Patents associated with the department of energy

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{"metadata":{"version":"1"},"inputs":{},"errors":{},"resultset":{"total":42133,"count":25,"number":0,"pages":1686,"result":[{"number":"9,275,844","artifact":"grant","title":"Apparatus and method for nanoflow liquid jet and serial femtosecond x-ray protein crystallography","filed_on":"2013-05-16","issued_on":"2016-03-01","published_on":"2013-11-21","abstract":"Techniques for nanoflow serial femtosecond x-ray protein crystallography include providing a sample fluid by mixing a plurality of a first target of interest with a carrier fluid and injecting the sample fluid into a vacuum chamber at a rate less than about 4 microliters per minute. In some embodiments, the carrier fluid has a viscosity greater than about 3 centipoise.","description":{"text":["STATEMENT OF GOVERNMENTAL INTEREST","This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","BACKGROUND OF THE INVENTION","Serial femtosecond (fs, 10 −15 seconds) crystallography (SFX) using X-ray Free-Electron laser (XFEL) radiation is an emerging method for three dimensional (3D) structure determination that extracts structural information from nanometer (nm, 10 −9 meters) to micron (micrometer, μm, 10 −6 meters) sized crystals. This method relies upon intense X-ray pulses that are sufficiently short to pass through the sample before the onset of significant radiation damage (diffraction-before-destruction). SFX therefore promises to break the correlation between sample size, damage and resolution in structural biology. In this approach, a liquid microjet is used to introduce randomly oriented crystals into the XFEL beam. Structures with less than 2 Ángström (Å, 1 Å=10 −10 meters) resolution have been solved using the method. SFX is unique from standard crystallography in that particle sizes on the order of microns dispersed in aqueous solutions are used instead of a single large crystal (that takes months of method development to grow) mounted on a loop or grid. One known method to deliver sample to the x-ray interaction region is the Gas Dynamic Virtual Nozzle (GDVN, e.g., see Shapiro, Chapman et al. 2008, DePonte et al., 2008, 2009, 2011, and Ganon-Calvo et al., 2010). A thin liquid jet is formed from a highly pressurized liquid reservoir and a high pressure sheath gas flow from concentric capillary tubes. The thin jet is subjected to femtosecond X-ray pulses (e.g., see Barty, Caleman et al. 2011%3b Chapman, Fromme et al. 2011%3b Hunter, DePonte et al. 2011%3b Lomb, Barends et al. 2011%3b Aquila, Hunter et al. 2012%3b Johansson, Arnlund et al. 2012%3b Koopmann, Cupelli et al. 2012).","SUMMARY OF THE INVENTION","Though suitable for many purposes, the known method for sample delivery suffers from one or more of the following disadvantages determined by inventors: (1) high sample consumption rate compared to precious sample amounts%3b (2) sample settling in the reservoir or transfer lines prior to analysis%3b (3) fluctuation of jet position%3b and (4) use of gas sheath and metal shield surrounding the liquid jet in a vacuum chamber. Current sample consumption rates are typically 10 to 16 microliters (μl, 1 μl=10 −6 liters) per minute (min). Sample consumption rates of less than about one μl/min are desirable to enable analysis of precious biological samples. Sample settling reduces data collection rates and increases the likelihood of clogging. Stability of the jet position is desirable because of the small size of the jet (1 micron) and the X-ray focus (0.1-1 micron). Access to the jet unimpeded by differential pumping shrouds, gas sheath flows or other components is highly desirable for performing time resolved crystallography experiments, such as measurements at several points along the liquid jet and downstream droplet cloud.","Improvements are disclosed here that allow stable, low consumption rate, accessible liquid jet with nanoscale and microscale targets, such as molecules, nanometer sized crystals (nanocrystals), cells or organelles, in vacuum. Such a liquid jet is called herein a nanoflow liquid jet and is suitable for SFX as well as for nanoparticle synthesis, ‘soft’ ionization of biomacromolecules for mass spectrometry, thin film generation, high harmonic generation, and pharmaceutical delivery.","In a first set of embodiments, a method includes providing a sample fluid by mixing a plurality of a first target of interest with a carrier fluid. The method includes injecting the sample fluid into a vacuum chamber at a rate less than about 4 microliters per minute.","In another set of embodiments, an apparatus includes a pump configured to apply pressure to a sample fluid and a capillary tube of inner diameter less than 100 microns in fluid communication with the pump, wherein the capillary tube is open at a distal end. The apparatus also includes a voltage source configured to apply a first voltage to the sample fluid inside the capillary tube, and a counter electrode configured to be charged at a different second voltage. The counter electrode has a shape that is axially symmetric and has a first end closest to an axis of symmetry and a second edge farthest from the axis of symmetry. The distal end of the capillary and the counter electrode are configured to be disposed inside a vacuum chamber","In another set of embodiments, a non-transitory computer-readable medium carries one or more sequences of instructions, wherein execution of the one or more sequences of instructions by one or more processors causes an apparatus to perform applying a first voltage to a sample fluid and a different second voltage to a counter electrode in a vacuum chamber. The apparatus is further caused to inject the sample fluid into the vacuum chamber at a rate less than about 4 microliters per minute.","Still other aspects, features, and advantages of the invention are readily apparent from the following detailed description simply by illustrating a number of particular embodiments and implementations, including the best mode contemplated for carrying out the invention. The invention is also capable of other and different embodiments, and its several details can be modified in various obvious respects, all without departing from the spirit and scope of the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.","DETAILED DESCRIPTION","A method and apparatus are described for nanoflow liquid jet and serial femtosecond X-ray protein crystallography. In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid unnecessarily obscuring the present invention. Various references are cited herein, both above and in the following. The entire contents of the cited references are hereby incorporated by reference as if fully set forth herein, except for terminology that is inconsistent with the terminology used herein. As used herein, the following terms and abbreviations have the meanings given in Table. 1."," TABLE 1 Terms and Definitions. Å Ángström, 1 Å = 10 −10 meters centipoise (symbol cP) is one one-hundredth of a poise CXI Coherent X-ray Imaging endstation of LCLS DNA Deoxyribonucleic acid - a double helix comprising two complementary sequences of nucleotide bases (each selected from a set of four nucleotides: adenine, thymine, cytosine, and guanine, represented by the letters A, T, C and G, respectively) electrospinning a variation of electrospray in which viscous solutes are used to overcome the charge repulsion that forms the electrospray and a thin liquid jet is formed instead. This process has found use in polymeric nanofiber manufacturing. Conventionally not done in vacuo. electrospray electrohydrodynamic atomization widely applied in nanoparticle synthesis, ‘soft’ ionization of biomacromolecules for mass spectrometry, thin film generation, and pharmaceutical delivery. Occurs at the exit of an open-ended capillary filled with a conductive liquid when exposed to an electric field of appropriate strength. Conventionally not done in vacuo. fs femtosecond, 1 fs = 10 −15 seconds. GDVN Gas Dynamic Virtual Nozzle - process to provide a fluid jet using high pressure and a gas sheath flow. LCLS Linac Coherent Light Source at SLAC National Accelerator Laboratory, Menlo Park, CA ml milliliter, 1 ml = 10 −3 Liters nm nanometer, 1 nm = 10 −9 meters parameter A term in an equation that is constant for a particular application or context, but can vary among different applications or contexts. PDB Protein Data Bank PEG polyethylene glycol peptide also called a protein fragment, a molecule comprising multiple amino acids, typically a shorter sequence of amino acids than a protein, poise (symbol P) is the unit of dynamic viscosity in the centimeter gram second (cgs) system of units and is equal to 1 gram per second per centimeter. protein A molecule comprising a long sequence of amino acids, selected from a set of 22 amino acids in humans. PS II Photosystem II, a protein responsible for oxidation of water using light from the sun. The light-driven, four-photon reaction is catalyzed by a Mn 4 CaO 5 cluster located at a lumenal side of PS II. RNA Ribonucleic acid - a molecule comprising a single sequence of nucleotide bases (each selected from a set of four nucleotides: adenine, uracil, cytosine, and guanine, represented by the letters A, U, C and G. SFX serial femtosecond crystallography, a process to determine atomic structure of molecules flowing past an high photon energy X-ray source that emits femtosecond pulses, which produces a series of X- ray scattering patterns siemens one siemens is equal to the reciprocal of one ohm, and is also referred to as the mho, and is a measure of electrical conductivity (reciprocal of resistance) and electrical admittance (reciprocal of impedance) viscosity a measure of the resistance of a fluid which is being deformed by either shear or tensile stress, such as a proportionality factor between a force applied per unit area of a fluid and resulting velocity gradient perpendicular to that area. variable a term in an equation that can assume multiple different values for a single application or context. XFEL X-ray Free-Electron laser radiation, based on using a relativistic electron beam as the lasing medium which moves freely through a magnetic structure, hence the term “free electron.” The free- electron laser has the widest frequency range of any laser type, and can be widely tunable to include very high frequency (high photon energy) X-rays. μl microliter, 1 μl = 10 −6 Liters μm micrometer, also called a micron, 1 μm = 10 −6 meters ","Some embodiments of the invention are described below in the context of serial femtosecond X-ray crystallography (SFX) of protein nanocrystals. However, the invention is not limited to this context. In other embodiments, filtered or unfiltered nanocrystals of other molecules, cells, viruses, organelles such as carboxysomes or single molecules are included in the sample fluid, or nanoflow liquid jet is used for one or more other purposes, such as nanoparticle synthesis, ‘soft’ ionization of biomacromolecules for mass spectrometry, thin film generation, high harmonic generation, and pharmaceutical delivery. In other embodiments, additional detection schemes can be used to probe the interaction of the X-ray pulse with the injected sample, such as analyzers used for spectroscopy or time-of-flight mass spectrometry. One or more of such detectors can be used separately or in parallel with the X-ray scattering detector. In other embodiments, synchrotron radiation or laser pulses from table-top lasers systems of any available wavelength are used. For the latter, synchronized timing with XFEL pulses can provide the means to make movies of molecular processes, perhaps even to femtosecond resolution, where the optical pulse pumps the molecules in a crystal and the X-rays probe the structure. In other embodiments, the molecules of interest are mixed with a reactant a known distance from the interaction region to provide study of chemical kinetics.","In the work presented here, solvent properties, such as 30% glycerol/10% polyethylene glycol (PEG), or 10% PEG/1.4 molar (M) sucrose in water, have been discovered for stable electrospinning in vacuo. Furthermore, it has been discovered that nanocrystals can be delivered in a one micron diameter jet in vacuo. These discoveries provide a new nanoflow source suitable for serial femtosecond crystallography (SFX) among other processes. These techniques for electrospinning in vacuo have opened the application of SFX to a much wider array of biological materials because it consumes about 50 times less sample than the current method based on GDVN. Furthermore, these techniques provide other advantages, such as the reduction of settling, the removal of a gas sheath that contaminates the x-ray scattering, and the removal of a metal shroud that limits the locations along the flow-focused liquid jet of GDVN where measurements can be made. In the work presented here, measurements can even be made inside the Taylor cone, providing typically a 50 micron (dependent on capillary inner diameter) X-ray path length through the sample.","FIG. 1 is a block diagram that illustrates example use of a gas dynamic virtual nozzle (GDVN) 130 for serial femtosecond X-ray crystallography. The GDVN 130 includes an inner capillary 132 and an outer capillary 134 . Sample fluid 133 is forced through the inner capillary 132 under pressure, while a gas 135 is forced through the outer capillary 134 under pressure. The result is a sample fluid jet 138 surrounded and focused by a gas sheath flow 139 . To reduce the gas load in a vacuum chamber 110 , a metal shroud 114 surrounds the gas sheath 139 and is differentially evacuated. For example, one low pressure vacuum is maintained outside the metal shroud by a first vacuum pump 112 a while a higher pressure vacuum is maintained inside the metal shroud by a second vacuum pump 112 b. ","When used for SFX, the sample fluid jet 138 is illuminated by an X-ray beam 124 from X-ray source 122 and the scattered emissions (photons) are recorded at an X-ray detector array 126 . The incident and scattered X-rays pass through ports in the metal shroud 114 . A disadvantage of this arrangement is that the position of the sample fluid jet 138 fluctuates so that the ports are not always ideally aligned. Also, the presence of the metal shroud 114 makes it difficult to measure the X-ray scattering at multiple different distances along the sample fluid jet 138 and the valuable high angle scattering from the sample can be shadowed from the detector array 126 . Furthermore, the X-ray scattering, even through the ports, is affected by the presence of the gas sheath flow 139 . In addition, target molecules in the low viscosity sample fluid tend to settle out in one or more pumps or reservoirs before reaching the GDVN 130 , causing the target molecules to be more sparse in the sample fluid jet, and, thus, reducing the number of useful measurements from the X-ray beam 124 .","Electrospray was attempted to circumvent the limitations of GDVN. Unexpectedly, it was observed that the synchrotron radiation severely perturbs the electrospray. Powder diffraction from crystal suspensions delivered to synchrotron radiation by GDVN has been recorded (Shapiro, Chapman et al. 2008). An attempt to repeat this experiment on crystals passing through the Taylor cone of an electrospray source at atmospheric pressure was performed at the Swiss Light Source cSAXS beamline using a fully closed gap configuration of the U19 undulator (4.6 mm) and 8 kilo-electron Volts (keV, 1 keV=10 3 electron Volts) X-rays focused into n approximately 5 micron×20 micron (100 square micron) footprint containing up to 10 12 photons/second. FIG. 1B through FIG. 1E are photographs that illustrate breakdown of electrospray from a 100 micron outer diameter capillary under exposure to X-rays at atmospheric pressures, before during and after exposure to synchrotron radiation. The result is that only the leading edge of the X-rays interacts with the electrospray. The Taylor cone compresses in less than 100 milliseconds (ms, 1 ms=10 −3 seconds) and does not return until about 1000 ms after a shutter of the X-ray source is closed. Thus no signal can be recorded from the electrospray after a time less than about 40 ms. These measurements show evidence that the destabilization occurs on a timescale shorter than about 10 ms, as the use of 10 ms exposures did not result in any detectable signals. It was concluded that rapid gas ionization by the incoming X-ray pulse destabilizes the electrospray and precludes the use of synchrotrons to probe the structure and dynamics of electrosprays and the particles within them.","Use of the LCLS X-ray laser alleviates this shortcoming by providing ultrabright and ultrashort X-ray pulses that pass through the electrospray before it is destabilized by gas ionization. The plasma created by the beam breaks down and recombines on the scale of microseconds, enabling probing of an electrospray operating at atmospheric pressure with a repetition rate of 1 Hz. It is suspected that the physical reformation of the Taylor cone is the rate limiting process. However, another unexpected problem was that geometrical constraints of the large X-ray beam path at CXI caused background scattering from the high concentration of gas molecules. This background scattering precluded recording of crystalline Bragg diffraction.","Thus, it was observed that atmospheric pressure electrosprays cannot be probed with synchrotron radiation without severe perturbations. X-rays lasers can probe electrosprays at atmospheric pressure with 1 Hz repetition rate, limited by the electrospray re-stabilization but suffer from background scattering by surrounding gas molecules.","Electrospun liquid jets of protein crystals in vacuo can be made to similar dimensions as liquid jets created using a gas dynamic virtual nozzle and provide a complementary sample delivery mechanism for SFX using X-ray lasers. However, without cryoprotectant added to carrier fluids, the jet breaks down due to freezing%3b and, the GDVN must be used, with all its limitations.","To reduce background scattering, conditions were determined for stable electrospray in vacuo absent a gas sheath. Glycerol was added as a cryoprotectant to overcome the limitation of immediate freezing at the capillary exit. Studies of glycerol electrosprays in vacuo have shown high stability at \u003c0.01 torr (1 torr=approximately 1.316×10 −3 atmosphere or 133.3 pascals, where 1 pascal is the SI units for pressure, one newton per square meter) (Ku and Kim 2003). Glycerol is also commonly used in crystal screens and as a cryoprotectant in synchrotron protein crystallography. Glycerol solutions of 25-30% by volume were discovered to be most effective. Highly viscous glycerol added a surprising extra advantage for SFX experiments by reducing the settling rate of crystals. Suspensions of crystals of sizes less than about 2 micron were stable for more than 12 hours. Similar to electrospray of solutions of pure glycerol, electrospun jets of crystal suspensions showed highest stability at pressures less than about 0.01 Torr.","FIG. 2A and FIG. 2B are block diagrams that illustrates two views of an example apparatus 200 for performing and testing nanoflow liquid jet serial femtosecond X-ray protein crystallography, according to an embodiment. The apparatus includes a reservoir 231 for holding a sample 251 , such as a mixture of nanocrystals with a viscous electrically conductive carrier fluid, as described in more detail below. In some embodiments, the apparatus includes an inline mixing apparatus to create the sample fluid from the molecules of interest and the carrier fluid, i.e. a simple T junction or more complex concentric flow apparatus. The reservoir is in fluid communication with a source of fluid pressure, such as syringe pump 232 that is in fluid communication with a capillary tube, such as silica capillary 236 with tapered open end. The pump 232 induces flow through an open distal end of the capillary tube. In the illustrated embodiment, the apparatus includes fluid flow sensor 233 configured to measure the rate of flow through the capillary tube. In another embodiment, pressure (10-50 pounds per square inch, psi, 1 psi=about 51.7 torr,) can be applied to a sample reservoir, with which the silica capillary 236 is in fluid communication, to induce flow through to the open distal end without any connectors. This embodiment is advantageous for minimizing potential for clogging due to crystal accumulation at a connector.","For electrospinning, the fluid is charged by a high voltage (HV) source 244 , such as a Stanford Research Systems 0-5 kiloVolt (kV, 1 kV=10 3 volts) or 10 kV power supply, connected to a metal union component 234 that transfers the voltage applied to a metal vessel to a conducting fluid, such as the sample fluid, contained in the vessel. The electrical current, in picoamperes (pA, 1 pA=10 −12 Amperes), which flows into the fluid to maintain the voltage is measured by an ammeter 242 . A counter electrode 246 is charged to a different voltage, e.g. to electrical ground in the illustrated embodiment. An opening in the proximal end of the counter electrode allows the flow of sample fluid to be collected neatly in a sample catcher 248 after passing the counter electrode 246 .","In the illustrated embodiment, the counter electrode is shaped as a cone with it apex removed, as depicted in FIG. 2C and FIG. 2D . FIG. 2C and FIG. 2D are block diagrams that illustrate a conical counter electrode with apex removed in oblique and plan views, respectively, according to an embodiment. That is, the counter electrode 246 has a shape that is axially symmetric and has a first end closest to an axis of symmetry and a second edge farthest from the axis. In some embodiments, the counter electrode has a more complex structure with multiple electrodes and multiple voltages. For example a segmented quad-electrode 247 , depicted in FIG. 2E and FIG. 2F with four segments 247 a through 247 d , respectively, making up the cone, each separately chargeable, would enable steering functionality. FIG. 2E and FIG. 2F are block diagrams that illustrate a quad-electrode conical counter electrode 247 with apex removed in oblique and plan views, respectively, according to an embodiment.","The counter electrode 246 (or 247 ) is disposed with the axis aligned with the flow of the sample fluid (e.g., the center of the capillary tube) and with the first edge closer than the second edge to an injection point at the open distal end of the capillary, e.g., silica capillary 236 where the sample fluid is injected toward the counter electrode 246 . The electrospray forms a Taylor cone 258 downstream of the distal end of capillary 236 followed by an electrospray jet 259 and, in some embodiments, a plume 257 . Tapering the distal open end of the capillary tube offers the advantage of enhancing formation of the Taylor cone 258 .","For electrospinning in vacuo, the capillary, e.g., silica capillary 236 , is passed into a vacuum chamber 210 through a feedthrough fitting 235 , such as a 1/16″ Swagelok fitting. In some embodiments, the capillary tube was fixed to a stepper 282 , such as an XYZ nanopositioning stage, to enable positioning of the tube distal end, and the jet emanating from it, relative to other components in the vacuum chamber 210 , as indicated by the double arrows in two dimensions. Vacuum pressures of about 10 −4 torr are achieved by the vacuum pump 212 . In various embodiments, the vacuum pressure is in a range from about 10 −5 torr to about 10 −2 torr. The vacuum pressure is monitored by pressure gauge 214 . The counter electrode 246 is disposed in the vacuum chamber with the axis aligned with the flow of the sample fluid in the vacuum chamber and with the first edge closer than the second edge to an injection point at the distal end of capillary 136 where the sample fluid is injected into the vacuum chamber.","To visualize the electrospray, in some embodiments, a light source, such as fiber optic lighting source 262 emits a light beam, e.g. light beam 263 , into the vacuum chamber 210 . In various other embodiments, an in-vacuum LED or in-vacuum pulsed laser acts as the light source. The transmitted light is detected at a video camera, such as formed by lenses 264 , stereomicroscope 266 , and charge coupled device (CCD) array 268 . In some embodiments, the electro spray is not visualized, and one or more of components 264 , 266 and 268 are omitted.","For SFX applications within vacuum chamber 210 , an X-ray source 122 , such as a XFEL, emits an X-ray beam 124 , such as serial femto second pulse X-ray beam, that intersects the electrospray, such as along electrospray jet 259 . Intersection of the X-ray beam 124 is controlled by stepper 282 moving the distal end so that the beam intersects at different portion of the fluid flow, either at Taylor cone 258 or jet 259 or plume 257 . Scattered X-ray photons are detected at the x-ray detector array 126 .","In some embodiments, a controller 280 is included to control one or more of syringe pump 232 , high voltage source 244 , fiber optic lighting source 262 , vacuum pump 212 and X-ray source 122 . In some embodiments the controller also receives or stores output, or both, from one or more of flow sensor 233 , ammeter 242 , pressure gauge 214 , and CCD array 268 . In various embodiments, the controller 280 comprises one or more computer systems as depicted in FIG. 12 or chip sets as depicted in FIG. 13 , or some combination. FIG. 2B depicts a perpendicular view in the direction indicated by the arrow labeled 2 B.","In FIG. 2B , vacuum chamber 210 , stepper 282 , feedthrough 235 , capillary 236 , Taylor cone 258 , electrospray jet 259 , plume 257 , counter electrode 246 and controller 280 are as described above. Apparent in this view are the X-ray source 122 and X-ray detector array 126 , as well as the X-ray beam 124 , also included in FIG. 2A and described above. Here, also shown, are Bragg scattered X-ray photons 127 not previously depicted.","The nanoscale dimensions of electrosprays, in particular the jet filament and the submicrometer droplet size distribution, have never been measured in situ because typical light scattering techniques cannot be extended to this scale (Smith, Flagan et al. 2002%3b Wortmann, Kistler-Momotova et al. 2007). However, the perturbation of biological materials transiting within these nanoscale electrospray regions has received recent interest because of the growth in applications of electrosprays to the characterization and preparation of biological materials. For example, tobacco mosaic virus has been shown to collapse during the electrospray process (Allmaier, Laschober et al. 2008) and the viability of bacteriophages is known to vary with applied electrospray voltage (Jung, Lee et al. 2009). Currently, the point during the electrospray process at which these changes in biomaterial structure are induced is not known. Insights into these structural perturbations are important to optimize electrospray delivery of biological materials to surfaces for applications such as biomimetic solar cell manufacture (Modesto-Lopez, Thimsen et al. 2009), injection into vacuum for mass spectrometry (Patriksson, Marklund et al. 2007) and single molecule x-ray diffractive imaging applications (Bogan, Benner et al. 2008%3b Bogan, Boutet et al. 2009)","SFX provides an opportunity to determine structural changes at various positions along the electrospray by measuring X-ray diffraction from materials inside of electrosprays. Due to the anatomy of an electrospray, signal changes are expected to be measured based on the position along the electrospray where the X-rays probe, and any structural changes induced in the target biomolecule.","FIG. 3 is a photograph 300 that illustrates example electrospray produced by apparatus of FIG. 2 , according to an embodiment. Evident is a distal end of a capillary tube, labeled a “needle tip” 310 in FIG. 3 , from which is extruded a Taylor cone 320 , a jet 322 and a plume 324 . In various embodiments, X-ray scattering measurements are made at position 331 in Taylor cone 320 , position 332 in jet 322 or at position 333 at a base of plume 324 .","Strong signals are expected from materials inside of the electrospray capillary at position 331 just outside the needle tip 310 in an experiment identical to Small-angle X-ray scattering (SAXS) measurements on liquids flowing through capillaries. In this position, the sample volume, ˜2×10 −8 cm 3 , is defined by the capillary diameter (50 μm) and the beam size (20 μm). For a solution of proteins with 10 12 particles per ml, this corresponds to 20,000 proteins in the exposure volume at any one instant. In position 332 of the jet 322 , materials are concentrated in space into a small filament of liquid \u003c1 μm in diameter. Here the sample volume is ˜2×10 −11 cm 3 . The highly confined sample region is ideally suitable for delivery of sample to the future submicron focus of LCLS and other XFELs. In the plume 324 , materials are divided into primary electrospray droplets 200-400 nm in diameter that are dispersed over a large volume, 100-1000 μm in diameter. It was expected that the expansion of the liquid into 20-200 times the original volume would require even longer integration times for adequate signal-to-noise ratios. At position 333 , conformational changes may be observed in the biomolecules as they transition into the gas phase.","Thus, there is interest in all three electrospray regions, including the Taylor cone 320 in the immediate vicinity of the nozzle tip, the thin electrostatic jet 322 emerging from the tip of the Taylor cone, and the plume 324 of fine droplets formed by Coulombic explosion in the jet. The conformation of several classes of biological particles (ranging from single proteins to larger macromolecular aggregates or crystals) can be characterized by x-ray scattering in an attempt to monitor conformational changes that occur during electrospray process. Analysis of the scattered intensity allows the study of particle dynamics in electrospray, such as hydrodynamic alignment, and structural modification of biological molecules caused by interaction with strong electric field, water shell evaporation and potentially even biological ion evaporation from the nanoscale droplets, a phenomenon predicted to occur on a picosecond (ps, 1 ps=10 −12 seconds) timescale (see, e.g., Marginean, Znamenskiy et al. 2006). The thin jet region is of particular interest for SFX since the jet can be used for nanocrystal delivery.","FIG. 4 is flowchart that illustrates an example method 400 for generating nanoflow liquid jet and serial femtosecond x-ray protein crystallography, according to one embodiment. Although steps are depicted as integral blocks in a particular order for purposes of illustration, in other embodiments, one or more steps or portions thereof are performed in a different order, or overlapping in time in series or parallel, or are omitted, or one or more steps are added, or the method is changes in some combination of ways.","In step 410 a sample fluid is prepared by mixing multiple copies of a target of interest, such as a molecule, crystal, cell or organelle of interest, with a carrier fluid. Thus, step 410 provides a sample fluid by mixing a plurality of a first target of interest with a carrier fluid. In some embodiments, about 10 9 copies of a target molecule are included per milliliter of sample fluid. In some embodiments, step 410 includes step 411 , in which nanoscale crystals are mixed with a viscous, electrically conductive carrier fluid, with conductivity similar to fluids used in well-known electrospray operation. Experimental embodiments included conductivities in a range of from about 0.5 to about 5 milliSiemens per centimeter (mS/cm, 1 milliSiemen, mS, =10 −3 Siemens, 1 centimeter, cm, =10 −2 meters). It was determined that below a value of approximately 0.5 mS/cm, the form of the electrospray starts suffering which requires higher and higher voltages which leads to the jet beginimg to suffer and fail. In some of these embodiments, about 10 9 nanocrystals of the target molecule are included per milliliter of sample fluid. Thus, in some embodiments, providing the sample fluid further comprises providing the sample fluid by mixing a plurality of nanoscale crystals of the first target of interest with the carrier fluid. In some embodiments, the nanoscale crystals are each smaller than about 500 nanometers in a largest dimension. In various embodiments, crystals of sizes from 0.2 microns to 20 micron have been measured at LCLS. In some embodiments, the viscosity of the carrier fluid is in a range from about 3 centipoise (cP) to about 5 cP. For example, in some embodiments, the carrier fluid comprises 30% by volume glycerol and 10% by volume polyethylene glycol (PEG) 2000.","In step 420 , the sample fluid is injected into a vacuum chamber at a rate less than about 4 microliters per minute, a rate that is a lower than is achievable with GDVN. In some embodiments, the injection rate is preferably even lower, at less than 1 microliters per minute. In some embodiments, the injection rate is about 0.1 to 0.5 microliters per minute. At about 0.3 microliters per minute, the target molecules or nanocrystals passes an x-ray focus at a rate of about 5000 per second.","In an illustrated embodiment, such nanoflow is achieved by steps 421 , 423 and 425 . In step 421 , a first voltage is applied to the sample fluid, e.g., at a fluid electrode such as metal union 234 or an electrode in contact with the sample reservoir, and a different second voltage is applied to the counter electrode 246 . In various embodiments, 1.7 kilovolts (kV, 1 kV=10 3 volts) to 5 kV are applied to one electrode and 0 to −5 kV applied to the other. For example, some embodiments operate with +2.3 kV in solution and −0.3 kV on the counter electrode and 6 millimeters (mm, 1 mm=10 −3 meters) to 8 mm distance between capillary and the counter electrode. In other embodiments, voltages are inverted to operate in negative mode electrospinning.","In step 423 , the vacuum chamber is evacuated to a pressure less than about 10 −2 Torr. Stable jetting is not observed at intermediate pressures above this level and below atmospheric pressure, consistent with prior work on pure glycerol and solat-doped glycerol solutions (e.g., see Ku, B. K. \u0026 Kim, 2003). In step 425 , pressure is applied to the sample fluid connected to the vacuum chamber by the single capillary tube, e.g., pressure is applied by syringe pump 232 in fluid communication with silica capillary 236 .","In various embodiments, the capillary tube has an inner diameter (ID) less than or equal to about 150 μm. For example, the fluid is injected through a single silicon capillary tube of ID about 50 microns to 150 microns ID, with both tapered and non-tapered distal end exits. Smaller capillaries are available commercially down to 5 micron inner diameter. Smaller capillaries lead to decreased flow rate and sample consumption but this is offset by increased likelihood for clogging. Capillaries smaller than 50 micron ID are most successful with pre-filtered solutions of less than 2 micron crystals, preferably less than 500 nm crystals In some embodiment, the sample fluid in the vacuum forms a jet less than about one micron in diameter.","In various embodiments, the vacuum chamber does not include a shroud to separate the vacuum chamber into two or more volumes pumped to different vacuum pressures as in a GDVN. In various embodiments, applied pressure injects the sample fluid into the vacuum chamber through a single silicon capillary tube without a sheath fluid flow introduced through a second concentric capillary tube as in a GDVN.","In step 431 , the focus of the X-ray source is positioned in the electrospray, for example, using nanoscale stepping motors 282 attached to the capillary 236 or feedthrough 235 . In step 433 , the sample fluid is exposed to the X-ray beam, such as femtosecond pulse high energy x-ray beams from XFEL source at Linac Coherent Light Source%27s (LCLS) Coherent X-ray Imaging (CXI) endstation. Thus, step 433 includes exposing a portion of the sample fluid in the vacuum chamber to a femtosecond pulse high energy X-ray beam. For example, measurements are made at 120 femtosecond pulses per second. In step 435 , the X-ray scattering is measured from each target molecule, or a nanocrystal of multiple copies of the target molecule, e.g., at an X-ray detector array. Thus step 435 includes measuring at an X-ray detector array an X-ray scattering pattern for the first target in the sample fluid in the vacuum chamber in response to exposing the portion of the sample fluid to the X-ray beam. The structure of the molecule is then deduced based on the measured scattering, using any method known in the art.","For 10 9 crystals per milliliter and a nanoflow rate of 0.3 microliters per minute, 5000 crystals pass the focus every second or 250 per sample period, providing enough targets to reliably interact with one femtosecond pulse during the sample period. For example, about ten to fifteen thousand samples of X-ray scattering are obtained per milliliter of sample. This is sufficient to provide statistically significant deduction of target molecule structure from randomly oriented target molecules, or crystals thereof. Due to the statistical nature of this random sampling, it is advantageous to have minimum sample flow required to replenish the sample between each X-ray pulse in order to preserve rare samples.","Tables 2A through 2E indicate X-ray source operation in various embodiments compared to other SFX operations."," TABLE 2A X-ray operating parameters. Crystal Micro-jet Total sample diffraction Flow rate diameter consumed patterns Crystal Sample (ul/min) (micron) (microliter) collected patterns/uL PSI 10 4 5139 112725 21.9 Lysozyme 12 to 16 Lysozyme 40 fs 10 4 850 16331 19.2 100 fs 10 4 230 6318 27.5 150 fs 10 4 381 4704 12.3 200 fs 10 4 375 2639 7.0 250 fs 10 4 319 1681 5.3 300 fs 10 4 322 2389 7.4 Cathepsin B 15 4 347 988 2.8 Reaction center 10 4 1000 1542 1.5 PSI-Fer, gs 10 4 1102 9086 8.2 5 us 10 4 611 6839 11.2 10 μs 10 4 451 3297 7.3 PSII 3~4 4 855 113632 132.9 Thermolysin   0.3 1 18 14043 780.2 50 μm ID Thermolysin 1~4 74 1064 14.4 75 μm ID Lysozyme, 10 4 2043 66442 18.4 40 fs Lysozyme, 5 fs 10 4 2774 40115 26.3 "," TABLE 2B X-ray operating parameters (continued). Protein Protein Protein concentration consumed Crystal concentration Sample (mg/ml) (mg) patterns/mg (M) Crystals/ml PSI 1 5.139 21935 1.00E−06 1.00E+09 Lysozyme 3.00E+10 Lysozyme 40 fs 1 0.85 19213 1.00E−06 100 fs 1 0.23 27470 1.00E−06 150 fs 1 0.381 12346 1.00E−06 200 fs 1 0.375 7037 1.00E−06 250 fs 1 0.319 5270 1.00E−06 300 fs 1 0.322 7419 1.00E−06 Cathepsin B 2 0.694 1424 1.00E+09 Reaction 5 5 308 center PSI-Fer, gs 3.50E−05 5 us 3.50E−05 10 us 3.50E−05 PSII 10 8.55 13290 5.00E+07 Thermolysin 14 0.252 55726 2.00E+10 50 um ID Thermolysin 14 1.036 1027 2.00E+10 75 um ID Lysozyme, 40 fs Lysozyme, 5 fs "," TABLE 2C X-ray operating parameters (continued). Resolution achieved X-ray energy Wavelength Pulse energy Photons Sample (A) (keV) (A) (mJ) per pulse PSI 8.5 1.8 6.9 1.00E+12 Lysozyme 10 2 6.2   \u003e1E+12 Lysozyme 40 fs 2 6.2 0.56 1.80E+12 100 fs 2 6.2 0.56 1.80E+12 150 fs 2 6.2 0.39 1.20E+12 200 fs 2 6.2 0.44 1.40E+12 250 fs 2 6.2 0.41 1.30E+12 300 fs 2 6.2 0.21 6.50E+11 Cathepsin B 8.5 1.9954 6.2 2.13 6.70E+12 Reaction center 2 6.17  \u003c10E+13 PSI-Fer, gs 2 6.9 3 5 us 2 6.9 3 10 us 2 6.9 3 PSII 6.5 9 5.00E+11 Thermolysin 9.73 1.27 50 um ID Thermolysin 9.73 1.27 75 um ID Lysozyme, 1.9 9.4 1.32 0.6 4.00E+11 40 fs Lysozyme, 5 fs 1.9 9.4 1.32 0.053 3.50E+10 "," TABLE 2D X-ray operating parameters (continued). X-ray focus Average PULSE Pulse X-ray fluence (um, irradiance X-ray pulses Sample duration (fs) (J/cm{circumflex over ( )}2 FWHM) (W/cm{circumflex over ( )}2) used PSI 10, 70, 200 900 7 1.00E+16 1.85E+06 lysozyme 70-400 1200-5300 10   4E+15 to 7.57E+16 Lysozyme 40 fs 70 10 1.40E+17 306000 100 fs 100 10 5.60E+16 82800 150 fs 150 10 2.80E+16 137000 200 fs 200 10 2.20E+16 135000 250 fs 250 10 1.60E+16 115000 300 fs 300 10 7.00E+15 116000 Cathepsin B 67.4 2.5 × 3 um 5.00E+17 83224 Reaction center 70 10 365035 PSI-Fer, gs 70 7 1.00E+17 396780 5 us 70 7 1.00E+17 219960 10 us 70 7 1.00E+17 162420 PSII 50 1.5 Thermolysin 50 1.5 50 um ID Thermolysin 50 1.5 75 um ID Lysozyme, 40 10 1.47E+06 40 fs Lysozyme, 5 fs 5 10 1997712 "," TABLE 2E X-ray operating parameters (continued). LCLS pulse rep rate Sample (Hz) Spots Reflections Reference PSI 6.00E+01 2.42E+06 3.38E+03 Chapman et al., Nature, 2011 lysozyme 60 Lomb et al., Phys Rev. B, 2011 Lysozyme 40 fs 60 Barty et al., Nature Photonics, 2011 100 fs 60 Barty et al., Nature Photonics, 2011 150 fs 60 Barty et al., Nature Photonics, 2011 200 fs 60 Barty et al., Nature Photonics, 2011 250 fs 60 Barty et al., Nature Photonics, 2011 300 fs 60 Barty et al., Nature Photonics, 2011 Cathepsin B 60 514 Koopman et al., Nature Methods, 2012 Reaction center 60 2247 Johannson et al., Nature Methods, 2012 PSI-Fer, gs 60 Aquila et al., Optics Express, 2012 5 us 60 Aquila et al., Optics Express, 2012 10 us 60 Aquila et al., Optics Express, 2012 PSII 120 Kern, PNAS, 2012 Thermolysin 120 Sierra, Laksmono, et al. 2012 50 um ID Thermolysin 120 Sierra, Laksmono, et al. 2012 75 um ID Lysozyme, 120 9921 Boutet, Science, 2012 40 fs Lysozyme, 5 fs 120 9743 Boutet, Science, 2012 ","FIG. 5A and FIG. 5B are block diagrams that illustrate spacing of components of the FIG. 2 apparatus for the Linac Coherent Light Source%27s (LCLS) Coherent X-ray Imaging (CXI) endstation, according to an embodiment. The CAD drawing of FIG. 5A depicts the spacing of various components between a vacuum chamber fitting 502 and the electrospray components 510 . The distance 504 a is 4.690 inches from a breadboard mount to the conflat flange 503 of vacuum chamber fitting 502 . The distance 504 b is 7.109 inches from a counter electrode mount to the conflat flange 503 of vacuum chamber fitting 502 . The distance 504 c is 10.359 inches from an XYZ nanopositioning motor mount to the conflat flange 503 of vacuum chamber fitting 502 . The distance 504 d is 15.520 inches from the top of a counter electrode 246 to the conflat flange 503 of fitting 502 . The distance 504 e is 16.149 inches from the bottom of a counter electrode 246 mount to the conflat flange 503 of vacuum chamber fitting 502 . The X direction denotes the x-ray beam path.","FIG. 5B is a diagram that depicts the electrospray components 510 and components useful for optical illumination of sample within the silica capillary 236 prior to formation of the jet, according to an embodiment. Spacing is indicated by scale bar 511 representing 1 centimeter (cm, 1 cm=10 −2 meters). This includes nanoscale stepping motor 512 and its mount 514 . Other components include a base mount 516 , a compression mount 518 for the silica capillary 236 , a laser dump 520 to capture light emitted from optical fibers 524 a , 524 b , 524 c , a compression clamp 522 to hold together the assembly of 236 , 518 and 520 and counter electrode 526 .","FIG. 6 is a photograph that illustrates example electrospray produced by apparatus of FIG. 5A and FIG. 5B , according to an embodiment. The tapered needle tip 610 exudes a Taylor cone 620 , nanoflow liquid jet 622 and start of plume 624 . FIG. 6 depicts a tapered fused silica capillary (74 μm×150 μm) needle tip 610 inside the CXI chamber, back-illuminated by a red LED and a laser (flowing the carrier solution described above), with a pressure of 3×10 −3 torr, inside the CXI chamber. Typical chamber pressure and liquid flow rate nominally ˜10 −5 torr and 0.4 μL/min.","The relative performance of the nanoflow electrospinning and the GDVN are compared in Table 3 for one embodiment."," TABLE 3 Electrospinning in vacuo comparison with GDVN Gas Dynamic Virtual Nozzle Electrospun Nanofiber in Parameters (Arizona State U.) vacuo (PULSE) Flow focusing Gas Electrokinetic phenomenon Capillary Diameter 40-50 μm 50, 75, 100, 150 μm Gas Sheath Helium \u003e300 psi none Liquid backing pressure \u003e200 psi 15-20 psi Sample consumption 5-40 μl/min 0.14-10 μl/min Jet diameter 1-20 μm 1-10 μm Observed hit rates at CXI ~2% ~2% (non-identical samples), to 25% Sample solvent Water, lipidic cubic phase 30% glycerol/10% PEG 2000 Sample delivery Rotating syringe mount/loop Microcentrifuge tube Sample volume (30 min) 300 μl 9, 90, 270 μl (50/75/100 μm ID capillary) Operating pressure for 10 −3 Torr, 10 −6 Torr with metal 7 × 10 −5 Torr, no metal shroud SFX sheath surrounding apparatus ","The electrostatic liquid jet illustrated in FIG. 6 is used to perform SFX with 20 times lower sample consumption rate, e.g., a flow rate of 500 nanoliters per minute. Experiments with both a 50 micron inner diameter capillary and a 75 micron inner diameter capillary are given in Table 4. This experiment consumed 0.046 ml of sample fluid and produced an average of 3 hits per second. Using GDVN, to index three times as many hits consumed 2.6 ml—not three times the volume, but 56 times the volume consumed by the nanoflow liquid jet in vacuo."," TABLE 4 Serial Femtosecond X-ray crystallography experimental statistics Inner % of diameter Time Total Total Total % of hits shots (microns) (minutes) shots hits indexed indexed indexed 50 68 489614 14043 4234 30 0.86 75 24.68 177671 1064 331 31 0.19 all 92.68 667285 15107 4565 30.5 0.68 ","In another embodiment, a new counter electrode was designed and built, and operated with a centered capillary. Long term (48 hour) testing of new design was performed with 30/10 glycerol/PEG 2000. Repeated 1.5 ml sample fluid, 24 hr tests were performed. New buffer conditions with Sucrose/PEG 2000 were explored. FIG. 7 and FIG. 8 are photographs that illustrate example reduction of sample fluid 820 collection on counter-electrodes 810 and 830 , according to an embodiment. It is concluded that new counter electrode design runs continuously for days with no sample buildup when capillary centered (75 um ID capillary, 1 μl/min flow rate). This is a huge improvement because, previously, intervention due to sample fluid collection 820 reaching the x-ray interaction region was required at 4 hrs. It was further concluded that: though multiple capillaries can be used, a single capillary will produce most reproducible jetting conditions%3b sucrose can substitute glycerol, and, in some embodiments, a Kapton heater is attached to the counter electrode to reduce sample fluid collection 820 .","In some experiments, injection of the samples into the interaction region was achieved by focusing the crystal suspension exiting a silica capillary (100 μm inner diameter) into a jet smaller than 10 μm in diameter using an electric potential of 2.1-2.5 keV between the capillary exit and a counter electrode 7 mm away. The crystal suspension flowed at 2.5-3.1 μl/min using a liquid backing pressure of 15-20 psi. Buffer B with 10% PEG 2000 does not electrospray in vacuum due to freezing at the nozzle exit. Glycerol was added as a cryoprotectant to eliminate freezing and enable formation of a stable cone-jet mode. Surprisingly, the combination of glycerol and PEG 2000 in the buffer also contributed to the low flow rate operation and reduced settling of the crystals during the experiment. The X-rays probed the liquid jet 50-100 μm from the exit of the capillary, exposing the crystal suspension to vacuum for fractions of a second.","In another embodiment, the X-ray diffraction pattern of PS II isolated from the thermophilic cyanobacterium Thermosynechococcus elongatus, was collected at the Coherent X-ray Imaging (CXI) instrument at LCLS using the single-shot approach. PS II microcrystals (˜10 μm) were injected into the LCLS X-ray beam in a liquid jet based on the electrohydrodynamic spraying of glycerol in vacuum using cone-jet mode. Several thousand diffraction images were collected at random crystal orientations. A single-shot diffraction pattern from a microcrystal exhibits Bragg spots up to 5.4 Å resolution. The Bragg spots are remarkably sharp and small, spreading over only a few pixels. This is likely due to the combination of low crystal mosaicity and the use of pixel-array detector technology with an extremely narrow point-spread function. The diffraction intensities varied strongly from shot to shot due to several factors, such as the size of the probed crystal volume, the quality of the microcrystals and orientation, and variations in the intensity of the beam due to the nature of the LCLS X-ray pulses.","Experiments were carried out at the CXI instrument at LCLS. FIG. 9 is a block diagram 900 that illustrates an experimental nanoflow liquid jet for SFX, according to an embodiment. This was the experimental setup for a SFX experiment at the LCLS CXI endstation. The endstation includes an interaction point 910 with a 10 square micron focus resulting from KB mirrors 923 focusing X-ray synchrotron radiation output by an undulator 921 located 420 meters upstream of the interaction point 910 . The KB mirrors 923 and undulator 921 collectively form an X-ray source 922 . The Bragg scattered photons 927 from a target at the interaction point 910 is captured at a CSPAD detector 926 located 93 millimeters (mm, 1 mm=10 −3 meters) downstream from the interaction point 910 .","A crystal suspension was prepared of 1-2 micron thermolysin crystals in 30% v/v glycerol, with 10% polyethylene glycol (PEG) 2000, CaCl 2 , dissolved in deionized water. The crystals were then filtered through an 8 μm pore size Nucleopore membrane (Whatman). A 100 μL aliquot of the sample (filtered crystal suspension 951 ) in a microcentrifuge tube was loaded into the pressurized cell 931 of a TSI electrospray aerosol generator (3980) from TSI Inc. of Shoreview, Minn. A solution high voltage (HV) electrode 944 was immersed in the sample 951 . A 114 cm long, 50 μm ID capillary 936 delivered the sample crystal suspension 951 to the interaction region inside the vacuum chamber through a 1/16″ Swagelok fitting. The capillary 936 was fixed to an XYZ nanopositioning stage (PI Micos PP-30 from PI USA of Auburn, Mass.) to enable positioning relative to the focused X-ray beam.","A counter electrode 946 was 1 cm in diameter and positioned 5 to 7 mm from the capillary exit. A sample catcher 948 backed up the counter electrode 946 . The nanoflow liquid jet 959 was visualized using a CXI microscope on-axis with the X-rays and was facilitated with illumination by a nanosecond pulsed laser (532 nm wavelength).","During operation, 2.5 kiloVolts (kV, 1 kV=10 3 volts) was applied to the solution high voltage (HV) electrode 944 and −0.2 kV was applied to the counter electrode 946 . An nanoflow liquid jet 959 flowing at 0.3 μl/min at flow sensor 933 was emitted from the 50 micron ID silica capillary 936 positioned less than about 1 mm from the XFEL interaction region surrounding interaction point 910 . Single pulse diffraction patterns from single crystals flowing in the nanoflow liquid jet were recorded on the CSPAD detector 926 at a 120 Hz repetition rate of the LCLS. Each 40 femtosecond pulse delivered an average of 3 milliJoules (mJ, 1 mJ=10 −3 Joules) focused at the interaction point 910 using 9.7 keV X-rays in beam 924 . Thus FIG. 9 depicts nanoflow liquid jet serial femtosecond crystallography at the Coherent X-ray Imaging endstation for protein nanocrystals in vacuo.","FIG. 10A is a block diagram that illustrates an experimental nanoflow liquid jet for SFX, according to another embodiment. The endstation includes an interaction point 1010 with a 3 square micron focus resulting from KB mirrors 1023 focusing X-ray synchrotron radiation output by an undulator 1021 located 420 meters upstream of the interaction point 1010 . The Bragg scattered photons 1027 from a target at the interaction point 1010 is captured at a CSPAD detector 1026 located 175 mm downstream from the interaction point 1010 .","A crystal suspension 1051 was prepared. A solution high voltage (HV) electrode 1044 was immersed in the sample 1051 . A 114 cm long, 50 μm ID capillary 1036 delivered the sample crystal suspension 1051 to the interaction region inside the vacuum chamber.","During operation, 2.5 kV was applied to the solution high voltage (HV) electrode 1044 and −0.2 kV was applied to the counter electrode 1046 . An nanoflow liquid jet 1059 flowing at 0.17 μl/min at flow sensor 1033 was emitted from the 50 micron ID silica capillary 1036 to interaction point 1010 . Single pulse diffraction patterns from single crystals flowing in the nanoflow liquid jet were recorded on the CSPAD detector from X-rays in beam 1024 .","FIG. 10B is a block diagram 1000 that illustrates panels 1060 of pixels that record X-ray scattering intensity 1020 from crystals in a nanoflow liquid jet of FIG. 10A , according to an embodiment. Thus FIG. 10B depicts serial femtosecond crystallography of electrospun thermolysin crystals in a nanoflow liquid jet. The image exhibits a sum of about 10,000 single-shot FEL diffraction patterns from 1-2 micron thermolysin crystals in different orientations. At the edge of the detector, a maximum resolution of 1.5 Å was achieved.","In other experimental embodiments, the CXI instrument at LCLS was operated at an energy of 9 keV with an average intensity of 3-5×10 11 photons/pulse, a pulse frequency of 120 Hz and a pulse duration of \u003c50 fs. The beam was focused to a size of about 1.5 μm full width at half maximum (FWHM) at the interaction region. Forward diffraction was measured using the CSPAD detector of the CXI instrument with a pixel size of 110×110 μm 2 and a total of 2.3 million pixels. The detector metrology was established using Ag behenate, microcrystals of thermolysin, and LCLS-provided optical data. Flux numbers were converted into deposited energy (dose) using the program RADDOSE.","PS II diffraction data was processed with a new software suite (cctbx.xfel from Lawrence Berkeley National Laboratory, Berkeley, Calif.) that builds upon components developed previously in the synchrotron context for picking Bragg spots (spotfinder Lawrence Berkeley National Laboratory, Berkeley, Calif.) and autoindexing (labelit Lawrence Berkeley National Laboratory, Berkeley, Calif.), and employs established methods for the integration of Bragg spot intensities by pixel summation. Individual reflections were scaled and merged without separately accounting for the partiality fraction of each observation. The structure was solved by molecular replacement using Phaser from University of Cambridge, Cambridge, United Kingdom.","In some embodiments, the injector is comprised of many off-the-shelf parts. The capillary is a tapered 1 m long borosilicate glass capillary, New Objective, Woburn, Mass., with inner diameters of 50 μm, 75 μm, and 100 μm. The reservoir used in Siena, Laksmono, et al., 2012, was a tapered Eppendorf, Hamburg, Germany, microcentrifuge tube that was placed inside of a pressure cell from a TSI, Inc., Shoreview, Minn., electrospray box. A more off-the-shelve reservoir has been developed and used in unpublished work. It involves a Shimadzu, Tokyo, Japan, autosampler vial which acts as the reservoir for the crystal suspension. There is a simpler 300 μL polypropylene vial with a PTFE/silicone septum. For better visibility of the sample, a 200 μL “Q-sert” glass autosampler vial is used. Both use plastic caps with a polymer septum which allows the capillary, platinum electrode, and pressure line to pierce through and interact with the fluid in the reservoir. Both the capillary and platinum electrode use Upchurch, Oak Harbor, Wash., polymer sleeves 1/16 inch×0.155 inch and 0.011 inch×0.025 inch, respectively, to easily pass in and out of the septum. The capillary tip and platinum electrode are submerged near the bottom of the reservoir, while ensuring that the sleeve is not submerged below the fluid level. The reservoir is pressurized by a nitrogen gas line that interfaces with a ¼ inch, 20 gage stainless steel blunt tip Luer Lock needle. Pressures of 0-20 psig are typically applied.","FIG. 11 is a graph 1100 that illustrates example flow rate measurement made during example electrospun liquid jets experiments using 30% glycerol and 10% PEG 2000 liquid for various capillaries inner diameter (50-100 μm), according to various embodiments. The horizontal axis 1102 indicates pressure difference applied by a the pump 932 or 1032 , in psi. The logarithmic vertical axis 1104 indicates flow rate in μl/min. Using a 100 micron inner diameter capillary, points along trace 1112 are obtained, with flow rates between about 2 and about 3 μl/min. Using a 75 micron inner diameter capillary, points along trace 1114 are obtained, with flow rates between about 0.8 and about 1.1 μl/min. Using a 50 micron inner diameter capillary, points along trace 1116 are obtained, with flow rates between about 0.12 and about 0.2 μl/min. Thus flow rates below about 3 μl/min are obtained. In contrast, flow rates from GDVN are much higher as indicated by region 1120 , e.g., at about 10 μl/min and above, even using greater pressure differences than on axis 1102 .","In embodiments for which results are depicted in FIG. 11 , sample flow rate was measured for a sample solution of 30% (by weight or volume, indicates by w/v) glycerol, 10% (w.v) PEG 2000, pH 6.5, 5 mM CaCl2, 100 mM MES buffer solution. The sample solution was emitted into vacuum from capillary tubes of inner diameter (ID) 50 microns, or 75 microns or 100 microns that were 114 cm long or 110 cm long or 120 cm long, respectively.","In some embodiments, carrier fluid comprises 10% by volume PEG 2000 and 30% sucrose solution with a sucrose concentration in a range from about 1.1 Molar to about 1.4 Molar. Table 5 summarizes flow rate for electrospun jet in vacuo with various sucrose concentrations and 10% PEG 2000 liquid through 100 cm long capillary with a 75 micron or 100 micron inner diameter."," TABLE 5 Flow rate for various sucrose concentrations and 10% PEG 2000 liquid in capillaries of different inner diameter (ID). Sucrose ID ΔP Flow Rate (Molar) (microns) (psi) (μl/minute) 1.1 75 15.7 0.73 1.1 75 17.7 0.75 1.1 75 19.7 0.79 1.2 75 15.7 0.58 1.2 75 17.7 0.62 1.2 75 19.7 0.66 1.4 75 15.7 0.33 1.4 75 17.7 0.40 1.4 75 19.7 0.53 1.1 100 15.7 1.84 1.1 100 17.7 2.15 1.1 100 19.7 2.43 1.2 100 15.7 1.5 1.2 100 17.7 1.7 1.2 100 19.7 1.81 1.4 100 15.7 1.15 1.4 100 17.7 1.2 1.4 100 19.7 1.41 ","Electrospun liquid jets have several features valuable for SFX experiments: simple design—no differential pumping shroud surrounds the jet and sample is loaded in a microcentrifuge tube, low flow rate (about 0.14 to about 3.1 μl/min), compatibility with highly viscous solutions (i.e. 30% glycerol) often used for biological samples, open silica capillary design enables fiber optical laser integration for future pump-probe experiments. Nanoflow liquid jet with protein crystals in vacuo complements the GDVN approach%3b and the ability of the nanoflow liquid jet to operate with few hundred nanoliter per minute flow rate opens SFX to a wider array of structural biology problems","The techniques presented here enable several applications. In general, the characteristics are: Lower sample consumption rate opens SFX to more precious samples%3b simple design allows for facile sample recovery%3b sample settling issue is resolved using highly viscous solutions%3b open access in the vacuum chamber facilitates complex experiments such as simultaneous x-ray emission spectroscopy/x-ray diffraction or time-resolved pump-probe experiments. National laboratory uses enabled include: SFX with 4th generation x-ray lasers like the LCLS and Next Generation Light Source%3b SFX at 3rd generation synchrotrons%3b other single-shot x-ray diffraction experiments such as virus imaging, catalytic nanomaterials, or solution scattering%3b and, sample delivery source for mass spectrometers. Commercial possibilities include SFX with 4th generation x-ray lasers like the LCLS and Next Generation Light Source%3b SFX at 3rd generation synchrotrons%3b other single-shot x-ray diffraction experiments such as virus imaging, catalytic nanomaterials, or solution scattering%3b and, sample delivery source for mass spectrometers.","Controller Hardware Overview","FIG. 12 is a block diagram that illustrates a computer system 1200 upon which an embodiment of the invention may be implemented. Computer system 1200 includes a communication mechanism such as a bus 1210 for passing information between other internal and external components of the computer system 1200 . Information is represented as physical signals of a measurable phenomenon, typically electric voltages, but including, in other embodiments, such phenomena as magnetic, electromagnetic, pressure, chemical, molecular atomic and quantum interactions. For example, north and south magnetic fields, or a zero and non-zero electric voltage, represent two states (0, 1) of a binary digit (bit). Other phenomena can represent digits of a higher base. A superposition of multiple simultaneous quantum states before measurement represents a quantum bit (qubit). A sequence of one or more digits constitutes digital data that is used to represent a number or code for a character. In some embodiments, information called analog data is represented by a near continuum of measurable values within a particular range. Computer system 1200 , or a portion thereof, constitutes a means for performing one or more steps of one or more methods described herein.","A sequence of binary digits constitutes digital data that is used to represent a number or code for a character. A bus 1210 includes many parallel conductors of information so that information is transferred quickly among devices coupled to the bus 1210 . One or more processors 1202 for processing information are coupled with the bus 1210 . A processor 1202 performs a set of operations on information. The set of operations include bringing information in from the bus 1210 and placing information on the bus 1210 . The set of operations also typically include comparing two or more units of information, shifting positions of units of information, and combining two or more units of information, such as by addition or multiplication. A sequence of operations to be executed by the processor 1202 constitutes computer instructions.","Computer system 1200 also includes a memory 1204 coupled to bus 1210 . The memory 1204 , such as a random access memory (RAM) or other dynamic storage device, stores information including computer instructions. Dynamic memory allows information stored therein to be changed by the computer system 1200 . RAM allows a unit of information stored at a location called a memory address to be stored and retrieved independently of information at neighboring addresses. The memory 1204 is also used by the processor 1202 to store temporary values during execution of computer instructions. The computer system 1200 also includes a read only memory (ROM) 1206 or other static storage device coupled to the bus 1210 for storing static information, including instructions, that is not changed by the computer system 1200 . Also coupled to bus 1210 is a non-volatile (persistent) storage device 1208 , such as a magnetic disk or optical disk, for storing information, including instructions, that persists even when the computer system 1200 is turned off or otherwise loses power.","Information, including instructions, is provided to the bus 1210 for use by the processor from an external input device 1212 , such as a keyboard containing alphanumeric keys operated by a human user, or a sensor. A sensor detects conditions in its vicinity and transforms those detections into signals compatible with the signals used to represent information in computer system 1200 . Other external devices coupled to bus 1210 , used primarily for interacting with humans, include a display device 1214 , such as a cathode ray tube (CRT) or a liquid crystal display (LCD), for presenting images, and a pointing device 1216 , such as a mouse or a trackball or cursor direction keys, for controlling a position of a small cursor image presented on the display 1214 and issuing commands associated with graphical elements presented on the display 1214 .","In the illustrated embodiment, special purpose hardware, such as an application specific integrated circuit (IC) 1220 , is coupled to bus 1210 . The special purpose hardware is configured to perform operations not performed by processor 1202 quickly enough for special purposes. Examples of application specific ICs include graphics accelerator cards for generating images for display 1214 , cryptographic boards for encrypting and decrypting messages sent over a network, speech recognition, and interfaces to special external devices, such as robotic arms and medical scanning equipment that repeatedly perform some complex sequence of operations that are more efficiently implemented in hardware.","Computer system 1200 also includes one or more instances of a communications interface 1270 coupled to bus 1210 . Communication interface 1270 provides a two-way communication coupling to a variety of external devices that operate with their own processors, such as printers, scanners and external disks. In general the coupling is with a network link 1278 that is connected to a local network 1280 to which a variety of external devices with their own processors are connected. For example, communication interface 1270 may be a parallel port or a serial port or a universal serial bus (USB) port on a personal computer. In some embodiments, communications interface 1270 is an integrated services digital network (ISDN) card or a digital subscriber line (DSL) card or a telephone modem that provides an information communication connection to a corresponding type of telephone line. In some embodiments, a communication interface 1270 is a cable modem that converts signals on bus 1210 into signals for a communication connection over a coaxial cable or into optical signals for a communication connection over a fiber optic cable. As another example, communications interface 1270 may be a local area network (LAN) card to provide a data communication connection to a compatible LAN, such as Ethernet. Wireless links may also be implemented. Carrier waves, such as acoustic waves and electromagnetic waves, including radio, optical and infrared waves travel through space without wires or cables. Signals include man-made variations in amplitude, frequency, phase, polarization or other physical properties of carrier waves. For wireless links, the communications interface 1270 sends and receives electrical, acoustic or electromagnetic signals, including infrared and optical signals, that carry information streams, such as digital data.","The term computer-readable medium is used herein to refer to any medium that participates in providing information to processor 1202 , including instructions for execution. Such a medium may take many forms, including, but not limited to, non-volatile media, volatile media and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 1208 . Volatile media include, for example, dynamic memory 1204 . Transmission media include, for example, coaxial cables, copper wire, fiber optic cables, and waves that travel through space without wires or cables, such as acoustic waves and electromagnetic waves, including radio, optical and infrared waves. The term computer-readable storage medium is used herein to refer to any medium that participates in providing information to processor 1202 , except for transmission media.","Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, a hard disk, a magnetic tape, or any other magnetic medium, a compact disk ROM (CD-ROM), a digital video disk (DVD) or any other optical medium, punch cards, paper tape, or any other physical medium with patterns of holes, a RAM, a programmable ROM (PROM), an erasable PROM (EPROM), a FLASH-EPROM, or any other memory chip or cartridge, a carrier wave, or any other medium from which a computer can read. The term non-transitory computer-readable storage medium is used herein to refer to any medium that participates in providing information to processor 1202 , except for carrier waves and other signals.","Logic encoded in one or more tangible media includes one or both of processor instructions on a computer-readable storage media and special purpose hardware, such as ASIC 1220 .","Network link 1278 typically provides information communication through one or more networks to other devices that use or process the information. For example, network link 1278 may provide a connection through local network 1280 to a host computer 1282 or to equipment 1284 operated by an Internet Service Provider (ISP). ISP equipment 1284 in turn provides data communication services through the public, world-wide packet-switching communication network of networks now commonly referred to as the Internet 1290 . A computer called a server 1292 connected to the Internet provides a service in response to information received over the Internet. For example, server 1292 provides information representing video data for presentation at display 1214 .","The invention is related to the use of computer system 1200 for implementing the techniques described herein. According to one embodiment of the invention, those techniques are performed by computer system 1200 in response to processor 1202 executing one or more sequences of one or more instructions contained in memory 1204 . Such instructions, also called software and program code, may be read into memory 1204 from another computer-readable medium such as storage device 1208 . Execution of the sequences of instructions contained in memory 1204 causes processor 1202 to perform the method steps described herein. In alternative embodiments, hardware, such as application specific integrated circuit 1220 , may be used in place of or in combination with software to implement the invention. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.","The signals transmitted over network link 1278 and other networks through communications interface 1270 , carry information to and from computer system 1200 . Computer system 1200 can send and receive information, including program code, through the networks 1280 , 1290 among others, through network link 1278 and communications interface 1270 . In an example using the Internet 1290 , a server 1292 transmits program code for a particular application, requested by a message sent from computer 1200 , through Internet 1290 , ISP equipment 1284 , local network 1280 and communications interface 1270 . The received code may be executed by processor 1202 as it is received, or may be stored in storage device 1208 or other non-volatile storage for later execution, or both. In this manner, computer system 1200 may obtain application program code in the form of a signal on a carrier wave.","Various forms of computer readable media may be involved in carrying one or more sequence of instructions or data or both to processor 1202 for execution. For example, instructions and data may initially be carried on a magnetic disk of a remote computer such as host 1282 . The remote computer loads the instructions and data into its dynamic memory and sends the instructions and data over a telephone line using a modem. A modem local to the computer system 1200 receives the instructions and data on a telephone line and uses an infra-red transmitter to convert the instructions and data to a signal on an infra-red a carrier wave serving as the network link 1278 . An infrared detector serving as communications interface 1270 receives the instructions and data carried in the infrared signal and places information representing the instructions and data onto bus 1210 . Bus 1210 carries the information to memory 1204 from which processor 1202 retrieves and executes the instructions using some of the data sent with the instructions. The instructions and data received in memory 1204 may optionally be stored on storage device 1208 , either before or after execution by the processor 1202 .","FIG. 13 illustrates a chip set 1300 upon which an embodiment of the invention may be implemented. Chip set 1300 is programmed to perform one or more steps of a method described herein and includes, for instance, the processor and memory components described with respect to FIG. 11 incorporated in one or more physical packages (e.g., chips). By way of example, a physical package includes an arrangement of one or more materials, components, and/or wires on a structural assembly (e.g., a baseboard) to provide one or more characteristics such as physical strength, conservation of size, and/or limitation of electrical interaction. It is contemplated that in certain embodiments the chip set can be implemented in a single chip. Chip set 1300 , or a portion thereof, constitutes a means for performing one or more steps of a method described herein.","In one embodiment, the chip set 1300 includes a communication mechanism such as a bus 1301 for passing information among the components of the chip set 1300 . A processor 1303 has connectivity to the bus 1301 to execute instructions and process information stored in, for example, a memory 1305 . The processor 1303 may include one or more processing cores with each core configured to perform independently. A multi-core processor enables multiprocessing within a single physical package. Examples of a multi-core processor include two, four, eight, or greater numbers of processing cores. Alternatively or in addition, the processor 1303 may include one or more microprocessors configured in tandem via the bus 1301 to enable independent execution of instructions, pipelining, and multithreading. The processor 1303 may also be accompanied with one or more specialized components to perform certain processing functions and tasks such as one or more digital signal processors (DSP) 1307 , or one or more application-specific integrated circuits (ASIC) 1309 . A DSP 1307 typically is configured to process real-world signals (e.g., sound) in real time independently of the processor 1303 . Similarly, an ASIC 1309 can be configured to performed specialized functions not easily performed by a general purposed processor. Other specialized components to aid in performing the inventive functions described herein include one or more field programmable gate arrays (FPGA) (not shown), one or more controllers (not shown), or one or more other special-purpose computer chips.","The processor 1303 and accompanying components have connectivity to the memory 1305 via the bus 1301 . The memory 1305 includes both dynamic memory (e.g., RAM, magnetic disk, writable optical disk, etc.) and static memory (e.g., ROM, CD-ROM, etc.) for storing executable instructions that when executed perform one or more steps of a method described herein. The memory 1305 also stores the data associated with or generated by the execution of one or more steps of the methods described herein.","Alternatives and Modifications","In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. Throughout this specification and the claims, unless the context requires otherwise, the word “comprise” and its variations, such as “comprises” and “comprising,” will be understood to imply the inclusion of a stated item, element or step or group of items, elements or steps but not the exclusion of any other item, element or step or group of items, elements or steps. Furthermore, the indefinite article “a” or “an” is meant to indicate one or more of the item, element or step modified by the article.","REFERENCES","The entire contents of each of the following are hereby incorporated by reference as if fully set forth herein, except as the terminology is inconsistent with the terminology presented herein. Allmaier, G. N., C. Laschober, \u0026 W. W. Szymanski (2008). “Nano ES GEMMA and PDMA, New Tools for the Analysis of Nanobioparticles—Protein Complexes, Lipoparticles, and Viruses.” Journal of the American Society for Mass Spectrometry 19: 1062-1068. Aquila, A., M. S. Hunter, et al. (2012). “Time-resolved protein nanocrystallography using an X-ray free-electron laser.” Optics Express 20(3): 2706-2716. Barty, A., C. Caleman, et al. (2011). “Self-terminating X-ray diffraction gates femtosecond serial nanocrystallography measurements.” Nature Photonics 6: 35-40. Benner, W. H., et al. (2008). “Non-destructive characterization and alignment of aerodynamically focused particle beams using single particle charge detection.” Journal of Aerosol Science 39: 917-928 Bogan, M. J., et al. (2008). “Single particle X-ray diffractive imaging.” Nano Letters 8: 310-316. Chapman, H., P. Fromme, et al. (2011). “Femtosecond x-ray protein nanocrystallography.” Nature 470: 73-77. DePonte, D. P., R. B. Doak, et al. (2009). “SEM imaging of liquid jets.” Micron, 40(4): 507-509. DePonte, D. P., K. Nass, et al. (2011). Sample injection for pulsed x - ray sources . Prague, Czech Republic, SPIE. DePonte, D. P., U. Weierstall, et al. (2008). “Gas dynamic virtual nozzle for generation of microscopic droplet streams.” J. Phys. D: Appl. Phys. 41: 195505. Ganon-Calvo, A. M., D. P. DePonte, et al. (2010). “Liquid Capillary Micro/Nanojets in Free-Jet Expansion.” Small 6(7): 822-824. Hunter, M. S., D. P. DePonte, et al. (2011). “X-ray Diffraction from Membrane Protein Nanocrystals.” Biophysical Journal 100(1): 198-206. Johansson, L. C., D. Arnlund, et al. (2012). “Lipidic phase membrane protein femtosecond nanocrystallography.” Nature Methods 9(3): 263-265. Jung, J. H., J. E. Lee, \u0026 S. S. Kim (2009). “Generation of Nonagglomerated Airborne Bacteriophage Particles Using an Electrospray Technique.” Analytical Chemistry 81: 2985-2990, doi:10.1021/ac802584z Koopmann, R., K. Cupelli, et al. (2012). “In vivo protein crystallization opens new routes in structural biology.” Nature Methods 9(3): 259-262. Ku, B. K., and S. S. Kim (2003). “Electrohydrodynamic spraying characteristics of glycerol solutions in vacuum.” Journal of Electrostatics 57(2): 109-128. Lomb, L., T. Barends, et al. (2011). “Radiation damage in protein serial femtosecond crystallography using an X-ray free-electron laser.” Physical Review B 84: 214111. Marginean, I., V. Znamenskiy, \u0026 A. Vertes (2006). “Charge Reduction in Electrosprays: Slender Nanojets as Intermediates.” Journal of Physical Chemistry B 110: 6397-6404, doi:10.1021/jp055708k Modesto-Lopez, L. B., E. J. Thimsen, A. M. Collins, R. E. Blankenship \u0026 P. Biswas (2009). “Electrospray-assisted characterization and deposition of chlorosomes to fabricate a biomimetic light-harvesting device.” Energy \u0026 Environmental Science 3: 216-222 Oshea, J. N., J. B. Taylor, et al. (2007). “Electrospray deposition of carbon nanotubes in vacuum.” Nanotechnology 18(3): 035707. Patriksson, A., E. Marklund, \u0026 D. van der Spoel (2007). “Protein structures under electrospray conditions.” Biochemistry 46: 933-945. Shapiro, D. A., H. N. Chapman, et al. (2008). “Powder diffraction from a continuous microjet of submicrometer protein crystals.” J. Synchrotron. Radiat. 15(Pt 6): 593-599. Sierra, R. G., H. Laksmono, et al. (2012). “Nanoflow electrospinning serial femtosecond crystallography.” Acta. Cryst. D. 68(Pt 11): 1584-1587. Smith, J. N., R. C. Flagan, \u0026 J. J. Beauchamp (2002). “Droplet evaporation and discharge dynamics in electrospray ionization.” Journal of Physical Chemistry A 106: 9957-9967. Swarbrick, J. C., J. B. Taylor, et al. (2006). “Electrospray deposition in vacuum.” Applied Surface Science 252(15): 5622-5626. Wortman, A., et al. (2007). “Shrinking Droplets in Electrospray Ionization and Their Influence on Chemical Equilibria.” Journal of the American Society for Mass Spectrometry 18: 385-393. "],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:","FIG. 1A is a block diagram that illustrates example use of gas dynamic virtual nozzle (GDVN) for serial femtosecond X-ray crystallography%3b","FIG. 1B through FIG. 1E are photographs that illustrate breakdown of electrospray under exposure to x-rays at atmospheric pressures%3b","FIG. 2A and FIG. 2B are block diagrams that illustrate two views of an example apparatus for performing and testing nanoflow serial femtosecond X-ray protein crystallography, according to an embodiment%3b","FIG. 2C and FIG. 2D are diagrams that illustrate a conical counter electrode with apex removed in oblique and plan views, respectively, according to an embodiment%3b","FIG. 2E and FIG. 2F are block diagrams that illustrate a quad-electrode conical counter electrode with apex removed in oblique and plan views, respectively, according to an embodiment%3b","FIG. 3 is a photograph that illustrates example nanoflow liquid jet produced by apparatus of FIG. 2 , according to an embodiment%3b","FIG. 4 is flowchart that illustrates an example method, according to one embodiment%3b","FIG. 5A and FIG. 5B are block diagrams that illustrate spacing of components of the FIG. 1 apparatus for the Linac Coherent Light Source%27s (LCLS) Coherent X-ray Imaging (CXI) endstation, according to an embodiment%3b","FIG. 6 is a is a photograph that illustrates example electrospray produced by apparatus of FIG. 5A and FIG. 5B , according to an embodiment%3b","FIG. 7 and FIG. 8 are photographs that illustrate example reduction of sample fluid collection on counter-electrode, according to an embodiment%3b","FIG. 9 is a block diagram that illustrates an experimental nanoflow liquid jet for SFX, according to an embodiment%3b","FIG. 10A is a block diagram that illustrates an experimental nanoflow liquid jet for SFX, according to another embodiment","FIG. 10B is a block diagram that illustrates panels of pixels that record X-ray scattering intensity from crystals in a nanoflow liquid jet of FIG. 10A , according to an embodiment%3b","FIG. 11 is a graph that illustrates example flow rate measurement made during example electrospun liquid jets experiments, according to various embodiments%3b","FIG. 12 is a block diagram that illustrates a computer system upon which an embodiment of the invention may be implemented%3b and","FIG. 13 illustrates a chip set upon which an embodiment of the invention may be implemented."]},"government_interest":"STATEMENT OF GOVERNMENTAL INTEREST This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,275,844","html":"https://www.labpartnering.org/patents/9,275,844","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,275,844"},"labs":[{"uuid":"b9bb03a5-2c32-4cba-a2e3-024938bcba78","name":"Brookhaven National Laboratory","tto_url":"https://www.bnl.gov/techtransfer/ ","contact_us_email":"tech@bnl.gov","avatar":"https://www.labpartnering.org/files/labs/1","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/b9bb03a5-2c32-4cba-a2e3-024938bcba78"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Michael J. Bogan","location":"San Francisco, CA, US"},{"name":"Hartawan Laksmono","location":"Sunnyvale, CA, US"},{"name":"Raymond G. Sierra","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A method comprising:providing a sample liquid by flowing a plurality of a first target of interest with a carrier liquid%3b andinjecting the sample liquid through a capillary tube at a rate of about 4 microliters per minute or less than 4 microliters per minute, without a gas sheath flow, to form a cone or jet at a first position outside the capillary tube,whereinthe first position is configured to intersect an X-ray beam%3bthe carrier liquid is electrically conductive%3b andinjecting the sample liquid further comprises injecting the sample liquid by applying a first voltage to the sample liquid upstream of the first position and a different second voltage to a counter electrode downstream of the first position."},{"idx":"00002","text":"A method as recited in claim 1, wherein injecting the sample liquid further comprises injecting the sample liquid at a rate of about 1 microliter per minute or less than 1 microliter per minute."},{"idx":"00003","text":"A method as recited in claim 1, wherein providing the sample liquid further comprises providing the sample liquid by flowing a plurality of nanoscale crystals of the first target of interest with the carrier fluid."},{"idx":"00004","text":"A method as recited in claim 3, wherein the nanoscale crystals are each about 500 nanometers or smaller than 500 nanometers in a largest dimension."},{"idx":"00005","text":"A method as recited in claim 1, wherein providing the sample liquid further comprises providing the sample liquid by flowing the carrier liquid in a concentric flow around the plurality of the first target of interest."},{"idx":"00006","text":"A method as recited in claim 1, wherein injecting the sample liquid further comprises injecting the sample liquid into a vacuum chamber through a capillary tube that terminates inside the vacuum chamber%3b the first position is inside the vacuum chamber%3b and the counter-electrode is disposed inside the vacuum chamber."},{"idx":"00007","text":"A method as recited in claim 6, wherein the viscosity of the carrier liquid is about 3 centipoise or greater than 3 centipoise."},{"idx":"00008","text":"A method as recited in claim 1, wherein the sample liquid in the jet has a diameter about equal to a diameter of the X-ray beam."},{"idx":"00009","text":"A method as recited in claim 8, wherein the sample liquid in the jet has a diameter of about one micrometer or less than one micrometer."},{"idx":"00010","text":"A method as recited in claim 6, wherein the vacuum chamber does not include a shroud to separate the vacuum chamber into two or more volumes pumped to different vacuum pressures."},{"idx":"00011","text":"A method as recited in claim 1, wherein injecting the sample liquid through the capillary tube further comprises injecting the sample liquid through a silicon capillary tube of diameter of about 25 micrometers, or about 95 micrometers or from 25 micrometers to 95 micrometers."},{"idx":"00012","text":"A method as recited in claim 1, wherein:the X-ray beam is a femtosecond pulse high energy X-ray beam%3b andthe method further comprises measuring at an X-ray detector array an X-ray scattering pattern for the first target in the sample liquid in response to exposing the cone or jet of the sample liquid to the X-ray beam."},{"idx":"00013","text":"A method as recited in claim 1, wherein the carrier liquid comprises 10% by volume PEG 2000 and 30% sucrose solution with a sucrose concentration of about 1.1 Molar or about 1.4 Molar or in a range from 1.1 Molar to 1.4 Molar."},{"idx":"00014","text":"An apparatus comprising:an inline mixing apparatus configured to produce a sample liquid from a plurality of a target of interest and an electrically conductive carrier fluid%3ba capillary tube in fluid communication with the inline mixing apparatus at a first end configured to supply the sample liquid inside the capillary tube, wherein the capillary tube is open at a distal end opposite to the first end%3ba voltage source configured to apply a first voltage to the sample liquid inside the capillary tube%3ba counter electrode configured to be charged at a different second voltage%3b anda source of an X-ray beam configured to intersect a cone or jet of the sample liquid at a first position between the distal end of the capillary tube and the counter electrode,whereina different concentric tube configured to provide a gas sheath flow is omitted."},{"idx":"00015","text":"An apparatus comprising:means for providing a sample liquid by flowing a plurality of a first target of interest with a carrier liquid%3b andmeans for injecting the sample liquid through a capillary tube at a rate of about 4 microliter per minute or less than 4 microliters per minute without a gas sheath flow to form a cone or jet at a first position outside the capillary tube,whereinthe first position is configured to intersect an X-ray beam%3bthe carrier liquid is electrically conductive%3b andinjecting the sample liquid further comprises injecting the sample liquid by applying a first voltage to the sample liquid upstream of the first position and a different second voltage to a counter electrode downstream of the first position."},{"idx":"00016","text":"A non-transitory computer-readable medium carrying one or more sequences of instructions, wherein execution of the one or more sequences of instructions by one or more processors causes an apparatus to perform:applying a first voltage to a sample liquid and a different second voltage to a counter electrode%3binjecting the sample liquid through a capillary tube at a rate of about 4 microliters per minute or less than 4 microliters per minute without a gas sheath flow, to form a cone or jet at a first position downstream of the capillary tube and upstream of the counter electrode%3b andcausing an X-ray source to generate an X-ray beam that intersects the cone or jet at the first position,wherein the sample liquid comprises a plurality of a target of interest in flow with an electrically conductive carrier fluid."},{"idx":"00017","text":"An apparatus as recited in claim 14, wherein the inline mixing apparatus is a concentric flow apparatus configured to flow the carrier liquid in a concentric flow around the plurality of the first target of interest."},{"idx":"00018","text":"An apparatus as recited in claim 15, wherein the means for providing the sample liquid further comprises means for providing the sample liquid by flowing the carrier liquid in a concentric flow around the plurality of the first target of interest."},{"idx":"00019","text":"A non-transitory computer-readable medium as recited in claim 16, wherein injecting the sample liquid further comprises causing the carrier liquid to flow in a concentric flow around the plurality of the first target of interest. "}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"167","main-group":"49","action-date":"2016-03-01","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","J","167","49","2016-03-01","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"16","main-group":"49","action-date":"2016-03-01","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"04","main-group":"49","action-date":"2016-03-01","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"B","version":"","subclass":"J","subgroup":"00","main-group":"4","action-date":"2016-03-01","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"N","subgroup":"20","main-group":"23","action-date":"2016-03-01","origination":"","symbol-position":"L"}],"document_number":"20130308756","document_published_on":"2013-11-21","document_kind":"","document_country":""},{"number":"9,287,598","artifact":"grant","title":"RF window assembly comprising a ceramic disk disposed within a cylindrical waveguide which is connected to rectangular waveguides through elliptical joints","filed_on":"2014-05-07","issued_on":"2016-03-15","published_on":"2014-11-13","abstract":"A high-power microwave RF window is provided that includes a cylindrical waveguide, where the cylindrical waveguide includes a ceramic disk concentrically housed in a central region of the cylindrical waveguide, a first rectangular waveguide, where the first rectangular waveguide is connected by a first elliptical joint to a proximal end of the cylindrical waveguide, and a second rectangular waveguide, where the second rectangular waveguide is connected by a second elliptical joint to a distal end of the cylindrical waveguide.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims priority from U.S. Provisional Patent Application 61/821,392 filed May 9, 2013, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under grant (or contract) no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","FIELD OF THE INVENTION","The present invention relates generally to high power microwave systems. More specifically, it relates to RF window designs for high power microwave devices such as klystrons.","BACKGROUND OF THE INVENTION","RF windows are used to separate high and low vacuum regions in high power microwave systems, such as klystrons. RF breakdowns in megawatt environments could damage the window. What is needed is an RF window to reduce electric and magnetic fields in the waveguide joints and the ceramic.","SUMMARY OF THE INVENTION","To address the needs in the art, a high-power microwave RF window is provided that includes a cylindrical waveguide, where the cylindrical waveguide includes a ceramic disk concentrically housed in a central region of the cylindrical waveguide, a first rectangular waveguide, where the first rectangular waveguide is connected by a first elliptical joint to a proximal end of the cylindrical waveguide, and a second rectangular waveguide, where the second rectangular waveguide is connected by a second elliptical joint to a distal end of the cylindrical waveguide.","In one aspect of the invention, the high-power microwave RF window is capable of supporting a traveling wave inside the ceramic disk.","According to another aspect of the invention, the high-power microwave RF window is capable of separating vacuum from atmospheric pressures in a klystron microwave system.","In a further aspect of the invention, the high-power microwave RF window is capable of operating in multi-tens of megawatt power environment.","According to one aspect of the invention, the high-power microwave RF window is capable of minimizing a normal component of an electric field on the surface of the ceramic disk, wherein a traveling wave is created inside the ceramic disk.","In yet another aspect of the invention, the high-power microwave RF window is capable of minimizing a surface magnetic and electric fields on the joints between the circular and rectangular waveguides.","DETAILED DESCRIPTION OF THE INVENTION","In ultra high power RF systems the window between vacuum and atmosphere is one of the components most prone to failure. Improving the reliability of this critical component in a high power environment will increase the reliability of the entire system and reduce the operation price.","In one aspect, the present invention provides a pillbox style RF window with elliptical joint between the circular and rectangular guide. Joint geometry is optimized to create a traveling wave inside the ceramic region and minimize the electric and magnetic field on the surfaces. The RF window is able to separate vacuum from atmosphere in high power microwave systems, such as klystrons. This window is designed to operate in multi-megawatt power environment without faults.","The current invention provides reduced electric and magnetic fields in ceramics and waveguide joints of RF windows. Specifically, the normal component of the electric field on the ceramic surface is minimized and a traveling wave is created inside the ceramic. This is achieved by optimizing the shape of the window and the geometry of the joint between the circular waveguide to the rectangular waveguide. The advantageous features of the window are achieved by optimizing the shape of the window and the geometry of the joint only and without additional matching elements. The matching elements increase complexity and decrease reliability, thus avoiding them is an important feature of this design. FIGS. 1 a - 1 b show perspective views of a high-power microwave RF window in full view and one quadrant view, respectively, according to one embodiment of the invention. As shown in FIG. 1 a , the high-power microwave window includes rectangular guides, circular guides, a ceramic disc and elliptical joints.","This RF window design has superior performance compared to any existing windows in high power RF sources and RF particle accelerators. It is applicable for industrial, medical, military and research applications.","The design can be used at any frequency, first by scaling all dimensions and then making minor optimization due to variation in manufacturing techniques and material properties for the given frequency.","An exemplary high-power microwave RF window was built and successfully tested at SLAC for the ILC prototype L-band positron source. A large number of accelerators in the world, including the SLAC linac operate at S-band. Thus this window, which operates comfortably at 65 MW peak power in S-band, is of great importance for many accelerators. Particular attention was paid to mitigate the high fields on the ceramic and the metal. Trapped and so-called ghost modes were investigated to assure that such modes are outside klystron bandwidths. The present invention can replace the pair of windows in the current the 5045 klystrons by a single window of this design.","To minimize the fields on the ceramic, the traveling wave window approach was implemented, according to one embodiment of the invention. Here, the basic design requirements of the window and the values achieved in simulation are presented in Table 1."," TABLE 1 S-Band Window Design Parameters Parameter Required Achieved Frequency (MHz) 2856 2856 3 dB BW (MHz) ≧20 ≧100 Reflection (S11) \u003c−20 dB \u003c−70 dB Peak Power (MW)    65 MW    65 MW Peak E on Ceramic (MV/m) Minimize 1.75 Peak H on Ceramic (KA/m) Minimize 17 Peak E (MV/m) Minimize 11 Peak H (KA/m) Minimize 20 ","The ceramic is housed in a circular waveguide. The inventors minimized the fields on the metal surfaces by optimizing the shape of the joint between the circular and rectangular waveguide. FIG. 1 b shows a quadrant of the window.","To characterize the exemplary embodiment, namely the S-band version of the window, the commercial code CASCADE™ was used for the initial simulations. CASCADE™ uses mode-matching for rapid S parameter analysis and optimization of 2-port passive waveguide components and calculation of frequency and Q of resonators. The 3-D finite-element code HFSS was then used for the final design. For the nominal case of ε=9.6 and thickness of 4 mm the reflection at 2856 MHz is less than −90 dB and the bandwidth at −20 dB is 50 MHz and more than 100 MHz at −3 dB. The reflection is less than −45 dB at 2856 MHz at ±0.2 mm from nominal.","Regarding reflection vs. frequency for the window with varying permittivity of the ceramic, keeping the ceramic thickness at 4 mm, the ceramic permittivity is varied in ε=0.2 increments on either side of the nominal. The reflection is less than −35 dB at 2856 MHz in the worst case of ε=9.6±0.4, which is satisfactory for a practical design.","The maximum electric and magnetic fields on the metal appear on the elliptically-shaped joint between the circular and rectangular waveguides FIGS. 2 a - 2 b show that at 65 MW through the window, the maximum electric field on the metal in area on the joints between circular and rectangular waveguides is 11 MV/m and the maximum electric field in the ceramic is 1.75 MV/m, and the maximum electric field on the joint is 1.75 MV/m.","FIGS. 3 a - 3 b show that the maximum magnetic field on the metal at the joints is 20 kA/m and the maximum magnetic field on the ceramic it is 17 KA/m as shown in FIG. 3 b. ","FIGS. 4-5 show plots of electric ( FIG. 4 ) and magnetic fields ( FIG. 5 ) versus the distance through the waveguide, which show E=1.75 MV/m on the centerline in the ceramic, and E=17.03 KA/m on the centerline in the ceramic, respectively, according to one embodiment of the invention.","As a comparison, the SLAC 5045 klystron uses a dual window, and each window has a maximum electric field of 11.6 MV/m on the circular to rectangular waveguide joint and 3.3 MV/m on the ceramic and 11.6 MV/m on the circular to rectangular waveguide joint and 3.3 MV/m on the ceramic with half of 65 MW transmitted through each window. The new design is a vast improvement considering that only one window is needed instead of two for the same function.","The trapped and ghost modes for this window were investigated. The study included the variation in the ceramic permittivity and thickness based on manufacturing variation. It was found that the nearest ghost mode is more than 200 MHz away from the nominal 2856 MHz mode. The closest trapped mode is more than 60 MHz away.","An exemplary S-band window is provided which comfortably operates at 65 MW, has much lower surface fields than the current S-band windows on the SLAC 5045 klystrons, and a single window of the design offered here can replace the dual window of the 5045.","The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive. Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. For example the cross-section of the of the window could have other shape than circular, or shape of the joint between the input waveguide and the waveguide with a window could be modified to accommodate specific manufacturing process.","All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIGS. 1 a - 1 b show perspective views of a high-power microwave RF window in full view and one quadrant view, according to one embodiment of the invention.","FIGS. 2 a - 2 b show perspective views of a surface electric field on a window quadrant scaled for 65 MW power transmitted through the whole high-power S-band RF window, according to one embodiment of the invention. The fields here are shown for a specific window, field magnitudes will be different in case of different frequency bands.","FIGS. 3 a - 3 b show perspective views of a surface electric field on a window quadrant scaled for 65 MW power transmitted through the whole high-power S-band RF window, according to one embodiment of the invention. The fields here are shown for a specific window, field magnitudes will be different in case of different frequency bands.","FIGS. 4-5 show plots of electric and magnetic fields on the centerline in the ceramic, respectively, according to one embodiment of the invention."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under grant (or contract) no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,287,598","html":"https://www.labpartnering.org/patents/9,287,598","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,287,598"},"labs":[{"uuid":"02bfeac1-ea4d-4356-8c61-b1e0259658d7","name":"Lawrence Berkeley National Laboratory","tto_url":"http://ipo.lbl.gov/","contact_us_email":"rbarcklay@lbl.gov","avatar":"https://www.labpartnering.org/files/labs/2","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/02bfeac1-ea4d-4356-8c61-b1e0259658d7"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Sami G. Tantawi","location":"Stanford, CA, US"},{"name":"Valery A. Dolgashev","location":"San Carlos, CA, US"},{"name":"Anahid D. Yeremian","location":"Menlo Park, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A high-power microwave RF window, comprising:a. a cylindrical waveguide, wherein said cylindrical waveguide comprises a ceramic disk concentrically housed in a central region of said cylindrical waveguide%3bb. a first rectangular waveguide, wherein said first rectangular waveguide is connected by a first elliptically-shaped joint to a proximal end of said cylindrical waveguide%3b andc. a second rectangular waveguide, wherein said second rectangular waveguide is connected by a second elliptically-shaped joint to a distal end of said cylindrical waveguide, wherein said elliptically-shaped joint spans from a flat surface of said rectangular waveguide to a wall of said cylindrical waveguide, wherein said elliptically-shaped joint is disposed to create a traveling wave inside said ceramic disk and disposed to minimize an electric field on a surface of said ceramic disk and disposed to minimize an electric field inside said ceramic disk."},{"idx":"00002","text":"The high-power microwave RF window according to claim 1, wherein said high-power microwave RF window is capable of supporting said traveling wave inside said ceramic disk."},{"idx":"00003","text":"The high-power microwave RF window according to claim 1, wherein said high-power microwave RF window is capable of separating vacuum from atmospheric pressures in a klystron microwave system."},{"idx":"00004","text":"The high-power microwave RF window according to claim 1, wherein said high-power microwave RF window is capable of operating in a multi-tens of megawatt power environment."},{"idx":"00005","text":"The high-power microwave RF window according to claim 1, wherein said high-power microwave RF window is capable of minimizing a normal component of an electric field on said ceramic disk."},{"idx":"00006","text":"The high-power microwave RF window according to claim 1, wherein said high-power microwave RF window is capable of minimizing a surface magnetic and electric fields on the first and second elliptical joints between the circular waveguide and the respective first and second rectangular waveguides. "}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"08","main-group":"1","action-date":"2016-03-15","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","P","08","1","2016-03-15","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"08","main-group":"1","action-date":"2016-03-15","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"36","main-group":"23","action-date":"2016-03-15","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"08","main-group":"5","action-date":"2016-03-15","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"10","main-group":"25","action-date":"2016-03-15","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"12","main-group":"23","action-date":"2016-03-15","origination":"","symbol-position":"L"}],"document_number":"20140333395","document_published_on":"2014-11-13","document_kind":"","document_country":""},{"number":"7,037,807","artifact":"grant","title":"Electric field induced spin-polarized current","filed_on":"2003-12-24","issued_on":"2006-05-02","published_on":"","abstract":"A device and a method for generating an electric-field-induced spin current are disclosed. A highly spin-polarized electric current is generated using a semiconductor structure and an applied electric field across the semiconductor structure. The semiconductor structure can be a hole-doped semiconductor having finite or zero bandgap or an undoped semiconductor of zero bandgap. In one embodiment, a device for injecting spin-polarized current into a current output terminal includes a semiconductor structure including first and second electrodes, along a first axis, receiving an applied electric field and a third electrode, along a direction perpendicular to the first axis, providing the spin-polarized current. The semiconductor structure includes a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant. In one embodiment, the semiconductor structure is a hole-doped semiconductor structure, such as a p-type GaAs semiconductor layer.","description":{"text":["STATEMENT OF GOVERNMENT SPONSORED RESEARCH","The present invention was made with support from the National Science Foundation under grant no. DMR-9814289 and with support from the US Department of Energy, Office of Basic Energy Sciences, under contract DE-AC03-76SF00515. The US Government has certain rights in the invention.","FIELD OF THE INVENTION","The invention relates to a spintronic device and, in particular, to a method of generating spin-polarized electric current in non-magnetic semiconductor materials by applying an electric field.","DESCRIPTION OF THE RELATED ART","Spintronics is a field of electronics in which the spin degree of freedom of an electron is utilized for operations of devices. In particular, spintronic devices made using semiconductors have been an important subject of research because of their potential applications in low power devices with integrated logic and storage functions. While effective spin injection into semiconductors is necessary for such spintronic devices, effective spin injection using only nonmagnetic semiconductors has been an elusive issue. No efficient methods of spin generation and injection in a semiconductor at room temperature have been reported up to now.","Generally, a ferromagnet is used to generate the spin current and inject the spin current into a semiconductor layer. For example, a ferromagnetic metal is often formed on a semiconductor layer for injecting spin current into the semiconductor layer. However, using ferromagnetic metals for spin injection is not practical for most semiconductor applications as ferromagnetic formation is not a common or usual semiconductor processing step and is thus more expensive to implement as specialized processing steps are required. More importantly, conductivity mismatch at the ferromagnet and semiconductor interface causes significant loss of spin polarization at the interface. Thus, only weakly spin-polarized current is injected from the ferromagnetic material into the semiconductor.","Spin injection from a ferromagnetic material into a semiconductor using a “spin filter” has also been demonstrated. U.S. Pat. No. 6,355,953 (Kirczenow) discloses using an atomically ordered interface between suitable ferromagnetic material and suitable semiconductor to create a spin filter. Depending on magnetization, spin current is either permitted or not permitted to flow through the spin filter. However, this method still requires the use of a ferromagnetic material and therefore suffers from the associated disadvantages.","Spin injection from a ferromagnetic electrode into a non-magnetic electrode through a nanocrystal doped with a single active paramagnetic ion has been demonstrated (See U.S. Patent Application 2003/0075772 to Efros et al). This kind of spintronic device requires specific and precise manufacturing steps as the electrodes and the nanocrystal have to be spaced apart at a tunneling distance. Thus, such a spintronic device is difficult to manufacture.","Spin injection from ferromagnetic semiconductors such as Ga 1-x Mn x As into non-magnetic semiconductor has been demonstrated. U.S. Pat. No. 6,482,729 (Ohno et al.) discloses one such technique. Nevertheless, the operating temperature T c is at most 110 K for Ga 1-x Mn x As spintronic devices which temperature is still too low for practical use at room temperature.","Thus, a spintronic device that uses conventional semiconductor material and generates spin polarized current in the absence of a magnetic field is desired.","SUMMARY OF THE INVENTION","In accordance with embodiments of the present invention, a device and a method for generating an electric-field-induced spin current is disclosed. A highly spin-polarized electric current can be generated using a semiconductor structure and an applied electric field across the semiconductor structure. The requirements to use ferromagnets or ferromagnetic semiconductor materials to generate the spin current are entirely obviated. The electric-field-induced spin current of the present invention overcomes the shortcomings of the conventional spin current generation devices using ferromagnetic materials. Another significant advantage of the present invention is that the electric-field-induced spin current can flow without dissipation, thus enabling a new generation of low power devices with integrated logic and storage capabilities.","According to one embodiment of the present invention, a device for injecting spin-polarized current into a current output terminal includes a semiconductor structure. The semiconductor structure includes a first end and an opposite second end disposed along the direction of a first axis. The semiconductor structure further includes a third end disposed along the direction of a second axis perpendicular to the first axis. A first electrode is formed on the first end of the semiconductor structure and a second electrode is formed on the second end of the semiconductor structure. The first and second electrodes are disposed to receive an applied electric field. A third electrode, being the current output terminal in the present embodiment, is formed on the third end of the semiconductor structure. The third electrode provides the spin-polarized current when an electric field is applied across the first and second electrodes. In accordance with the present invention, the semiconductor structure includes a hole-doped semiconductor structure or an undoped zero-gap semiconductor structure and includes a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant.","In one embodiment, the hole-doped semiconductor structure includes a hole-doped semiconductor structure with finite bandgap or zero bandgap. In another embodiment, the semiconductor structure includes an undoped semiconductor of zero bandgap.","In another embodiment, the semiconductor structure includes a hole-doped semiconductor structure of a semiconductor material selected from the group of Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, α-Sn, HgSe, HgTe and alloys of these semiconductor materials.","In an alternate embodiment, a second electric field is applied to the semiconductor structure. The second electric field is applied between the third electrode and the current output terminal. In this manner, a spin-polarized current accompanying a charge current is generated at the current output terminal.","According to another aspect of the present invention, a spintronic device for injecting spin current into a ferromagnetic electrode, a spin LED, and a magnetic switching device can be formed using the electric-field-induced spin current of the present invention.","The present invention is better understood upon consideration of the detailed description below and the accompanying drawings.","DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS","In accordance with the principles of the present invention, a device and a method for generating a highly spin-polarized electric current utilizes a semiconductor structure and an applied electric field across the semiconductor structure. The semiconductor structure includes a hole-doped semiconductor structure of finite bandgap, a hole-doped semiconductor structure of zero bandgap, or an undoped semiconductor of zero bandgap. In one embodiment, an electric field is applied across a hole-doped semiconductor material having a strong spin orbit coupling energy to generate the spin polarized electric current. The spin current, referred herein as an “electric-field-induced spin current,” can be generated at room temperature and is free from rapid relaxation of spins. Because the spin-polarized electric current is generated in a semiconductor material without the use of metallic ferromagnet or ferromagnetic semiconductor, efficient spin injection in a semiconductor can be realized as the spin current is generated inside a semiconductor material itself. As a result, a strongly spin-polarized current can be generated even at room temperature. The spin current thus generated is characterized by a long spin relaxation time making the device of the present invention suitable for practical use.","In the present technology of electronics, motions of electrons are controlled to realize various functions. In such devices, electrons are regarded merely as charged particles and a voltage is applied to move an electron%27s center of mass through materials. However, electrons have another degree of freedom called a spin. The electronic “spin” is a property of the electron and describes the orientation of the electron by its quantum state as “up” or “down.” Spintronics is a newly developed field of electronics where the spin degree of freedom is utilized. Spintronics devices built using only semiconductors are more attractive for practical use because in semiconductors, carrier transport can be easily controlled, as in conventional diodes and transistors. In accordance with the present invention, a device and a method is disclosed for realizing efficient injection of spin-polarized electronics into semiconductors and thereby overcoming many of the limitations of the conventional spintronic devices.","In one embodiment, the device and associated method of the present invention realize an electric-field-induced spin current in conventional hole-doped (p-type) semiconductors. In hole-doped semiconductors, the structure of the valence bands plays major roles in the realization of the present invention. The valence bands in semiconductors with diamond or zincblende structure are made up of p orbitals, and are six-fold degenerate at wavevector k=0. The spin-orbit coupling leads to a splitting of valence bands into four-fold degenerate P 3/2 and two-fold degenerate P 1/2 levels. In a large class of semiconductors, including Si, Ge, GaAs and InSb, the P 3/2 levels form the top of the valence bands, which are separated from S-like conduction bands. Therefore, the valence bands are four-fold degenerate at k=0. These four bands are described by the Hamiltonian known as Luttinger Hamiltonian. For a given wave vector k, the Hamiltonian has two eigenvalues, where each eigenvalue is doubly degenerate. Each doublet is a Kramers doublet, whose degeneracy is ensured by the time reversal and inversion symmetry of the Hamiltonian. They are referred to as the light-hole (LH) and heavy-hole (HH) bands in semiconductors. The light-hole and the heavy-hole bands are split because of the spin-orbit interaction among the P 3/2 levels. The two energy levels cross at the band center k=0. In semiconductors with zincblende structure, such as GaAs, inversion symmetry breaking causes an additional splitting in the LH and HH bands. This splitting is quite small and can be neglected at room temperature.","The spintronic device of the present invention utilizes the effect of the spin-orbit coupling. The spin-orbit coupling gives rise to various phenomena in physics. In an article entitled “Dissipationless Quantum Spin Current at Room Temperature,” published in Science 301, 1348 (2003), authored by the same inventors hereof, the inventors disclosed that in conventional hole-doped semiconductors, the spin-orbit coupling causes a spin-polarized current by applying only an electric field. The size of the effect was evaluated and the inventors found that the spin-polarized current is almost the same or even more than the usual charge current.","It has been known that this physical phenomenon occurs also by the extrinsic spin-orbit coupling between the electron and the random impurity atoms. This extrinsic effect is therefore proportional to the amount of “dirt” in the system, which is very small in the high purity semiconductor materials employed in the semiconductor industry today. The reliance on “dirt” also has unwanted side effects on the transport properties and the performance of the device. To the contrary, the inventors of the present invention are the first to present findings in the aforementioned Science paper where the spin-polarized current is generated by the intrinsic spin-orbit coupling between the electrons and the applied electric field. This intrinsic effect is sufficiently large for practical use and is free from dissipation from impurities.","The electric field induced spin current can be quantitatively understood in terms of the “Berry%27s phase” accumulated by the electron motion. The Berry phase effect requires a coupling of spin and orbital motion of electrons, i.e. the spin-orbit coupling. Depending on the spin direction of the hole, together with the lattice effect, the hole motion will obtain an additional component coming from the Berry phase. This additional motion is perpendicular to both the wavevector k and the applied electric field E, and is opposite for the opposite orientations of spins. Semiclassical equation of motion for the hole is written as:"," ℏ ⁢ ⁢ k . = eE , x . = 1 ℏ ⁢ ⁢ ∂ E ⁢ ⁢ ( k ) ∂ k + k . × F ⁢ ⁢ ( k ) , ( 1 ) where F(k) is a curvature term coming from the Berry phase effect. The Berry curvature F(k) is determined from the wavefunction. For example, in the Luttinger Hamiltonian together with the spherical approximation, this F(k) is proportional to |k| −3 k. It becomes larger when k approaches zero, which is a result of the k-space structure of wavefunctions having a monopole at k=0 coming from touching of the light-hole and heavy-hole bands there.","FIG. 1 shows the trajectory of the hole motion for illustrating how the hole motion is affected by this Berry-phase term. The trajectory can be obtained by integrating equation (1) over the time t. Referring to FIG. 1 , the two arrows denote the direction of the spins. The last term in equation (1) causes a spin current perpendicular to both the electric field E and the direction of the spin S. For example, by applying an electric field E z along the z-axis, the spin current at zero temperature, with spin parallel to the x axis, flowing to the y direction is given by:"," j xy = eE z 12 ⁢ ⁢ π 2 ⁢ ⁢ ( 3 ⁢ k F H - k F L ) , ( 2 ) where k F H and k F L are the Fermi wavevector of the heavy-hole and light-hole bands, respectively. The spin current equation is rotationally invariant, with the covariant form given by: j ij =σ s ε ijk E k ,  (3) where ε ijk is a fully antisymmetric tensor with ε xyz =1. More recently, a full quantum mechanical calculation based on the Kubo formula by the same authors hereof finds a quantum correction to the semiclassical result of equation (2), where the spin conductivity is given by"," σ s = e 6 ⁢ ⁢ π 2 ⁢ ⁢ ( k F H - k F L ) . ","The fundamental response equation (3) is invariant under the reversal of the arrow of time, and shows that it is possible to induce a dissipationless spin current by an electric field in conventional semiconductors. That is, the spin of the electrons can be transported without any loss of energy, or dissipation. In one embodiment, an electric field along the z direction can induce a spin current along the y direction, with the spin polarization aligned in the x direction. Although actual motion of holes is intervened by scatterings coming from impurities, electron—electron interaction and so forth, the spin current itself is not affected by these scattering events. In other words, the spin conductivity given by equation (2) is completely independent of the mean free path and relaxation rates, and all states below the Fermi energy contribute to the spin current.","The size of the spin current can be estimated. In p-GaAs with the hole density n=10 19 cm −3 , the mobility of the holes at room temperature is μ=50 cm 2 /Vsec. This value corresponds to the conductivity a σ=enμ˜80Ω −1 cm −1 . The unit of the spin conductivity σ s is converted to be the same as that of the conductivity to facilitate comparison. A term σ′ s is defined as σ′ s =(2e/ )σ 5 and can be roughly estimated as"," σ s ′ ∼ e 2 h ⁢ n 1 ⁢ / ⁢ 3 ∼ 80 ⁢ ⁢ Ω - 1 ⁢ cm - 1 . Therefore σ and σ′ s are of the same order for n=10 19 cm −3 . For lower carrier concentration, σ′ s becomes larger than σ. For n=10 16 cm −3 , for example, σ˜0.6Ω −1 cm −1 and σ′ s ˜7Ω −1 cm −1. ","As discussed above, the present invention discloses the generation of a dissipationless spin current in a hole-doped semiconductor, including semiconductor of either finite (non-zero) or zero bandgap, or an undoped semiconductor of zero bandgap by an electric field. The electric-field-induced spin-polarized electric current can be applied to build various spintronic devices. The following description discusses several embodiments of spintronic devices which can be built using the electric-field-induced spin current of the present invention. Of course, the description below is illustrative only and one of ordinary skill in the art would appreciate that other spintronic devices can be built based on these principles to enable the construction of more sophisticated computing devices.","Spin Injection into Semiconductor Devices","FIG. 2 is a schematic diagram illustrating a spintronic device for injecting an electric-field-induced spin current into semiconductors according to one embodiment of the present invention. Because the spin current of the present invention is generated in a semiconductor material, the spin current is particularly useful for spin injection into semi-conductors. In contrast with spin injection into semiconductors from metallic ferromagnet, spin injection using the electric-field-induced spin current of the present invention is free from the problems of conductance mismatch as the injector and the recipient of the spin current are both semiconductors. In other words, by generating the spin current in a semiconductor material, the spin current can be efficiently transported to other regions of the semiconductor, minimizing or eliminating loss of spin polarization.","Referring to FIG. 2 , a spintronic device 10 for spin injection into semiconductors is shown. Spintronic device 10 includes a hole-doped semiconductor structure 11 having a first end and an opposite second end disposed on a first axis. A first electrode 12 is formed on the first end and a second electrode 13 is formed on the second end of the semiconductor structure. Semiconductor structure 11 further includes a third end disposed along the direction of a second axis perpendicular to the first axis. A third electrode 14 is formed on the third end and forms a current output terminal 15 of the spintronic device. To inject spin current into a recipient semiconductor material, the recipient semiconductor material (not shown) can be coupled across terminal 15 and a terminal 16 , opposite and on the same axis as terminal 15 , of spintronic device 10 .","When an electric field V 1 is applied across first and second electrodes 12 and 13 , a spin current (spin-polarized holes or spin-polarized electrons) will flow out of current output terminal 15 . The spin current can thus be injected into the desired recipient semiconductor material by coupling the recipient semiconductor material to terminals 15 and 16 .","In the present description, the terms “spin current” and “spin-polarized current” are used to refer to the current generated as a result of the manipulation and transport of the electron spin. In general, there are two types of spin currents. A “pure” spin current refers to a spin current where the up spin and down spin are exactly equal and counter propagate. Thus, there is no net electric current. On the other hand, a spin-polarized current exists where there are more up-spin moving in one direction than down-spin in the same direction. Thus, there is an electric current flowing but the current is spin polarized. In other words, the spin current accompanies a charge current. In the present description, the terms “spin current” and “spin-polarized current” refer to both types of spin current: the pure spin current and the spin-polarized current with a charge current.","FIG. 3 is a schematic diagram illustrating a spintronic device for injecting an electric-field-induced spin current into semiconductors according to an alternate embodiment of the present invention. The spintronic device of FIG. 2 generates a spin-polarized current that is a pure spin current by the application of an electric field across first and second electrodes 12 and 13 . On the other hand, the spintronic device of FIG. 3 generates a spin-polarized current that accompanies a charge current by applying two electric fields in perpendicular direction to each other.","Referring to FIG. 3 , spintronic device 20 includes a hole-doped semiconductor structure 21 having a first end and an opposite second end disposed on a first axis. A first electrode 22 is formed on the first end and a second electrode 23 is formed on the second end of the semiconductor structure. A first electric field V 1 is applied across the first and second electrodes. Semiconductor structure 21 further includes a third end and a fourth end disposed along the direction of a second axis perpendicular to the first axis. A third electrode 24 is formed on the third end of semiconductor device 21 . In the present embodiment, a second electric field V 2 is applied across third electrode 24 and a current output terminal 25 of the spintronic device. To inject spin current into a recipient semiconductor material, the recipient semiconductor material (not shown) can be coupled across current output terminal 25 and a fourth electrode 26 formed on the fourth end of spintronic device 20 .","In spintronic device 20 , a second electric field V 2 is applied between third electrode 24 and current output terminal 25 . The second electric field, together with the first electric field, generates a spin polarized current at current output terminal 25 that is accompanied by a charge current.","The hole-doped semiconductor structure used in spintronic devices 10 and 20 of FIGS. 2 and 3 can be a p-type semiconductor made of a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant (k=1.38×10 −23 J/K). In one embodiment, the semiconductor material has a spin orbit coupling energy that is greater than approximately 30 meV.","In one embodiment, the hole-doped semiconductor structure includes a p-type semiconductor structure having a doping level of approximately 10 16 to 10 20 atoms/cm 3 .","Furthermore, in one embodiment, the electric field V 1 applied across the first and second electrodes is a DC electric field in the range of 10 3 V/cm to 10 6 V/cm. In other embodiments, the electric field V 1 can be an AC electric field.","As a result of the application of the first electric field V 1 ( FIG. 2 ) or the first and second electric fields V 1 and V 2 ( FIG. 3 ), a spin current is generated and can be injected into a recipient semiconductor structure. In FIGS. 2 and 3 , the recipient semiconductor structure into which spin current is injected is not shown. In most applications, the recipient semiconductor structure and the hole-doped semiconductor structure are formed as an integral semiconductor device, such as an integrated circuit. As such, the third electrode shown in FIGS. 2 and 3 is illustrative only and does not depict an actual physical implementation of the third electrode. In actual implementation, the third electrode is merely the interface between the hole-doped semiconductor structure and the recipient semiconductor structure.","Moreover, the spin current can be injected into a recipient semiconductor structure of either p-type or n-type conductivity. In particular, it is generally more desirable to inject spin current into n-type semiconductors because the spin relaxation time for electrons is much longer than that of holes. For instance, the spin lifetime of electrons in GaAs is of the order of 100 psec at room temperature, 10 3 times longer than that of holes, and by suppressing the D%27yakonov-Perel%27 mechanism, which is one of the major mechanisms for spin relaxation, the spin relaxation time could be even as long as 2 nsec.","As mentioned above, spin injection from ferromagnetic semiconductors, such as (Ga,Mn)As, into n-GaAs through the p-n junction has been successfully demonstrated. However, the prior art structure requires the use of a ferromagnetic semiconductor. The spin injection generated by the spintronic devices of the present invention is achieved by replacing the ferromagnetic semiconductor (Ga,Mn)As with a conventional hole-doped semiconductor layer, such as a p-GaAs layer under an electric field. By eliminating the use of a ferromagnet, the spintronic device of the present invention can be manufactured using standard semiconductor fabrication processes and can be readily applied to construct various types of computing devices.","Spin Injection Device Into Ferromagnet","According to one embodiment of the present invention, a spin injection device into a ferromagnetic electrode can be constructed using the electric-field-induced spin current of the present invention. FIG. 4 is a schematic diagram of a spin injection device for injecting a spin current into a ferromagnetic electrode according to one embodiment of the present invention. Referring to FIG. 4 , a spin injection device 30 includes a hole-doped semiconductor structure 31 attached to a ferromagnetic electrode 32 . The magnetization of the ferromagnetic electrode 32 is along ±x-direction. In the present embodiment, the hole-doped semiconductor structure 31 is a p-type GaAs layer having first and second electrodes disposed along the z-direction for receiving an applied electric field V 1 .","When the electric field is applied along the z-direction between the first and second electrodes, an electric current J Z is induced in the spin injection device 30 and a spin current j xy will flow along the +y direction. The electric current I, flowing out of the ferromagnetic electrode 32 , is a function of the direction of magnetization M.","Although ferromagnetic metals can be used as the ferromagnetic electrode 32 , the use of ferromagnetic metals to receive the spin current is not efficient due to conductance mismatch between the metal and the semiconductor structure. The spin polarization will be reduced at the metal-semiconductor boundary. Alternately, doped ferromagnetic semiconductors are more suitable for use with the spin injection device 30 since the conductance mismatch between the doped ferromagnetic semiconductor and the semiconductor structure is lessened.","By attaching spin injection device 30 to the ferromagnetic electrode 32 , the spin current j xy induces an electric current I when the magnetization of the ferromagnet is along +x-direction while less current is observed for magnetization in the −x-direction. In realistic situation, the ratio of the electric currents I(+x)/I(−x) is determined by that of the tunneling probabilities for parallel and anti-parallel spins at the interface with the electrode. This ratio is still expected to be well larger than unity. This difference can be used as a read head for magnetic data storage, as will be described in more detail below with respect to magnetic switching devices.","Spin LED","According to another embodiment of the present invention, the electric-field-induced spin current is used to construct a spin light emitting device (spin LED). FIG. 5 is a schematic diagram of a spin LED according to one embodiment of the present invention. Referring to FIG. 5 , a quantum well structure 51 is sandwiched between a hole-doped (p-type) semiconductor layer 52 and an electron-doped (n-type) semiconductor layer 53 . First and second electrodes 54 , 55 are attached on opposite sides of hole-doped semiconductor layer 52 and a first electric field V 1 is applied across the first and second electrodes 54 , 55 . A second electric field V 2 is applied between the hole-doped semiconductor layer 52 and the electron-doped (n-type) semiconductor layer 53 for guiding the holes into the quantum well.","When electric field V 1 is applied between the first and second electrodes 54 , 55 , the spin current, that is, spin-polarized holes, will flow into the quantum well. The spin-polarized holes will recombine with electrons coming from the electron-doped semiconductor layer 53 . As a result, a circularly polarized light is emitted from the quantum-well layer 51 .","Prior to the present invention, spin LED can only be made using ferromagnetic semiconductor. For example, a prior art spin LED structure has been proposed where the quantum well structure of (In,Ga)As is sandwiched by p-type (Ga,Mn)As and n-GaAs. However, in accordance with the present invention, ferromagnetic semiconductor is not needed. Instead, a conventional p-type semiconductor layer under and electric field is used to replace the ferromagnetic dilute semiconductor (Ga,Mn)As used in the prior art devices. The spin LED thus formed is more conducive to practical implementation.","The hole-doped (p-type) semiconductor layer 52 of spin LED 50 can be constructed in the same manner as described above with reference to the hole-doped semiconductor structure of the spintronic devices of FIGS. 2 and 3 . In particular, the hole-doped (p-type) semiconductor layer includes a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant. In one embodiment, the semiconductor material has a spin orbit coupling energy that is greater than approximately 30 meV.","Magnetic Switching Device","According to another embodiment of the present invention, the electric-field-induced spin current is used to construct a magnetic switching device. When spin current is injected into a ferromagnet, the spin current will exert a torque on the magnetization of the ferromagnet. By exploiting the effect that the magnetization of a ferromagnet can be controlled by a spin current, a magnetic switching device can be derived with the ferromagnet being the media for recording data. U.S. Pat. No. 5,695,864 to J. C. Slonczewski describes such a magnetic switching device. The magnetic switching device described in the %27864 patent involves attaching a second ferromagnet with fixed magnetization and injecting spin-polarized current from the fixed magnetization ferromagnet into the first ferromagnet acting as the recording medium. In contrast to the prior art device, a magnetic switching device can be constructed using the electric-field-induced spin current of the present invention in place of the fixed magnetization ferromagnet. Thus, the magnetic switching device does not include any magnetic elements except for the ferromagnetic recording media itself. By eliminating the ferromagnet used to generate the spin current, the magnetic switching device of the present invention has advantages in magnetic recording applications because the switching device is free from errors caused by switching other recorded bits by mistake.","FIG. 6 is a schematic diagram of a spin-current induced magnetic switching device according to one embodiment of the present invention. Referring to FIG. 6 , magnetic switching device 60 includes five layers: a nonmagnetic conductor layer 61 , a hole-doped semiconductor layer 62 , a nonmagnetic conductor layer 63 , a magnetic conducting layer 64 and a nonmagnetic conductor layer 65 . The two nonmagnetic conductor layers 61 and 65 serve as electrodes, and an electric field V 2 is applied between the electrodes to introduce an electric current flowing through these five layers. The electric field V 2 functions as a current supply and can be in the form of an applied voltage or an applied current (that is, a voltage source or a current source). The magnetic conducting layer 64 is either ferromagnetic or ferrimagnetic, having a spontaneous or changeable magnetic moment. The easy axis of the magnetization of magnetic layer 64 has been put to the z direction.","Hole-doped semiconductor layer 62 includes electrodes 66 and 67 disposed on opposite ends thereof (the y-direction). By applying an electric field V 1 on the semiconductor layer 62 in the vertical (y) direction through electrodes 66 and 67 , a spin current will flow into the magnetic layer 64 through the nonmagnetic conductor layer 63 . The spins of this spin current are aligned along the z direction. Therefore this spin current will reverse the magnetization of the magnetic layer 64 if the initial magnetization of the magnetic layer is antiparallel to the spin direction of the spin current. Mathematically, if they are exactly antiparallel, there will occur no magnetization switching. Nevertheless, in reality there is disorder and thermal fluctuation of the magnetization, causing a slight change of the magnetization direction, and magnetization switching always takes place.","The spin direction of the spin current can be reversed by inverting the sign of the applied electric field V 1 between the electrodes 66 and 67 . By controlling the spin direction, the magnetization of the magnetic layer 64 can be controlled. By regarding the +z and −z magnetization as 0 and 1, the two magnetization states can serve as one “bit” in a magnetic data storage application.","The hole-doped semiconductor layer 62 of magnetic switching device 60 can be constructed in the same manner as described above with reference to the hole-doped semiconductor structure of the spintronic devices of FIGS. 2 and 3 . In particular, the hole-doped (p-type) semiconductor layer includes a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant. In one embodiment, the semiconductor material has a spin orbit coupling energy that is greater than approximately 30 meV.","Furthermore, in FIG. 6 , the non-magnetic conductor layers 61 and 63 are shown as separate layers from the hole-doped semiconductor layer 62 . However, in actual implementation, the non-magnetic conductor layers 61 and 63 can merely be integral parts of the hole-doped semiconductor layer 62 . That is, layers 61 , 62 and 63 can be replaced by a single non-magnetic hole-doped semiconductor layer. In conventional magnetic devices using a fixed magnetization ferromagnet for generating the spin current, the non-magnetic conductor layer 61 is used to form an electrode for receiving the electric field V 2 and the non-magnetic conductor layer 63 is used to isolate the spin-generating ferromagnet and the ferromagnet recording medium. However, in accordance with the present invention, because no ferromagnetic material is used for spin generation and the spin generation is provided by a semiconductor material under an electric field, the semiconductor material can form the electrode for receiving the applied electric field V 2 and can also form the interface to the magnetic layer 64 .","Advantages","The electric-field-induced spin current of the present invention provides many advantages over conventional devices and method for generating spin current. As compared to prior art devices, the electric-field-induced spin current of the present invention improves appreciably the efficiency of spin injection into semiconductors. Furthermore, the electric-field-induced spin current is non-dissipative, and does not accompany any Joule heating. The non-dissipative nature of the spin current is a feature that is useful in building electronics devices with low power consumption.","Another advantage of the electric-field-induced spin current is that the magnitude of the spin current is considerably large, even at room temperature. Equation (2) above describes the spin current at zero temperature. For finite temperature, the equation is modified only through the Fermi distribution function. For example, for GaAs at room temperature with n=10 9 cm −3 , the nominal value of the energy difference between the light-hole (LH) and heavy-hole (HH) bands at the same wavenumber is 0.1 eV, and it largely exceeds both the temperature (˜0.025 eV) and the width of the energy levels broadened by a momentum relaxation /τ p ˜0.006 eV. Thus the value of the spin current remains of the same order as in the zero temperature.","An important advantage of the electric-field-induced spin current of the present invention is that the spin-polarized current does not undergo rapid relaxation of spins. It is known that the hole spins relax very rapidly to an unpolarized state, with the short relaxation time τ s ˜100 fsec at room temperature. This is because the rapid momentum relaxation always accompanies the spin relaxation, due to the strong spin-orbit interaction in the valence band.","Nevertheless, in the steady state, a spin current induced by an electric field is free from such rapid relaxation of spins of holes. The electric-field-induced spin current is a purely quantum mechanical effect with equilibrium spin/momentum distribution. Thus, the electric-field-induced spin current is not affected by the rapid relaxation of hole spins. Only when the spin/momentum distribution deviates from equilibrium, for example, in the case of spin accumulation at the boundaries of the semiconductor structure, will the rapid relaxation of holes become effective.","Another important advantage of the electric-field-induced spin current of the present invention is that the spin-polarized current can be injected into other semiconductor structures or materials without suffering the conductivity mismatch problem typically associated with ferromagnetic spin injecting devices. Furthermore, because the amount of carrier doping in the semiconductor structure can be adjusted, the doping level can be selected to match the conductivity of the recipient semiconductor device. Thus, any conductance mismatch can be strictly minimized.","Alternate Embodiments and Modifications","In the embodiments described above, the hole-doped semiconductor structure used to form the spintronic device of the present invention is sometimes implemented as a p-type GaAs. The use of GaAs as the hole-doped semiconductor structure is illustrative only and other semiconductor materials can also be used. For instance, other semiconductors whose highest valence band is a fourfold degenerate p 3/2 band at Γ point in the cubic lattice, namely Γ 5 in the absence of the spin-orbit coupling or γ 8 in the presence of it, can be used as well. This class contains Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, C(diamond), AlP, BP, BAs and their alloys. Hence, by using hole-doped semiconductors described above, an electric-field-induced spin current can be generated. In particular, semiconductor materials with spin-orbit coupling energy larger than the thermal energy at room temperature (300 K), i.e., the room temperature times the Boltzmann constant, are ideal because the electric-field-induced spin current survives at room temperature. This class of hole-doped semiconductors includes Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe and their alloys.","In some semiconductors including α-Sn, HgSe and HgTe, the fourfold degenerate band Γ 8 at the Γ point are split into a conduction band and a valence band, both having twofold degeneracy. They are called zero-gap semiconductors which refer to semiconductors with a zero bandgap. These semiconductors are also among the materials that can be used to generate the electric-field-induced spin current in accordance with the present invention. When the zero-gap semiconductors are used, the electric-field-induced spin current can be generated with or without carrier doping of the semiconductor structure. Thus, in some embodiments of the present invention, an undoped semiconductor material can be used to generate the electric-field-induced spin current.","Furthermore, the hole-doped semiconductor structure used for generating the electric-field-induced spin current can be formed in a bulk or in a layer. That is, the semiconductor structure can be formed in a three-dimensional form or in a two-dimensional form.","Also, in the above embodiments, the term “axis” is used to describe the relative direction of the applied electric field, the spin polarization and the resultant spin current. For example, the electric field is applied in a first axis while the spin current flows in the second axis, the second axis being perpendicular to the first axis. The spin polarization is in the direction of a third axis perpendicular to both the first and the second axes. Moreover, in some cases, the above description uses the Cartesian coordinates (x,y,z) to describe the directional relationship of the electric field, the spin current and the spin polarization as in three perpendicular axes. However, the term “axis” used in the present description and in the claims is not intended to restrict the present invention to operate in a Cartesian coordinate system only. Rather the term “axis” is used herein to describe the main line of motion of the respective subject matter (e.g. electric field or spin current).","In addition, the use of the Cartesian coordinates (x,y,z) in the present description is illustrative only and is not intended to limit the practice and implementation of the electric-field induced spin current of the present invention in the Cartesian coordinate space only. In particular, the spin current equation (3) derived above is independent of any specific coordinate systems. Thus, the directional relationship of the three perpendicular axes of the electric field, the spin current and the spin polarization can be expressed in any coordinate systems that describe positional relationship in the three dimensional space. In one embodiment, the three perpendicular axes of the electric field, the spin current and the spin polarization is expressed in the cylindrical coordinates (r,φ,z).","The above detailed descriptions are provided to illustrate specific embodiments of the present invention and are not intended to be limiting. Numerous modifications and variations within the scope of the present invention are possible. The present invention is defined by the appended claims."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 shows the trajectory of the hole motion for illustrating how the hole motion is affected by the anomalous velocity drift term caused by the Berry phase.","FIG. 2 is a schematic diagram illustrating a spintronic device for injecting an electric-field-induced spin current into semiconductors according to one embodiment of the present invention.","FIG. 3 is a schematic diagram illustrating a spintronic device for injecting an electric-field-induced spin current into semiconductors according to an alternate embodiment of the present invention.","FIG. 4 is a schematic diagram of a spin injection device for injecting a spin current into a ferromagnetic electrode according to one embodiment of the present invention.","FIG. 5 is a schematic diagram of a spin LED according to one embodiment of the present invention.","FIG. 6 is a schematic diagram of a spin-current induced magnetic switching device according to one embodiment of the present invention."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED RESEARCH The present invention was made with support from the National Science Foundation under grant no. DMR-9814289 and with support from the US Department of Energy, Office of Basic Energy Sciences, under contract DE-AC03-76SF00515. The US Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/7,037,807","html":"https://www.labpartnering.org/patents/7,037,807","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=7,037,807"},"labs":[{"uuid":"69cb3598-6fdc-4f43-89cf-a0791ffccf22","name":"Lawrence Livermore National Laboratory","tto_url":"https://ipo.llnl.gov/","contact_us_email":"pitcock1@llnl.gov","avatar":"https://www.labpartnering.org/files/labs/3","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/69cb3598-6fdc-4f43-89cf-a0791ffccf22"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Shuichi Murakami","location":"Yokohama, JP, US"},{"name":"Naoto Nagaosa","location":"Tokyo, JP, US"},{"name":"Shoucheng Zhang","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A device for injecting spin-polarized current into a current output terminal comprising:a semiconductor structure comprising%3ba first end and an opposite second end disposed along the direction of a first axis, and a third end disposed along the direction of a second axis perpendicular to the first axis%3ba first electrode formed on the first end of the semiconductor structure%3ba second electrode formed on the second end of the semiconductor structure, wherein the first and second electrodes are disposed to receive an applied electric field%3b anda third electrode being the current output terminal formed on the third end of the semiconductor structure, the third electrode providing the spin-polarized current when an electric field is applied across the first and second electrodes,wherein the semiconductor structure comprises a hole-doped semiconductor structure or an undoped zero-gap semiconductor structure and further comprises a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant."},{"idx":"00002","text":"The device of claim 1, wherein the semiconductor structure comprises a hole-doped semiconductor structure of finite bandgap or zero bandgap."},{"idx":"00003","text":"The device of claim 2, wherein the hole-doped semiconductor structure comprises a semiconductor material selected from the group of Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, α-Sn, HgSe, HgTe and alloys of these semiconductor materials."},{"idx":"00004","text":"The device of claim 1, wherein the semiconductor structure comprises an undoped zero-gap semiconductor structure selected from the group of semiconductor materials with zero bandgap."},{"idx":"00005","text":"The device of claim 4, wherein the undoped zero-gap semiconductor structure comprises a semiconductor material selected from the group of α-Sn, HgTe and HgSe."},{"idx":"00006","text":"The device of claim 1, wherein the semiconductor structure comprises a semiconductor material whose spin orbit coupling energy is greater than approximately 30 meV."},{"idx":"00007","text":"The device of claim 2, wherein the hole-doped semiconductor structure comprises a p-type semiconductor structure having a doping level of approximately 1016 to 1020 atoms/cm3."},{"idx":"00008","text":"The device of claim 1, wherein the electric field applied across the first and second electrodes comprises a DC electric field in the range of 103 V/cm to 106 V/cm applied across the first and second electrodes."},{"idx":"00009","text":"The device of claim 1, wherein the electric field applied across the first and second electrodes comprises an AC electric field applied across the first and second electrodes."},{"idx":"00010","text":"The device of claim 1, wherein the spin-polarized current has a spin polarization aligned in the direction of a third axis, the third axis being perpendicular to the first axis and to the second axis."},{"idx":"00011","text":"The device of claim 10, wherein the first axis, the second axis and the third axis have directional relationship described in Cartesian coordinates."},{"idx":"00012","text":"The device of claim 10, wherein the first axis, the second axis and the third axis have directional relationship described in cylindrical coordinates."},{"idx":"00013","text":"The device of claim 1, wherein the semiconductor structure further comprises a fourth end opposite to the third end, the semiconductor structure providing the spin-polarized current to a recipient semiconductor structure coupled across the third end and the fourth end of the semiconductor structure."},{"idx":"00014","text":"The device of claim 13, wherein the semiconductor structure and the recipient semiconductor structure are formed as an integral semiconductor structure."},{"idx":"00015","text":"A device for injecting spin-polarized current into a current output terminal comprising:a semiconductor structure comprising a hole-doped semiconductor structure or an undoped zero-gap semiconductor structure and further comprising a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant, the semiconductor structure comprising:a first end and an opposite second end disposed along the direction of a first axis, and a third end and an opposite fourth end disposed along the direction of a second axis perpendicular to the first axis%3ba first electrode formed on the first cad of the semiconductor structure%3ba second electrode formed on the second end of the semiconductor structure, wherein the first and second electrodes are disposed to receive a first applied electric field%3b anda third electrode formed on the third end of the semiconductor structure, wherein the third electrode and the current output terminal are disposed to receive a second applied electric field,wherein the third electrode provides the spin-polarized current at the current output terminal when the first electric field is applied across the first and second electrodes, and the second electric field is applied across the third electrode and the current output terminal."},{"idx":"00016","text":"The device of claim 15, wherein the semiconductor structure comprises a hole-doped semiconductor structure of finite bandgap or zero bandgap."},{"idx":"00017","text":"The device of claim 15, wherein the semiconductor structure comprises a semiconductor material whose spin orbit coupling energy is greater than approximately 30 meV."},{"idx":"00018","text":"The device of claim 16, wherein the hole-doped semiconductor structure comprises a semiconductor material selected from the group of Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, α-Sn, HgSe, HgTe and alloys of these semiconductor materials."},{"idx":"00019","text":"The device of claim 16, wherein the hole-doped semiconductor structure comprises a p-type semiconductor structure having a doping level of approximately 1016 to 1020 atoms/cm3."},{"idx":"00020","text":"The device of claim 15, wherein the semiconductor structure comprises an undoped zero-gap semiconductor structure selected from the group of semiconductor materials with zero bandgap."},{"idx":"00021","text":"The device of claim 20, wherein the undoped zero-gap semiconductor structure comprises a semiconductor material selected from the group of α-Sn, HgTe and HgSe."},{"idx":"00022","text":"A spintronic device comprising:a semiconductor structure comprising:a first electrode formed on a first end of the semiconductor structure%3ba second electrode formed on a second end opposite to the first end of the semiconductor structure, the first end and the second end being disposed along the direction of a first axis%3b anda third electrode formed on a third end of the semiconductor structure, the third end being disposed along the direction of a second axis perpendicular to the first axis, the third electrode providing a spin-polarized current when an electric field is applied across the first and second electrodes,wherein the semiconductor structure comprises a hole-doped semiconductor structure or an undoped zero-gap semiconductor structure and further comprises a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant%3b anda ferromagnetic structure coupled to the third electrode of the semiconductor structure for receiving the spin-polarized current, the ferromagnetic structure having a first magnetization direction and a second magnetization direction opposite to the first magnetization direction,wherein the spin-polarized current flows in the ferromagnetic structure when the ferromagnetic structure has the first magnetization direction and the spin-polarized current is reduced in the ferromagnetic structure when the ferromagnetic structure has the second magnetization direction."},{"idx":"00023","text":"The device of claim 22, wherein the semiconductor structure comprises a hole-doped semiconductor structure of finite bandgap or zero bandgap."},{"idx":"00024","text":"The device of claim 22, wherein the semiconductor structure comprises a semiconductor material whose spin orbit coupling energy is greater than approximately 30 meV."},{"idx":"00025","text":"The device of claim 23, wherein the hole-doped semiconductor structure comprises a semiconductor material selected from the group of Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, α-Sn, HgSe, HgTe and alloys of these semiconductor materials."},{"idx":"00026","text":"The device of claim 23, wherein the hole-doped semiconductor structure comprises a p-type semiconductor structure having a doping level of approximately 1016 to 1020 atoms/cm3."},{"idx":"00027","text":"The device of claim 22, wherein the semiconductor structure comprises an undoped zero-gap semiconductor structure selected from the group of semiconductor materials with zero bandgap."},{"idx":"00028","text":"The device of claim 27, wherein the undoped zero-gap semiconductor structure comprises a semiconductor material selected from the group of α-Sn, HgTe and HgSe."},{"idx":"00029","text":"A circularly polarized light emitting device comprising:a quantum well structure coupled between a hole-doped semiconductor layer and an electron-doped semiconductor layer%3bthe hole-doped semiconductor layer comprising a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant and further comprising:a first electrode formed on a first end of the hole-doped semiconductor layer%3ba second electrode formed on a second end opposite the first end of the hole-doped semiconductor layer, the first end and the second end being disposed along the direction of a first axis%3b anda third electrode formed on a third end of the hole-doped semiconductor layer, the third end being disposed along the direction of a second axis perpendicular to the first axis and at the interface between the quantum well structure and the hole-doped semiconductor layer, the third electrode providing a spin-polarized current when an electric field is applied across the first and second electrodes,wherein the hole-doped semiconductor layer injects the spin-polarized hole current into the quantum well structure to be recombined with electrons provided by the electron-doped semiconductor layer to generate circularly polarized light."},{"idx":"00030","text":"The device of claim 29, wherein hole-doped semiconductor layer comprises a hole-doped semiconductor material of finite bandgap or zero bandgap."},{"idx":"00031","text":"The device of claim 29, wherein hole-doped semiconductor layer comprises a semiconductor material whose spin orbit coupling energy is greater than approximately 30 meV."},{"idx":"00032","text":"The device of claim 29, wherein the hole-doped semiconductor layer comprises a semiconductor material selected from the group of Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, α-Sn, HgSe, HgTe and alloys of these semiconductor materials."},{"idx":"00033","text":"The device of claim 29, wherein the hole-doped semiconductor layer comprises a p-type semiconductor layer having a doping level of approximately 1016 to 1020 atoms/cm3."},{"idx":"00034","text":"A spin-current induced magnetic switching device, comprising:a layered structure comprising a first layer of a non-magnetic semiconductor layer, a second layer of a magnetic conducting material having a changeable magnetic moment and a third layer of a non-magnetic conductor wherein the first and third layers comprise electrodes for passing an electrical current through the layered structure along a first axis perpendicular to the interfaces between the layers%3b anda current supply connected to the first and third layers for passing an electric current through the first and second layers for switching the changeable magnetic moment of the second layer,wherein the semiconductor layer comprises a hole-doped semiconductor layer or an undoped zero-gap semiconductor layer and further comprises a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) dimes the Boltzmann constant, the semiconductor layer comprising:a first electrode formed on a first end of the semiconductor layer%3ba second electrode formed on a second end opposite the first end of the semiconductor layer, the first end and the second end being disposed along the direction of a second axis perpendicular to the first axis%3b anda third end being disposed along the direction of the first axis and at the interface between the first layer and the second layer,wherein the semiconductor layer provides a spin-polarized current at the third end along the direction of the first axis when an electric field is applied across the first and second electrodes, the spin-polarized current having a spin polarization aligned in the direction of a third axis, the third axis being perpendicular to both the first axis and the second axis, which spin polarization flows through the first layer to the second layer for establishing a spin polarization of electrons in the second layer."},{"idx":"00035","text":"The device of claim 34, wherein the semiconductor layer comprises a hole-doped semiconductor layer having finite bandgap or zero bandgap."},{"idx":"00036","text":"The device of claim 34, wherein the semiconductor layer comprises a semiconductor material whose spin orbit coupling energy is greater than approximately 30 meV."},{"idx":"00037","text":"The device of claim 35, wherein the hole-doped semiconductor layer comprises a semiconductor material selected from the group of Si, Ge, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnSe, ZnTe, CdTe, α-Sn, HgSe, HgTe and alloys of these semiconductor materials."},{"idx":"00038","text":"The device of claim 35, wherein the hole-doped semiconductor layer comprises a p-type semiconductor layer having a doping level of approximately 1016 to 1020 atoms/cm3."},{"idx":"00039","text":"The device of claim 34, wherein the current supply comprises a second applied electric field."},{"idx":"00040","text":"The device of claim 34, wherein the current supply comprises an applied voltage."},{"idx":"00041","text":"The device of claim 34, wherein the non-magnetic semiconductor layer comprises:a fourth layer of a non-magnetic conductor disposed along the direction of the first axis coupled to the current supply%3b anda fifth layer of a non-magnetic conductor disposed along the direction of the first axis coupled to the second layer of magnetic conducting material."},{"idx":"00042","text":"The device of claim 34, wherein the semiconductor layer comprises an undoped zero-gap semiconductor layer selected from the group of semiconductor materials with zero bandgap."},{"idx":"00043","text":"The device of claim 42, wherein the undoped zero-gap semiconductor layer comprises a semiconductor material selected from the group of α-Sn, HgTe and HgSe."},{"idx":"00044","text":"The device of claim 1, wherein the semiconductor structure comprises a hole-doped semiconductor layer of a semiconductor material whose spin orbit coupling energy is greater than room temperature (300 Kelvin) times the Boltzmann constant, the device further comprising:a quantum well structure coupled between the hole doped semiconductor layer and an electron-doped semiconductor layer, the third end of the hole-doped semiconductor layer being disposed at the interface between the hole-doped semiconductor layer and the quantum well structure,wherein the hole-doped semiconductor layer injects the spin-polarized hole current into the quantum well structure to be recombined with electrons provided by the electron-doped semiconductor layer to generate circularly polarized light."},{"idx":"00045","text":"The device of claim 1, wherein the semiconductor structure comprises a non-magnetic semiconductor layer, the device further comprising:a layered structure comprising a first layer of the non magnetic semiconductor layer, a second layer of a magnetic conducting material having a changeable magnetic moment and a third layer of a non-magnetic conductor, the third end of the non-magnetic semiconductor layer being at the interface between the first layer and the second layer, wherein the first and third layers comprise electrodes for passing an electrical current through the layered structure along the second axis perpendicular to the interfaces between the layers%3b anda current supply connected to the first and third layers for passing an electric current through the first and second layers for switching the changeable magnetic moment of the second layer,wherein the semiconductor layer provides a spin-polarized current at the third end along the direction of the second axis when an electric field is applied across the first and second electrodes, the spin-polarized current having a spin polarization aligned in the direction of a third axis, the third axis being perpendicular to both the first axis and the second axis, which spin polarization flows through the first layer to the second layer for establishing a spin polarization of electrons in the second layer."}],"cpc":[],"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"L","subgroup":"00","main-group":"21","action-date":"2006-05-02","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"L","subgroup":"326","main-group":"21","action-date":"2006-05-02","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"L","subgroup":"479","main-group":"21","action-date":"2006-05-02","origination":"","symbol-position":"L"}],"document_number":"","document_published_on":"","document_kind":"","document_country":""},{"number":"9,410,806","artifact":"grant","title":"System and method for gyroscope zero-rate-offset drift reduction through demodulation phase error correction","filed_on":"2013-08-26","issued_on":"2016-08-09","published_on":"2015-02-26","abstract":"A circuit for processing signals from a gyroscope includes a first that generates an in-phase demodulated signal and a second demodulator that generates a quadrature-phase demodulated signal with reference to in-phase and quadrature-phase modulated signals, respectively, from the gyroscope. The circuit includes a digital processor that receives the demodulated in-phase and quadrature phase signals from the demodulators and generates an output signal corresponding to a rotation of the gyroscope along a predetermined axis with reference to the in-phase demodulated signal and the quadrature-phase demodulated signal to remove a portion of the quadrature-phase signal from the in-phase signal.","description":{"text":["TECHNICAL FIELD","This disclosure relates generally to gyroscopic sensors and, more particularly, to circuits for correcting error in an output signal from a gyroscopic sensor.","BACKGROUND","Gyroscopes are often used for sensing a rotation or an attitude of an object along one or more axes of rotation. For example, gyroscopes have long been used in naval vessels, aircraft, and spacecraft to identify rotation of the craft and for use in stability control systems. More recently, gyroscopes have been incorporated in micro-electromechanical (MEMS) devices. While classical gyroscopes rotate around an axis, MEMS gyroscopes typically include vibrating elements that are formed using photolithographic processes in an integrated circuit that is suitable for mounting to a printed circuit board or with other electronic components. As the MEMS device rotates around an axis, the plane of oscillation for the vibrating element tends to remain constant, and a modulated electrical signal from the MEMS sensor corresponds to the attitude of the support for the MEMS device around the axis. Some MEMS devices include multiple vibrating gyroscope elements that enable sensing of rotation along multiple axes in a three-dimensional space.","State of the art MEMS gyroscopes are used in a wide range of devices including, but not limited to, smartphones, tablets, and other portable electronic devices. For example, many portable devices include a display screen that displays text and graphics in either a portrait or a landscape orientation. A MEMS gyroscope in the mobile electronic device generates signals corresponding to the rotation of the device between the landscape and portrait orientations, and a microprocessor in the mobile electronic device adjusts the graphical display based on the signals from the gyroscope. Additional uses for MEMS gyroscopes in mobile devices include, but are not limited to, user input and inertial navigation applications.","While MEMS gyroscopes have become popular in compact electronic devices, the structure and operating conditions for existing MEMS gyroscopes introduce errors into the signals that are generated in the gyroscope. For example, the different manufacturing tolerances and fluctuating operating temperatures of MEMS gyroscope generate a quadrature signal error in the output of the signal from the vibrating sensing element in the gyroscope. A demodulation phase error is introduced due to the delays in the mechanical sensing element and electronic components that receive the modulated analog signals from the gyroscopic sensor and generate demodulated digital signals that are suitable for processing with digital microprocessors. Existing solutions for mitigating the offset drift errors include complex closed-loop feedback circuits that increase the cost, complexity, and electrical power consumption of the gyroscopic sensor system. Thus, improvements to circuits that process signals generated in vibrational gyroscopic sensors with reduced offset drift error would be beneficial.","SUMMARY","In one embodiment, a sensor circuit generates output signals corresponding to an output of a gyroscope sensor with the sensor circuit removing some or all of an offset drift from the output signal of the gyroscope. The circuit includes a first demodulator configured to receive a modulated signal from an output of a sensing element in the gyroscope, the first demodulator generating an in-phase demodulated signal with reference to the modulated signal, a second demodulator configured to receive the modulated signal from the output of the sensing element in the gyroscope, the second demodulator generating a quadrature-phase demodulated signal with reference to the modulated signal, and a digital processor configured to receive the demodulated in-phase signal from an output of the first demodulator and the demodulated quadrature-phase signal from an output of the second demodulator. The digital processor is configured to generate an output signal corresponding to a rotation of the gyroscope along a predetermined axis with reference to the in-phase demodulated signal and the quadrature-phase demodulated signal to remove a portion of the quadrature-phase signal from the in-phase signal.","DETAILED DESCRIPTION","The description below and the accompanying figures provide a general understanding of the environment for the system and method disclosed herein as well as the details for the system and method. In the drawings, like reference numerals are used throughout to designate like elements.","As used herein, the term in-phase signal refers to a signal from a sensor, such as a gyroscope sensor, that carries information from the sensor corresponding to a property that the sensor measures during operation. For example, the in-phase signal from a vibratory gyroscope is a modulated signal that corresponds to a motion of a vibrating element in the gyroscope sensor.","As used herein, the term quadrature-signal refers to another signal from the sensor that has a quadrature phase (90° phase offset) from the in-phase signal. The quadrature-phase signal is also referred to as a quadrature error signal. Ideally, the in-phase signal is completely separated from the quadrature-phase signal. However, in practical circuits, the phase-offset error can make measurement of only the in-phase signal difficult.","As used herein, the term phase-offset error refers to an error in the measurement of signals from a gyroscopic sensor that are produced by a time delay between the generation of the sensor signal and the measurement of the sensor signal. Inherent delays in the sensing elements of a gyroscope or other components in a circuit that measures the signal from sensor produce a phase-offset error. The phase-offset error results in a portion of the quadrature phase signal being shifted in time to overlap with a portion of the in-phase signal. Thus, the phase-offset error results in an inclusion of a portion of the quadrature-phase error signal being included in the measured in-phase signal, which can result in unacceptably large errors in the measurement of the output of the gyroscope. The phase-delay error varies between individual gyroscope sensors and measurement circuits, and can vary over time due to the physical configuration of the gyroscopic sensor on a mounting substrate and due to environmental factors such as ambient temperature. As described in more detail below, a signal processing circuit measures both the in-phase and quadrature-phase signals, and removes a portion of the quadrature-phase signal from the measurements of the in-phase signal to reduce or eliminate measurement errors that the phase-offset error produces in the measured signal from the gyroscopic sensor.","FIG. 1 is a functional diagram of a system 100 that includes a gyroscopic sensor 102 and an in-phase quadrature-phase (I/Q) demodulator 120 that demodulates a modulated output signal from the gyroscopic sensor 102 . In the gyroscope a vibrating member oscillates at a predetermined frequency to generate an in-phase modulated force 104 that produces an in-phase rate signal corresponding to a rotation of the gyroscope sensor. The gyroscope 102 also experiences a quadrature-phase force 108 that is phase-shifted by"," 90 ⁢ ° ⁢ ⁢ ( π 2 ⁢ radians ) from the in-phase force 104 . The quadrature-phase force 108 produces an oscillation in a sense mass 116 whenever the gyroscopic sensing element 102 is in operation. When the gyroscopic sensing element 102 rotates, the in-phase force 104 also produces an oscillation of the sense mass 116 in addition to the quadrature-phase force 108 as a vector sum depicted by the node 112 in FIG. 1 . The sense mass 116 oscillates within the gyroscopic sensor 102 , and electrodes on the sense mass 116 form a capacitor with fixed electrodes in the gyroscopic sensor 102 . When the gyroscopic sensor 102 rotates, both the in-phase force 104 and quadrature-phase force 108 , which are summed at the node 112 for illustrative purposes in FIG. 1 , introduce a modulated motion of the sense mass 116 other than the natural oscillation of the sense mass 116 . The modulated motion of the sense mass 116 generates a modulated capacitance signal within the gyroscopic sensor 102 that can be measured using electrical circuits.","The sense mass 116 is characterized by a transfer function H s (jω). The sense mass 116 oscillates in response to the rate and quadrature forces. The sense mass 116 experiences a delay in oscillation when acted upon by the rate and quadrature forces that produce an oscillating motion in the sense mass 116 during rotation of the gyroscope. The delay produces a phase-offset error that results in a portion of the quadrature-phase signal 108 being measured during the measurement of the in-phase signal 104 . The phase-offset error is approximated with the following equation: φ≈φ(T 0 )ƒ(T 0 ,T), where T 0 is a predetermined reference temperature, and T is the current operating temperature of the gyroscope. The value of φ(T 0 ) is identified empirically through a calibration process at the reference temperature T 0 , such as during manufacture of the gyroscope or through a calibration process. The function ƒ(T 0 ,T) is approximated as ƒ(T 0 ,T)≈c 0 +c 1 T where c 0 =b 0 kT 0 and c 1 =b 1 (a 0 T 0 +a 1 T 0 2 +a 2 T 0 3 . . . a n T 0 n+1 ). The numeric values of the coefficients b 0 ,b 1 , and a 0 . . . a n are identified empirically during a calibration process that measures samples from the gyroscope while the gyroscope operates at the reference temperature T 0 .","In the system 100 , the in-phase demodulator 124 generates a demodulated signal corresponding to the in-phase component of the output signal from the sense mass 116 . In the configuration of FIG. 1 , the in-phase module 132 introduces a unity gain to the demodulated in-phase signal from the demodulator 124 . In another configuration, the gain of the in-phase module 132 corresponds to the value of cos(φ) instead of the unity gain. The quadrature-phase demodulator 128 generates the demodulated quadrature-phase signal. The phase change of φ=−φ corresponding to the identified phase error φ. Thus, the phase-offset error correction module 136 multiplies the demodulated quadrature-phase signal by a scaling factor of φ=−φ, which corresponds to the identified phase error φ, with a negative (−) scaling factor that is used to subtract a portion of the demodulated quadrature-phase signal from the corresponding in-phase signal. The I/Q demodulator 120 removes a portion of the quadrature-phase signal that is included in the measured in-phase signal due to the phase delay error. An adder 140 generates an output signal from the combined in-phase and scaled quadrature-phase demodulated signals. In the embodiment of FIG. 1 , the adder 140 generates the difference between the in-phase demodulated signal and the scaled quadrature-phase demodulated signal. In another configuration, the adder unit 140 is a subtraction unit that generates a difference between the in-phase signal and the scaled quadrature-phase signal when the scaling factor φ=φ instead of the φ=−φ scaling factor that is illustrated in FIG. 1 .","FIG. 2 is a schematic diagram of one embodiment of system 200 including an I/Q demodulator that is electrically connected to an output of a vibratory gyroscope to reduce or eliminate phase delay error in the output signal of the gyroscope. The system 200 includes a gyroscopic sensing element 202 , sensing channels 208 A, 208 B, and 208 C, capacitance to voltage converter 220 , amplitude regulator 224 , phase-lock loop (PLL) 228 , a temperature sensor 236 , and a digital processing device 244 .","In the system 200 , the sensing element 202 is a vibratory gyroscope such as a MEMS gyroscope that is used in mobile electronic devices or any other suitable vibratory gyroscope. In the embodiment of FIG. 2 , the sensing element 202 includes a sensing element that senses rotation about three sensing axes 204 A, 204 B, and 204 C, each of which is configured to generate a signal corresponding to the motion of a vibrating element and corresponding rotation of the gyroscope along each of an x, y, and z axis, respectively. The x, y, and z axes correspond to three orthogonal axes of rotation in the physical world. In another embodiment, the gyroscope includes only one axis or a different configuration of multiple sensing elements that are arranged on multiple axes. A drive axis 206 receives an electric drive signal that generates oscillation in the vibrating members of each of the sensing axes 204 A, 204 B, and 204 C. The drive axis 206 drives the sense mass at a predetermined frequency to enable each of the axes 204 A- 204 C to oscillate at a predetermined frequency.","In FIG. 2 , the sensing channel 208 A is electrically connected to the output of the sensing axis 204 A. The sensing channel 208 A includes a capacitance to voltage converter 210 that generates a voltage signal in response to a modulated electrical capacitance output from the sensing axis 204 A. In one embodiment, the PLL 228 is implemented using a wideband type-II semiconductor PLL formed with a low phase-noise property to prevent reciprocal mixing of the quadrature error signal with the demodulation clock signal. In the system 200 , the sensing channels 208 B and 208 C are configured in the same manner as the sensing channel 208 A to generate digital data corresponding to demodulated signals from the sensing axes 204 B and 204 C, respectively. The sensing channel 208 A further comprises an I/Q demodulator that includes an in-phase demodulator 212 and a quadrature-phase demodulator 216 . Both the in-phase demodulator 212 and quadrature-phase demodulator 216 are electrically connected to the output of the capacitance to voltage converter 210 to receive the modulated output voltage signal from the sensing axis 204 A. In the embodiment of FIG. 2 , the in-phase demodulator 212 and quadrature-phase demodulator 216 are implemented as chopper circuits that demodulate the output of the capacitance to voltage converter 210 in response to switching signals from the in-phase and quadrature-phase outputs of the PLL 228 . As described in more detail below, the in-phase demodulator 212 is connected to the in-phase output of the PLL 228 , and the quadrature-phase demodulator 216 is connected to the quadrature output of the PLL 228 with a"," π 2 ⁢ radians (90°) phase offset from the in-phase output signal. The in-phase demodulator 212 and quadrature-phase demodulator 216 generate demodulated analog signals corresponding to the in-phase and quadrature-phase components, respectively, of the modulated output signal from the sensing axis 204 A. Analog to digital converters (ADCs) 214 and 218 generate digital output data corresponding to the outputs of the demodulators 212 and 216 , respectively. In one embodiment, the ADCs 214 and 218 are delta-sigma modulators that include single-bit fourth order ADC 214 and second order ADC 218 that oversample the analog signals from the demodulators 212 and 216 .","In the system 200 , the drive axis 206 receives an electrical drive signal from an amplitude regulator circuit 224 . The amplitude regulator circuit 224 controls the amplitude of the electrical drive signal for the drive axis 206 in the sensing element 202 , which maintains the amplitude of the oscillation for the sensing element 202 at a predetermined level. The PLL 228 and the amplitude regulator 224 controls the drive axis 206 in a closed-loop configuration, with the output of the drive axis 206 being supplied to a capacitance to voltage converter 220 that generates an output voltage corresponding to the oscillation of the drive axis 206 . The PLL 228 receives the output signal from the capacitance to voltage converter 220 and generates a tracking signal output to control the frequency and phase of the signal to the drive axis 206 . The PLL 228 generates a time varying signal that tracks the inherent frequency of oscillation of the moving member in the gyroscopic sensing element 202 . The PLL 228 generates an in-phase output signal that controls the operation of the amplitude regulator 224 to operate the drive axis 206 , and the in-phase output signal from the PLL 228 also controls the in-phase demodulator 212 . The PLL 228 includes a phase-delay circuit that generates a shifted quadrature-phase output with a shifted-phase of"," π 2 ⁢ radians (90°) from the in-phase signal to control the operation of the quadrature-phase modulator 216 .","In the system 200 , the drive axis 206 and the demodulators 212 and 216 are all driven by the output signals from a single PLL 228 . As described above, the sensing axes 204 A- 204 C and other components in the system 200 introduce a phase-offset error in the in-phase and quadrature-phase output signals from the sensing element 202 . The in-phase and quadrature-phase signals from the PLL 228 are also supplied to the demodulators 212 and 216 . Prior-art sensing circuits attempt to filter or separate the quadrature-phase signal from the in-phase signal since only the in-phase signal includes useful information from the sensing element in the gyroscope 200 . In the system 200 , however, the quadrature-phase component of the signal from the sensing element 202 is not discarded. Instead, the quadrature-phase demodulator 216 and ADC 218 generate digital data corresponding to the demodulated quadrature-phase signal. As described in more detail below, the demodulated quadrature-phase signal is scaled according to the phase-offset error in the system 200 , and the scaled quadrature-phase signal component is removed from the in-phase component of the output signal to reduce or eliminate the effects of the phase-offset error in an output signal.","In the system 200 , the temperature sensor 236 includes a temperature sensing element 238 and an ADC 240 . In one embodiment, the temperature sensing element 238 is a proportional-to-absolute temperature (PTAT) sensor element. The temperature sensing element 238 generates an analog signal corresponding to the temperature of the sensing element 202 , and the ADC 240 converts the analog signal into a digital data for additional processing by the processor 244 . In one embodiment, the ADC 240 is an incrementally operated second-order delta-sigma modulator. The temperature sensor 236 provides temperature data that are used to identify a scaling factor for the quadrature-phase demodulated signal data. The magnitude of the phase-offset error and corresponding overlap between the measured in-phase signal and the quadrature-phase error signal depend upon the temperature of the sensing element 202 .","In the system 200 , the digital processor 244 is embodied as a microprocessor, microcontroller, digital signal processor (DSP), application specific integrated circuit (ASIC), field programmable gate array (FPGA), or any other digital processing device that is configured to receive digital demodulated signal data from the in-phase ADC 214 , quadrature-phase ADC 218 , and the temperature sensor ADC 240 . In one embodiment, the entire system 200 including the mechanical sensing element 202 , the sensing channels 208 A- 208 C, temperature sensor 236 , amplitude regulator 224 , PLL 228 , and the digital backend 244 are integrated into a single physical package using, for example, a CMOS process, MEMS process. Additional embodiments include combinations of the mechanical, analog electrical, and digital electronic components of the system 200 . In the embodiment of FIG. 2 , the digital processor 244 is further configured to receive data from ADCs in the sensing channels 208 B and 208 C to enable monitoring of the sensing axes 204 B and 204 C, respectively, in the sensing element 202 .","FIG. 2 depicts a schematic configuration of the operations that the digital processor 244 performs to generate digital output data corresponding to the signal from the sensing element 202 . In the embodiment of FIG. 2 , the processor 244 applies low-pass filters 248 , 250 , and 252 to the digital data from the temperature sensor 236 , in-phase demodulator 212 , and quadrature-phase demodulator 216 , respectively. The processor 244 multiplies the filtered output reading of the temperature sensor 236 by the constant value c 1 with the multiplier 256 and adds the constant value c 0 with the adder 260 . The values of the constants c 0 and c 1 are predetermined constants that are stored in a memory associated with the digital processor 244 and are described above with reference to the function ƒ(T 0 ,T). The output of the adder 260 corresponds to the result of the ƒ(T 0 ,T) equation where T is the capacitance temperature reading for the sensing element 202 that is received from the temperature sensor 236 . The processor 244 includes a multiplier 264 that multiplies the output of the adder 260 by the digital data corresponding to the quadrature-phase demodulated signal from the filter 252 to generate digital data corresponding to a scaled version of the demodulated quadrature-phase signal data. As described above, the multiplier 264 also introduces a negative factor (φ=−φ) to the multiplication process to produce a negative scaled value corresponding to the demodulated quadrature-phase signal data.","The digital processor 244 uses an adder 268 to add the digital data for the in-phase signal from the filter 250 to the scaled quadrature-phase error signal output of the multiplier 264 to generate a combined output signal. The combined output signal from the adder 268 corresponds to a difference between the measured in-phase signal and scaled quadrature-phase error signal. Thus, since the phase-offset error in the system 200 introduces a portion of the quadrature-phase error signal into the in-phase signal, the digital processor 244 removes the quadrature-phase component from the in-phase demodulated signal data with the adder 268 . As described above, the digital processor 244 dynamically adjusts the scaling factor based on the temperature data from the temperature sensor 236 and with reference to calibration data for the gyroscopic sensing element 202 to compensate for changes in the phase-offset error that occur during operation of the system 200 . In one embodiment, the digital processor 244 executes stored program instructions as part of a software program to perform the functions of the filters 248 , 250 , and 252 , multipliers 256 and 264 , and the adders 260 and 268 .","Those skilled in the art will recognize that numerous modifications can be made to the specific implementations described above. Therefore, the following claims are not to be limited to the specific embodiments illustrated and described above. The claims, as originally presented and as they may be amended, encompass variations, alternatives, modifications, improvements, equivalents, and substantial equivalents of the embodiments and teachings disclosed herein, including those that are presently unforeseen or unappreciated, and that, for example, may arise from applicants/patentees and others."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 is a block diagram of functional units in a circuit that monitors an output of one or more axes of a gyroscope and removes an offset drift error from the gyroscope output.","FIG. 2 is a schematic diagram of a circuit that monitors outputs of a gyroscope along one or more axes and removes an offset drift error from the gyroscope output."]},"government_interest":"","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,410,806","html":"https://www.labpartnering.org/patents/9,410,806","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,410,806"},"labs":[{"uuid":"e2af34a8-8b90-4726-9edf-fa75fede52e8","name":"National Renewable Energy Laboratory","tto_url":"https://www.nrel.gov/workingwithus/technology-transfer.html","contact_us_email":"Eric.Payne@nrel.gov","avatar":"https://www.labpartnering.org/files/labs/4","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/e2af34a8-8b90-4726-9edf-fa75fede52e8"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Chinwuba D. Ezekwe","location":"Albany, CA, US"}],"assignees":[{"name":"Robert Bosch GmbH","seq":1,"location":{"city":"Stuttgart","state":" DE","country":" US"}}],"claims":[{"idx":"00001","text":"A circuit for processing signals from a gyroscope comprising:a first demodulator configured to receive a modulated signal from an output of a sensing element in the gyroscope, the first demodulator generating an in-phase demodulated signal with reference to the modulated signal%3ba second demodulator configured to receive the modulated signal from the output of the sensing element in the gyroscope, the second demodulator generating a quadrature-phase demodulated signal with reference to the modulated signal%3b anda digital processor configured to receive the demodulated in-phase signal from an output of the first demodulator and the demodulated quadrature-phase signal from an output of the second demodulator, the digital processor being configured to:generate an output signal corresponding to a rotation of the gyroscope along a predetermined axis with reference to the in-phase demodulated signal and the quadrature-phase demodulated signal to remove a portion of the quadrature-phase signal from the in-phase signal."},{"idx":"00002","text":"The circuit of claim 1, the digital processor being further configured to:generate a scaled datum corresponding to a product of a datum of the quadrature-phase signal multiplied by a scaling factor to reduce an absolute value of the digital datum%3bgenerate the output signal with another datum corresponding to a difference between a datum corresponding to the in-phase signal and the scaled datum."},{"idx":"00003","text":"The circuit of claim 2 further comprising:a temperature sensor configured to generate a signal corresponding to a temperature of the gyroscope."},{"idx":"00004","text":"The circuit of claim 3, the temperature sensor further comprising:a proportional to absolute temperature (PTAT) sensor element%3b andan analog to digital converter (ADC) electrically connected to an output of the PTAT sensor element and configured to generate digital temperature data corresponding to the signal generated by the PTAT."},{"idx":"00005","text":"The circuit of claim 3 wherein the digital processor is operatively connected to an output of the temperature sensor and the digital processor is further configured to:receive data corresponding to the temperature of the gyroscope from the temperature sensor%3badjust the scaling factor with reference to the temperature of the gyroscope%3b andmultiply the datum corresponding to the quadrature-phase signal by the adjusted scaling factor to reduce an absolute value of the digital datum corresponding to the quadrature-phase signal."},{"idx":"00006","text":"The circuit of claim 1 further comprising:a phase lock loop circuit operatively connected to the first demodulator and the second demodulator, the phase lock loop being configured to:receive a signal corresponding to motion of a drive axis in the gyroscope%3bgenerate a first signal to control the first demodulator, the first signal being generated with a first phase at a predetermined frequency in response to the signal from the drive axis%3b andgenerate a second signal with a second phase at the predetermined frequency to control the second demodulator, the second phase being different than the first phase."},{"idx":"00007","text":"The circuit of claim 6 wherein the second phase differs from the first phase by approximately π/2 radians."},{"idx":"00008","text":"The circuit of claim 6 further comprising:a capacitance to voltage converter electrically connected to an output of the drive axis in the gyroscope%3b andthe phase lock loop circuit being electrically connected to an output of the capacitance to voltage converter to enable the phase lock loop circuit to receive the signal from the drive axis in the gyroscope."},{"idx":"00009","text":"The circuit of claim 1 further comprising:a capacitance to voltage converter electrically connected to the output of the sensing element in the gyroscope%3bthe first demodulator being electrically connected to an output of the capacitance to voltage converter to receive the modulated signal from the capacitance to voltage converter%3b andthe second demodulator being electrically connected to the output of the capacitance to voltage converter to receive the modulated signal from the capacitance to voltage converter."},{"idx":"00010","text":"The circuit of claim 1 further comprising:a first ADC electrically connected to the output of the first demodulator and configured to generate digital data corresponding to the in-phase demodulated signal%3ba second ADC electrically connected to the output of the second demodulator and configured to generate digital data corresponding to the quadrature-phase demodulated signal%3b andthe digital processor being connected to an output of the first ADC to receive the digital data corresponding to the in-phase demodulated signal and the digital processor being connected to an output of the second ADC to receive the digital data corresponding to the quadrature-phase demodulated signal."},{"idx":"00011","text":"The circuit of claim 10 wherein the first ADC and the second ADC are delta-sigma modulators."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"C","subgroup":"5776","main-group":"19","action-date":"2016-08-09","origination":"","symbol-position":"F","further":["01","","H","B","US","G","","C","5776","19","2016-08-09","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"P","subgroup":"00","main-group":"21","action-date":"2016-08-09","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"C","subgroup":"5776","main-group":"19","action-date":"2016-08-09","origination":"","symbol-position":"L"}],"document_number":"20150057959","document_published_on":"2015-02-26","document_kind":"","document_country":""},{"number":"9,869,648","artifact":"grant","title":"High density grids","filed_on":"2015-09-29","issued_on":"2018-01-16","published_on":"2016-01-21","abstract":"An X-ray data collection grid device is provided that includes a magnetic base that is compatible with robotic sample mounting systems used at synchrotron beamlines, a grid element fixedly attached to the magnetic base, where the grid element includes at least one sealable sample window disposed through a planar synchrotron-compatible material, where the planar synchrotron-compatible material includes at least one automated X-ray positioning and fluid handling robot fiducial mark.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application is a continuation-in-part of U.S. patent application Ser. No. 14/750,470 filed Jun. 25, 2015, which is incorporated herein by reference. U.S. patent application Ser. No. 14/750,470 filed Jun. 25, 2015 claims priority to U.S. Provisional Patent Application 62/017,594, filed Jun. 26, 2014, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy and under contract GM103393 awarded by the National Institutes of Health. The Government has certain rights in the invention.","FIELD OF THE INVENTION","The present invention relates generally to X-ray data collection and sample preparation for X-ray data collection. More particularly, the invention relates to X-ray sample grids compatible with automated sample mounting systems used at synchrotron beamlines and the magnets used on sample goniometers and positioning stages.","BACKGROUND OF THE INVENTION","As structural biologists tackle ever more challenging systems, the development of efficient methods to deliver large quantities of crystals for X-ray diffraction studies is increasingly important. Proteins that are difficult to crystallize will often produce only small crystals that yield only a few degrees of diffraction data before succumbing to the damaging effects of radiation exposure. For many systems, obtaining a complete dataset to high resolution using very small crystals is possible through the use of microfocus synchrotron beams and the collection and combination of data from multiple crystals. The structural information accessible from very small or very radiation sensitive crystals may be extended through the application of femtosecond crystallography (FX), an emerging method that capitalizes on the extremely bright, short time-scale X-ray pulses produced by X-ray free electron lasers (XFELs). This approach exploits a ‘diffraction before destruction’ phenomenon where a still diffraction pattern is produced by a single X-ray pulse before significant radiation induced electronic and atomic rearrangements occur within the crystal. Since the area of the crystal exposed to the X-ray pulse is completely destroyed after each shot, multiple crystals are required for these experiments. If larger crystals are available, different areas of the crystal may be exposed to obtain multiple stills from a single crystal. In addition, FX confronts another major challenge in structural enzymology by providing a means to determine catalytically accurate structures of radiation sensitive metalloenzymes, which may undergo structural rearrangement upon photo-reduction of the metal center at a synchrotron. In most cases, these experiments also require a large quantity of samples as each area of the crystal can only be exposed once. High throughput crystallization and the implementation of automated sample mounting systems at synchrotron light sources have made data collection from multiple crystals approachable, however challenges still exist. The process of sample exchange using automated mounting systems, which includes mounting a crystal, centering a crystal for data collection, and dismounting the crystal can take between 35 seconds to a few minutes. While this time scale may be suitable for experiments that require screening of at most a few hundred crystals, higher efficiency methods are required for more challenging endeavors at both the synchrotron and XFEL sources. Furthermore, harvesting crystals for data collection can be another time consuming step. Crystal manipulation robots are being developed to automate this process, however crystal harvesting is still primarily done by hand.","One approach for efficient sample delivery and diffraction quality screening is the use of high-density sample containers that hold crystals in known locations coupled with the use of a high-speed sample goniometer for rapid sample positioning. Examples of high-density sample mounting containers for room temperature data collection include microfluidic chips and micro-crystals traps. What is needed is a simple, inexpensive, high density crystal mounting device for data collection at cryogenic or room temperatures, which is compatible with most automated mounting systems and sample storage containers and enables rapid positioning of multiple crystals.","SUMMARY OF THE INVENTION","To address the needs in the art, an X-ray data collection grid device is provided that includes a magnetic base that is compatible with robotic sample mounting systems used at synchrotron beamlines, a grid element fixedly attached to the magnetic base, where the grid element includes at least one sealable sample window disposed through a planar synchrotron-compatible material, where the planar synchrotron-compatible material includes at least one automated X-ray positioning and fluid handling robot fiducial mark.","In one aspect of the invention, the magnetic base includes a shape that is compatible with sample goniometers disposed at synchrotron beam lines and is compatible with automated sample-pin exchange robotic systems. In one aspect, the magnetic base is compatible with an Advanced Light source (ALS) puck, a uni-puck, an MSC magazine, or a Stanford Synchrotron Radiation Light source (SSRL) cassette. In a further aspect the automated sample-pin exchange robotic systems include SSRL Automated Mounter, ALS Sample Exchange Robot, ACTOR, or a Cryogenic Automated Transfer System (CATS) robotic system.","In another aspect of the invention, the synchrotron-compatible material includes polycarbonate, acrylonitrile butadiene styrene, cyclic olefin copolymer or other polymer material.","According to a further aspect of the invention, the sample window includes a single window, an array of sample holes or an array of the windows, where the array of sample holes or the array of windows comprise a diameter in a range of 50 μm to 2.5 mm.","In yet another aspect of the invention, the fiducial mark includes a hole, a mark, a dimple, a corner or an edge of the planar synchrotron-compatible material. In one aspect, the fiducial mark hole has a diameter in a range of 5 μm to 200 μm.","According to one aspect of the invention, the rectangular planar synchrotron-compatible material includes a thickness in a range of 25 μm to 300 μm.","In a further aspect of the invention, the at least one sealable window includes a transparent sheet that includes of graphene, holey carbon, mylar, polyamide, polyimide film with silicone adhesive, or polymers. In one aspect, the transparent sheet includes a thickness in a range of 100 nm to 20 μm.","DETAILED DESCRIPTION","The current invention provides an X-ray data collection grid device having a magnetic base that is compatible with robotic sample mounting systems used at synchrotron beamlines, a grid element fixedly attached to the magnetic base, where the grid element includes at least one sealable sample window disposed through a planar synchrotron-compatible material that includes polycarbonate, acrylonitrile butadiene styrene, cyclic olefin copolymer or other polymer material, where the planar synchrotron-compatible material includes at least one automated X-ray positioning and fluid handling robot fiducial mark. The fiducial mark includes a hole, a mark, a dimple, a corner or an edge of the planar synchrotron-compatible material. In one aspect, the fiducial mark hole has a diameter in a range of 5 μm to 200 μm.","According to the invention, the X-ray data collection grid device significantly improves the efficiency of data collection by allowing multiple samples to be mounted simultaneously by the sample mounting robots currently ulitized at synchrotron and XFEL light sources, according to one embodiment. Current automated sample mounting systems mount and dismount a sample in approximately 30 seconds to 2 minutes. In one embodiment, the grid holds 76 samples, meaning that it can save up to approximately 150 minutes of wasted in mounting time. The grid device, according to the current invention, also reduces sample alignment time because all samples contained in a grid undergo the alignment procedure simultaneously. This alignment procedure may be fully automated. Subsequently, grid ports (also referred to as windows) are automatically positioned into the X-ray beam (or measurement position) and data is automatically collected for each grid ports. Depending on the measurement integration time and detector properties, the entire data collection process takes can take from only a few seconds to minutes, where automated screening for 76 samples mounted individually can take several hours. The compact nature of the grid device allows for greater efficiency in storage and transportation of samples. The use of grid devices with SSRL cassettes increases the sample capacity of a cassette from 96 samples to up to 7200 samples (or more).","In a further embodiment, the current invention also serves as a scaffold for crystal growth. Tools have been developed to enable compatibility with commercial liquid handling robots including the Art Robbins Gryphon and Labcyte Echo550. After protein sample and precipitating agents have been deposited on grids, they may be incubated in specialized crystal growth contains which support hanging or sitting drop experiments and LCP crystallization experiments (see FIG. 5A ). By growing crystals directly on the data collection grid device, the crystal harvesting step may be bypassed, which not only saves time, but protects the sample from human handling.","In a further embodiment, the grid device may hold multiple samples in separate ports for X-ray data collection. Samples may include microcrystals, suspensions of crystals, amorphous material, and sample fluids. X-ray data collection may include methods such as diffraction quality screening, X-ray scattering experiments, or X-ray absorption experiments.","Grids allow for higher throughput preparation and screening of protein and small molecule microcrystals. This is critical for reducing the time and cost involved in protein and macromolecular structure determination, the characterization of potential drug leads, and the identification of drug binding sites, for example during fragment based drug design.","According to further embodiments, specialized grid related tools are used to aid in mounting samples in the grid ports, incubating grids in controlled environments, and holding and positioning the grid during X-ray experiments.","An exemplary embodiment of the invention is described and shown herein, where the body of the grid includes a 25 μm to 300 μm thin sheet of polycarbonate with ( FIG. 1A ) a single sample window, and with multiple rows of holes cut into it, as shown in FIGS. 1B-1C . According to a further aspect of the invention, the sample window can be a single window, an array of sample holes or an array of the windows, where the array of sample holes or the array of windows have a diameter in a range of 50 μm to 2.5 mm. The fiducial mark includes a hole, a mark, a dimple, a corner or an edge of the planar synchrotron-compatible material. In one aspect, the fiducial mark hole has a diameter in a range of 5 μm to 200 μm.","In practice, the grid ports may be filled with liquid, crystals may be mounted in the holes by hand, suspensions of crystals may be loaded in to the holes, by hand using a loop or piettor or, using a liquid handling robot, or crystals may be grown in the holes by loading them with a protein sample and precipitating agent. Samples contained in grids may be stored at room temperature or cryogenic temperatures, where the glue and plastics used to fabricate grids is compatible with room and cryogenic temperatures, according to one embodiment.","The grids are affixed into a magnetic base (such as a stainless steel Hampton-style base) compatible with automated sample mounting systems used at synchrotron beamlines (such as the Stanford SAM system, the ALS robot and the Rigaku ACTOR robot) as well as the magnets used on sample goniometers and positioning stages ( FIG. 2A ). According to the invention, the magnetic base has a shape that is compatible with sample goniometers disposed at synchrotron beam lines and is further compatible with automated sample-pin exchange robotic systems. In one aspect, the magnetic base is compatible with an ALS puck, a uni-puck, an MSC magazine, or an SSRL cassette. In a further aspect the automated sample-pin exchange robotic systems include S SRL Automated Mounter, ALS Sample Exchange Robot, ACTOR or a CATs robotic system.","While affixing grids to a magnetic base, a specialized jig may be used to prevent grids from tilting in the base as glue sets ( FIG. 2B ), according to one aspect of the invention. For example, grids affixed to a Hampton magnetic base fit inside cryotongs, the ports of uni-puck enclosures ( FIG. 3A ) and SSRL cassettes ( FIG. 3B ).","In one embodiment, a specialized holder is used to store grids at a controlled humidity. This is useful for for crystal growth by vapor diffusion, for crystal loading and other experiments. The container may be filled with fluids or dessicants to control the grid environment ( FIGS. 4A, 4B ).","According to one embodiment, a specialized holder is used to position a grid surrounded by precipitating agent within a glass sandwich to facilitate crystal growth in lipidic cubic phase on the grid ( FIG. 5B ). In a further aspect of the invention, the transparent sheet of the sealable window can be glass, graphene, holey carbon, mylar, polyamide, polyimide film with silicone adhesive, or polymer. In one aspect, the transparent sheet includes a thickness in a range of 100 nm to 20 μm.","In a further embodiment, a specialized adaptor with an SBS plate compliant footprint is used to hold a grid in the destination plate position of liquid handling robots (such as the Labcyte Echo550 or Art Robbins Instruments Gryphon) to receive a liquid sample, or solid liquid suspension ( FIGS. 6A-6C ). In this example, the grid is indexed against two metal plates protruding from the adaptor so that sample ports are in the correct position to receive sample ( FIG. 6B ). Further, specialized grid related tools are used to aid in hand mounting samples in the grid ports.","In a further embodiment, routines in a Blu-Ice/DCSS experimental control system are used for semi-automated grid alignment, fully automated positioning of grid ports, rastering, and automated data collection. Crystal positions may be mapped in relation to the grid fiducial marks for subsequent automated centering.","According to other embodiments of the current invention, new features include a mounting device that is both capable of holding multiple samples in separate ports on a single magnetic base, and compact enough to fit within a single port of a uni-puck enclosure or SSRL cassette, and cryotongs. The current invention is both compatible with liquid handling robots, and useful for x-ray diffraction, small angle scattering, or x-ray absorption data collection. The current invention is compatible with a specialized incubation chamber for the growth of crystals directly in the ports of a multiport mounting device, and compatible with a specialized tray, which allows crystals to be grown in lipidic cubic phase directly in the ports of a multiport mounting device within a glass sandwich. Further, the current invention can be used with a specialized holder having indexing plates for the positioning of a multiport mounting device that is pre-glued to a magnetic base in the destination plate position of a liquid handling robot to receive sample, and a automated alignment procedure, which makes use of a grid pattern of sample ports to index sample locations for rapid data collection during x-ray diffraction, small angle scattering, or X-ray absorption experiments. Further, the invention can be used with thin, optically clear, polycarbonate sheeting that results in minimal X-ray absorption and low X-ray scattering background.","The grid element invention enables efficient automated data collection from a large number of crystals that will only survive a few X-ray exposures or small rotational ranges during data collection. Since crystals are held in known locations, rapid and precise automated crystal positioning into the X-ray beam path is possible. In addition, grids may also serve as a scaffold for crystal growth and are compatible with many liquid handling robots, allowing for increased automation in crystal growth and harvesting.","In an exemplary embodiment, the grid scaffold includes of a piece of 100 μm thick polycarbonate plastic with laser cut rows of holes (or ports). This polycarbonate scaffold is affixed to a standard magnetic base to produce the ‘grid assembly’ ( FIG. 1B-1C ). A specialized bonding jig is used to hold the polycarbonate scaffold inside the magnetic base as the epoxy sets ( FIG. 2A-2B ). Grid ports may hold either large crystals, or groups of smaller crystals, in known locations. The current grid layout has 74 ports that can include 400 μm, 200 μm, and 125 μm diameters, along with 4 fiducial markers ( FIG. 1B ), however the size and arrangement of ports may be altered to better suit different experimental setups. Grids may have an additional thin polymer film affixed to one face to better hold samples within ports, or to serve as a scaffold for sitting or hanging drop crystallization experiments. The 5 μm thick polycarbonate film in this exemplary embodiment has minimal X-ray absorption and low X-ray scattering background.","The grid elements have been used in combination with goniometer based instrumentation installed at the Linac Coherent Light Source (LCLS) X-ray Pump Probe (XPP) station for XFEL diffraction experiments. During these experiments, the Stanford Automated Mounter was used to mount grids containing crystals onto the goniometer. In this example, the size of the grid was maximized to expand the cassette capacity from 96 to more than 7200 sample locations while reliably fitting inside the port of a SSRL cassette ( FIG. 2C ). Grid assemblies are also compatible with uni-puck storage containers.","To control these experiments, automated routines were added to the experimental control software Blu-Ice/DCSS. To define the position of all grid ports in relation to the X-ray beam position, an automated alignment procedure takes advantage of the predefined spatial arrangement of the laser cut grid ports. This process begins by first defining the position of the edge of the grid by rotating it until it is edge-on in the software video display to move the edge of the grid into the X-ray beam position. If the grid is tilted in this view, two positions may be identified to define the translation path.","Next the grid is rotated by 90 degrees to put the face-on view of the grid. Four ports on the outer corners of the grid are then identified which act as fiducial markers to define the port locations and the grid rotation ( FIG. 1B ). This procedure calibrates all of the grid ports to the coordinate system of the goniometer and beam interaction region. For crystals that closely match the size of each grid port, data collection may then be carried out automatically%3b each port is automatically centered into the X-ray interaction region and exposed. Alternatively, automated data collection may be paused and a different area of the port may be selected for exposure using a manual “click-and-shoot” procedure.","Helical data collection may also be setup across longer crystals within grid ports. A spreadsheet, specifying which grid ports contain crystals, may be uploaded in advance so that empty ports are automatically skipped during data collection.","In cases where a group of small crystals is present inside a port, X-ray raster searches may be performed on the entire grid port, or on a smaller area within the port. Rastering is often performed at synchrotrons with low doses of radiation to locate crystals. At an XFEL, a raster mode of data collection is done with a full dose of radiation to collect data from multiple crystals in a grid port, or to collect data from multiple locations on a single crystal. The entire grid port may be rastered automatically using the Blu-ice/DCSS software by using a pull-down menu to choose the port, and a suitable circular area is automatically defined, or a smaller area containing crystals may be rastered by defining the edges of a polygon from within the software display. Moreover, the exact position of small crystals placed randomly within a grid window may be mapped in relation to the fiducial marks prior to data collection using microscopy, or a raster search using low dose X-rays. After running the automated alignment procedure, positioning software applies the crystal map to rapidly position these crystals into the X-ray beam position.","This automation may be further incorporated into automated software workflows for fully automated multi-crystal data collection strategies.","Grids may be manually filled with crystals. Crystals can be viewed during this process by positioning the grid assembly underneath a microscope with the use of a magnetic holder. Grid ports can be prefilled with cryo-protectant oil such as paratone-N, or paraffin to prevent crystal dehydration. A fine needle may be used to apply oil to each grid port. A cryo-loop may be used as a tool to remove a crystal from the crystallization tray, coat the crystal with a thin layer of oil, and then transfer it to an appropriately sized grid port. It is helpful to match the size of the cryo-loop tool to a port size in the grid. Filling all ports in a grid may be impractical because crystals may degrade over time in the cryo-protectant oil. Testing is necessary to determine the maximum timeframe for filling grids with a particular sample and oil. This may be accomplished by filling a grid with crystals and recording the loading time for each port. Diffraction data may then be collected and compared for crystals with known exposure times to the oil. Crystals of myoglobin were mounted in grids in this manner for FX experiments at LCLS XPP. During these experiments, still diffraction patterns were collected from 932 crystals in 32 grids%3b of these, 739 stills were included in a final dataset that was fully complete to 1.5 Å resolution.","Grid ports may be covered with a thin polymer film or sleeve to prevent evaporation and sample dehydration. This modification enables grids to be used for room temperature data collection of protein crystals in water based cryoprotectants, or other evaporation sensitive samples. This approach was used for room temperature screening of protein crystals at LCLS-XPP. A polycarbonate backing was glued to one face of a grid with epoxy. A suspension of protein crystals was pipetted over the open grid ports, and a loop was used to drag crystals into the ports ( FIG. 2A ). A second sheet of polycarbonate was placed over the open ports and held in place by capillary action ( FIG. 5C ). Minimal evaporation was observed over the course of 30 minutes.","Crystals may be grown directly inside grid ports. To fill grids with crystallization solutions for this purpose, an adaptor was developed that holds a grid assembly in the destination plate position of liquid handling robots ( FIG. 6A ). A neoprene lined torsion clip grips the magnetic base of the grid assembly and holds it in place. Grids are indexed against two metal surfaces to ensure accurate reproducible drop placement ( FIG. 6B ). The adaptor has been successfully tested with the Labcyte Echo550 ( FIG. 6C ), the Art Robbins Gryphon, and the TTP Labtech Mosquito. After sample has been deposited on grids, the grids may be incubated in specialized crystal growth containers, which support hanging or sitting drop experiments and LCP crystallization experiments.Liquid handling robots may also be used to dispense suspensions of protein microcrystals, or other solid liquid suspensions into grids.","A grid vapor diffusion chamber was developed to hold a grid in a controlled environment for incubation of sitting or hanging drop crystallization experiments ( FIGS. 4A-B ). The chambers are capped with transparent X-seal crystallization supports, or sealed with transparent tape so that crystal growth may be monitored with a microscope. Silicone O-rings are used to ensure a tight seal around the grid scaffold ( FIG. 4B ) or around the pin base. A thin film of vacuum grease may be applied to the O-rings to improve sealing. A well in the base of the chamber holds up to 350 μL of desiccant below the grid. To demonstrate that grids may be used as scaffolds for crystal growth, sitting drop vapor diffusion experiments were set up on grids using lysozyme as a test case. An Echo550 liquid handler was used to dispense drops of protein and precipitant solution onto a grid with a thin polycarbonate backing. Grids were then incubated in a vapor diffusion chamber drop side up, with desiccant for 5 days. Lysozyme crystals grew on the grids, and the Echo550 liquid handler was used to dispense drops of cryo-protectant on top of the crystallization drops.","In instances in which crystals are manually loaded into grids using water based cryoprotectant, vapor diffusion chambers may be used to prevent evaporation of the sample and cryoprotectant. Grids may be positioned in the vapor diffusion chamber during crystal loading, and liquid may be added to the well of the chamber. The chamber may be opened to allow a crystal to be transferred to the grid, and sealed again in between transfers to maintain a humid environment for the grid. This method may be used for protein crystals, as well as for other evaporation sensitive samples. For example this approach was used to load grids with crystals of a large multi-protein-DNA complex. To accomplish this, a grid was coated with cryoprotectant and placed in a vapor diffusion chamber with cryoprotectant solution in the well. Two microscopes were used to aid visualization of the crystallization tray and the grid in the vapor diffusion chamber. Crystals were transferred from the crystallization tray into the grid using cryo-loops. The chamber was loosely sealed between transfers to maintain humidity. The grids were then flash-frozen and used to screen crystals of the protein-DNA complex at both LCLS-XPP and at SSRL beamline 12-2 producing diffraction patterns to 3.3 Å and 3.7 Å resolution.","LCP crystallization experiments may also be performed on grids with the use of a specialized holder that incorporates full grid assemblies, eliminating the need to manually cut glass or plastic crystallization chambers containing crystals for data collection. The tray holds an assembly in which a grid containing cubic phase is incubated in precipitating solution in a glass sandwich ( FIG. 5B ). The grid LCP tray assembly includes two siliconized glass slides, for example 1 mm thick double sided tape, and a tray with a support for a magnetic base and glass slides. The grid is sandwiched between the two sheets of glass and is surrounded by precipitating agent. To aid in removal, a thin polycarbonate sheet may be laid on top of the grid and under the top glass plate.","Proof of principal LCP crystallization experiments were performed on grids using an adaptation of a protocol for the growth of lysozyme crystals in LCP as a test case. An Art","Robbins Gryphon was used to dispense cubic phase into grid ports, and grids were incubated with precipitating agent in the glass sandwich. Lysozyme crystals up to 100 μm in size were observed in grid ports after 16 hours of incubation.","High density sample mounting devices dramatically reduce the amount of time needed for multi-crystal data collection. Data collection of crystals held in loops requires that each crystal be individually mounted on the goniometer, centered in the X-ray beam, and then dismounted. Automated alignment of crystal containing loops can take between 15 to 30 seconds each, depending on the beamline hardware and software. The time required to mount and dismount a sample varies, however even if sample exchange requires 25 seconds, sample exchange, alignment and exposure for 1000 crystals in loops would consume at least 12 hours of beam time. Furthermore, a 1000 samples mounted individually in loops would require 11 SSRL cassettes or 62 uni-pucks for storage. The sample mounting grid enables more than 70 conventionally sized crystals (˜100-300 μm in diameter) to be mounted on the goniometer at once, or many thousands of micro-crystals, circumventing much of the time involved in sample exchange. Time is further saved because alignment is performed once for the entire grid, after which the position of each sample location is automatically calculated by the Blu-Ice/DCSS control software. When conventionally sized crystals are used, the use of grids to screen 1000 crystals would reduce the time spent on sample exchange and alignment from about 12 hours to under 1 hour, and a single uni-puck would be sufficient to hold 1000 samples. Additionally, a single grid port may also be filled with multiple micro-crystals, in which case thousands of crystals may be mounted on the goniometer at once.","Since crystals may be grown directly on grids, crystal harvesting may be avoided entirely during room temperature data collection. Plastic sleeves and backings may be used to lessen the effects of evaporation. Grids may alternatively be transferred directly from an incubation chamber to a goniometer outfitted with a humidity controlled air-stream.","The use of grids for screening LCP conditions will be a very powerful tool for enabling researchers to use grids for both the collection of entire datasets and also to screen conditions for subsequent use of LCP injectors.","The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive.","Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. For example variations in embodiments of the current invention include the size, number, and position of the grid holes, the size, shape, or thickness of the grids, the use of different plastics to fabricate the grids with different optical properties, the use of different materials to fabricate the grids with different properties regarding the adhesive force exerted on liquids, and the grids may have a thin polycarbonate sheet affixed to one or both sides to better contain sample within grid holes, where thin sheets or membranes of other materials may also be used for this purpose. Further variations include improved methods for affixing a grid to a magnetic base, variations in the materials or specifications of vapor diffusion chambers for grids, variations in the materials or specifications of the LCP grid assembly, and variations in the materials or specifications of the grid adaptor.","All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIGS. 1A-1C show the body of grids having a sheet of polycarbonate with ( FIG. 1A ) a single sample window, and ( FIG. 1B-1C ) multiple rows of holes, according to one embodiment of the invention.","FIGS. 2A-2C show the grids affixed into a magnetic base compatible with automated sample mounting systems used at synchrotron beamlines as well as the magnets used on sample goniometers and positioning stages, and the grids affixed to a magnetic base, a specialized jig is used to prevent grids from tilting in the base as glue sets, according to one embodiment of the invention.","FIGS. 3A-3B show the grids affixed to a magnetic base, the ports of uni-puck enclosures, and SSRL cassettes, according to one embodiment of the invention.","FIGS. 4A-4B show a specialized holder used to store grids at a controlled humidity for crystal growth by vapor diffusion, where the container may be filled with fluids or dessicants to control the grid environment, according to one embodiment of the invention.","FIGS. 5A-5C show ( FIG. 5A ) a grid implemented in a hanging drop crystallization experiment, ( FIG. 5B ) a specialized holder is used to position a grid surrounded by precipitating agent within a glass sandwich to facilitate crystal growth in lipidic cubic phase on the grid, ( FIG. 5C ) two sheets of window seals placed over the open windows and held in place by capillary action, according to one embodiment of the invention.","FIGS. 6A-6C show a specialized adaptor with an SBS plate compliant footprint used to hold a grid in the destination plate position of liquid handling robots to receive a liquid sample, or solid liquid suspension, according to one embodiment of the invention.","FIGS. 7A-7B show ( FIG. 7A ) an edge-on view of a grid with polycarbonate backing during data collection at LCLS-XPP, where, according to one embodiment of the invention, an Echo 550 liquid handling robot was used to position droplets of a crystal suspension inline with grid ports immediately prior to flash freezing in liquid nitrogen, and ( FIG. 7B ) two protein crystals positioned over a grid port during data collection at LCLS-XPP, where hole is clearly visible in the top crystal where it has been exposed to the X-ray beam. The bottom crystal is still intact."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy and under contract GM103393 awarded by the National Institutes of Health. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,869,648","html":"https://www.labpartnering.org/patents/9,869,648","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,869,648"},"labs":[{"uuid":"0e20ecf3-77df-45a2-9c36-10780c968d5c","name":"Oak Ridge National Laboratory","tto_url":"https://www.ornl.gov/technology-transfer","contact_us_email":"partnerships@ornl.gov","avatar":"https://www.labpartnering.org/files/labs/5","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/0e20ecf3-77df-45a2-9c36-10780c968d5c"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Aina E. Cohen","location":"Pacifica, CA, US"},{"name":"Elizabeth L. Baxter","location":"San Jose, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"An X-ray data collection grid device, comprising:a. a magnetic base, wherein said magnetic base is compatible with robotic sample mounting systems used at synchrotron beamlines%3bb. a grid element fixedly attached to said magnetic base, wherein said grid element comprising a planar synchrotron-compatible material, wherein said grid element comprises at least one sealable sample window disposed through said planar synchrotron-compatible material, wherein said planar synchrotron-compatible material comprises at least one automated X-ray positioning and fluid handling robot fiducial mark."},{"idx":"00002","text":"The X-ray data collection grid device of claim 1, wherein said magnetic base comprises a shape that is compatible with sample goniometers disposed at synchrotron beam lines and is compatible with automated sample-pin exchange robotic systems."},{"idx":"00003","text":"The X-ray data collection grid device of claim 2, wherein said magnetic base is compatible with an ALS puck, a uni-puck, an MSC magazine, or an SSRL cassette."},{"idx":"00004","text":"The X-ray data collection grid device of claim 2, wherein said automated sample-pin exchange robotic systems comprise SSRL Automated Mounter, ALS Sample Exchange Robot, ACTOR, or a CATs robotic system."},{"idx":"00005","text":"The X-ray data collection grid device of claim 1, wherein said planar synchrotron-compatible material comprises polycarbonate, acrylonitrile butadiene styrene, cyclic olefin copolymer or other polymer material."},{"idx":"00006","text":"The X-ray data collection grid device of claim 1, wherein said at least one sealable sample window comprises a single window, an array of sample holes, or an array of windows, wherein said array of sample holes or said array of windows comprise a diameter in a range of 50 μm to 2.5 mm."},{"idx":"00007","text":"The X-ray data collection grid device of claim 1, wherein said at least one automated X-ray positioning and fluid handling robot fiducial mark comprises a hole, a mark, a dimple, a corner or an edge of said planar synchrotron-compatible material."},{"idx":"00008","text":"The X-ray data collection grid device of claim 7, wherein said hole has a diameter in a range of 5 μm to 300 μm."},{"idx":"00009","text":"The X-ray data collection grid device of claim 1, wherein said planar synchrotron-compatible material comprises a thickness in a range of 25 μm to 300 μm."},{"idx":"00010","text":"The X-ray data collection grid device of claim 1, wherein said at least one sealable sample window comprises a transparent sheet selected from the group consisting of graphene, holey carbon, mylar, polyamide, polyimide film with silicone adhesive, and polymers."},{"idx":"00011","text":"The X-ray data collection grid device of claim 10, wherein said transparent sheet comprises a thickness in a range of 100 nm to 20 μm."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"N","subgroup":"20025","main-group":"23","action-date":"2018-01-16","origination":"","symbol-position":"F","further":["01","","H","B","US","G","","N","20025","23","2018-01-16","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"N","subgroup":"10","main-group":"23","action-date":"2018-01-16","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"N","subgroup":"20","main-group":"23","action-date":"2018-01-16","origination":"","symbol-position":"L"}],"document_number":"20160019994","document_published_on":"2016-01-21","document_kind":"","document_country":""},{"number":"9,863,057","artifact":"grant","title":"Coated substrate apparatus and method","filed_on":"2014-04-28","issued_on":"2018-01-09","published_on":"2014-10-30","abstract":"A coated substrate is formed with aligned objects such as small molecules, macromolecules and nanoscale particulates, such as inorganic, organic or inorganic/organic hybrid materials. In accordance with one or more embodiments, an apparatus or method involves an applicator having at least one surface patterned with protruded or indented features, and a coated substrate including a solution-based layer of objects having features and morphology attributes arranged as a function of the protruded or indented features.","description":{"text":["FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT","This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy and under contract 0705687 awarded by the National Science Foundation. The Government has certain rights in this invention.","FIELD","Aspects of various embodiments are directed to thin film coatings, their application and both related apparatuses and methods.","BACKGROUND","Solution coating of organic semiconductors can be utilized for achieving low-cost manufacturing of electronics. Frequently, the electronics require a large-area of coverage while maintaining flexibility. In order to achieve low-cost manufacturing of these types of electronics, rapid coating speed is preferred. However, industrial-scale production poses challenges to the control of thin film morphology.","Controlling thin film morphology during solution shearing can be difficult in light of crystal defects that can form during application of the film. Solution shearing features of a film impose mass transport limitations during the coating process, which can lead to void formation and dendritic growth. This can hinder efficient charge transport due to charge carrier trapping at the prevalent grain boundaries. The transport limitation is not unique to solution shearing, but is commonly observed in other fast coating methods. These and other matters have presented challenges to coating substrates for a variety of applications","SUMMARY","Various example embodiments are directed to thin film coatings, their application and both related apparatuses and methods as well as implementation thereof.","According to an example embodiment, an apparatus includes an applicator having at least one surface patterned with protruded or indented features, and a coated substrate including a solution-based layer of objects having a plurality of features and morphology attributes (nano-sized, micron-sized, millimeter-sized or molecule level) that are attained as a function of the protruded or indented features.","Another embodiment is directed to a method as follows. The effect of patterns is characterized when a coating is generated using an applicator having at least one surface patterned with protruded or indented features. The characterizing is modeled based upon at least one attribute corresponding to the protruded or indented features, including shape, height, thickness, distance separating the protruded or indented features, and randomness of location of the protruded or indented features. Based on the characterizing, the applicator having the at least one surface patterned with protruded or indented features is used to generate the patterns in a solution of crystal-forming molecules on a substrate. In some implementations, the applicator is used to direct or align crystalline morphology attributes of the crystal-forming molecules as a function of the protruded or indented features. In other implementations, characterizing the effect of patterns includes characterizing the effect of an interconnected network having two-dimensional or three-dimensional features.","Another embodiment is directed to a method as follows. A substrate is coated with a solution-based layer of objects. An applicator having at least one surface patterned with protruded or indented features is used to control features and morphology attributes (nano-sized, micron-sized, millimeter-sized or molecule level) of the objects with the protruded or indented features. In some implementations, the features and morphology attributes are set using shape and distances between the protruded or indented features to control the flow of fluid in the solution-based layer to orient the objects. Further, patterned features on the substrate may be used to control nucleation of crystalline structures from the objects by controlling the evaporation of solvent from the solution-based layer. In some implementations, components are reacted during deposition or post deposition of the solution-based film while using the applicator to coat the film.","The above discussion/summary is not intended to describe each embodiment or every implementation of the present disclosure. The figures and detailed description that follow also exemplify various embodiments.","While various embodiments discussed herein are amenable to modifications and alternative forms, aspects thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the disclosure including aspects defined in the claims. In addition, the term “example” as used throughout this application is by way of illustration, and not limitation.","DETAILED DESCRIPTION","Aspects of the present disclosure are believed to be applicable to a variety of different types of devices, systems and arrangements involving fluid-enhanced crystal-engineering that allows for a high degree of morphological control of solution-printed thin films. Certain aspects of the present disclosure utilize a micropillar patterned application structure (e.g., a blade) to induce recirculation in the ink for enhancing crystal growth. Additionally, in certain embodiments, the micropillar patterned application structure controls the curvature of the ink meniscus which controls crystal nucleation. Other embodiments and features are exemplified in the claims and in the appendices included in the underlying provisional application to which benefit is claimed.","Various aspects of the present disclosure are directed toward apparatus or methods, as exemplified or supported by the underlying description and further discussion in the provisional application to which benefit is claimed. The apparatus and methods involve a substrate, and a film provided on the substrate. The film includes a plurality of objects such as single-crystalline structures that have a high degree of alignment with respect to one other. Additionally, in various embodiments the width of the individual structures is greater than approximately 50 μm.","In certain embodiments, each of the plurality of single-crystalline structures has a width at least between 200 μm and 1 mm. Additionally, certain embodiments of apparatus and methods, consistent with the present disclosure, also include a nucleation control pattern provided on the substrate. The nucleation control pattern assists in alignment of the plurality of single-crystalline structures. Additionally, as seen in the figures, a high degree of alignment of the plurality of single-crystalline structures can be characterized by the plurality of single-crystalline structures being at least 20 degrees or 30 degrees in the same direction. Further, in other embodiments, the high degree of alignment is characterized by the plurality of single-crystalline structures being within 10 degrees of a parallel axis of the substrate. In order to determine whether the single-crystalline structures are highly aligned, cross-polarized light is directed at the substrate and film, and if the domains of the plurality of single-crystalline structures extinguish at the same time, there is a high degree of alignment.","In certain embodiments, the film is provided to the substrate by applying a solution using an applicator that has a plurality of fluid-mixing structures (e.g., pillars, concave structures, microfluidic channels). In this manner, the plurality of fluid-mixing structures provides a single-crystalline film having high degree of alignment. Additionally, in other embodiments, the film is a highly controlled structure, with a crystalline size, and alignment is produced by applying a solution to the substrate using an applicator including a plurality of fluid-mixing structures. Further, the film can also be provided by applying a solution to the substrate using an applicator including a plurality of fluid-mixing structures to induce and control a concentration of the solution distributed throughout the film. The solution can be applied with the substrate being at a controlled temperature. Additionally, the film is often applied to the substrate at a controlled shearing speed.","In certain embodiments, the plurality of fluid-mixing structures provided with the applicator is between 1 μm and 1 mm in height or depth. Additionally, in other embodiments, each of the plurality of fluid-mixing structures is separated by a pitch distance between 50 nm and 1 mm. Further, the plurality of fluid-mixing structures can be separated by a pitch distance that is approximately equal to the height of the plurality of fluid-mixing structures.","In certain embodiments, applying the film to the substrate includes inducing recirculation of the solution near a drying front of the solution, and in other embodiments still, applying the film to the substrate includes controlling a curvature of the solution meniscus. Additionally, in certain embodiments, utilizing fluid-mixing structures on an applicator to apply the film to the substrate decreases mass depletion regions in the single-crystalline film. In certain more specific embodiments, in applying the film to the substrate, an applicator (having a plurality of fluid-mixing structures) is advanced along the substrate at a height above the substrate that is approximately equal to the height of the plurality of fluid-mixing structures.","Various embodiments of the present disclosure are also directed toward application of a solution to a substrate, which results in a film on the substrate having a plurality of single-crystalline structures each of which has a high degree of alignment with respect to the other single-crystalline structures. The film can be provided using a number of difference processes, including, for example a slot-die coater, or a roll-to-roll processing technique.","Various embodiments may be implemented in conjunction with different types of apparatuses. For instance, some embodiments are directed to a thin film used in electronic applications, such as in bulk heterojunction solar cells, touch screens, organic devices and electrodes as may be implemented in a multitude of electrical applications.","In some embodiments, a micropillar patterned printing blade is used to induce recirculation in the ink for enhancing crystal growth, with the curvature of the ink meniscus used to control crystal nucleation. Fast coating and patterning of millimeter-wide, centimeter-long, highly-aligned single-crystalline organic semiconductor thin films can be achieved. For instance, thin films of 6,13-bis(triisopropylsilylethynyl) pentacene (TIPS-pentacene) can be formed having lattice-strained single-crystalline domains and average and maximum mobilities of 8.1±1.2 cm2 V-1 s-1 and 11 cm2 V-1 s-1, as may be implemented with non-equilibrium single-crystalline domains in high-performance, large-area printed electronics.","Various embodiments are directed to fluid flow-enhanced alignment of objects, such as objects from which crystals are grown (and, e.g., alignment of such as-grown crystals). These and other embodiments are implemented for controlling thin film morphology during coating of the film, such as coating involving solution shearing, for mitigating or preventing defects during film formation (e.g., for preventing crystalline defects). A component such as a blade or other tool is patterned with microstructures, such as micropillars, and engaged with the solution to enhance mass transport, such as by dragging or otherwise moving the microstructures through the film. This approach can address issues that may, for example, relate to laminar flow in micron-thick films (e.g., including ink), which may impose mass transport limitations and lead to undesirable conditions such as void formation and dendritic growth, and hinder efficient charge transport due to charge carrier trapping at prevalent grain boundaries. Enhancing mass transport in this regard can reduce or eliminate such aspects as void formation and dendritic growth, addressing charge carrier trapping issues.","The spacing and arrangement of the microstructures can be tailored to particular applications. In some embodiments, a spacing (period) between microstructures is less than 100 microns, or otherwise set to match a domain size in the reference film being prepared (the domain size being relevant to the film preparation without using microstructures). The cross-section and shape of the microstructures may also be set to suit particular embodiments in this regard. In some implementations, the microstructures are arranged to facilitate recirculation behind the microstructures as they move through the film. Narrow spacing can be implemented to induce rapid flow expansion following acceleration through the gap between the structures, so as to facilitate lateral mass transport (e.g., perpendicular to the shearing direction). This approach can be implemented with unidirectional coating techniques (e.g., solution shearing, slot-die printing, doctor blading, or zone casting), in which evaporation-driven connective flow occurs mainly along the blade/tool movement direction.","Another embodiment is directed to an apparatus including an applicator having one or more surfaces (e.g., top or bottom) patterned with features that protrude from or into the applicator. A coated substrate includes a solution-based layer of objects having features and morphology attributes (e.g., nano-sized, micron-sized, millimeter-sized or molecule level) that are attained as a function of the protruded or indented features. The objects may include, for example, small molecules, macromolecules, and nanoscale particulates, and can be inorganic, organic or inorganic/organic hybrid objects.","The patterned features are implemented in a variety of manners to suit particular embodiments. In some implementations, the features set the direction of the morphology attributes based on a fluidic mix of the objects in the coating. The shape, spacing and arrangement of the features may be controlled to set the resulting morphology.","The features and morphology attributes of the coated substrate are also set in various manners, to suit particular embodiments. In some embodiments, the coated substrate includes patterned features that control the flow of the solution and spatial distribution of the objects on the substrate. In certain embodiments, the objects include at least one of crystal-forming molecules and inorganic molecules, and the coated substrate includes patterned features that operate with the protruded or indented features of the applicator to control both nucleation and growth of crystalline structures from the objects. For instance, phase separation as relating to nucleation, growth of crystalline structures and/or spinodal decomposition from the objects can be used to control the objects. In some embodiments, the solution-based layer exhibits morphology attributes including domain size of respective objects in the coated film that are controlled with the protruded or indented features (e.g., for polymers, small molecules, inorganic materials, nano or micro-objects including one of particles, rods, wires, and tubes, or a combination of different ones of the types of objects). In some embodiments, the solution includes one or more of crystal-forming molecules, inorganic materials and other objects having a features including directed crystalline morphology attributes arranged by the protruded or indented features.","In certain embodiments, the substrate includes patterned features having boundary regions with intersecting edges that nucleate the objects along the boundary regions by directing flow of the objects in the solution and controlling evaporation of solvent from the solution (e.g., to pattern the solution-based layer relative to surface patterning on the substrate). For instance, the intersecting edges may be implemented to, as a meniscus of the solution-based layer passes an intersection of the edges, pin a contact line of the solution at the intersection of the edges until the objects nucleate at the contact line. In some implementations, the intersecting edges operate to evaporate solvent from the solution-based layer and deposit a crystalline or a non-crystalline coating on the substrate that includes ones of the objects that are dissolved or suspended in the solvent. The patterned features may, for example, facilitate deposition of a crystalline or a non-crystalline coating on the substrate by controlling evaporation of a solvent from the solution, in which the coating includes substances chemically derived from the objects that were dissolved or suspended in the solvent. In some implementations, the patterned features form the chemically-derived substances during or after coating of the substrate by at least one of chemical and thermal interaction with at least one of the applicator and the coated substrate.","Another embodiment is directed to forming a film including single-crystalline structures from a solution, upon a substrate having a nucleation control pattern. The structures are nucleated via the nucleation control pattern, and meniscus curvature and fluid flow are used to create aligned crystals. Using this approach, each structure has a nucleated crystalline lattice aligned with respect to others of the structures relative to the nucleation control pattern. For instance, aligned single-crystalline structures can be grown with a width of at least 50 μm while aligning the single-crystalline structures with a micropillar-patterned printing blade. Further, fluid-mixing structures of the blade can be used to decrease mass depletion regions in the solution, prior to nucleating the plurality of single-crystalline structures, induce microphase separation of the solution by increasing the nucleation density, and/or induce recirculation of the solution near a drying front thereof. In certain implementations, cross-polarized light is used to concurrently extinguish domains of the plurality of single-crystalline structures.","Another embodiment is directed to a plurality of substrate-grown single-crystalline structures arranged in a layer and with each of the structures having a nucleated crystalline lattice aligned with respect to others of the plurality of single-crystalline structures relative or corresponding to a nucleation control pattern. The substrate-grown single-crystalline structures exhibit alignment of the single-crystalline structures along the nucleation control pattern.","Turning now to the Figures, FIG. 1 shows a flow diagram for forming a thin film, in accordance with another example embodiment. At block 100 , a substrate is provided with a solution-based layer. At block 110 , fluid flow is generated in the solution-based layer, by introducing applicator features. For instance, protrusions or indentations of an applicator can be introduced into a substrate or other material of the applicator, and engage with the solution. Such features may, for example, have spacing and sizes that facilitate alignment. At block 120 , characteristics of the substrate are optionally used to initiate nucleation, such as by pinning fluid flow to initiate nucleation of single-crystal structures. Other embodiments involve the alignment of non-crystalline structures. At block 130 , objects from the solution are aligned, via the fluid flow as implemented by the applicator. This alignment may, for example, involve controlled single-crystalline growth, such as in embodiments in which bock 120 is implemented. At block 140 , a formed coating is provided with the aligned objects, as may be used for a variety of devices such as thin-film electronic devices including those discussed in the underlying provisional application to which benefit is claimed.","FIG. 2 shows an apparatus and approach 200 to forming a film on a substrate, in accordance with another example embodiment. A tool 210 includes a plurality of microstructures, including microstructure 212 labeled by way of example, that interact with a coating 220 to form a film 222 on a substrate 230 (e.g., which may be heated by way of example). The microstructures are pulled through the film 222 in a direction as shown by the arrow, to mitigate defects in the formation of the film 222 . For instance, by using microstructures patterned in a manner that enhances mass transport in the film, defects can be reduced or eliminated.","FIG. 3 shows a microstructure apparatus 300 , in accordance with another example embodiment. The microstructure apparatus 300 includes a plurality of microstructures (e.g., micropillars), with an example size reference and microstructure 310 labeled by way of example. Inset 320 shows a top view of the microstructures. A cross-section of the microstructures is crescent-shaped, and can be implemented with the arch of each microstructure being directed against a flow direction of fluid through which the apparatus is drawn, to facilitate flow separation from the surface of the microstructures. The microstructures operate to generate recirculation behind the microstructures. The narrow microstructure spacing induces rapid flow expansion following acceleration through the gap between the microstructures, so as to facilitate lateral mass transport (perpendicular to the shearing direction). This approach may be implemented with unidirectional coating techniques such as solution shearing, slot-die printing, doctor blading, and zone casting, in which evaporation-driven connective flow occurs mainly along the blade movement direction.","FIG. 4 shows a microstructure apparatus 400 and corresponding flow patterns in a film as the microstructures are moved in the film, in accordance with another example embodiment. The apparatus 400 may, for example, be implemented in accordance with the apparatus 300 shown in FIG. 3 . Microstructure 410 is labeled by way of example, with flow lines shown passing around the crescent-shape of the microstructures, which generate recirculation and lateral currents behind the pillars. There is little to no velocity in flow in front of and behind the crescent-shape, with high velocity (e.g., 1.3 mm/s) laterally between the microstructures, with flow direction shown by the arrow.","The use of microstructures, such as micropillar-patterned shearing blades as may be consistent with the apparatus 300 in FIG. 3 , can significantly improve thin-film morphology of various types of objects in solution. In some embodiments, TIPS-pentacene is sheared from its mesitylene solution to form crystalline structures having a domain size on the millimeter scale, with drastically reduced grain boundary densities (e.g., relative to such structures formed without such a shearing blade). This approach can be implemented to produce structures with a low void fraction and virtually no dendritic growth. In some embodiments, the micropillars of about 35 μm wide and 42 μm tall are used to effect these flow characteristics.","In some embodiments, single-crystalline domains are achieved by controlling fluid mixing and also controlling the nucleation process of crystalline structures in the fluid. This entails controlling the spatial distribution and the density of nucleation events, by controlling solvent evaporation. In some embodiments, the curvature of a contact line is modified by surface patterning of a substrate upon which the film is formed, to anchor nucleation at spots where the radius of curvature is the highest in which crystal nucleation preferentially occurs at highly convex points along the contact line. The shape of the contact line is modulated by patterning the substrate with solvent-wetting and non-wetting regions, using a combination of photolithography and surface energy patterning (e.g., using PTS (phenyltrichlorosilane) and crystalline OTS (octadecyltrichlorosilane) to create the wetting and non-wetting regions, respectively).","Referring again to FIG. 2 , in some implementations, the substrate 230 is patterned with wetting regions including triangular-shaped portions including portion 224 , which facilitates crystallization. The tip of the triangular regions points towards the approaching meniscus of the coating 220 (e.g., ink). As the meniscus passes, the contact line is temporarily pinned at the boundary of the triangles, until nucleation occurs at the sharp tips. The triangular design defines a wedge shaped meniscus that funnels the convective supply of solute towards the tip, which facilitates nucleation anchoring by lowering the nucleation induction time. In some implementations, asymmetric aspects of the triangle portions eliminate twin boundary formation. Following the triangles is a series of narrow slits that arrest the growth of undesired crystallites, which are otherwise difficult to eliminate simply by nucleation control given the stochastic nature of nucleation.","In certain embodiments, a fluid-enhanced crystal engineering approach involves controlling both nucleation and crystal growth. In certain implementations, millimeter-wide, centimeter-long TIPS-pentacene single-crystalline domains are formed using a combination of fluid flow and surface-based nucleation control. Resulting domains may, for example, extinguish cross-polarized light simultaneously, indicating a high degree of crystallographic alignment. Single-crystalline domains coated using this approach may exhibit a smooth and uniform texture, with minimal voids. In some implementations, the number of voids is reduced by increasing film thickness or lowering coating speed.","Such approaches are applicable to large-area, high-throughput coating with controlled domain locations. In some implementations, an array of large TIPS-pentacene single crystalline domains is formed covering an area of approximately 1×3 cm 2 within 50 seconds, with a high probability (e.g., 70%) of forming single crystals. In other implementations, a probability of single-crystal formation is increased to above 90% by narrowing domains to 500 μm and 200 μm in width, reducing surface defects (e.g., by tuning a slit as discussed above), while maintaining the same printing speed.","FIG. 5 shows an apparatus 500 having structures (including structure 510 ) aligned via an applicator, in accordance with another example embodiment. The structures include in-plane molecular structure of TIPS-pentacene crystal with a b-axis aligned with the shearing direction, at φ=0° as shown. The overall grain orientation distribution and the dominant crystal growth axis are shown on the (010) reflection (along line 520 and lines parallel thereto) with the momentum transfer vector qxy=0.81, qz=0.21. This reflection may be used for comprehensive sampling, since at the corresponding diffraction condition, the X-ray illuminates all grains almost perpendicularly to the shearing direction. Phi-scans confirm the high degree of alignment of single-crystalline domains, with an angular spread of diffraction peaks of about 3 degrees (around) φ=80°). The (010) diffraction peak may be at φ=81.3° when the b axis of TIPS-pentacene is perfectly aligned with the shearing direction (φ=0°). The crystallographic b axis of the TIPS-pentacene is aligned with the shearing direction, within sample placement error. This crystal orientation may be implemented to enhance charge transport. Further, these approaches can be similarly used with materials other than TIPS-pentacene.","In various applications as implemented with FIG. 5 , out-of-plane coherence lengths can be set at 16±2 nm, by imparting a common out-of-plane molecular packing throughout almost the entire thickness of the film. The single-crystalline domains are formed with in-plane correlation lengths both parallel and perpendicular to the shearing direction. The correlation length perpendicular to the shearing direction can be increased by enhancing mass transport in the lateral direction (e.g., using a micropillar-patterned blade such as shown in FIG. 2 ).","In some implementations, crystal morphology is controlled while tuning molecular packing of crystalline materials such as TIPS-pentacene, to optimize the charge carrier mobility. Non-equilibrium molecular packing states are achieved by tuning film thickness and solvent. In some implementations, multiple polymorphs of crystalline material are formed with incremental changes in unit cell geometry relative to equilibrium, with non-equilibrium packing states achieved via confined molecular motion near the substrate. For instance, by taking advantage of the thickness-dependent molecular packing, non-equilibrium crystal lattices can be achieved by lowering solution concentration instead of increasing shearing speed, thereby maintaining film morphology while tuning molecular packing. In some implementations involving TIPS-pentacene, it has been recognized/discovered that the solvent mesitylene can be used to obtain non-equilibrium molecular packing of TIPS-pentacene at lower shearing speed (e.g., relative to using toluene).","Various embodiments are directed to solution coating of various soluble organic compounds, addressing mass-transport limited crystal growth and random nucleation in high-throughput crystalline film formation. For instance, such morphology control can be applied to an organic semiconductor molecule, 4T-TMS (trimethylsilyl-substituted quarterthiophene) to form single-crystalline thin films of 4T-TMS that exhibit a herringbone packing motif.","FIG. 6 shows patterned microstructures 600 , in accordance with another example embodiment. A plurality of hexagonal-shaped microstructures, including microstructure 610 , are shown in a pillar formation. These pillars may be used in an array, such as with an applicator as shown in FIG. 2 (e.g., in place of and/or in addition to the crescent-shaped structures as shown therein). In some embodiments, the microstructure 610 has a diameter of 2-3 μm, a height of 6 μm (AR: 2˜3), and a spacing length between the structures of 1.5˜2 μm (spacing ratio: 0.5˜1).","The embodiments and specific applications discussed herein and in the above-referenced provisional application may be implemented in connection with one or more of the above-described aspects, embodiments and implementations, as well as with those shown in the appended figures. One or more of the items depicted in the present disclosure and in the provisional application to which benefit is claimed can also be implemented in a more separated or integrated manner, or removed and/or rendered as inoperable in certain cases, as is useful in accordance with particular applications. In view of the description herein, those skilled in the art will recognize that many changes may be made thereto without departing from the spirit and scope of the present disclosure."],"drawings":["DESCRIPTION OF THE FIGURES","Various example embodiments may be more completely understood in consideration of the following detailed description in connection with the accompanying drawings, in which:","FIG. 1 shows a flow diagram for forming a thin film, in accordance with an example embodiment%3b","FIG. 2 shows an apparatus and approach to forming a film on a substrate, in accordance with another example embodiment%3b","FIG. 3 shows a microstructure arrangement, in accordance with another example embodiment%3b","FIG. 4 shows flow patterns in a film as microstructures are moved in the film, in accordance with another example embodiment%3b","FIG. 5 shows structures aligned via a an applicator, in accordance with another example embodiment%3b and","FIG. 6 shows patterned microstructures, in accordance with another example embodiment."]},"government_interest":"FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy and under contract 0705687 awarded by the National Science Foundation. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,863,057","html":"https://www.labpartnering.org/patents/9,863,057","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,863,057"},"labs":[{"uuid":"2efd2261-1434-4297-8eb6-c40cbde9cb49","name":"Pacific Northwest National Laboratory","tto_url":"https://www.pnnl.gov/industry","contact_us_email":"jennifer.lee@pnnl.gov","avatar":"https://www.labpartnering.org/files/labs/6","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/2efd2261-1434-4297-8eb6-c40cbde9cb49"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Zhenan Bao","location":"Stanford, CA, US"},{"name":"Ying Diao","location":"Stanford, CA, US"},{"name":"Stefan Christian Bernhardt Mannsfeld","location":"Palo Alto, CA, US"},{"name":"Chee-Keong Tee","location":"Stanford, CA, US"},{"name":"Hector A. Becerril-Garcia","location":"Rexburg, ID, US"},{"name":"Yan Zhou","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"An apparatus comprising:an applicator including a shearing blade having at least one surface patterned with protruded or indented features%3b anda coated substrate including a solution-based layer of objects having a plurality of features and morphology attributes including at least one of nano-sized, micron-sized, millimeter-sized and molecule level, being configured and arranged as a function of the protruded or indented features, wherein the protruded or indented features of the applicator are separated by a pitch distance of between 50 nm and 1 mm such that application with the solution causes formation of a film on the substrate having the plurality of features and morphology attributes."},{"idx":"00002","text":"The apparatus of claim 1, wherein the features are configured and arranged to set the direction of the morphology attributes based on a fluidic mix of the objects in the coating, and wherein the attributes include nano-sized objects."},{"idx":"00003","text":"The apparatus of claim 1, wherein the coated substrate includes patterned features configured and arranged to control flow of the solution and spatial distribution of the objects on the substrate and wherein the attributes include micron-sized objects."},{"idx":"00004","text":"The apparatus of claim 1, whereinthe objects include at least one of crystal-forming molecules and inorganic molecules, andthe coated substrate includes patterned features that are configured and arranged with the protruded or indented features of the applicator to control both nucleation and growth of crystalline structures from the objects."},{"idx":"00005","text":"The apparatus of claim 1, wherein the solution-based layer exhibits the morphology attributes including domain size of respective objects in the solution-based layer that are configured and arranged as a function of the protruded or indented features, wherein types of the objects include at least one of:polymers,small molecules,inorganic materials,nano or micro-objects including one of particles, rods, wires, and tubes, anda combination of different ones of the types of the objects."},{"idx":"00006","text":"The apparatus of claim 1, wherein the solution-based layer includes a solution of at least one of crystal-forming molecules, inorganic materials and other objects having a plurality of features including directed crystalline morphology attributes configured and arranged as a function of the protruded or indented features."},{"idx":"00007","text":"The apparatus of claim 1, whereinthe objects include at least one of crystal-forming molecules, inorganic molecules and other objects, andthe substrate includes patterned features having boundary regions with intersecting edges configured and arranged to nucleate the objects along the boundary regions by directing flow of the objects in the solution and controlling evaporation of solvent from the solution."},{"idx":"00008","text":"The apparatus of claim 7, wherein the intersecting edges are configured and arranged to, as a meniscus of the solution-based layer passes an intersection of the edges, pin a contact line of the solution at the intersection of the edges until the objects nucleate at the contact line."},{"idx":"00009","text":"The apparatus of claim 7, wherein the solution-based layer is patterned relative to surface patterning on the substrate."},{"idx":"00010","text":"The apparatus of claim 7, wherein the intersecting edges are configured and arranged to facilitate evaporation of a solvent from the solution-based layer and therein deposit a crystalline or a non-crystalline coating on the substrate, the coating including ones of the objects that are dissolved or suspended in the solvent."},{"idx":"00011","text":"The apparatus of claim 7, wherein the patterned features are configured and arranged to facilitate deposition of a crystalline or a non-crystalline coating on the substrate by controlling evaporation of a solvent from the solution, and wherein the coated substrate includes substances chemically derived from the objects that were dissolved or suspended in the solvent."},{"idx":"00012","text":"The apparatus of claim 11, wherein the patterned features are configured and arranged to form the chemically-derived substances during or after coating of the substrate by at least one of chemical and thermal interaction with at least one of the applicator and the coated substrate."},{"idx":"00013","text":"The apparatus of claim 1, whereinthe objects include at least one of crystal-forming molecules and inorganic molecules, andthe coated substrate includes patterned features that are configured and arranged with the protruded or indented features of the applicator to control phase separation including at least one of nucleation, growth of single crystalline structures and spinodal decomposition from the objects."},{"idx":"00014","text":"The apparatus of claim 1, wherein the coated substrate includes directed or aligned crystalline morphology attributes set as a function of the protruded or indented features."},{"idx":"00015","text":"The apparatus of claim 1, wherein the morphology attributes includes shape and distances between the protruded or indented features being configured and arranged to control flow of fluid in the solution-based layer, and using the controlled flow of fluid to orient the objects."},{"idx":"00016","text":"The apparatus of claim 1, further including patterned features on the substrate being configured and arranged to control nucleation of crystalline structures from the objects by controlling evaporation of solvent from the solution-based layer."},{"idx":"00017","text":"The apparatus of claim 1, further including reactive components present during deposition or post deposition of the solution-based layer."},{"idx":"00018","text":"The apparatus of claim 1, wherein the shearing blade has a micro-pillar pattern formed by the protruded or indented features."},{"idx":"00019","text":"The apparatus of claim 1, wherein the protruded or indented features are configured to interact with the solution to form a film on the substrate responsive to movement of the applicator relative to the coated substrate or movement of the coated substrate relative to the applicator."},{"idx":"00020","text":"The apparatus of claim 1, wherein the protruded or indented features include pillars or indented pillar shapes in an array, each protruded or indented features having a height or depth of between 1 um and 1 mm."}],"cpc":{"class":"30","value":"","source":"H","status":"B","country":"US","section":"C","version":"","subclass":"B","subgroup":"02","main-group":"7","action-date":"2018-01-09","origination":"","symbol-position":"F","further":["30","","H","B","US","C","","B","02","7","2018-01-09","","F"]},"ipc":[{"class":"30","value":"","source":"H","status":"B","country":"US","section":"C","version":"","subclass":"B","subgroup":"02","main-group":"7","action-date":"2018-01-09","origination":"","symbol-position":"F"},{"class":"30","value":"","source":"H","status":"B","country":"US","section":"C","version":"","subclass":"B","subgroup":"54","main-group":"29","action-date":"2018-01-09","origination":"","symbol-position":"L"}],"document_number":"20140318440","document_published_on":"2014-10-30","document_kind":"","document_country":""},{"number":"9,966,598","artifact":"grant","title":"High capacity prelithiation reagents and lithium-rich anode materials","filed_on":"2015-09-29","issued_on":"2018-05-08","published_on":"2016-03-31","abstract":"Described here is a method for making an anode of a rechargeable battery, comprising incorporating a composition comprising Li.sub.xM into the anode, wherein M is a Group 14 element. Also described here is an anode comprising a composition comprising Li.sub.xM, wherein M is a Group 14 element, and a rechargeable battery comprising the anode.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims the benefit of U.S. Provisional Patent Application No. 62/057,957 filed Sep. 30, 2014, the content of which is incorporated herein by reference in its entirety.","FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT","This invention was made with Government support under Contract No. DE-AC02-76SF00515, awarded by U.S. Department of Energy. The Government has certain rights in the invention.","BACKGROUND","Rechargeable lithium-ion batteries are widely used for consumer electronics and exhibit great potential for electrical vehicle and grid-scale energy storage. The first charging process, in which lithium ions and electrons move from cathode to anode, is important for lithium-ion battery operation. When the potential of the anode is below ˜1 V versus Li metal, the organic electrolyte is reduced on the anode surface to form a layer of solid electrolyte interphase (SEI) that is composed of a complex composition of inorganic and organic lithium compounds. In addition, some lithium may be trapped in the electrode upon lithiation. As a result, the first charging process irreversibly consumes a fraction of the lithium ions, giving rise to a net loss of storage capacity. Such first cycle irreversible capacity loss is usually compensated by additional loading of cathode materials in current lithium-ion batteries. However, lithium metal oxide cathodes have much lower specific capacity (mostly less than ˜200 mAh/g) than anodes. Excessive loading of cathode material causes appreciable reduction of battery specific energy and energy density. It is therefore attractive to develop an alternative method that suppresses this loss and consequently increases the 1 st cycle Coulombic efficiency.","Addressing first cycle capacity loss is important for the successful commercialization of graphite anodes. With graphite anodes, 5-20% of the lithium from the cathode is typically consumed to form the SEI, corresponding to an appreciable amount of inactivated cathode material. In the past two decades, the 1 st cycle Coulombic efficiency of graphite anodes has increased from \u003c80% to 90-95% through optimization of material quality, electrolyte, and additives. Further improvement is likely to result from pre-compensation or prelithiation of the electrodes.","Besides graphite anodes, prelithiation presents exciting opportunities for next generation high capacity anode materials such as Si, Ge, Sn, SiO x , GeO x , SnO 2 , TiO 2 and P, which have a large first cycle capacity loss. For example, Si is a particularly attractive anode material, due to its high specific capacity of ˜4200 mAh/g, excellent material abundance, and well-developed industrial infrastructure for manufacturing. In the past several years, there has been exciting progress in addressing the issues associated with large volume change (\u003e300%) during lithium insertion and extraction by designing nanostructured Si including nanowires and core-shell nanowires, hollow particles and tubes, porous materials, Si/C nanocomposites and by using improved binders. One of the remaining issues for Si anodes is the large capacity loss in the first cycle. The 1 st cycle Coulombic efficiency is typically very low, in the range of 50 to 80%, in spite of a few reports with higher values of ˜85%.","The 1 st cycle Coulombic efficiency can be improved by prelithiation. Anode prelithiation has been previously achieved by inducing electrical shorting between anode materials and lithium metal foil. It involves the fabrication of a temporary battery, a process which is difficult to scale up. In addition, prelithiation of thick electrode with Li foil is time consuming, as it involves the diffusion of Li ions across the entire anode. Another approach is to use stabilized lithium metal powder (SLMP) to pre-compensate the first cycle irreversible capacity loss of different anode materials, such as graphite and Si-CNT composite. However, SLMP faces many practical challenges yet to be addressed, including large particle size and difficulty to scale up. It is therefore highly desirable to develop alternative microparticles or nanoparticles for prelithiation.","SUMMARY","One aspect of some embodiments of the disclosure relates to a method for making an anode of a rechargeable battery, comprising incorporating a composition comprising Li x M into the anode, wherein M is a Group 14 element. x indicates the atomic ratio of Li to M and can be, for example, about 5:1 or less, about 4:1 or less, about 3:1 or less, or about 2:1 or less, and down to about 1:1, about 1:3, or about 1:6. In some embodiments, x is between about 5:1 to about 4:1 or between about 4:1 to about 3:1.","The Group 14 element can be selected from, for example, graphite (C), silicon (Si), germanium (Ge), tin (Sn), lead (Pb), and flerovium (Fl). In some embodiments, the composition comprises Li x C. In some embodiments, the composition comprises Li x Si. In some embodiments, the composition comprises Li x Ge. In some embodiments, the composition comprises Li x Sn.","In some embodiments, the composition comprises nanoparticles or microparticles that comprise Li x M. In some embodiments, the composition comprises nanoparticles or microparticles that comprise Li x Si, Li x Ge, and/or Li x Sn. In some embodiments, the composition comprises nanostructures that comprise Li x M, such as nanoparticles, having at least one dimension in the range of about 1 nm to about 1 μm, such as about 500 nm or less, about 400 nm or less, about 300 nm or less, or about 200 nm or less, and down to about 100 nm, and down to about 50 nm, down to about 20 nm, down to about 10 nm, or less. In some embodiments, the composition comprises microstructures that comprise Li x M, such as microparticles, having at least one dimension in the range of about 1 μm to about 1 mm, such as about 500 μm or less, about 100 μm or less, about 50 μm or less, or about 10 μm or less, down to about 5 μm, down to about 2 μm, or less.","In some embodiments, the composition comprises crystalline Li x Si, and, in other embodiments, the composition comprises amorphous Li x Si. In some embodiments, the composition comprises crystalline Li x Ge, and, in other embodiments, the composition comprises amorphous Li x Ge. In some embodiments, the composition comprises crystalline Li x Sn, and, in other embodiments, the composition comprises amorphous Li x Sn.","In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising a lithium compound and (b) a plurality of Li x M domains embedded in the matrix. The matrix can comprise, for example, an oxide, a fluoride, a sulfide, or a nitride of lithium. In some embodiments, the matrix comprises Li 2 O and/or LiF. In some embodiments, the nanoparticles or microparticles comprise at least 3, or at least 5, or at least 10, or at least 20, or at least 50, or at least 100 Li x M domains embedded in the matrix. In some embodiments, the embedded Li x M domains have an average size of about 1 nm to about 200 nm, such as about 100 nm or less, about 70 nm or less, about 50 nm or less, or about 30 nm or less, and down to about 20 nm, and down to about 10 nm, down to about 5 nm, down to about 2 nm, or less.","In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising Li 2 O and/or LiF and (b) a plurality of Li x Si domains embedded in the matrix. In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising Li 2 O and/or LiF and (b) a plurality of Li x Ge domains embedded in the matrix. In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising Li 2 O and/or LiF and (b) a plurality of Li x Sn domains embedded in the matrix. In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising Li 2 O and/or LiF and (b) Li x Si and Li x Sn domains embedded in the matrix. In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising Li 2 O and/or LiF and (b) Li x Si and Li x Ge domains embedded in the matrix. In some embodiments, the nanoparticles or microparticles comprise (a) a matrix comprising Li 2 O and/or LiF and (b) Li x Ge and Li x Sn domains embedded in the matrix. In some embodiments, the nanoparticles or microparticles comprise a composite of Li x Si and at least one metal (e.g., Fe, Ni, Co, and other metals).","In some embodiments, the nanoparticles or microparticles comprise (a) a protective coating comprising Li 2 O and/or LiF and (b) a Li x M core encapsulated by the protective coating. In some embodiments, the nanoparticles or microparticles comprise (a) a protective coating comprising Li 2 O and/or LiF and (b) a Li x Si core encapsulated by the protective coating. In some embodiments, the nanoparticles or microparticles comprise (a) a protective coating comprising Li 2 O and/or LiF and (b) a Li x Ge core encapsulated by the protective coating. In some embodiments, the nanoparticles or microparticles comprise (a) a protective coating comprising Li 2 O and/or LiF and (b) a Li x Sn core encapsulated by the protective coating.","In some embodiments, the nanoparticles or microparticles comprise a core-shell nanostructure, wherein the core comprises Li x M and the shell comprises the protective coating. In some embodiments, the protective coating is a passivation layer. In some embodiments, the protective coating comprises an oxide, such as Li 2 O, SiO 2 , TiO 2 , or another metal oxide. In some embodiments, the protective coating comprises a sulfide, or a fluoride, or a nitride, or a carbonate, or inorganic lithium salts. In some embodiments, the protective coating comprises an organic lithium compound. In some embodiments, the protective coating comprises a mixture of inorganic and organic lithium compounds. Different surfactants can be used to modify the surface of Li x M. Surfactants, such as —OH, —SH, —NH 2 , —PH 2 , —F, —Cl, —Br, and —I terminated long hydrocarbon chains, can be reduced on the surface of Li x M to form a dense coating. This kind of coating, a mixture of inorganic and organic lithium compounds, can improve the dry air and moisture stability of Li x M. In some embodiments, the protective coating comprises polymers, such as polydimethylsiloxane (PDMS). In some embodiments, the protective coating comprises graphene, graphene oxide, reduced graphene oxide, graphitic carbon, amorphous carbon and other carbon materials. In some embodiments, the protective coating comprises metallic materials. In some embodiments, the protective coating has a thickness of about 200 nm or less, or about 100 nm or less, or about 50 nm or less, or about 20 nm or less, or about 10 nm or less, or about 5 nm or less.","In some embodiments, the nanoparticles or microparticles can further comprise a thin layer formed by solvent decomposition during slurry processing, which could be due to the reducing power of Li x M.","In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to dry air (dew point=−50° C.) for 1 day. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to dry air (dew point=−50° C.) for 3 days. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to dry air (dew point=−50° C.) for 5 days.","In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to ambient air for 1 hour. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to ambient air for 3 hours. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to ambient air for 6 hours. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to ambient air for 12 hours.","In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 20% relative humidity (RH) for 1 hour. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 20% RH for 3 hours. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 20% RH for 6 hours. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 20% RH for 12 hours.","In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 10% RH for 1 hour. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 10% RH for 3 hours. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 10% RH for 6 hours. In some embodiments, the Li x M-containing nanoparticles or microparticles are capable of retaining at least 50%, or at least 60%, or at least 70%, or at least 80%, or at least 90% of its capacity after exposure to air of 10% RH for 12 hours.","In some embodiments, the composition comprising Li x M is incorporated as the anode material. In some embodiments, the composition comprising Li x M is incorporated as a prelithiation reagent to prelithiate an anode material.","In some embodiments, the anode material comprises carbon. In some embodiments, the anode material comprises graphite. In some embodiments, the anode material comprises Si. In some embodiments, the anode material comprises SiO. In some embodiments, the anode material comprises Ge. In some embodiments, the anode material comprises Sn. In some embodiments, the anode material comprises TiO 2 or SnO 2 . In some embodiments, the anode material comprises P.","In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:2 or less, or about 1:3 or less, or about 1:4 or less, or about 1:5 or less, or about 1:8 or less, or about 1:10 or less, or about 1:15 or more, or about 1:20 or more, or about 1:30 or more.","In some embodiments, the method comprises mixing the prelithiation reagent and the anode material in at least one binder and one solvent to form a slurry, wherein the solvent has a dielectric constant of about 20 or less. In some embodiments, the solvent has a dielectric constant of about 15 or less. In some embodiments, the solvent has a dielectric constant of about 10 or less. In some embodiments, the solvent has a dielectric constant of about 8 or less. In some embodiments, the solvent comprises an ether, an aromatic hydrocarbon, or both. In some embodiments, the solvent is selected from one or more of polar aprotic organic solvents. In some embodiments, the solvent is selected from one or more of non-polar organic solvents. In some embodiments, the solvent comprises 1,3-dioxolane (DOL), dimethyl ether (DME), tetrahydrofuran (THF), and/or other ethers. In some embodiments, the solvent comprises toluene, hexane, benzene and/or other hydrocarbons. In some embodiments, the binder for the slurry process comprises polyvinylidene fluoride (PVDF), and/or poly(styrene-co-butadiene).","In some embodiments, the mixing of the prelithiation reagent and the anode material in slurry and/or the coating of the slurry is processed in an ambient environment. In some embodiments, the mixing of the prelithiation reagent and the anode material in slurry and/or the coating of the slurry is processed in a low-humidity environment. In some embodiments, the prelithiation reagent is processed at a relative humidity of about 20% or less, or about 10% or less, or about 5% or less, or about 1% or less.","In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 2%, or at least about 5%, or at least about 10%, or at least about 15%, or at least about 20%. In some embodiments, the first cycle Coulombic efficiency of the anode after prelithiation is at least about 80%, or at least about 85%, or at least about 90%, or at least about 95%, or at least about 98%, or at least about 99%.","In some embodiments, the method comprises reacting nanoparticles or microparticles of a Group 14 element or compound thereof with Li to obtain the composition comprising Li x M. In some embodiments, the method comprises reacting nanoparticles or microparticles of a Group 14 element or compound thereof with Li to obtain the nanoparticles or microparticles comprising Li x M. In some embodiments, the method comprises reacting nanoparticles or microparticles of a Group 14 element or compound with Li metal foil under mechanical stirring at an elevated temperature (e.g., about 180-300° C., or higher). In some embodiments, the method comprises exposing the nanoparticles or microparticles comprising Li x M to some amounts of oxygen to form a passivation layer on the nanoparticles or microparticles, which can prevent Li x M from further oxidization in dry air.","In some embodiments, the method comprises reacting nanoparticles or microparticles of Si with Li to obtain a composition comprising Li x Si, such as nanoparticles or microparticles having Li x Si—Li 2 O core-shell structure.","In some embodiments, the method comprises reacting nanoparticles or microparticles of SiO with Li to obtain a composition comprising Li x Si, such as Li x Si—Li 2 O composites each comprising a Li 2 O matrix embedded with Li x Si domains.","In some embodiments, the method comprises reacting nanoparticles or microparticles of SiO 2 with Li to obtain a composition comprising Li x Si, such as Li x Si—Li 2 O composites each comprising a Li 2 O matrix embedded with Li x Si domains.","In some embodiments, the method comprises reacting nanoparticles or microparticles of Ge with Li to obtain a composition comprising Li x Ge, such as nanoparticles or microparticles having Li x Ge—Li 2 O core-shell structure.","In some embodiments, the method comprises reacting nanoparticles or microparticles of GeO 2 with Li to obtain a composition comprising Li x Ge, such as Li x Ge—Li 2 O composites each comprising a Li 2 O matrix embedded with Li x Ge domains.","In some embodiments, the method comprises reacting nanoparticles or microparticles of Sn with Li to obtain a composition comprising Li x Sn, such as nanoparticles or microparticles having Li x Sn—Li 2 O core-shell structure.","In some embodiments, the method comprises reacting nanoparticles or microparticles of SnO 2 with Li to obtain a composition comprising Li x Sn, such as Li x Sn—Li 2 O composites each comprising a Li 2 O matrix embedded with Li x Sn domains.","In some embodiments, the method comprises reacting nanoparticles or microparticles of SnF 2 or SnF 4 with Li to obtain a composition comprising Li x Sn, such as Li x Sn—LiF composites each comprising a LiF matrix embedded with Li x Sn domains.","In some embodiments, the method comprises reacting nanoparticles or microparticles of metal silicide (e.g., FeSi 2 , NiSi 2 , CoSi 2 , and other transition metal silicide) with Li to obtain a composition comprising metal-Li x Si (e.g., Fe—Li x Si composites, Ni—Li x Si composites, Co—Li x Si composites, and other metal-Li x Si composites).","In some embodiments, the method comprises reacting a combination of two or more Group 14 element(s) and/or compound(s) thereof with Li. In one embodiment, the method comprises reacting SiO—SnF 4 composites with Li to obtain Li x Si— Li x Sn—Li 2 O—LiF composites.","Another aspect of some embodiments of the disclosure relates to an anode comprising the composition comprising Li x M. In some embodiments, the composition comprising Li x M is incorporated as the anode material. In some embodiments, the composition comprising Li x M is incorporated as a prelithiation reagent to prelithiate an anode material present in the anode. In some embodiments, the anode further comprises a binder and/or a conductive material.","Another aspect of some embodiments of the disclosure relates to a rechargeable battery comprising the anode comprising Li x M.","A further aspect of some embodiments of the disclosure relates to a method for making an anode of a rechargeable battery, comprising prelithiating an anode material with a prelithiation reagent comprising Li x M, such as Li x Si, wherein the prelithiation reagent improves first cycle Coulombic efficiency of the anode.","In some embodiments, the prelithiation reagent comprises nanostructures, such as nanoparticles, having at least one dimension in the range of about 1 nm to about 1000 nm, such as about 500 nm or less, about 400 nm or less, about 300 nm or less, or about 200 nm or less, and down to about 50 nm, down to about 20 nm, down to about 10 nm, or less. In some embodiments, the prelithiation reagent comprises microstructures, such as microparticles, having at least one dimension in the range of about 1 μm to about 1 mm, such as about 500 μm or less, about 100 μm or less, about 50 μm or less, or about 10 μm or less, down to about 5 μm, down to about 2 μm, or less.","In some embodiments, the prelithiation reagent comprises a nanostructure comprising Li x M, where x indicates the atomic ratio of Li to M and can be, for example, about 5:1 or less, about 4:1 or less, about 3:1 or less, or about 2:1 or less, and down to about 1:1, about 1:3, or about 1:6, or less.","In some embodiments, the prelithiation reagent comprises particles having at least one dimension of about 1000 nm or less. In some embodiments, the prelithiation reagent comprises particles having at least one dimension of about 500 nm or less. In some embodiments, the prelithiation reagent comprises particles having at least one dimension of about 200 nm or less.","Particles of the prelithiation reagent can have any of a variety of shapes, such as spheroidal, tetrahedral, tripodal, disk-shaped, pyramid-shaped, box-shaped, cube-shaped, cylindrical, tubular, wire-shaped, branch-shaped, and a number of other geometric and non-geometric shapes. Particles of the prelithiation reagent can be an aggregation of a number of small particles that are about 2 or more, about 5 or more, about 10 or more, about 100 or more, or about 1000 or more. Particles of the prelithiation reagent can have aspect ratios that are about 3 or more, or less than about 3.","In some embodiments, the prelithiation reagent comprises Li 21 M 5 (i.e., where x=21:5). In some embodiments, the prelithiation reagent comprises Li 22 M 5 (i.e., where x=22:5). In some embodiments, the prelithiation reagent comprises Li 15 M 4 (i.e., where x=15:4). In some embodiments, the prelithiation reagent comprises Li 13 M 4 (i.e., where x=13:4). In some embodiments, the prelithiation reagent comprises Li 7 M 3 (i.e., where x=7:3). In some embodiments, the prelithiation reagent comprises Li 12 M 7 (i.e., where x=12:7). In some embodiments, the prelithiation reagent comprises LiM (i.e., where x=1). In some embodiments, the prelithiation reagent comprises Li 7 M 2 (i.e., where x=7:2). In some embodiments, the prelithiation reagent comprises Li 13 M 5 (i.e., where x=13:5). In some embodiments, the prelithiation reagent comprises Li 5 M 2 (i.e., where x=5:2). In some embodiments, the prelithiation reagent comprises Li 2 M 5 (i.e., where x=2:5). In some embodiments, the prelithiation reagent comprises LiM 6 (i.e., where x=1:6). In some embodiments, the prelithiation reagent comprises Li 11 M 6 (i.e., where x=11:6). In some embodiments, the prelithiation reagent comprises Li 9 M 4 (i.e., where x=9:4). In some embodiments, the prelithiation reagents comprises crystalline Li x M compounds, and, in other embodiments, the prelithiation reagent comprises amorphous Li x M compounds.","In some embodiments, the anode material comprises carbon. In some embodiments, the anode material comprises graphite. In some embodiments, the anode material comprises Si. In some embodiments, the anode material comprises SiO, or SiO 2 . In some embodiments, the anode material comprises Ge. In some embodiments, the anode material comprises Sn. In some embodiments, the anode material comprises TiO 2 or SnO 2 . In some embodiments, the anode material comprises P.","In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:2 or less. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:3 or less. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:4 or less. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:5 or less. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:8 or less. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:10 or less. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:15 or more. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:20 or more. In some embodiments, the weight ratio between the prelithiation reagent and the anode material is about 1:30 or more.","In some embodiments, the method comprises reacting Si nanoparticles or microparticles with Li metal to obtain Li x Si nanoparticles or microparticles. In some embodiments, the method comprises reacting Si nanoparticles with Li metal foil under mechanical stirring at an elevated temperature (e.g., about 180-300° C., or higher). In some embodiments, the method comprises exposing the Li x Si nanoparticles or microparticles obtained to some amounts of oxygen to form a passivation layer on the Li x Si nanoparticles or microparticles, which can prevent Li x Si from further oxidization in dry air.","In some embodiments, the mixing of the prelithiation reagent and the anode material in slurry and/or the coating of the slurry is processed in a low-humidity environment. In some embodiments, the prelithiation reagent is processed at a relative humidity of about 30% or less. In some embodiments, the prelithiation reagent is processed at a relative humidity of about 20% or less. In some embodiments, the prelithiation reagent is processed at a relative humidity of about 10% or less. In some embodiments, the prelithiation reagent is processed at a relative humidity of about 5% or less. In some embodiments, the prelithiation reagent is processed at a relative humidity of about 1% or less.","In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 2%. In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 5%. In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 10%. In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 15%. In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 20%. In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 30%. In some embodiments, the prelithiation reagent improves the first cycle Coulombic efficiency of the anode by at least about 50%.","In some embodiments, the first cycle Coulombic efficiency of the anode after prelithiation is at least about 80%. In some embodiments, the first cycle Coulombic efficiency of the anode after prelithiation is at least about 85%. In some embodiments, the first cycle Coulombic efficiency of the anode after prelithiation is at least about 90%. In some embodiments, the first cycle Coulombic efficiency of the anode after prelithiation is at least about 95%. In some embodiments, the first cycle Coulombic efficiency of the anode after prelithiation is at least about 100%.","A further aspect of some embodiments of the disclosure relates to a composition comprising an anode material mixed with a prelithiation reagent comprising Li x M, as described herein. In some embodiments, the composition further comprises a solvent having a dielectric constant of about 20 or less, as described herein. In some embodiments, the composition is a mixture comprising the anode material, the prelithiation reagent, the solvent, and other optional components such as a binder and a carbon additive. In some embodiments, the composition is a slurry comprising the anode material, the prelithiation reagent, the solvent, and other optional components such as a binder and a carbon additive. In some embodiments, the composition is an anode obtained by coating the slurry and drying the coated slurry.","A further aspect of some embodiments of the disclosure relates to a rechargeable battery comprising an anode, wherein the anode comprises or is obtained from the composition described herein, and wherein the prelithiation reagent improves first cycle Coulombic efficiency of the anode.","These and other features, together with the organization and manner of operation thereof, will become apparent from the following detailed description when taken in conjunction with the accompanying drawings.","DETAILED DESCRIPTION","Introduction.","Silicon is a high-performance anode material for next generation lithium ion batteries, with an order of magnitude higher capacity than traditional graphite anode. In recent years, challenges of Si anode materials associated with large volume change (300%) during lithium insertion and extraction are largely addressed by well-designed nanostructures. However, the common issue associated with these anode materials is the increased solid electrolyte interphase (SEI) formation on high-surface-area nanostructures during the first cycle. The process consumes an appreciable amount of lithium, resulting in irreversible loss of capacity and low Coulombic efficiency (50-80%), while a value of at least 90% is desired for real applications. Such capacity loss is usually compensated by additional loading of cathode materials in commercial lithium ion batteries. However, the lithium metal oxide cathodes have lower specific capacity than the anodes. The excessive loading of cathode material causes appreciable reduction of battery energy density. It is therefore desirable to suppress such loss so as to increase the 1st cycle Coulombic efficiency.","Li x Si/Li 2 O Core-Shell Nanoparticles","Overcoming the first cycle Coulombic loss is important for lithium ion batteries, which results mostly from the formation of SEI and lithium trapping at the anodes. It is discovered that Li x Si—Li 2 O core-shell nanoparticles afford an excellent prelithiation reagent with high specific capacity to compensate the first cycle loss. A facile and scalable synthesis method of these nanoparticles has been developed by direct reaction of Si nanoparticles with lithium metal. Li x Si—Li 2 O core-shell nanoparticles are compatible with conventional slurry process and exhibit high capacity under the dry air conditions with the protection of Li 2 O passivation shell, indicating these nanoparticles are compatible with the industrial battery fabrication process. Both Si and graphite anodes are successfully prelithiated with these nanoparticles to achieve high 1st cycle Coulombic efficiencies of 94% to 100%.","Li x Si—Li 2 O core-shell NPs can be mixed with various anode materials to increase the 1st cycle Coulombic efficiency. It suppresses the undesired consumption of Li from cathode materials during SEI formation. The approach is generally applicable to various anode materials involving complex nanostructures, and thus a breakthrough for practical implementation of high-performance nanomaterials in lithium ion batteries.","Described here are chemically synthesized core-shell nanoparticles of Li x Si—Li 2 O (see, e.g., FIG. 1 ) as an excellent prelithiation reagent, which can be mixed with various anode materials during slurry processing. Li x Si nanoparticles exhibit multiple attractive properties for prelithiation: 1) Fully lithiated Li x Si alloy has a sufficiently low potential of around 10 mV versus Li/Li + to prelithiate all types of anodes including graphite, Si, Ge and Sn. 2) Li x Si has very high specific capacity (about 4200 mAh/g of Si, about 2000 mAh/g of Li 4.4 Si) for pre-storing lithium, so a small percentage of material is used for prelithiation. 3) Nanoscale Li x Si-Li 2 O particles (about 100˜200 nm) are helpful for distributing pre-stored Li uniformly across the anodes. Furthermore, using nanoscale Li x Si—Li 2 O particles as prelithiation reagent is less likely to disturb the whole structure of the electrode. 4) Nanoscale Li x Si particles provide a localized lithium source to realize fast prelithiation of anode materials, compared to the process of inducing electrical shorting between anode materials and lithium metal foil. 5) Li x Si can benefit from the mature manufacturing infrastructure of the Si industry for scale up and low-cost manufacturing.","Another challenge associated with anode prelithiation is the high chemical reactivity of prelithiation reagents, which make them difficult to survive multiple processing steps (exposure to air and solvents, slurry mixing, coating and baking) during battery electrode fabrication. A protective coating is therefore desired. However, this coating should be activated later to ensure quick lithium ion diffusion for prelithiation, as Li x Si is a reactive prelithiation reagent.","Thus, also described here is how to protect and de-protect Li x Si using a Li x Si—Li 2 O core-shell nanostructure. It is found that: 1) The core-shell nanoparticles rapidly react with solvents containing active protons such as water and alcohol. The slow reaction with oxygen, however, allows the formation of a dense Li 2 O shell that protects the Li x Si core in dry air environments over the long term. This is desirable since these nanoparticles are compatible with the low humidity environment of a dry room, commonly used in battery manufacturing. 2) For solvents without active protons, it is found that Li x Si can survive in low polarity solvents such as ether and toluene during slurry processing. Highly polar solvents such as N-methyl-2-pyrrolidinone (NMP) and organic carbonate can weaken the protection of the Li 2 O shell and react with the Li x Si core, making them poor candidates for solvents in slurry processing. At the end of the battery assembly process, carbonate electrolyte is injected, directly resulting in the activation of the facile lithium diffusion into anode materials. This is believed to be the first example of prelithiation of anode materials with stabilized Li x Si nanoparticles.","Synthesis and Characterizations of Li x Si—Li 2 O Nanoparticles.","Li x Si nanoparticles were synthesized by mechanical stirring of a stoichiometric mixture (1:4.4) of Si nanoparticles (˜50 nm in diameter) and Li metal foil at 200° C. for 6 hours in a glove box (Ar-atmosphere, H 2 O level \u003c0.1 ppm and O 2 level \u003c3 ppm). In the process, the color of the powder changes from brown to black, indicating the formation of the Li x Si alloy. Due to trace oxygen in the glove box, a dense Li 2 O passivation layer will form outside the Li x Si NPs, resulting in the formation of Li x Si—Li 2 O core-shell NPs and preventing Li x Si from further oxidizing. The Li 2 O passivation layer was evidenced by experimental characterization. Transmission electron microscopy (TEM) images were taken immediately after exposure of the samples to the electron beam to minimize the impact of the electron beam on the nanoparticles. TEM image ( FIG. 2A ) and SEM image ( FIG. 5A ) show that the size of the Li x Si NPs ranges from 100 to 200 nm, which is larger than the size of Si nanoparticles (50 nm) due to volume expansion and some aggregation of particles during the alloying process. The magnified TEM image ( FIG. 2B ) shows a thin passivation layer (˜10 nm thick) on the surface of the Li x Si NPs.","Compositional analysis of the Li x Si NPs was acquired by electron energy loss spectroscopy (EELS) in the TEM. EELS is ideal for Li mapping, since the shallow Li K-edge has a high ionization cross-section, which is about 10-100 times greater than that of other light elements like oxygen. Oxygen mapping is therefore performed with longer exposure time per step. Compared with the scanning transmission electron microscopy (STEM) image in FIG. 2C , the corresponding EELS oxygen map ( FIG. 2D ) reveals that oxygen is concentrated in the passivation layer of the core-shell NPs. To avoid possible beam damage through consecutive scans, a different region is selected for Li and Si mapping. STEM image ( FIG. 2E ) and corresponding EELS elemental mapping reveals the spatial distribution of Li ( FIG. 2F ) and Si ( FIG. 2G ), respectively. According to the elemental maps, Li is distributed throughout the entire nanoparticle, whereas Si is distributed in the internal part of the nanoparticle. Both images and elemental maps demonstrate that the nanoparticles form a core-shell structure, composed of a core of Li x Si and a shell of Li 2 O. Furthermore, X-ray diffraction of the product ( FIG. 2H ) reveals the crystalline nature of the core-shell nanoparticles formed by Li 21 Si 5 and Li 2 O. The broad background comes from the Kapton tape used to protect the samples from moisture in the air. Li 21 Si 5 , a variation of the Li 22 Si 5 phase with ordered vacancies, is the most thermally stable phase among the crystalline lithium silicides.","Electrochemical Performance.","To study the electrochemical properties of the Li x Si—Li 2 O NPs, half cells were fabricated with Li metal as a counter electrode. 1.0 M LiPF 6 in a mixture of 1:1 w/w ethylene carbonate/diethyl carbonate, 10 vol % fluoroethylene carbonate, and 1 vol % vinylene carbonate was used as the electrolyte. To find a proper solvent for the slurry process, Li x Si—Li 2 O NPs were mixed with carbon black (Super P) and PVDF (65:20:15 by weight) in different solvents to form a slurry, which was then drop cast on copper foil and dried under vacuum. The entire battery electrode preparation process from the slurry formation to drop casting and drying were performed in a dry air glove box (dew point=−50° C.). The capacities of the resulting electrodes were studied by delithiating the samples to 1 V directly. FIG. 3A shows that there is almost no Li capacity extracted from the Li x Si—Li 2 O NPs processed with N-methyl-2-pyrrolidinone (NMP) solvent. With ethylene carbonate (EC) solvent, the Li x Si—Li 2 O NPs show a small Li extraction capacity of ˜300 mAh/g, indicating that most of the stored Li is not active. Excitingly, Li x Si—Li 2 O NPs are compatible with 1,3-dioxolane (DOL) and toluene ( FIG. 3A ), showing high extraction capacities of 1200-1400 mAh/g, which is sufficient to qualify it as a prelithiation reagent. Among these solvents, it appears that the difference lies in polarity (Dielectric constant: NMP 32.2, EC 89.8, DOL 7.1, toluene 2.4). The more polar solvents (e.g., NMP and EC) are more reactive than the less polar solvents (e.g., DOL and toluene). The detailed reaction mechanism is shown in FIG. 7 . Because PVDF binder does not dissolve in toluene to form an uniform slurry, DOL is selected in the following experiments.","To evaluate the electrochemical behavior of the Li x Si—Li 2 O NPs, normal deep galvanostatic lithiation/delithiation was used. FIG. 3B shows the voltage profiles of the 1 st and 2 nd cycles. Li x Si—Li 2 O NPs were first lithiated to 0.01 V, and then delithiated to 1 V at a rate of C/20 (The specific capacity is calculated based on the mass of Si in the electrode. 1C=4.2 A g −1 Si). The open circuit voltage (OCV) of Li x Si—Li 2 O NPs was less than 0.2 V, which is significantly lower than that of crystalline Si NPs. The capacity preloaded into Si NPs is 1310 mAh/g, determined by subtracting the first lithiation capacity from the delithiation capacity. After the 1 st cycle, the voltage profile is similar to normal Si anodes. But the 2 nd cycle Coulombic efficiency of the Li x Si—Li 2 O NPs is 96%, still higher than that of Si NPs (93%) ( FIG. 9A ). During the slurry process, DOL will likely decompose on the surface of the Li x Si—Li 2 O core-shell NPs to form a thin coating due to the strong reducing power of Li x Si ( FIG. 5B ). The reaction consumes part of the Li stored in the Li x Si—Li 2 O NPs, and a significant amount of electrochemically active Li is preserved as the prelithiation reagent.","FIG. 3C demonstrates that Li x Si—Li 2 O NPs can be used as a prelithiation reagent to improve the 1 st cycle Coulombic efficiency of normal Si NP anodes. The anodes were made by forming a slurry of Si NPs, Li x Si—Li 2 O NPs, carbon black and PVDF binder with a mass ratio of 50:15:20:15. The dimensions of the Li x Si—Li 2 O NPs are similar to that of Si NPs, so the Li x Si-Li 2 O NPs were more uniformly distributed in the electrode compared with a large-size prelithiation reagent. After a coin cell was fabricated, it took 6 h for the anode to reach equilibrium. The first cycle voltage profile reveals an OCV of 0.20V, much lower than that of the control cell, which indicates partial prelithiation of the Si NPs. The capacity of the Li x Si—Li 2 O NPs compensates the irreversible capacity loss of the Si NPs in the first cycle. Therefore, the 1 st cycle Coulombic efficiency increased from 76% to 94%. In addition, the lithiation capacity due to SEI formation decreases, due to the pre-formation of SEI during the prelithiation process. The electrochemical cycling performance was evaluated using deep lithiation/delithiation cycling from 1 to 0.01 V. The Li x Si—Li 2 O NPs exhibited improved cycling performance over Si NPs at C/20 as displayed in FIG. 3D . By using Li x Si—Li 2 O NPs as anode material, enough void space formed during the delithiation can be pre-built into the electrode structure to accommodate the volume expansion during the subsequent lithiation process. Accordingly, the introduction of Li x Si—Li 2 O NPs into Si NP anodes did not affect the cycling performance of Si NPs (The specific capacity was based on the total mass of Si in the electrode. 1C=4.2 A g −1 Si).","Li x Si—Li 2 O NPs can also be used to compensate the irreversible capacity loss of existing graphite anodes as shown in the first cycle voltage profiles ( FIG. 3E ). Graphite anodes composed of mesocarbon microbeads (MCMB) graphite and PVDF binder (90:10 by weight) were measured in a voltage window from 0.005 to 2 V as a control. In FIG. 3E , the MCMB graphite voltage profile reveals a sloping region between 0.7 and 0.2 V, corresponding to SEI formation during first cycle lithiation. As a result, the first lithiation capacity of MCMB graphite is higher than the theoretical capacity of graphite (372 mAh/g), whereas the 1 st cycle Coulombic efficiency is just 75%. Prelithiation of the MCMB graphite by Li x Si—Li 2 O NPs (mass ratio 81:9) yields a 1 st cycle Coulombic efficiency of 99%. The electrochemical potential of the electrode is close to 0.2 V, indicating partial prelithiation of MCMB graphite. The incorporation of Li x Si—Li 2 O NPs decreases the typical lithiation capacity, due to the pre-formation of SEI during the prelithiation process. As shown in the table in FIG. 3E , the 1 st cycle Coulombic efficiency of MCMB anodes can be adjusted by tuning the amount of Li x Si—Li 2 O additive. The 1 st cycle Coulombic efficiency ranges from 96% to 104% by varying the mass ratio of MCMB to Li x Si—Li 2 O NPs from 83:7 to 80:10. The MCMB/Li x Si—Li 2 O composites (mass ratio of 83:7 and 80:10) exhibited stable cycling performance at C/20 for the first three cycles and C/5 for the following cycles (1C=372 mA g −1 C) as displayed in FIG. 3F . The specific capacity was based on the mass of MCMB graphite and Si in the Li x Si—Li 2 O additives. The capacities of MCMB/Li x Si—Li 2 O composites are slightly higher than that of the control graphite cell, contributed by the capacity stored in the Li x Si—Li 2 O NPs. The incorporation of Li x Si—Li 2 O NPs into the MCMB graphite electrode does not damage the structure of the electrode during cycling. As a result, the cycling performance of MCMB graphite is not affected. Furthermore, Li x Si—Li 2 O additives also improve the 2 nd cycle Coulombic efficiency of MCMB and Coulombic efficiency of the subsequent cycles is comparable to cells without additives ( FIG. 9B ). Prelithiation of graphite flakes by Li x Si—Li 2 O NPs (mass ratio 83:7) shows consistent results, increasing 1 st cycle Coulombic efficiency from 87% to 99% ( FIG. 10A ). Graphite/LiFePO 4 full cells are used to investigate the effect of Li x Si—Li 2 O particles on full cell performance. One full cell is composed of graphite flake anode prelithiated with Li x Si—Li 2 O particles (graphite flakes:Li x Si—Li 2 O:PVDF=83:7:10), whereas another one is composed of an anode with regular graphite flakes (graphite flakes:PVDF=90:10). The cells are measured in the voltage window from 2.5 V to 3.8 V at C/10 ( FIG. 12A ). The rate and cell capacity are both presented based on the mass of LiFePO 4 in the cathode. The voltage profile reveals a plateau between 2.6 and 3.2 V, corresponding to the SEI formation in the anode during charging. After incorporating Li x Si—Li 2 O particles into the anode, the open circuit voltage before cycling is about 2.3 V, significantly higher than 0.8 V for regular full cell. As shown by the voltage profile, the incorporation of Li x Si—Li 2 O NPs compensates the irreversible Li consumption resulting from SEI formation. Accordingly, the 1 st cycle Coulombic efficiency increases from 77.6% to 90.8%. In the following cycles, the cell with Li x Si—Li 2 O NPs consistently shows a higher capacity than the regular cell ( FIG. 12B ).","Stability of Li x Si—Li 2 O NPs.","FIG. 4A is a TEM image showing that the Li x Si—Li 2 O core-shell nanostructure remains after 3 days of exposure to dry air (dew point=−50° C.), although a thicker passivation layer of ˜20 nm is observed, as compared to the original 10 nm-thick layer. X-ray diffraction ( FIG. 4B ) analysis confirms that the sample exposed to dry air for 3 days is still composed of crystalline Li 21 Si 5 and Li 2 O. There is no substantial change in the XRD pattern as compared with the sample without exposure to dry air. The capacities of the Li x Si—Li 2 O NPs exposed to dry air for different numbers of days were studied by delithiating the Li x Si—Li 2 O NPs to 1 V directly ( FIG. 4C ). After exposure to dry air for one day, there is 1175 mAh/g capacity, a 9% decay from time zero. After 5 days of exposure, the Li x Si—Li 2 O NPs still exhibit a capacity of 880 mAh/g (line 1 in FIG. 4C ), showing high capacity retention of 70%. The capacity of the Li x Si—Li 2 O NPs decays slowly with exposure time. The Li x Si—Li 2 O NPs stored in dry air for various durations were added into MCMB graphite to optimize the 1 st cycle Coulombic efficiency (MCMB:Li x Si—Li 2 O NPs=8:1 by weight). The corresponding cells were tested in the voltage window of 0.005-2 V. The first cycle voltage profiles of the MCMB/Li x Si—Li 2 O composites ( FIG. 13B ) indicate that Li x Si—Li 2 O NPs stored in dry air for 5 days are still active enough to prelithiate MCMB graphite, yielding a 20% improvement in the 1 st cycle Coulombic efficiency. More attractively, Li x Si—Li 2 O NPs exhibit excellent dry air stability even at elevated temperatures. MCMB/Li x Si—Li 2 O composites baked at 45° C. for 1 h in dry air exhibit a 1 st cycle Coulombic efficiency of 101.6%. Li x Si—Li 2 O NPs after baking at 65° C. can still effectively prelithiate MCMB graphite to counteract the first cycle capacity loss as shown in FIG. 14 . To test humidity stability, the Li x Si—Li 2 O nanoparticles were stored in an air box with different dew points for 6 h. The capacity of the samples in air with different humidity was studied by discharging the samples to 1 V directly ( FIG. 4D ). The electrochemical performance demonstrates that 6 h of exposure to air with dew point of −30° C. does not affect the capacity. Even in air with a dew point of −10° C., the Li x Si—Li 2 O nanoparticles still exhibit a capacity of 819 mAh/g. However, the Li x Si—Li 2 O NPs were completely converted to LiOH under high humidity, as confirmed by the XRD pattern in FIG. 4B .","Additional Characterizations.","Electrochemical characterization ( FIG. 3B ) shows that the amount of Li preloaded into the Si NPs is 1310 mAh/g for Si. Li was partially consumed to form a Li 2 O passivation layer to protect Li x Si from further oxidation. During the slurry process, DOL decomposes on the surface of the nanoparticles to form a thin layer due to the strong reducing power of Li x Si, further consuming a fraction of the Li. However, the remaining capacity of the Li x Si—Li 2 O NPs is still sufficient as a prelithiation reagent, higher than most Li-rich cathode materials. Compared with the conventional approach of extra loading of cathode materials, prelithiation using Li x Si—Li 2 O NPs more effectively increases the specific energy and energy density of batteries. Li x Si—Li 2 O core-shell NPs can be mixed with various anode materials in the slurry process to achieve improved 1 st cycle Coulombic efficiency. Nanoscale Li x Si particles provide uniform and localized Li distribution to realize fast prelithiation of anode materials. Cycling performance of anode materials is negligibly affected by the addition of prelithiation reagents. The low material loading and particle dimensions are less likely to disturb the structure of the electrode. In addition, void spaces will be formed through delithiation of the Li x Si additive which accommodates the volume expansion during the next lithiation process.","As shown in FIG. 4C , the capacity retention is 91% after exposure to dry air for 1 day indicating that the Li x Si—Li 2 O NPs are sufficiently stable to undergo battery fabrication process in a dry room. Li x Si—Li 2 O NPs exposed to dry air for 5 days are still active enough to prelithiate MCMB graphite, which yields a 20% improvement in the 1 st cycle Coulombic efficiency (line 4 in FIG. 13B ), indicating the potential for long-term storage. The dry air stability can be attributed to the unique core-shell nanostructure. The dense Li 2 O passivation layer has a remarkable effect in preventing Li x Si NPs from thermally oxidizing in dry air.","In summary, an one-step thermal alloying process to synthesize Li x Si—Li 2 O core-shell NPs has been demonstrated. These nanoparticles exhibit high capacity under dry air conditions with the protection of the Li 2 O passivation shell, indicating that Li x Si—Li 2 O NPs are compatible with industrial battery fabrication processes in a dry room. Both commercial Si nanoparticles and graphite are prelithiated with Li x Si—Li 2 O NPs, which improves the 1 st cycle Coulombic efficiency and suppresses the undesired consumption of Li from cathode materials during SEI formation. The approach is generally applicable to various anode materials involving complex nanostructures. In addition, Li x Si alloy also serves as an anode material to pair with all high capacity lithium-free cathodes for next generation high-energy-density lithium-ion batteries.","Li x Si/Li 2 O Composites","Disclosed here is an one-pot thermal alloying process to synthesize Li x Si/Li 2 O composites, using low-cost SiO or SiO 2 as starting materials as shown in FIG. 15 . The extraction capacities of Li x Si/Li 2 O composites derived from SiO and SiO 2 were 2120.7 mAh/g and 1543.2 mAh/g based on the mass of SiO and SiO 2 , respectively. Active Li x Si nanodomains embedded in a robust Li 2 O matrix allows the unparalleled stability in both dry and humid air. Besides negligible capacity decay in dry air, Li x Si/Li 2 O composites exhibited a high capacity retention of 1240.3 mAh/g after 6 h exposure to ambient air (\u003e35% RH). Due to the sufficiently low potential, Li x Si/Li 2 O composites can be mixed with various anode materials such as SiO, Sn and graphite during slurry processing to increase the 1 st cycle CE. Aside from being employed as the prelithiation additive, Li x Si/Li 2 O composites also afford remarkable battery performance as the anode material. With stable cycling performance and consistently high CEs (e.g., 99.81% at 7 th cycle and stable at 99.87% for later cycles), this material can replace Li metal anode in Li—O 2 and Li—S batteries.","Synthesis and Characterizations of Li x Si/Li 2 O Composites.","Both SiO and SiO 2 can be used as the starting materials to form Li x Si/Li 2 O composites. Large SiO particles (−325 mesh) were first ground to obtain a fine powder via planetary ball-milling operated at a grinding speed of 400 rpm for 6 h. Subsequently, the SiO powder was made to react with molten Li with the color transition from dark red to black immediately upon contact. To guarantee uniform lithiation, the mixture of SiO NPs and Li metal (500 mg:509 mg, the mass ratio is determined by the chemical reaction in FIGS. 16A-16F .) was heated at 250° C. under mechanical stirring inside a tantalum crucible at 200 rpm for at least 1 day in a glove box (Ar-atmosphere, O 2 level \u003c1.2 ppm and H 2 O level \u003c0.1 ppm). Similar to ball-milled SiO NPs, sol-gel synthesized SiO 2 NPs reacted with molten Li to form Li x Si/Li 2 O composites at the same condition. Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) were utilized to characterize the morphology of the SiO and SiO 2 NPs before and after thermal lithiation. After ball-milling for 6 h, the size of most SiO NPs was in the range of 50-250 nm, as shown in FIG. 16A and FIG. 21A . The size of derived Li x Si/Li 2 O composites was larger than that of original SiO NPs due to the volume expansion and some degree of particle aggregation during the alloying process. FIG. 16D and FIG. 21B show SiO 2 NPs with a narrow size distribution around 90 nm. After thermal lithiation, the morphology of NPs remained while the size changed to 200 nm due to volume expansion as indicated in FIG. 16E . To investigate the spatial distribution of various elements, electron energy loss spectroscopy (EELS) mapping was performed on a Li x Si/Li 2 O particle under the scanning transmission electron microscopy (STEM) mode. To obtain Si and O maps, long exposure time per step can be performed. However, Li signal cannot be detected under such condition because of the heavy beam damage through consecutive scans. Therefore, Li element mapping was obtained first at short exposure time followed by Si and O mapping at the same place with longer exposure time per step. Compared with the STEM image, the corresponding EELS elemental mapping reveals that Li, Si and O elements were uniformly distributed, indicating the formation of a homogeneous Li x Si/Li 2 O composite. Furthermore, X-ray diffraction (XRD) confirms the complete transformation of amorphous SiO and SiO 2 ( FIG. 22 ) to crystalline Li 22 Si 5 and Li 2 O during the thermal alloying process ( FIG. 16F ). The broad background of the XRD patterns primarily comes from the Kapton tape covering the sample surface to eliminate or reduce side reactions with moisture and oxygen in the air. The intensity ratio of Li 22 Si 5 to Li 2 O in lithiated SiO is higher than that in lithiated SiO 2 , since the lithiation of SiO can produce more active phase determined by the chemical reaction in FIGS. 16A-16F .","Electrochemical Performance.","To measure the real capacity of the synthesized Li x Si/Li 2 O composites and eliminate or reduce capacity loss during the slurry coating process, lithiated SiO and SiO 2 were dispersed in cyclohexane and then drop casted on copper foil. Half cells were fabricated by using Li metal as both the counter and the reference electrode. The capacities of lithiated SiO and SiO 2 were studied by charging the cells to 1.5V at a rate of C/50 (1 C=2.67 A/g for SiO and 1 C=1.96 A/g for SiO 2 . FIG. 17A ). The extraction capacities of lithiated SiO and SiO 2 were 2120.7 mAh/g and 1543.2 mAh/g, respectively based on the mass of SiO and SiO 2 . If calculated based on the mass of Si, the capacities were 3332.5 mAh/g and 3306.8 mAh/g respectively, which are close to the theoretical specific capacity of Si. The open circuit voltage (OCV) of Li x Si/Li 2 O composites was around 0.1 V, confirming that the majority of SiO and SiO 2 have been successfully lithiated. To make anodes, Li x Si/Li 2 O composites were mixed with super P and polyvinyldifluoride (PVDF) (65:20:15 by weight) in tetrahydrofuran to form a slurry, which was then drop casted on copper foil. Due to the high reactivity of Li x Si, slurry solvents with higher polarity should be avoided. The lithiated SiO electrode prepared via the slurry coating process demonstrated an extraction capacity of 2059.2 mAh/g, indicating a 97% capacity retention compared to that without the slurry process ( FIG. 23 ). The galvanostatic discharge/charge profile of SiO 2 NPs (SiO 2 :Super P:PVDF=65:20:15 by weight, line 3 in FIG. 17A ) showed little delithiation capacity after the first lithiation cycle, indicating that the sol-gel synthesized SiO 2 NPs are electrochemically inactive as an anode material. However, due to the thermal lithiation process, the inactive SiO 2 NPs can be successfully converted into high capacity anode. The flat plateau at 0.4V in the delithiation profile ( FIG. 17A ) and the strong oxidation peak at 0.7 V in the cyclic voltammetry profile of lithiated SiO 2 ( FIG. 17B ) and SiO ( FIG. 24 ) further confirmed the formation of highly crystalline Li x Si, consistent with the XRD result.","Due to the sufficiently low potential, Li x Si/Li 2 O composites are readily mixed with various anode materials such as SiO, Sn and graphite during slurry processing and serve as excellent prelithiation reagents. Lithiated SiO NPs were mixed with SiO, super P, and PVDF in a weight ratio of 10:55:20:15 in a slurry, which was then drop casted on copper foil. During the cell assembly, lithiated SiO NPs were spontaneously activated upon the addition of the electrolyte, which provide additional Li ions to the anode for the partial lithiation of the SiO NPs and the formation of the SEI layer. After the cell assembly, it took 6 h for the anode to reach equilibrium. Both the SiO cell with lithiated SiO additive and the bare SiO control cell were first lithiated to 0.01 V and then delithiated to 1 V at C/50 ( FIG. 17C . 1 C=2.67 A/g for SiO, the mass of the active materials includes SiO in the lithiated SiO additive). The 1 st cycle CE of the SiO control cell was 52.6%, since a large portion of Li was desired for the reaction with SiO to form electrochemically inactive components. The OCV of SiO with lithiated SiO additive is 0.35 V, much lower than that of the control cell. That means lithiated SiO additive compensates the Li consumption for SEI formation and silica conversion, so the curve directly reaches the anode lithiation voltage region. Therefore, the 1 st cycle CE increased considerably to 93.8%. Similarly, tin NPs were also successfully prelithiated with lithiated SiO NPs, thereby improving the 1 st cycle CE form 77.7% to 101.9% (tin:lithiated SiO=60:5 by weight, shown in FIG. 25 ). As the final products of lithiated SiO and SiO 2 are the same, lithiated SiO 2 also serves as a prelithiation reagent. Similarly, lithiated SiO 2 were mixed with graphite and PVDF in a weight ratio of 6:84:10 to compensate the irreversible capacity loss of graphite. Without incorporation of lithiated SiO 2 , the voltage profile of graphite control cell in FIG. 17D revealed a plateau around 0.7 V, corresponding to the formation of SEI during the lithiation process. After prelithiation, the OCV of graphite with lithiated SiO 2 additive decreased to 0.31 V, and the 1 st cycle CE increases from 87.4% to 99.7%. At the same weight ratio, the 1 st cycle CE of graphite with lithiated SiO additive is 104.5%, due to the relatively higher capacity of lithiated SiO ( FIG. 26 ).","Li x Si/Li 2 O composites afford remarkable battery performance both as anode additives and as anode materials. Aside from improved 1 st CE, graphite prelithiated with lithiated SiO and lithiated SiO 2 follow the trend of the graphite control cell and exhibit stable cycling performance at C/20 for the first 3 cycles and C/5 for the following cycles (1C=372 mAh/g, FIG. 17E ). Cells with prelithiation reagents consistently show slightly higher capacity than graphite control cell, contributed by the capacity of lithiated SiO and lithiated SiO 2 . Due to the nanoscale dimension and the small amount, prelithiation reagents tend to be embedded in the interstices of graphite microparticles. Li x Si/Li 2 O composites maintain the remarkable cyclability of commercial graphite. The commercial graphite with Li x Si/Li 2 O prelithiation reagents suppresses the undesired consumption of Li from cathode materials, which in turn increases the energy density of the full cell. Li x Si/Li 2 O composites not only can improve current lithium ion technology, but are also useful for the next generation lithium ion battery. The cycling stability of Li x Si/Li 2 O composites was tested at C/50 for the first 2 cycles and C/2 for the following cycles as shown in FIG. 17F . The cell capacities initially decreased due to rate change, and then increased to maintain a stable cycling performance at a high capacity of 960.6 mAh/g (The capacity is based on the mass of SiO. 1 C=2.67 A/g for SiO). If the capacity is based on the mass of Si, the retention capacity after 400 cycles was 1509.5 mAh/g, a value more than three times of the theoretical capacity of graphite. Using Li x Si/Li 2 O composites as anode materials, the CE increased to 99.81% after just 6 cycles. Such result stands contrast to previous reports in which it usually took several hundred cycles for Si anode to reach this value. Moreover, in normal Si anodes, SEI rupture and reformation results in decreased CE, especially in later cycles, while the average CE from the 200 to 400 cycles of Li x Si/Li 2 O composites was as high as 99.85% as indicated in the top curve in FIG. 17F . There are several characteristics of the Li x Si/Li 2 O composites that lead to superior battery performance. First, the Li x Si nano domains are already in their expanded state and sufficient space has been created during the electrode fabrication. Due to the small domain size and void space, Li x Si will not pulverize or squeeze each other during cycling and the Li 2 O inactive phase could serve as mechanical buffer to further alleviate the stress and volume change during lithiation/delithiation of the Si phase. In addition, unlike conventional Si anode that exposes reactive Li x Si phase to the electrolyte, the vast majority of Li x Si phase of the Li x Si/Li 2 O composites is enclosed in the stable Li 2 O matrix. Therefore, the Li 2 O inactive phase not only improves dimensional stability but also serves as an artificial SEI to reduce side reactions between active Li x Si domains and electrolytes, contributing to the high initial and following CEs. With high Li amount, stable cyclability and high CE, Li x Si/Li 2 O composites can be paired with lithium-free cathode exhibiting high capacity, such as S, in order to achieve high energy density in lithium ion battery.","Stability of Li x Si/Li 2 O Composites.","The improved stability allows for safe handling and reduces the requirement on industrial battery fabrication environment, which in turn can decrease battery manufacturing cost. The average dimension of Li x Si domain increased along with the increasing alloying time, as confirmed by the XRD patterns in FIG. 27 . The domain size is increased from 23 nm to 30 nm by extending the heating time from 3 to 5 days. Usually, the stability in air increases when the crystalline size increases. Therefore, the sample for stability test was prepared by mechanically stirring of a mixture of SiO and Li at 250° C. for 5 days. To test the dry air stability, lithiated SiO was stored in dry air (dew point=−50° C.) with varying durations. The retention capacity is determined by charging the cell to 1.5 V at C/20 directly (lithiated SiO:Super P:PVDF=65:20:15). As shown in FIG. 18A , Li x Si/Li 2 O composites exhibited remarkable dry air stability with negligible (9%) capacity decay after 5 days of exposure and the trend of capacity decay is much slower compared with Li x Si/Li 2 O core-shell NPs (inset in FIG. 18A ). FIG. 18B shows the capacity retention of Li x Si/Li 2 O composites, Li x Si/Li 2 O core-shell NPs and fluorinated molecular modified Li x Si NPs in the air with different humidity levels for 6 h, from which the superior stability of the Li x Si/Li 2 O composites is demonstrated. In previous reports, little capacity was extracted when the humidity level was higher than 20% RH. Li x Si/Li 2 O composites still exhibited a high extraction capacity of 1382.9 mAh/g, after exposure to humid air with 20% RH ( FIG. 28 ). To further test whether Li x Si/Li 2 O composites are stable enough for the whole battery fabrication process, the remaining capacities of Li x Si/Li 2 O composites in ambient air with different durations were studied. The humidity range of the test room is from 35% RH to 40% RH. After 3 h, there was merely 15% capacity decay. As shown in FIG. 29A , lithiated SiO exposed to ambient air for 3 h is still reactive enough to prelithiate graphite material (graphite:lithiated SiO:PVDF=84:6:10 by weight), achieving a perfect 1 st cycle CE of 100.1%. The TEM image ( FIG. 29B ) indicates the morphology and surface finish remained intact after 6 h exposure to the ambient air. Although the XRD spectrum revealed small peaks belonging to LiOH, the intensity of Li x Si peaks confirmed Li x Si to have remained as the majority composition after 6 h exposure. Consistently, line 3 in FIG. 18C shows Li x Si/Li 2 O composites with an extraction capacity of 1240.3 mAh/g, suggesting that Li x Si/Li 2 O composites are compatible with industrial battery fabrication environment.","DFT Simulation and Reasons for Improved Stability.","To understand the reason for the unparalleled stability of Li x Si/Li 2 O composites in the air, DFT simulation was performed to study the interaction between O in Li 2 O and Li in Li 22 Si 5 . For simplicity, cleavage along (001) plane of Li 22 Si 5 is performed, and the binding energy is calculated between O at different positions in Li 2 O with Li at the center of (001) plane of Li 22 Si 5 , as shown in FIG. 19A . The binding energy between O atoms at (½ ½ 0), (100), (010) position of Li 2 O and surface Li is −2.2079 eV, −2.1945 eV and −2.1987 respectively, much larger than the binding energy between Li and the nearest Si in (001) plane of Li 22 Si 5 with a value of −0.7293 eV. Compared with Li 2 O/Li x Si core-shell structure, uniform Li x Si/Li 2 O composites exhibit larger contact surface between Li 2 O and Li x Si ( FIG. 19B ). Therefore, Li x Si/Li 2 O composites provide stronger binding between O in Li 2 O and Li in Li 22 Si 5 , which effectively lowers the total Gibbs energy of Li x Si/Li 2 O composites. The different behaviors of the Li x Si/Li 2 O composites and the Li x Si/Li 2 O core-shell NPs under TEM electron beam directly corroborate the simulation result ( FIG. 20 ). Once the Li x Si/Li 2 O core-shell NPs were exposed to the electron beam in the TEM, Li metal started to grow outside and the whole structure collapsed after 1 min. On the contrary, Li x Si/Li 2 O composites were stable under electron beam at the same condition. The particle shrinked slightly after 1 min exposure time, suggesting stronger binding to Li, that is consistent with the DFT simulation. There is also an additional factor contributing to the inferior stability of the core-shell NPs. Namely, absent complete encapsulation, any pinhole will provide pathway for inner Li x Si to react with O 2 and water vapor in air, which leads to loss of capacity as shown in FIG. 19B . In Li x Si/Li 2 O composites, Li x Si nanodomains are uniformly embedded in a robust Li 2 O matrix, such that each Li x Si nanodomain has localized Li 2 O protection. Even if some Li x Si nanodomains are sacrificed due to the presence of pinholes on the surface, the inner Li 2 O still serves as a localized protection layer to prevent inner Li x Si nanodomains from further oxidation.","In summary, Li x Si/Li 2 O composites were synthesized via an one-pot thermal alloying process using SiO and SiO 2 as the starting material. The product revealed a unique structure with substantially homogeneously dispersed active Li x Si nanodomains embedded in a robust Li 2 O matrix, which endowed the composite an unparalleled stability. Besides negligible capacity decay in dry air, Li x Si/Li 2 O composites exhibited a high capacity of 1240.3 mAh/g after 6 h exposure to ambient air (\u003e35% RH). The improved stability reduces the requirement on industrial battery fabrication environment, which in turn can reduce manufacturing cost. As a prelithiation reagent, the Li x Si/Li 2 O composites were demonstrated to be effective to compensate the 1 st cycle irreversible capacity loss for both intercalation and alloying anodes and can be generally applied to advanced nanostructured materials with large 1 st cycle irreversible capacity loss. Moreover, the composites are also capable of functioning as an anode material, which exhibits stable cycling performance and consistently high CEs (99.81% at 7 th cycle and stable at 99.87% for 400 cycles). Such Li rich anode material can replace the dendrite-forming lithium metal anodes in next generation high-energy-density batteries, such as Li—O 2 and Li—S batteries. In addition, the synthetic approach disclosed here offers an economical route to large-scale manufacturing.","WORKING EXAMPLES","Example 1.1—Synthesis of Li","Si NPs (˜50 nm, MTI, Inc.) were dried under vacuum for 24 h to remove trapped water. 140 mg of Si NPs were mixed with 154 mg of Li metal foil (99.9%, Alfa Aesar). The Li x Si NPs were synthesized by mixing the Si NPs and lithium foil at 200° C. under mechanical stirring for 6 hours in a glove box (Ar-atmosphere, H 2 O level \u003c0.1 ppm and O 2 level \u003c3 ppm).","Example 1.2—Material Characterization","SEM and TEM images were taken using a FEI XL30 Sirion SEM and a FEI Tecnai G2 F20 X-TWIN, respectively. A FEI Titan 80-300 environmental transmission electron microscope was employed for EELS mapping collection at an acceleration voltage of 300 kV. The energy resolution of the EELS spectrometer is about 0.9 eV as measured by the full width at half-maximum of the zero-loss peak. EELS mapping data was acquired using a C2 aperture size of 50 mm and a camera length of 48 mm. To minimize sample drift during the STEM EELS mapping, the mapping drift was corrected every 30 pixels. The energy window of the EELS was 40-145 eV for Li (Li K edge, 54.7 eV) and Si (Si L2, 3 edge 99.2 eV) peaks and 510-615 eV for 0 (O K edge, 532 eV) peak. X-ray diffraction patterns were obtained on a PANalyticalX%27Pert, Ni-filtered Cu Kα radiation. Li x Si NPs are sensitive to ambient moisture so the samples were sealed with Kapton tape (DuPont) in the glove box before XRD characterization.","Example 1.3—Electrochemical Measurements","Si NPs (˜50 nm, MTI, Inc.), MCMB graphite (MTI, Inc), carbon black (Super P, TIMCAL, Switzerland), and polyvinylidene fluoride binder (PVDF, Kynar HSV 900) were dried under vacuum for 24 h to remove trapped water. To prepare the working electrodes, various materials were dispersed uniformly in 1,3-dioxolane (DOL) to form a slurry. (Anode materials and mass ratio are based on specific cells.) The slurry was then cast onto a thin copper foil and dried under vacuum. Coin-type cells (2032) were assembled in an Ar-filled glove box using a Li metal foil as counter/reference electrode. The electrolyte is 1.0 M LiPF 6 in 1:1 w/w ethylene carbonate/diethyl carbonate (EMD Chemicals), 1 vol % vinylene carbonate and 10 vol % fluoroethylene carbonate (Novolyte Technologies). Cyclic voltammetry measurements were carried out on a BioLogic VMP3 system. Galvanostatic cycling was carried out using an MTI 8 Channel battery tester. The total mass loading of the Si based anode was 0.7-1.0 mg cm −2 and a typical total mass loading of the graphite based anode was 2.0-2.5 mg cm −2 .","Example 2.1—Synthesis of Li","To obtain SiO NPs, the large SiO particles (˜325 mesh, Sigma Aldrich) were ball-milled at a grinding speed of 400 rpm for 6 h. To synthesize 90 nm SiO 2 NPs, ammonia hydroxide solution (1 ml NH 4 OH (Fisher Scientific), 5 ml H 2 O and 15 ml ethanol (Fisher Scientific)) was poured into tetraethyl orthosilicate solution (1 ml TEOS (99.999% trace metal basis, Sigma Aldrich) and 15 ml ethanol) while stirring. The reaction was left at 55° C. under stirring at 500 rpm for 2 hr. The reaction was quenched by adding ethanol into the mixture, and the NPs were cleaned and collected by centrifuging at 5000 rpm for 3 times. Both SiO and SiO 2 NPs were dried under vacuum for 48 h and then heated to 120° C. in the argon glove box for 24 h to remove trapped O 2 and H 2 O. SiO or SiO 2 NPs were heated to 250° C., followed by the addition of Li metal foil (99.9%, Alfa Aesar). The ratios of SiO to Li and SiO 2 to Li were determined by the chemical equation in FIGS. 16A-16F . The mixture was heated at 250° C. under mechanical stir at 200 rpm for at least 1 day in an Ar glove box (H 2 O level \u003c0.1 ppm and O 2 level \u003c1.2 ppm).","Example 2.2—DFT Simulation","First-principles calculations were performed within the density-functional theory (DFT) framework, as implemented in the Materials Studio version 5.5. The electron exchange and correlation interaction is described by the generalized gradient approximation (GGA) method. The following valence electron configurations are used: Si (3s 2 3p 3 ), O (2s 2 2p 4 ) and Li (2s 1 ). After checking for convergence, 450 eV was chosen as the cut-off energy of the plane-wave basis for the Kohn-Sham states. All atomic positions and lattice vectors were fully optimized using a conjugate gradient algorithm to obtain the unstrained configuration. Atomic relaxation was performed until the change of total energy was less than 10 −5 eV and all the forces on each atom were smaller than 0.01 eV/Å.","Example 2.3—Characterizations","Powder X-ray diffraction patterns were obtained on a PANalytical X%27Pert diffractometer with Ni-filtered Cu Kα radiation. SEM and TEM images were taken using a FEI XL30 Sirion SEM and FEI Tecnai G 2 F20 X-Twin microscope (at a acceleration voltage of 200 kV), respectively. TEM videos were also taken on Tecnai microscope with a magnification of 13500 and a spot size of 5. Compositional analysis of the lithiated nanoparticles was obtained by electron energy loss spectroscopy (EELS) mapping collection using an FEI Titan 80-300 environmental transmission electron microscope (TEM) at the acceleration voltage of 300 kV. The energy resolution of the EELS spectrometer was 0.8 eV as measured by the full width at half-magnitude of the zero-loss peak. EELS mapping data were acquired using a C2 aperture size of 50 mm and a camera length of 60 mm. To obtain the range of Li, Si, and O at the same particle, the dual detector was employed with a different acquisition time of 0.2 and 2 seconds for low and high-loss range, respectively. The energy window of the EELS was 40-145 eV for Li (Li K edge, 54.7 eV) and Si (Si L2,3 edge 99.2 eV) peaks and 510-615 eV for 0 (O K edge, 532 eV) peak. Mapping images were collected after extracting the peaks of Li—K, Si-L, and O—K edges at 54.7, 99.2, and 532 eV, respectively.","Example 2.4—Electrochemical Measurements","Cyclic voltammetry measurements were performed on a BioLogic VMP3 system. Galvanostatic cycling was performed using a 96-channel battery tester (Arbin Instrument). Anode materials including SiO, graphite and Sn NPs (Sigma Aldrich), carbon black (Super P, TIMCAL, Switzerland), and polyvinylidenefluoride binder (PVDF, Kynar HSV 900) were dried under vacuum for 24 h to remove trapped water. To prepare the working electrodes, anode materials were dispersed uniformly in tetrahydrofuran (THF, Sigma Aldrich) to form a slurry, which was then casted onto a copper foil and dried under vacuum. Anode materials and mass ratio are tailored for specific cells. Typically, the mass loading of Li x Si/Li 2 O composites based cells was 0.8-1.5 mg/cm 2 and the mass loading of graphite based cells was 2.0-3.0 mg/cm 2 . The working electrodes were assembled in 2032-type coin cells (MTI Corporation) with Li metal both as the reference and counter electrodes. The electrolyte was 1.0 M LiPF 6 in 1:1 w/w ethylene carbonate/diethyl carbonate (BASF).","Example 3.1—Additional Synthesis Examples","Starting material (e.g., graphite, Sn, SnO 2 , SnF 2 , SnF 4 , Ge, GeO 2 , FeSi 2 , NiSi 2 , CoSi 2 , and SiO—SnF 4 composite) is dried under vacuum for 48 h and then heated at 120° C. (set point temperature of hot plate) in the glove box for 12 h to remove trapped water. Starting materials are heated at 200° C. in a tantalum crucible with cap, and then Li metal foil (99.9%, Alfa Aesar) is added inside. The ratio of starting materials to Li metal is based on the specific reaction equation. After lithium starts melting, the hot plate temperature is increased by 20° C. and then hold at the temperature. Li alloy were synthesized by heating the starting materials and lithium foil at 200° C. on hot plate under mechanical stirring at 200 rpm for 3 days in a glove box (Ar-atmosphere, H 2 O level \u003c0.1 ppm and O 2 level \u003c1.2 ppm). It is recommended to maintain the H 2 O level\u003c1 ppm or O 2 level\u003c6 ppm. For small amounts of starting materials, 6 h is sufficient. For gram-synthesis, the heating time can increase to several days to ensure the complete reaction. For starting materials with low melting point, such as Tin, synthesis temperature should be below the melting point of starting materials. For starting materials with high melting point, the final products are the same crystalline phase, when the temperature is in the range of 200° C. to 400° C. The materials synthesized with longer time and higher temperature will have larger crystalline size.","Example 3.2—Characterizations of Lithiated Sn, SnP","The characterization of lithiated Sn is shown in FIGS. 30, 31A-31F, 32A-32D, 33A-33D . The characterization of lithiated SnO 2 is shown in FIGS. 34A-34C . The characterization of lithiated SiO—SnF 4 composite is shown in FIGS. 35A-35B . The characterization of lithiated FeSi 2 is shown in FIGS. 36A-36B .","As used herein, the singular terms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to a molecule can include multiple molecules unless the context clearly dictates otherwise.","As used herein, the terms “substantially,” “substantial,” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, the terms can refer to a range of variation of less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.","Additionally, amounts, ratios, and other numerical values are sometimes presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth.","In the foregoing description, it will be readily apparent to one skilled in the art that varying substitutions and modifications may be made to the invention disclosed herein without departing from the scope and spirit of the invention. The invention illustratively described herein suitably may be practiced in the absence of any element or elements, limitation or limitations, which is not specifically disclosed herein. The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention that in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention. Thus, it should be understood that although the present invention has been illustrated by specific embodiments and optional features, modification and/or variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scopes of this invention."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 shows schematic diagrams showing Si NPs reacting with melted Li to form Li x Si NPs. A dense passivation layer is formed on the Li x Si NPs after exposure to trace amounts of oxygen, preventing the Li x Si alloy from further oxidation in dry air. As-synthesized Li x Si—Li 2 O core-shell NPs, compatible with the existing battery manufacturing environment, can be mixed with various anode materials during slurry processing and serve as an excellent prelithiation reagent.","FIGS. 2A-2H show characterization of Li x Si—Li 2 O core-shell NPs. ( FIG. 2A ) TEM image of Li x Si—Li 2 O NPs. ( FIG. 2B ) Magnified TEM image reveals the core-shell nanostructure. ( FIG. 2C ) STEM image of Li x Si—Li 2 O NPs, and ( FIG. 2D ) the corresponding EELS map of O distribution. ( FIG. 2E ) STEM image of Li x Si—Li 2 O NPs. Corresponding EELS maps of ( FIG. 2F ) Li distribution and ( FIG. 2G ) Si distribution. ( FIG. 2H ) XRD pattern reveals the core-shell nanoparticles composed of crystalline Li 21 Si 5 and Li 2 O.","FIGS. 3A-3F show electrochemical characteristics. ( FIG. 3A ) First cycle delithiation capacity of Li x Si—Li 2 O NPs, using different solvents to form the slurry. ( FIG. 3B ) Galvanostatic discharge/charge profiles of Li x Si—Li 2 O NPs in 1 st and 2 nd cycles. ( FIG. 3C ) First cycle voltage profiles of Si NPs/Li x Si—Li 2 O and Si NPs show that the incorporation of Li x Si—Li 2 O additive compensates the 1 st cycle capacity loss of Si NPs. ( FIG. 3D ) Cycling performance of Li x Si—Li 2 O NPs, Si NPs/Li x Si—Li 2 O and the control Si NPs at C/20 (1C=4.2 A g −1 Si, the capacity is based on the total mass of Si in the electrodes). The top line is the Coulombic efficiency of Si NPs/Li x Si—Li 2 O composite. ( FIG. 3E ) First cycle voltage profiles of mesocarbon microbeads (MCMB)/Li x Si—Li 2 O (81:9 by weight) show Li x Si—Li 2 O NPs improve the 1 st cycle Coulombic efficiency of MCMB. The table shows that the 1 st cycle Coulombic efficiency is tuned by the amount of Li x Si—Li 2 O additives. ( FIG. 3F ) Cycling performance of MCMB/Li x Si—Li 2 O composites with different weight ratios at C/20 for first three cycles and C/5 for the following cycles (1C=0.372 A g −1 C, the capacity is based on the mass of the total active materials, including MCMB and Si in Li x Si—Li 2 O NPs). The top line is the Coulombic efficiency of MCMB/Li x Si—Li 2 O composite (80:10 by weight).","FIGS. 4A-4D show stability of Li x Si—Li 2 O NPs. ( FIG. 4A ) TEM image of Li x Si—Li 2 O NPs after 3 days of exposure to dry air. ( FIG. 4B ) XRD patterns of Li x Si—Li 2 O NPs without exposure to dry air, exposed to dry air for 3 days, and under ambient conditions. ( FIG. 4C ) The capacity retention of Li x Si—Li 2 O NPs exposed to dry air with varying durations. The inset shows the trend of capacity decay. ( FIG. 4D ) The capacity retention of Li x Si—Li 2 O NPs exposed to air at different humidity levels.","FIGS. 5A-5C show ( FIG. 5A ) SEM image of the Li x Si—Li 2 O NPs%3b ( FIG. 5B ) TEM image of the Li x Si—Li 2 O NPs, stirred in DOL for 6 h%3b ( FIG. 5C ) XRD patterns of Li x Si—Li 2 O NPs in DOL for 6 h and Li x Si—Li 2 O NPs 6 h exposure in dry air.","FIGS. 6A-6C show electron energy loss (EELS) spectra of the Li x Si—Li 2 O NPs showing the presence of ( FIG. 6A ) Li, ( FIG. 6B ) Si, and ( FIG. 6C ) O.","FIG. 7 shows reaction mechanisms with different solvents.","FIGS. 8A-8C show ( FIG. 8A ) specific capacity of the Li x Si—Li 2 O NPs cycled at various rates from C/20 to 1C in the potential window of 0.01 to 1 V versus Li/Li + . 1C=4.2 A g −1 Si%3b ( FIG. 8B ) cyclic voltammetry (CV) measurements of Si/Li x Si—Li 2 O NPs and Si NPs at a scan rate of 0.1 mV s −1 over the potential window of 0.01 to 1.5 V versus Li/Li + %3b and ( FIG. 8C ) CV of MCMB/Li x Si—Li 2 O composites and MCMB graphite at a scan rate of 0.1 mV s −1 over the potential window of 0.01 to 2.0 V versus Li/Li + .","FIGS. 9A-9C show ( FIG. 9A ) Coulombic efficiency versus cycle number of Li x Si—Li 2 O NPs, Li x Si—Li 2 O NPs added Si NPs, and Si NPs%3b ( FIG. 9B ) Coulombic efficiency and ( FIG. 9C ) accumulated irreversible capacity versus cycle number of MCMB/Li x Si—Li 2 O composites with different weight ratios, with MCMB:Li x Si—Li 2 O=80:10 shown in (1), MCMB:Li x Si—Li 2 O=83:7 shown in (2), and a control graphite cell shown in (3).","FIGS. 10A-10B show ( FIG. 10A ) first cycle voltage profiles of graphite flakes/Li x Si—Li 2 O (83:7 by weight) and graphite flakes control cell%3b and ( FIG. 10B ) cycling performance of graphite flakes/Li x Si—Li 2 O and graphite flakes control cell. The top line is the Coulombic efficiency of graphite flakes/Li x Si—Li 2 O composite.","FIGS. 11A-11B show ( FIG. 11A ) SEM image of LiFePO 4 from MTI%3b and ( FIG. 11B ) the 1 st cycle voltage profile of LiFePO 4 half-cell.","FIGS. 12A-12B show ( FIG. 12A ) first cycle voltage profiles of graphite/LiFePO 4 full cell with and without Li x Si—Li 2 O nanoparticles%3b and ( FIG. 12B ) cycling performance of full cell with and without Li x Si—Li 2 O nanoparticles. The top line is the Coulombic efficiency of full cell with Li x Si—Li 2 O nanoparticles.","FIGS. 13A-13B show ( FIG. 13A ) the trend of capacity decay with air humidity%3b and ( FIG. 13B ) first cycle voltage profiles of MCMB added with Li x Si—Li 2 O NPs exposed to dry air for varying time (MCMB: Li x Si—Li 2 O=80:10 by weight).","FIG. 14 shows first cycle voltage profiles of MCMB/Li x Si—Li 2 O NPs composites (80:10 by weight) heated at 45° C. and 65° C. for 1 h.","FIG. 15 shows schematic diagrams of an one-pot thermal alloying process to synthesize Li x Si/Li 2 O composites. Low-cost SiO or SiO 2 are employed as the starting materials. Li x Si/Li 2 O composites exhibit unparalleled stability both in dry and humid air atmosphere, which are readily mixed with various anode materials during slurry process to serve as an excellent prelithiation reagent.","FIGS. 16A-16F show characterizations of SiO and SiO 2 NPs before and after thermal lithiation. TEM images of ( FIG. 16A ) ball-milled SiO NPs and ( FIG. 16B ) lithiated SiO NPs. ( FIG. 16C ) STEM image of lithiated SiO NPs and the corresponding EELS maps of Li, Si and O distributions. TEM images of ( FIG. 16D ) sol-gel synthesized SiO 2 NPs and ( FIG. 16E ) lithiated SiO 2 NPs. ( FIG. 16F ) XRD patterns of lithiated SiO NPs and SiO 2 NPs.","FIGS. 17A-17F show electrochemical characteristics. ( FIG. 17A ) First cycle delithiation capacity of lithiated SiO NPs (line 2) and SiO 2 NPs (line 1). Galvanostatic lithiation/delithiation profile of SiO 2 NPs in 1 st cycle (line 3). The capacity is based on the mass of SiO or SiO 2 in the anode. ( FIG. 17B ) Cyclic voltammetry measurement of lithiated SiO 2 NPs at a scan rate of 0.1 mV s −1 over the potential window from 0.01 to 2 V versus Li/Li + . ( FIG. 17C ) First cycle voltage profiles of SiO NPs/lithiated SiO composite (55:10 by weight, line 2) and SiO control cell (line 1) show lithiated SiO NPs improve the 1 st cycle Coulombic efficiency of SiO. ( FIG. 17D ) First cycle voltage profiles of graphite/lithiated SiO 2 composite (84:6 by weight, line 2) and graphite control cell (line 1). ( FIG. 17E ) Cycling performance of graphite/lithiated SiO 2 composite (84:6 by weight, line 1), graphite/lithiated SiO composite (84:6 by weight, line 2) and graphite control cell (line 3) at C/20 for first three cycles and C/5 for the following cycles (1C=0.372 A/g C, the capacity is based on the mass of the active materials, including graphite, SiO and SiO 2 in Li x Si/Li 2 O composites). The top line is the Coulombic efficiency of graphite/lithiated SiO 2 composite. ( FIG. 17F ) Cycling performance of lithiated SiO NPs and SiO control cell at C/50 for first two cycles and C/2 for the following cycles (1 C=2.67 A/g and the capacity is based on the mass of SiO NPs). The top line is the Coulombic efficiency of lithiated SiO NPs.","FIGS. 18A-18D show stability of Li x Si/Li 2 O composites. ( FIG. 18A ) The remaining capacities of lithiated SiO NPs exposed to dry air with varying duration. The inset shows the trend of capacity decay. ( FIG. 18B ) Capacity retention of Li x Si/Li 2 O composites (line 3), Li x Si/Li 2 O core-shell NPs (line 1) and fluorinated molecular modified Li x Si NPs (line 2) after 6 h storage in the air with different humidity levels. ( FIG. 18C ) The remaining capacities of lithiated SiO NPs in ambient air (35% RH-40% RH) with different durations. ( FIG. 18D ) XRD patterns of lithiated SiO NPs exposed to ambient air for 6 h (upper) and to humid air (10% RH) for 6 h (lower).","FIGS. 19A-19C show DFT simulation and reasons for improved stability. ( FIG. 19A ) DFT simulation is performed by cleaving along (001) plane of Li 22 Si 5 and calculating the binding energy between O at different positions in Li 2 O with Li at (001) plane of Li 22 Si 5 . (FIG. 19 B) Schematic diagram shows the difference between Li x Si/Li 2 O composites and Li x Si/Li 2 O core-shell NPs. ( FIG. 19C ) The table shows the binding energy of different bonds.","FIG. 20 shows different behaviors of Li x Si/Li 2 O composites and Li x Si/Li 2 O core-shell NPs under TEM electron beam with varying duration.","FIGS. 21A-21C show SEM images of ( FIG. 21A ) ball-milled SiO NPs, ( FIG. 21B ) sol-gel synthesized SiO 2 NPs, and ( FIG. 21C ) thermal lithiated SiO NPs.","FIG. 22 shows XRD patterns of ball-milled SiO NPs (upper) and sol-gel synthesized SiO 2 NPs (lower).","FIG. 23 shows first cycle delithiation capacity of the lithiated SiO electrode prepared via the slurry coating process (Li—SiO NPs:Super P:PVDF=65:20:15 by weight).","FIG. 24 shows cyclic voltammetry measurement of lithiated SiO NPs at a scan rate of 0.1 mV s −1 over the potential window from 0.01 to 2 V versus Li/Li + .","FIG. 25 shows first cycle voltage profiles of tin/lithiated SiO composite (60:5 by weight, line 2) and tin control cell (line 1). The capacity is based on the mass of the active materials, including tin NPs and SiO in lithiated SiO NPs.","FIG. 26 shows first cycle voltage profiles of graphite/lithiated SiO composite (84:6 by weight, line 1) and graphite control cell (line 2). The capacity is based on the mass of the active materials, including graphite and SiO in lithiated SiO NPs.","FIG. 27 shows XRD patterns of thermal lithiated SiO NPs with heating time of 3 days (upper) and 5 days (lower).","FIG. 28 shows first cycle delithiation capacities of lithiated SiO NPs exposed to air for 6 h at different humidity levels.","FIGS. 29A-29B show ( FIG. 29A ) first cycle voltage profile of graphite added with lithiated SiO NPs, exposed to ambient air for 3 h (84:6 by weight). ( FIG. 29B ) TEM image of lithiated SiO NPs exposed to ambient air for 6 h.","FIG. 30 shows schematic diagrams of Sn NPs reacting with melted Li to form Li x Sn NPs.","FIGS. 31A-31F show characterizations of tin NPs before and after thermal lithiation. ( FIG. 31A ) SEM image, ( FIG. 31B ) TEM image and (c) XRD pattern of tin NPs. ( FIG. 31D ) SEM image, ( FIG. 31E ) TEM image and ( FIG. 31F ) XRD pattern of Li x Sn alloy.","FIGS. 32A-32D show ( FIG. 32A ) Galvanostatic lithiation/delithiation profile of lithiated tin NPs in 1 st cycle. ( FIG. 32B ) First cycle voltage profiles of tin NPs/lithiated tin composite (6:2 by weight, line 2) and tin control cell (line 1) show lithiated tin NPs improve the 1 st cycle Coulombic efficiency of tin. ( FIG. 32C ) First cycle voltage profiles of graphite/lithiated tin (75:15 by weight, line 2) and graphite control cell (line 1). ( FIG. 32D ) Cycling performance of graphite/lithiated tin composite (line 1) and graphite control cell (line 2) at C/20 for first three cycles and C/5 for the following cycles.","FIGS. 33A-33D show stability of lithiated tin NPs. ( FIG. 33A ) The remaining capacities of lithiated tin NPs exposed to dry air with varying duration. The inset shows the trend of capacity decay. ( FIG. 33B ) Capacity retention of lithiated tin NPs after 6 h storage in the air with different humidity levels. ( FIG. 33C ) The remaining capacities of lithiated tin NPs in ambient air (35% RH-40% RH) with different durations. ( FIG. 33D ) XRD patterns of lithiated tin NPs in ambient air (35% RH-40% RH) with different durations.","FIGS. 34A-34C show ( FIG. 34A ) XRD pattern ( FIG. 34B ) Cyclic voltammetry measurement and ( FIG. 34C ) delithiation capacity of lithiated SnO 2 .","FIGS. 35A-35B show ( FIG. 35A ) TEM image and ( FIG. 35B ) XRD pattern of lithiated SiO—SnF 4 composite.","FIGS. 36A-36B show ( FIG. 36A ) XRD pattern and ( FIG. 36B ) charge capacity of lithiated FeSi 2 ."]},"government_interest":"FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with Government support under Contract No. DE-AC02-76SF00515, awarded by U.S. Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,966,598","html":"https://www.labpartnering.org/patents/9,966,598","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,966,598"},"labs":[{"uuid":"be353232-fcbd-4417-9643-f034964759a2","name":"National Energy Technology Laboratory","tto_url":"http://www.netl.doe.gov/business/tech-transfer ","contact_us_email":"NETLPartnering@netl.doe.gov","avatar":"https://www.labpartnering.org/files/labs/7","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/be353232-fcbd-4417-9643-f034964759a2"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Yi Cui","location":"Stanford, CA, US"},{"name":"Jie Zhao","location":"Stanford, CA, US"},{"name":"Zhenda Lu","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A method for making an anode of a rechargeable battery, comprising mixing a prelithiation reagent composition and an anode material selected from the group consisting of carbon, graphite, Si, Ge, SiO, SiO2, TiO2, SnO2 and P,wherein the prelithiation reagent composition comprises nanoparticles or microparticles comprising (a) a matrix of at least one of Li2O or LiF and (b) a plurality of LixM domains embedded in the matrix,wherein M is a Group 14 element, and x is an atomic ratio of Li to M, wherein x is 5:1 or less,wherein the prelithiation reagent composition prelithiates the anode material and improves a first cycle Coulombic efficiency of the anode by at least 2%, and wherein the first cycle Coulombic efficiency of the anode is at least 90%."},{"idx":"00002","text":"A method for making an anode of a rechargeable battery, comprising mixing a prelithiation reagent composition and an anode material selected from the group consisting of carbon, graphite, Si, Ge, SiO, SiO2, TiO2, SnO2 and P,wherein the prelithiation reagent composition comprises nanoparticles or microparticles comprising (a) a protective coating of at least one of Li2O or LiF and (b) a LixM core encapsulated by the protective coating,wherein M is a Group 14 element, and x is an atomic ratio of Li to M, wherein x is 5:1 or less,wherein the prelithiation reagent composition prelithiates the anode material and improves a first cycle Coulombic efficiency of the anode by at least 2%, and wherein the first cycle Coulombic efficiency of the anode is at least 90%."},{"idx":"00003","text":"The method of claim 1 or 2, wherein the composition comprises at least one of LixC, LixSi, LixGe, or LixSn."},{"idx":"00004","text":"The method of claim 1 or 2, comprising mixing the prelithiation reagent composition and the anode material in at least one solvent to form a slurry, wherein the solvent has a dielectric constant of 20 or less."},{"idx":"00005","text":"The method of claim 1 or 2, further comprising reacting nanoparticles or microparticles of the Group 14 element or compound thereof with Li to obtain the prelithiation reagent composition comprising LixM."},{"idx":"00006","text":"The method of claim 1 or 2, further comprising reacting Li with nanoparticles or microparticles of at least one of graphite, Si, SiO, SiO2, Ge, GeO2, or metal silicide to obtain the prelithiation reagent composition comprising ."},{"idx":"00007","text":"The method of claim 1 or 2, wherein x is 1:6 or greater."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"364","main-group":"4","action-date":"2018-05-08","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","M","364","4","2018-05-08","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"38","main-group":"4","action-date":"2018-05-08","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"0525","main-group":"10","action-date":"2018-05-08","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"36","main-group":"4","action-date":"2018-05-08","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"052","main-group":"10","action-date":"2018-05-08","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"02","main-group":"4","action-date":"2018-05-08","origination":"","symbol-position":"L"}],"document_number":"20160093884","document_published_on":"2016-03-31","document_kind":"","document_country":""},{"number":"8,398,790","artifact":"grant","title":"Proximally self-locking long bone prosthesis","filed_on":"2012-01-17","issued_on":"2013-03-19","published_on":"2012-05-17","abstract":"A femoral stem hip implant for insertion into a surgically created aperture in a femur includes a monolithic femoral stem made of shape memory material. The stem is configured to be inserted into the aperture, has a proximal portion and a longitudinal axis. The shape memory material within the proximal portion has a cross-section perpendicular to the longitudinal axis. At least a portion of the shape memory material within the proximal portion is in a compressed state by application of a plurality of compressive forces at a temperature below an austenitic finish temperature of the shape memory material so that the cross-section expands through shape memory effect via the formation of austenite in response to a temperature increase after insertion into the aperture thereby causing a locking-force to be exerted against an inner surface of the aperture, the locking force being sufficient to stabilize the implant in the aperture.","description":{"text":["CROSS REFERENCE TO RELATED APPLICATIONS","The present application is a continuation of U.S. patent application Ser. No. 13/091,592, filed on Apr. 21, 2011 now U.S. Pat. No. 8,137,486, which is a continuation of U.S. patent application Ser. No. 12/424,885, filed on Apr. 16, 2009, now U.S. Pat. No. 7,947,135, which in turn is a divisional of U.S. patent application Ser. No. 12/054,678, filed Mar. 25, 2008, now U.S. Pat. No. 8,062,378, which claims priority to U.S. Provisional Patent Application Ser. No. 60/919,969, filed Mar. 26, 2007, U.S. Provisional Patent Application Ser. No. 60/911,427, filed Apr. 12, 2007, U.S. Provisional Patent Application Ser. No. 60/911,633, filed Apr. 13, 2007, U.S. Provisional Patent Application Ser. No. 60/943,199, filed Jun. 11, 2007, and U.S. Provisional Patent Application Ser. No. 60/991,952, filed Dec. 3, 2007, the disclosures of which are hereby incorporated herein, in their entirety, by reference.","TECHNICAL FIELD","The invention generally relates to medical implants and, more particularly, the invention relates to materials, structures and methods of using medical implants.","BACKGROUND","Damage to a joint of a patient may result from a variety of causes, including osteoarthritis, osteoporosis, trauma, and repetitive overuse. Osteoarthritis is a condition characterized by damage of the joint cartilage and resulting inflammation and pain. The cause of hip osteoarthritis is not known for certain, but is thought to be “wear and tear” in most cases. Some conditions may predispose the hip to osteoarthritis%3b e.g., a previous fracture of the joint. In osteoarthritis of the hip, the cartilage cushion may be thinner than normal, leaving bare spots on the bone. Bare bone on the head of the femur grinding against the bone of the pelvic socket causes mechanical pain. Fragments of cartilage floating in the joint may cause inflammation in the joint lining, which may also cause pain. Rheumatoid Arthritis (R.A.) starts in the synovium and is mainly “inflammatory”. The cause is not known%3b however, it is known that the condition leads to an eventual destruction of the joint cartilage. Bone next to the cartilage is also damaged%3b it becomes very soft, frequently making the use of an un-cemented implant impossible. Lupus is another form of hip arthritis that is mainly “inflammatory”. Osteonecrosis is a condition in which part of the femoral head dies. This dead bone can not stand up to the stresses of walking. As a result, the femoral head collapses and becomes irregular in shape. The joint then becomes more painful. The most common causes of osteonecrosis are excessive alcohol use and excessive use of cortisone-containing medications.","Implanted prosthetics have been used to replace various components of an affected joint. For example, total hip joint replacement (arthroplasty) surgeries are becoming more prevalent. One common arthroplasty technique uses a cemented femoral implant (i.e., a prosthesis). Undesirably, cemented implants often loosen, causing pain and requiring subsequent surgeries. Alternatively, cementless implants often require an extended period of bone-ingrowth in order for a patient to regain full use of the joint. During the recovery period, the patient with a cementless implant is often required to use crutches or other weight-bearing mechanical assistance to avoid fully loading the implant.","For the structure of the femur prior to arthroplasty, the load distribution can be essentially resolved into an axial component, two bending moments and a torsional moment, which depend on leg stance. The distribution of these load components is changed after the arthroplasty. Conventional methods of prosthesis fixation allow for transfer of axial loads to the bone mainly through shear stresses at the bone-implant interface. (The muscles attached to the femur transfer load and moments as before the arthroplasty). The bending moment is effectively transferred to the bone, primarily through a contact between the prosthesis and the bone in two or more localized regions. In addition, the great disparity in the stiffness of a metallic prosthesis and the surrounding bone reduces bending displacements, changing the bending moment distribution in the surrounding bone.","Conventional femoral prostheses include an elongated stem for insertion into a surgically created cavity in a bone. The elongated stem may provide for accelerated integration of the prosthesis and an early recovery, but potentially at the expense of long-term stability. Because biomechanical forces will be transferred to distal regions of the implanted prosthesis (i.e., “distal bypass”), bone resorption may occur in more proximal portions of the bone—a process known as “stress shielding.” This bone resorption is a consequence of a natural process in which bone remodels in response to applied stresses. Bone density tends to increase in response to applied stress and decrease in response to removal of stress. Proximal bone resorption, along with a levering effect of a long stem, may cause loosening of the prosthesis over time.","An additional source of implant failure results from acetabular wear particles, which induce an inflammatory response in the patient. The resulting chronic inflammation may cause bone loss through osteolysis.","A further source of cemented implant failure is through degradation of the cement over the course of several decades. For this reason, practitioners disfavor the use of cemented implants in younger people.","Most femoral implants are introduced by hammering the stem into an aperture in the bone to create an interference fit. This procedure carries a risk of fracturing the bone, which is estimated by some sources to be in the range of 1-3%.","Recently, “stemless” implants have been begun to be adopted in Europe. See, e.g., Santori, “Proximal load transfer with a stemless uncemented femoral implant” J. Ortopaed Traumatol (2006) 7:154-160. Stemless implants may avoid at least some stress shielding by selectively transferring loads to more proximal bone regions. However, because of inherently lower primary (initial) stability, these stemless implants may require a longer recovery period than conventional stemmed implants and patients must limit weight bearing (e.g., by using crutches) during recovery. Advani, U.S. Pat. No. 6,379,390, discloses a stemless hip prosthesis that includes a cable for wrapping around a reconstructed femur in order to secure the prosthesis.","The success of a hip replacement can be adversely affected by periprosthetic infection, which can have immense financial and psychological costs. Common measures, including the use of body exhaust systems, laminar airflow, prophylactic antibiotics, and various other precautions, have been successful in reducing the incidence of periprosthetic infection. Despite these measures, it is believed that deep infection still occurs after 1 to 5 percent of joint replacements. The incidence is even higher in some high risk patients, such as patients with diabetes, patients with remote history of infection, and patients with inflammatory arthropathies.","Orthopedic scientists have been attempting to design a biologically active implant surface that prevents periprosthetic infection. One strategy is to apply drugs to the surface of implants, such as cemented or cementless implants. Current cementless hip and knee implants, for example, are wedged into the femoral or tibial bone by means of a hammering the implant with a mallet to drive the implant into the pre-drilled bone cavity. A tight interference fit between the implant and femoral bone, however, may undesirably scrape and/or squeegee off any drugs applied to the surface of the implant stem.","Shape memory materials are known in the art. See, for example, Mantovi, D., “Shape Memory Alloys Properties and Biomedical Applications,” Journal of Materials (2000). In particular, shape memory alloys, the most common of which is Nitinol, a nickel-titanium alloy, exist in a martensitic state below a first temperature and an austenitic state above a second temperature. Because the different states have different geometries, a temperature change can lead to a change in shape of an object made from shape memory material.","Nitinol exhibits various characteristics depending on the composition of the alloy and its thermal and work history. For example, the transition temperature or range may be altered. Nitinol can exhibit 1-way or 2-way shape memory effects. A 1-way shape-memory effect results in a substantially irreversible change upon crossing the transition temperature, whereas a 2-way shape-memory effect allows the material to repeatedly switch between alternate shapes in response to temperature cycling. Two-way shape-memory typically requires a cyclic working of the material%3b this is commonly performed by cyclically pulling on the material in tension. Additionally, Nitinol may be used in a pseudoelastic mode based on the formation of stress-induced martensite. Pseudoelastic Nitinol is typically employed at a temperature well above its transition temperature.","One common use of Nitinol in medical devices is its use in arterial stents. To this end, much research has been performed to test the life cycles and other wear properties of Nitinol wires. At least one study found that Nitinol wire has a mode of failure due to bending and compression that is not found in other materials such as austenitic stainless steel.","SUMMARY OF EMBODIMENTS","In accordance with one embodiment of the invention, a femoral stem hip implant for insertion into a surgically created aperture in a femur includes a monolithic femoral stem made of shape memory material. The stem is configured to be inserted into the aperture and have a proximal portion and a longitudinal axis. The shape memory material within the proximal portion has a cross-section perpendicular to the longitudinal axis. At least a portion of the shape memory material within the proximal portion is in a compressed state by application of a plurality of compressive forces at a temperature below an austenitic finish temperature of the shape memory material so that the cross-section of the shape memory material expands through shape memory effect via the formation of austenite in response to a temperature increase after insertion into the aperture thereby causing a locking-force to be exerted against an inner surface of the aperture. The locking force is sufficient to stabilize the implant in the aperture.","In accordance with another embodiment of the invention, a femoral stem hip implant for insertion into a surgically created aperture in a femur includes a monolithic femoral stem made of shape memory material. The stem is configured to be inserted into the aperture and have a proximal portion and a longitudinal axis. The shape memory material within the proximal portion has a cross-section perpendicular to the longitudinal axis. At least a portion of the shape memory material within the proximal portion is in a compressed state by application of a plurality of compressive forces at a temperature below an austenitic finish temperature of the shape memory material so that the cross-section of the shape memory material expands through shape memory effect via the formation of austenite in response to a temperature increase after insertion into the aperture thereby causing a locking-force to be exerted against an inner surface of the aperture. The locking force is sufficient to stabilize the implant in the aperture. The implant further includes a connection feature integral to the stem and configured to connect to an acetabular ball.","In accordance with another embodiment of the invention, a femoral stem hip implant for insertion into a surgically created aperture in a femur includes a non-sleeved femoral stem made of shape memory material. The stem is configured to be inserted into the aperture and have a proximal portion and a longitudinal axis. The shape memory material within the proximal portion has a cross-section perpendicular to the longitudinal axis. At least a portion of the shape memory material within the proximal portion is in a compressed state by application of a plurality of compressive forces at a temperature below an austenitic finish temperature of the shape memory material so that the cross-section of the shape memory material expands through shape memory effect via the formation of austenite in response to a temperature increase after insertion into the aperture thereby causing a locking-force to be exerted against an inner surface of the aperture. The locking force is sufficient to stabilize the implant in the aperture.","In some embodiments, the portion of the shape memory material within the proximal portion may be in the compressed state by the application of compressive forces and tensile forces. The compressive forces may be applied by at least one of a forging process and a pressing process. The shape memory material may be in the compressed state such that a varying radial expansion along the length of the shape memory material results in response to the temperature increase. The shape memory material in the proximal portion may be in the compressed state such that a varying radial expansion in the proximal portion results in response to the temperature increase. The stem has a distal portion and the shape memory material within the distal portion may be in an untrained state. The stem has a distal portion and the shape memory material within the distal portion may be in the compressed state. The shape memory material may be in the compressed state such that the proximal portion radially expands by a different amount than the distal portion in response to the temperature increase. At least 70% of the cross-section may be occupied by shape memory material or the entirety of the cross-section may be occupied by shape memory material. The implant may include at least one of a porous surface coating, a drug coating, and a collagen coating The hip implant may include at least one of a textured surface and a porous surface. The shape memory material may be Nitinol, and/or a titanium-niobium alloy. The stem may have a distal portion having two or more branches.","DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS","Illustrative embodiments of the present invention include prostheses for use in arthroplasty. By way of explanation, examples are given of femoral prosthetics, but the invention also pertains to other long-bone prosthetics, including those used for implantation in a humerus, tibia, fibula, radius, or ulna. Unless noted otherwise, the prostheses described herein include an expanding shape-memory portion that exerts an active locking force upon a proximal bone region due to a shape-memory transition. As a result, a patient with the prosthesis may enjoy a shortened recovery due to increased primary stability. The locking force may also exclude wear particles from the prosthesis-bone junction, and may induce an increase in bone density in the proximal bone, thereby improving the long-term stability of the implant, and perhaps extending the use of cementless implants to include additional patient populations.","Furthermore, embodiments of the present invention prevent stress-shielding by allowing for increased diaphyseal flexibility through the use of a stemless design or a flexible distal shaft portion. In embodiments, a majority of the bone-locking force (e.g., at least 70% of, at least 90% of, or substantially all) is applied to region of the bone that is no more distal than the metaphysis, no more distal than the lesser trochanter, or to the region of the calcar femorale.","FIG. 1 a shows a prosthesis 100 in accordance with an illustrative embodiment of the present invention. The prosthesis 100 includes a body 110 (also referred to as a “shaft”) that is inserted into a resected long bone of a patient. The body 110 is structured to transfer a load produced by the weight of a patient to a femur of the patient. A neck 120 acts as a connection feature for connection to a ball (not shown) that is suitable for insertion into an acetabulum of the patient or prosthetic acetabular cup.","The body 110 is constructed, in whole or in part, from a shape memory material. For example, the body may be entirely constructed of a shape memory alloy such as Nitinol. Alternately, the body 110 includes a coating of shape memory material fused to a solid core. The body may 110 also be hollow or porous with sufficient material remaining present to bear the weight of the patient. In an embodiment, a majority of the body 110 may be entirely composed of a shape memory material as measured in a cross section taken orthogonally to an axis defined by the bone in which it is implanted. Alternately, the cross-section may be characterized by a majority of shape-memory material or at least 70% shape-memory material. In addition to Nitinol, other suitable shape-memory material may be used, including Ti—Nb alloys, suitably robust shape-memory plastics, composite materials, and materials produced using nanotechnology, which may be increasingly discovered as that art progresses.","As discussed below, the shape memory material provides an active bone-locking force, the majority of which is at or above (i.e., proximal to) the level of the metaphysis. The locking force actively applies an outwardly directed force upon a bone in which it is inserted and thereby increases primary stability (i.e., stability that is not a result of bone-ingrowth). Thus, the bone-locking force of the prosthesis 100 differs from the contributions to long-term stability caused by bone-ingrowth. However, the body 110 or other portions of the prosthesis may include features, such as textured or porous surfaces, that are designed to promote osseointegration for additional long-term stability.","The shape-memory material is integral to the bone-locking portion and changes shape in response to a temperature change. In various embodiments, the shape memory material may utilize one or more of a 1-way shape memory effect, and a 2-way shape memory effect. Nitinol and other shape memory alloys may be more flexibly that conventional alloys used in long-bone prosthetics. Additionally, to increase flexibility, a pseudoelastic shape-memory material may be used for portion of the body 110 . The flexibility of the body 110 may allow a recoverable strain similar to that of a normal bone. According to embodiments, the shape-memory effect need not be the maximal expansion achievable for a given material. In contrast, the shape-memory material may be prepared in a manner that causes it to expand by a predetermined sub-maximal amount in the absence of a bone. Accordingly, when implanted into a resected femur, the so-prepared shape memory material will apply a corresponding force, which may be less than the maximal force achievable for a shape-memory bone-locking region of a given size. For example, while Nitinol may be used to achieve as much as an 8% shape change, a Nitinol body may prepared in a manner that causes it to expand by less than 8% or, more preferably, less than 5% or less than 1%. The degree of force applied may be optimized to balance short-term and long-term stability of the prosthesis by applying sufficient force to give suitable initial stability while avoiding either over-compression of the bone and associated pressure-induced necrosis or bone-fracture.","The prosthesis 100 includes several optional features. A lateral flare 130 of body 110 may help stabilize the prosthesis in the bone by using a high femoral neck cut and “round-the-bend” insertion technique as is known in the art in conjunction with the Proxima™ line of femoral prosthetics (DePuy, Leeds, UK). The lateral flare may have a proximal section 140 and a distal section 150 . However, in an alternate embodiment shown in FIG. 1 b , the lateral flare 130 is omitted%3b a design change for which the bone-locking expansion of the body 110 may compensate by providing offsetting or comparable short-term stability. In the embodiment of either FIG. 1 a or 1 b , a short stem 160 may be included, and may be flat, rounded, tapered or pointed. The stem 160 of the present invention allows the flexibility of the femoral diaphysis to be maintained in order to increase the long-term stability of the implantation. Flexibility may be maintained by using a short stem 160 that does not extend into the diaphysis of the bone. Alternately, only a minority of the stem length may extend into the diaphysis. In embodiments described below, the stem does extend into the diaphysis to improve short-term stability, but is flexible. As is known in the art, the prosthesis may be sterilized prior to use. As discussed in more detail below, the prosthesis 100 may also include anti-rotation features such as facets 170 .","FIG. 2 shows a flow diagram for a method of implantation in accordance with an embodiment of the invention. First, a sterile prosthesis is selected in a size that is appropriate for the patient (step 200 ). The prosthesis is at a temperature below its transition temperature (e.g., chilled by refrigeration or storage on ice, or at room temperature with a transition temperature that is between room temperature and body temperature). Selection of the prosthesis may be aided by using a stencil on an x-ray, or using computer-guided techniques. The prosthesis may be a standard size, or custom-made for a particular patient. In any case, the prosthesis may be chosen to provide adequate stability, without damaging the bone during implantation.","The bone is resected and an aperture (i.e., a cavity) is surgically created in the bone using reamers and broaches, as is known in the art (step 210 ). The body 110 , which includes the bone-locking portion in its compressed state, is inserted into the aperture so that the bone-locking portion is situated in the metaphysis (step 220 ). Typically, a broach or other tool may be used that is calibrated for use with a particular prosthesis to give a desired fit. As a result, a bone-to-prosthesis gap of an approximately predetermined size is created at the junction of the aperture and prosthetic surface. In an embodiment, when implanted into an average-sized patient, the body 110 will extend by less than or equal to 5 inches into the aperture.","As the bone-locking portion of the body 110 approaches or surpasses its transition temperature, a martensite to austenite transition of the shape-memory material becomes thermodynamically favored. As a result, the bone-locking portion will radially expand, filling the gap left at the junction. Additionally, the bone-locking portion may possess a potential for further radial expansion, were it to be hypothetically unconstrained by bone. Accordingly, the bone-locking portion exerts a radially outward bone-locking force upon the bone at the junction. As a result of the application of bone-locking force, the prosthesis 100 is more securely lodged in the aperture than a conventional prosthesis made without the use of shape-memory material (step 230 ). In accordance with an embodiment of the invention, the prosthesis 100 is inserted into the aperture and its position adjusted prior to full locking expansion. If the prosthesis is capable of 2-way shape-memory or stress-induced martensite behavior, as discussed below with reference to FIG. 6 , the prosthesis 100 may be cooled to return it to a contracted form in order to unlock it for purposes of repositioning or removal and replacement.","According to an embodiment, the shape-memory alloy bone-locking portion, which may be the entire prosthesis 100 , expands throughout its volume to apply outwardly radial locking-force to thereby seal the junction between the prosthesis 100 and the bone. To enhance, the seal, a sealing portion of the body 110 (e.g., a proximal portion or the entire body) may be substantially uninterrupted%3b e.g., with no grooves, holes or other substantial discontinuities in its exterior surface.","The bone-locking force may increase primary stability (i.e., the initial stability immediately after implantation) to thereby reduce patient recovery times and allow greater weight-bearing during patient recovery. In various embodiments, the bone-locking force may provide the majority of, at least 70% of, or substantially all of the forces contributing to primary stability. The bone-locking force may also increase long-term stability (e.g., to 50 years or more). Without wanting to be bound by the scientific explanation, long-term stability may be increased by promoting elevated bone density and osseointegration in the vicinity of the bone-prosthesis interface based on the ability of bone to remodel in response to the radially applied stresses. The ability to increase bone density may be useful to patients with low bone density%3b e.g. those with osteoporosis. Accordingly, the prosthesis may be used with or without cement according to the circumstances. Moreover, because the bone-locking force is applied in the proximal regions of the bone, there is little or substantially no stress-shielding due to subtrochantric or other distal buttressing. For example, the majority of, at least 70% of, at least 90% of, or substantially all of the force may be applied to regions no more distal than the trochanter minor (lesser trochanter), at or above the level of the metaphysis, at the epiphysis, or in the vicinity of the calcar femorale. Furthermore, the bone-locking force may act to sealingly exclude wear debris or other particles from entering the junction and avoid corresponding adverse effects. Additionally, the bone-locking force may reduce cyclic micromotions of the prosthesis 100 relative to the bone in which it is implanted. Such micromotions may be associated with long term instability of a reconstructed bone.","Another advantage of using an expanding bone-locking portion is that with such a device, it is not necessary to use a tight interference fit between the prosthesis and the aperture, and accompanying insertion by hammering, as is common with conventional cementless prostheses. Accordingly, a larger gap may be used (e.g., a 0.5 to 5 mm gap). Expansion of the prosthesis may be selected to apply a desired bone-locking force for a given gap size. Increasing the gap size may militate for using a prosthesis capable of a greater degree of expansion. By preventing scraping associated with forcible insertion of a prosthesis in an aperture, increasing the initial gap size may prevent damage to the bone and avoid the creation of wear particles. Additionally, by eliminating the need for hammering, or if hammering is used, by reducing the required force, use of the prosthesis 100 reduced the chance of fracturing the bone. Nonetheless, in some instances, it may be desirable to use only a small gap to aid in aligning and maintaining the alignment of the implant prior to the expansion and corresponding application of locking force. The prosthesis may be held in its correct orientation within the bone during the expansion process until the expansion has proceeded to a degree sufficient to stabilize the prosthesis within the bone. The temperature change may occur through warming of the prosthesis due to heat from the body of the patient or external heaters may be used to accelerate the process.","In addition, an increased gap allows for the prosthesis to optionally be surrounded by a gap-filling material that bridges the junction between the prosthesis and the bone. Optionally, the gap-filling material may be strongly or loosely attached to the prosthesis. The gap-filling material may include a variety of materials including a membrane, gel, fibrous or woven mesh, foam, or a plastic or metal sleeve. The gap-filling material may be applied to the prosthesis prior to insertion into the aperture, or, alternately, injected directly into the gap. As discussed below, the gap-filling material may be a metal foam, collagen, or other suitable material.","The gap-filling material may play a variety of functions. The gap-filling material may improve the seal formed at the junction to thereby exclude particles. For this purpose, a deformable, gel, paste or collar may be used. The deformable material may include or consist of collagen (e.g., a collagen membrane). Similar materials may be used to improve the fit and stability of the implant. If cement is to be used in the procedure, the cement may act as a gap-filling material. The gap-filling material may act as a scaffold for bone growth. The gap-filling material may include substances that encourage bone growth. For example, the gap-filling material may include a peptide hydrogel (e.g., Puramatrix™, 3DM Inc.). The gap-filling material may also include growth factors such as peptide growth factors that are known in the art to enhance bone growth. The gap-filling material may include an antimicrobial or antifungal substance (e.g., small molecule antibiotics or colloidal silver). The various biologically active substances mentioned, or others, may be released from a gap-filling matrix material in a time-released manner.","In accordance with illustrative embodiments, an implant formed from shape memory alloy has a drug (e.g., a small or large molecule antibiotic, anti-inflammatory, or growth factor) applied to it either internally and/or externally. Specifically, in illustrative embodiments, a drug coated, self-expanding implant should not scrape or interfere with the bone during insertion, keeping the coated surface intact (if the surface is coated). The implant will then radially expand to contact the femoral bone, which will locally deploy the antibiotics in the proper place against the bone tissue. The processes used to apply the drug or drug/polymer solutions to the prosthesis 100 can be based on one of the following methods (among others): dipping, ultrasonic spray coating, painting (air brush), ink jet coating, and deposition along the stem using syringes. Some techniques combine one of the deposition methods above with a continuous stem rotation to eliminate the excess fluid. The drug and polymer solutions can be deposited very precisely (location and amount) onto the surface of body 110 . Complex coatings using multiple different drugs or drug concentrations, or different polymers deposited onto the prosthesis 100 , will prevent the coating from scraping off during insertion into the bone. Drug coatings may also be applied to a porous surface of the prosthesis.","FIG. 3 shows an embodiment of the present invention, in which a Nitinol prosthesis 100 is embedded in a femur 300 . The body 110 is wedged in the proximal (epiphyiseal/metaphyseal) bone such that the majority of the prosthesis is located at or above the lesser trochanter 310 . An optional lateral flare is wedged by the greater trochanter 320 . A ball 330 is attached to the neck 120 . The distal-most tip 340 of the body 110 extends to the proximal portion of the medullary canal. In this embodiment, the distance from the tip 340 to a neck junction 360 between the ball 330 and the neck 120 is designated as the length of the prosthesis. The length may be, for example, less than or equal to 5 inches.","In order to provide diaphyseal flexibility and proximal locking, in an embodiment, the length/width ratio of the prosthesis is less than or equal to 5. In a preferred embodiment, the length/width ratio is less than or equal to 4. In the embodiment, of FIG. 1 a , the length/width ratio is about equal to 3. The length/width ratio is defined by implanting the prosthesis into a resected bone or suitable model thereof (e.g., an animal bone or reamed plaster cast of a bone). The length (l) is defined as the distance from a projection line 380 drawn from the centroid of a plane defined by the neck junction 360 to a line 370 parallel to an axis defined by the shaft of the femur 300 to a second projection line 390 drawn from the tip 340 to the line 370 . The width (w) is defined as the longest line that can be drawn that is perpendicular the axis of the shaft.","In addition to the proximal bone-locking action of the shape memory material, additional features may be included to enhance long-term stability. For example, as shown in FIG. 4 , the body 110 may be decorated by protrusions 400 such as barbs, teeth, tangs or flutes, which may also be constructed from shape memory material and trained to lockingly expand upon elevation of the temperature. Additionally, the body 110 may include a textured surface, which may be constructed from fused beads, wire mesh, porous hydroxyapetite, or grooves and ribs. The textured surface may be applied by vapor deposition or sintering.","The protrusions 400 may assist in preventing rotation of the prosthesis 100 within the aperture. Additional features and methods may be included to disfavor detrimental rotation of the prosthesis 100 . The prosthesis may be eccentric (i.e., deviating from cylindrical, conical or frustoconical). In a specific eccentric embodiment, the proximal portion of the body 110 may include facets 170 (as shown in FIG. 1 a ). The eccentricity could also be characterized by an oval or clover-leaf cross section. In use, a correspondingly eccentric bore is created in the bone 300 , and the prosthesis is inserted. After warming and expansion, and because shape-memory material is used in the proximal portion of the body 110 , the prosthesis 100 will be locked in a manner that is resistant to torsional displacement. For example, 6 facets 170 may be used and a complementary (hexagonal) proximal aperture created. Protrusions 400 may compensate for a prosthesis 100 that is somewhat round in cross-section%3b e.g., the prosthesis 100 shown in FIG. 1 b. ","The proximal portion of the body 110 may also include a bottle-bore shape%3b i.e., having a taper so that the portion adjoining the neck is narrower than the immediately distal portion. When a corresponding proximal aperture is used, the proximal body will expand to create an implantation that is resistant to proximally-directed dislodgement. The opposite configuration may also be used—the most proximal body portion may be wider than the immediately distal portion and a corresponding cavity created in the proximal aperture. Accordingly, the resulting implantation will resist distally-directed dislodgement. In addition, both of these effects may be combined as with a threaded arrangement or series of circumferential ribs in the proximal body 110 and corresponding grooves created in the proximal bone aperture.","As mentioned above, the body 110 is designed to permit flexure of the bone shaft and this may be accomplished by use of a shortened or stemless prosthesis, which, by not extending significantly into the diaphysis, may avoid the stiffening of the diaphysis associated with stemmed prostheses. A body 110 that is predominantly constructed from a shape memory alloy will have a high degree of flexibility. For example, Nitinol has an elastic modulus of 48 GPa and Ti-26Nb has an elastic modulus of 80 GPa, whereas Co—Cr—Mo, 316-L stainless steel and Ti-gAl-4V have elastic moduli of 230, 200 and 110, respectively. Thus, the shape memory alloys Nitinol and Ti-26Nb have an elastic moduls that is closer to the elastic modulus of cortical bone (15 GPa) than conventional prosthetic materials. A more flexible prosthesis will reduce the load-sharing ratio between the prosthesis and the bone in which it is implanted and will minimize stress-shielding accordingly. A closer matching of elasticity between the prosthesis and bone may also reduce interfacial shear stresses.","Optionally, the prosthesis 100 may expand by a first amount in a first region and by a second amount in a second region. For example, FIG. 5 shows an illustrative embodiment in which a proximally locking short or stemless body is connected to an elongated flexible shaft 500 . The flexible shaft 500 may be composed of a material that is flexible, and may be composed of a material that is as flexible or more flexible than stainless steel. The flexible shaft 500 may also include pores, a roughened surface, a bioactive coating, or other features designed to promote ingrowth to enhance long-term stability of the prosthesis. In an embodiment, the flexible shaft 500 is composed of pseudoelastic Nitinol or martensitic Nitinol (which may be unworked). The stem may also be composed of Nitinol that has been trained to expand to a lesser degree (including not at all) than the programmed expansion of body 110 . In another embodiment, the flexible shaft 500 is split into 2 or more branches with a central gap to permit bending of the branches in response to applied bending moments. The branches may be composed of a shape memory alloy or other material.","In accordance with an embodiment of the invention, the elastic modulus varies along the proximal-distal axis of the implant. This may be accomplished by selectively training a shape-memory alloy. The proximal portion of the implant may be trained to expand at body temperature and contract at another temperature so as to secure the implant through application of force to the proximal portion of a bone. In contrast, the distal portion of the implant may be untrained or trained in a different manner so as to create a lower elastic modulus in the distal portion. In a specific embodiment, Nitinol is used as the shape-memory alloy and is trained to expand in the proximal portion of a stem, and untrained in the distal portion%3b the untrained Nitinol is in its martensitic state and is more flexible than the trained austenitic Nitinol.","If the expansion of the body 110 in response to a temperature shift causes elongation of the body 110 , the tip of the prosthesis may expand in a manner that compresses the bone marrow. Accordingly, it may be desirable to remove a portion of the marrow immediately below the distal extent of the prosthetic. This gap may be filled with a gap-filling material, which may be a resilient material and/or one of the materials mentioned above with respect to the filling of the prosthesis-bone junction.","The prosthesis 100 may also be modular, meaning that the shape-memory proximal portion may be assembled with other portions in order to give a better fit for a given patient. For example, a proximal locking portion may be assembled with a stem, neck, and ball. In an embodiment, the body 110 is made from nitinol, and the neck is made from another alloy that is more resistant to bending-induced fracture.","In accordance with an embodiment of the invention, FIG. 6 shows a flow diagram for a method of manufacturing a proximally self-locking prosthesis. A Nitinol workpiece (e.g., a billet) is selected. The Nitinol material may be selected to have an austenite finish temperature (A f ) that is at or below body temperature (about 37° C. for a human) so that the resulting prosthesis 100 will be in an expanded form after implantation. For example, the prosthesis 100 may have an A f of 30° C. The prosthesis 100 is formed to net shape at a temperature above A f , i.e., to the final expanded shape after expansion (step 600 ). The forming step 600 may include one or more of machining, forging, casting, sintering or hot-isostatic-pressing.","The formed implant is then “trained” using a thermo-mechanical treatment regime (step 610 ). Training may be commenced by heat treating the prosthesis and then cooling in order to establish the martensitic state. The training generally includes straining the material to altering the shape at a lowered temperature. In an embodiment, the compression includes forging in a manner that applies compressive forces having at least a component that is orthogonal to a central axis of the prosthesis 100 (e.g. an axis drawn from the tip 160 to the centroid of the neck 120 , or an axis corresponding to the axis of a bone in which the prosthesis 100 will be implanted). Optionally, or in addition, forces may be applied with at least a component that is orthogonal to the central axis of a bone in which it is implanted (e.g. as described with reference to FIG. 3 ). When performed at a temperature below A f , this process is referred to as “cold-working”. The forging process may include swaging or rotary swaging. Mechanical forge presses, screw presses, hydraulic presses, swage or pointer machines can be employed to train the prosthesis 100 . Alternately, the prosthesis 100 may be pulled (i.e., tensioned on a 2-column tensile pulling machine) longitudinally to both extend its length and decrease its width. Although the pulling process may be simpler, the forging process may allow for a greater degree of control in the compression. For example, certain regions of the prosthesis may be selectively compressed or compressed to varying degrees. In an embodiment, the prosthesis 100 is forged to generate varying compression along its length. For example, because untrained Nitinol is generally more flexible than trained Nitinol, differential training may be used to provide proximal locking while maintaining greater distal flexibility in a stemmed or stemless prosthesis 100 . Multiple discreet locking regions may also be formed by machining raised zones (e.g., patches, ridges, or bumps) and then compressing those zones. A combination of forging and pulling steps may also be used to train the prosthesis 100 . The use of forging may enable the creation of short or stemless shape-memory prosthesis 100 and allow for the creation of complex shapes such as the later-flare design of FIG. 1 a. ","For two-way shape-memory effect (SME) training, the prosthesis 100 may be cooled to below the martensite finish temperature (Mf) of the material and deformed to the desired shape. It is then heated to a temperature above A f and allowed freedom to take its austenitic shape. The procedure is repeated (e.g., 20-30 times). The prosthesis 100 now assumes its programmed compressed shape upon cooling to below M f and to the expanded shape when heated to above A f .","Alternately, stress induced martensite (SIM) training may be employed. For SIM training, the prosthesis 100 is deformed to a compressed shape just above its martensite start temperature (M s ) to generate stress-induced martensite and then cooled to below its M f (martensite finish temperature). Upon subsequent heating above A f , the prosthesis 100 takes its original austenitic shape. This procedure is repeated (e.g., 20-30 times). Alternately, other metallurgical techniques that are known in the art to produce 2-way SME may be employed.","The expansion of a 2-way shape memory alloy component differs from the thermal expansion that may occur in a conventional alloy in at least the following ways: (i) SME components exhibit martensite to austenite transformations at a crystal level, (ii) SME components may be trained to either expand or contract, (iii) the percentage shape change due to thermal expansion is usually −0.001% per ° C., while the shape change due to SME can be as much as two orders of magnitude greater%3b (iv) the temperature ranges at which a shape-memory alloy exhibits a SME can be adjusted by thermo-mechanical treatment%3b (v) the SME material may exhibit a hysteresis in its temperature/displacement profile%3b (vi) the SME material may exhibit hyperbolic temperature/displacement behavior.","A 1-way shape-memory effect bone-locking portion may be employed. The 1-way SME material will decompress and expand upon heating, but will not regain its original shape upon subsequent cooling. Thus, a 1-way SME prosthesis 100 should be kept at low temperature and/or mechanically constrained prior to use. The 1-way SME material may be Nitinol that has been compressed only once in training. The use of 1-way SME may be advantageous in terms of preventing long-term material fatigue-failure that may occur due to repetitive austenite to martensite transitions that may be induced by the repeated stresses applied during use.","In a specific illustrative embodiment, the process includes hot-forging the prosthesis 100 to near net shape at a temperature above A f , finish-machining the forged piece to net shape, and training the prosthesis 100 at lower temperature (e.g., below A f ) to radially compress the prosthesis 100 by less than 8%, or, more preferably, less than 5% or less than 1%.","After training (step 610 ), the prosthesis 100 may be passivated and/or coated to provide a protective layer in order to discourage corrosion, improve biocompatibility, to promote osseointegration, or a combination of the foregoing. Passivation may include prolonged exposure to elevated temperature in the presence of oxygen in order to build a metal oxide layer. A metal foam or other porous metal material, of about 2 mm thickness for example, may serve to promote osseointegration and as a gap-filling material to improve the proximal seal by deforming radially and circumferentially to fill the gap and any deformities in the aperture. The porous metal material described in U.S. Pat. No. 6,063,443 and that commercialized as Trabecular Metal™ (Zimmer, Inc.) may be a suitable porous metal material. The porous material may also be porous Nitinol. An explanation of sterilization and surface treatments may be found in Shabalovskaya, S., “Surface, corrosion and biocompatibility aspects of Nitinol as an implant material”, Bio-Medical Materials and Engineering 12 (2002) 69-109 69. Sterilization (step 630 ) may be accomplished through a variety of means including steam, heat, ethylene oxide, plasma, electron or gamma irradiation. Surface coating may include the application of a porous coating including a metal foam, such as titanium foam.","In accordance with an embodiment, the prosthesis 100 includes one or more radially extending features that are structured to sit above the femoral cut. FIG. 7 shows a prosthesis 100 with a lateral projection 700 that is positioned to sit proximal to the femoral cut after implantation and to provide additional safeguarding against unwanted distal displacement of the prosthesis in the aperture. FIG. 8 shows a prosthesis 100 with a proximal skirt 800 . The skirt 800 may be made of shape-memory material. Optionally, the skirt 800 may be shape memory material and may be trained to curve distally upon elevation of temperature and shifting to its austenitic state, thereby surrounding the proximal portion of the bone and preventing acetabular wear particles from entering the prosthesis-bone junction. Alternately, conventional material such as stainless steel or other biocompatible alloy may be used in a statically curved or flat configuration.","In accordance with an embodiment of the invention, a prosthetic 100 includes a Nitinol body 110 of sufficiently short length to avoid bending-induced fracture over the lifetime of a prosthetic or of a patient. By confining the Nitinol portion primarily or entirely to regions at or above the metaphysis, bending-induced fracture of the prosthesis is avoided due to the absence of a long stem with a bending moment. As discussed below, computer modeling of a short-stemmed prosthesis 100 indicates sufficient robustness of the short-stemmed design when exposed to cyclic compressive forces simulating use in a patient having a prosthesis implanted in the proximal bone.","In an embodiment, the bone-locking region creates a bone-locking force that creates a sufficient primary stability so that a 2.5 kN force applied to the prosthesis causes a micromovement of the implant relative to the bone of no more than 50 microns.","In accordance with an embodiment, the prosthesis 100 does not fracture during application of an endurance test. The endurance test may be conducted according to ISO 7206-4 (including the 1995 and 2002 standards) and may include embedding the prosthesis in an embedding medium and applying 5,000,000 cycles of application of a cyclic load of 2 kN with a minimum load of 300N and a maximum load of 2.3 kN. The embedding medium is a casting medium that will not crack or break under the load applied during testing, and will not exhibit excessive deformation or creep, and is reproducible in strength and other characteristics, and has a modulus of elasticity between 3 GPa and 6 GPa. The prosthesis 100 may be constructed of Nitinol and have a sufficiently short stem length to meet the ISO 7206-4 standard.","Example 1","Finite Element Modeling of a Long-Stemmed Implant","A computational model of a long-stemmed Nitinol prosthesis was created using finite element modeling techniques. The results warn that long-stemmed prosthetics with Nitinol stems may be susceptible to bending-induced fracture.","FIGS. 9 a and 9 b show a finite element model geometries used and designated as “Hip A” and “Hip B” respectively. The material properties for the finite element analyses were assumed to be linear elastic and isotropic. CoCrMo and Nitinol used in these analyses were assumed to follow Hooke%27s Law, and frictional forces could be neglected since the applied force was much higher than the frictional forces. All finite element models were assumed to be linear and un-cemented. The force(s) transmitted from walking were assumed to be transmitted from the femur into the implant, where the force then was transmitted to the ball. From there, the force was then transmitted into the liner and cup. The force transmitted from the liner/ball interaction was assumed to be equal to the applied force due to the press fit between the two objects. The force applied to the hip stem was varied from 2.5 to 7.5 kN, but any force can be extrapolated from these two forces. The force was assumed to be completely transmitted from the acetabulum to the ball on the hip stem, with no losses in between. These forces were chosen because a typical gait cycle generates up to 7 times the body weight at the hip joint.","The force acting on the ball of the hip stem was varied from 2.5 to 7.5 kN. There were three different constraint conditions used: the distal end of the hip prosthesis was constrained, at and below the mid plane of the stem, and lastly at and below where the neck protrudes from the hip prosthesis.","Austenitic and martensitic Nitinol was applied to the stem and neck of hip designs. The ball of the implant was CoCr. This research was performed to determine the effects of applying Nitinol to the stem.","The maximum stresses 900 occur above the region of fixation, as shown in FIGS. 9 c and 9 d . The maximum stress 900 for the hip design B ( FIGS. 9 b and 9 d ) was 9.07 MPa when austenitic Nitinol was used, and 9.41 MPa when the martensitic Nitinol was applied. For hip A ( FIGS. 9 a and 9 c ), the maximum Von Mises stresses were 6.60 and 7.14 MPa for the austenitic and martensitic Nitinol, respectively.","FIG. 10 shows the fatigue curve for Nitinol. Tables 2 and 3 show the results of the fatigue analysis for Nitinol in comparison to Cobalt Chromium, Titanium and Stainless Steel.","The expected life of the Nitinol implants is much less than the other materials, although the maximum von Mises stress values were much less.","The von Mises stress values for the austenitic and martensitic Nitinol were less than the CoCr, Ti, and SS. The maximum stress values occurred proximal to the region of fixation. The maximum stress for the austenitic Nitinol was higher than the martensitic. The modulus of elasticity for the low temperature Nitinol was roughly 40% of that of the high temperature.","The fatigue lives show a significant decrease in Nitinol than other materials. The expected number of cycles until failure was estimated from the SN curve of FIG. 10 . The expected number of years before failure for the Nitinol design was estimated to be between 0.07 and 37 years, which was clearly less than for comparable CoCrMo and stainless steel (SS) prostheses."," TABLE 1 List of properties used for the analyses Modulus of Elasticity (E) Poissons Material 10 6 psi Ratio (n) Bone 0.5 0.30 CoCrMo 25 0.29 Nitinol 10.9 0.30 (Austenite) Nitinol 4.06 0.30 (Martensite) "," TABLE 2 Fatigue results for a SF = 1.0 Hip A Hip B SF = 1.0 yrs yrs CoCrMo 100.0 100.0 SS 100.0 100.0 Ti 100.0 100.0 Nitinol (Austenite) 37.0 6.05 Nitinol (Martensite) 33.9 6.05 "," TABLE 3 Fatigue results for a SF = 1.5 Hip A Hip B SF = 1.5 yrs yrs CoCrMo 22.9 100.0 SS 100.0 100.0 Ti 100.0 87.7 Nitinol (Austenite) 4.76 0.07 Nitinol (Martensite) 3.43 0.07 ","Example 2","Finite Element Modeling of an Implant According to FIG.","To confirm the hypothesis that a short-stemmed Nitinol prosthesis 100 with a lateral flare according to FIG. 1 a would be sufficiently robust, further finite element modeling was performed to simulate the fatigue endurance strength properties of a short-stemmed prosthesis. A quasi-static analyses was performed with the commercial finite element analysis (FEA) code ABAQUS/Standard version 6.5-1. Three dimensional elements and a large displacement formulation were used. Two material models were used for this report: the first was a Nitinol material model assuming a superelastic response with an A f temperature of 30° C. and a typical stainless steel material with approximately 20% cold work was chosen as a baseline for comparison. Two finite element models were created to examine the effect of mesh refinement on the accuracy of the solution. The number of degrees of freedom for the base model and the fine model were 44853 and 111138, respectively. The difference in the results between the two models was considered negligible, so a mesh with refinement consistent with the base mesh was selected. Following the ISO+7206−4−2002 testing standard, the load path was determined by defining the axis of the hip implant using 0.1 and 0.4 CT distances (CT is the distance from the tip of the implant to the center of the implant head) and offsetting this by 10 degrees (alpha in Table 1 of the ISO standard). This was the on axis loading scenario. The implant was embedded to a depth of 0.4 CT from the center of the ball. The effect of the boundary conditions in the location of the embedded material was examined and it was found that there was no effect on the location of the maximum stresses and strains near the head of the implant. Following standard ISO+7206−4−2002, off axis loading was defined following the procedure for on axis loading with an additional rotation of the load path by 9 degrees from the plane of the hip implant (beta in Table 1 of the ISO standard). The following table summarizes the results for the on axis and off axis load cases considered."," TABLE 4 Summary of the results. Maximum Principal Load Max Strain vonMises Load Case Material [kN] [percent] Stress [MPa] On Axis Nitinol 2.5 0.264 119 Stainless 2.5 0.050 119 Steel Off Axis Nitinol 2.5 0.292 131 Stainless 2.5 0.056 131 Steel ","The stresses for both the Nitinol and stainless steel prostheses when loaded to 2.5 kN were similar and below typical levels associated with survival to 10M cycles (“Metallic materials”, J. R. Davis, editor, Handbook of Materials for Medical Devices, page 30. ASM International, 2003.). The strains for the Nitinol prosthesis were five times larger than for the stainless steel component, as would be expected based on the difference in elastic modulus for the two materials. However, the 0.25% strain experienced by the Nitinol component is still below typical values assumed for survival out to 400 million cycles (A. R. Pelton, X. Y. Gong, and T. W. Duerig, “Fatigue testing of diamond shaped specimens.”, Proceedings of the International Conference on Superelastic and Shape Memory Technologies, 2003). A contour plot of vonMises stress for off axis loading of 2.5kN is shown in FIG. 11 .","Several conclusions may be drawn in comparing the long-stemmed Nitinol prostheses of Example 1 with the abbreviated Nitinol prosthesis of example 2. For a long-stemmed prosthesis, the bending moment is applied through the intramedullary stem and results in stress concentrations at the medial and distal lateral ends of the prosthesis. The axial load and torsional moments are transferred to the bone across the bone-prosthesis interface, resulting in high interface shear stresses that may cause the stem to fracture due to fatigue. In contrast, the short-stemmed prosthesis locks proximally in the metaphysis and, as a result, significantly reduces or eliminates interface shear stresses in the intramedullary canal. The short-stem has no bending moments in the diaphysis, but bears axial and compressive loads in the metaphysis. The active locking force of the short-stemmed prosthesis will provide torsional support and anchoring while increasing the physiological loading of the proximal femur. The result is a more natural stress distribution across a proximal femur cross section. Thus stress-shielding may be effectively minimized, and concerns about fatigue failure due to bending moments of the stem are reduced or removed.","In an alternative embodiment, pseudoelastic shape-memory material is used without a temperature-induced transition to cause a locking-force. The prosthesis 100 has a pseudoelastic bone-locking portion with an A f that is below 37° C. (e.g. A f =30° C.). In this case the pseudoelastic prosthesis may be inserted forcibly into the aperture (e.g., with a hammer). The resiliency of the pseudoelastic material will then provide the locking force. In a related embodiment, the pseudoelastic prosthesis is constrained by a rigid sleeve (e.g., a hard plastic sleeve). After insertion of the constrained prosthesis into the bone aperture, the sleeve is removed. The prosthesis may be coated or wrapped with a gap-filling material such as collagen before insertion into the sleeve. After removing the sleeve, the gap-filling material will bridge the bone-prosthesis interface. Use of the sleeve may avoid or mitigate the need for forcible insertion into the aperture and will protect any coatings or gap filling materials from scraping forces.","In another embodiment, the shape-memory material does change phase in response to a temperature change, but only partially. For example, a shape memory material with a wide transition temperature range that overlaps body temperature may be employed.","A further embodiment includes a method of revising a prosthesis implantation. A prosthesis with a 2-way shape-memory bone-locking portion is cooled to induce formation of martensite that is sufficient to loosen the prosthesis so that it may be removed with minimal damage to the bone.","The described embodiments of the invention are intended to be merely exemplary and numerous variations and modifications will be apparent to those skilled in the art. All such variations and modifications are intended to be within the scope of the present invention as defined in the appended claims."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","The foregoing features of the invention will be more readily understood by reference to the following detailed description, taken with reference to the accompanying drawings, in which:","FIG. 1 a depicts a prosthesis in accordance with an embodiment of the present invention%3b","FIG. 1 b schematically shows a prosthesis of FIG. 1 a implanted in a bone in accordance with an alternate embodiment of the invention%3b","FIG. 2 depicts a flow diagram for a method of performing an arthroplasty in accordance with an embodiment of the present invention%3b","FIG. 3 schematically shows the prosthesis of FIG. 1 a implanted in a bone%3b","FIG. 4 depicts a prosthesis that is decorated with projections%3b","FIG. 5 depicts a prosthesis with a flexible stem in accordance with an embodiment of the invention%3b","FIG. 6 depicts a flow diagram for a method of manufacturing a prosthesis in accordance with an embodiment of the present invention%3b","FIG. 7 depicts a prosthesis with a lateral projection in accordance with an embodiment of the present invention%3b","FIG. 8 depicts a prosthesis with a proximal skirt in accordance with an embodiment of the present invention%3b","FIGS. 9 a and 9 b depict finite element models of a long-stemmed prosthesis%3b","FIGS. 9 c and 9 d depict finite element model output corresponding to FIGS. 9 a and 9 b , respectively%3b","FIG. 10 is a chart showing output of the finite element model in accordance with the model of FIG. 9 %3b and","FIG. 11 shows a finite element model of the prosthesis of FIG. 1 a."]},"government_interest":"","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/8,398,790","html":"https://www.labpartnering.org/patents/8,398,790","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=8,398,790"},"labs":[{"uuid":"2694f894-8072-490e-b9ef-647eb2643b73","name":"Argonne National Laboratory","tto_url":"http://www.anl.gov/technology/technology-development-and-commercialization","contact_us_email":"amitchell@anl.gov","avatar":"https://www.labpartnering.org/files/labs/8","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/2694f894-8072-490e-b9ef-647eb2643b73"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Matthew V. Fonte","location":"Charlestown, MA, US"}],"assignees":[{"name":"MX Orthopedics, Corp.","seq":1,"location":{"city":"Billerica","state":" MA","country":" US"}}],"claims":[{"idx":"00001","text":"A femoral stem hip implant for insertion into a surgically created aperture in a femur, the implant comprising:a monolithic femoral stem made of shape memory material, the stem configured to be inserted into the aperture, the stem having a proximal portion and a longitudinal axis, the shape memory material within the proximal portion having a cross-section perpendicular to the longitudinal axis, at least a portion of the shape memory material within the proximal portion being in a compressed state by application of a plurality of compressive forces at a temperature below an austenitic finish temperature of the shape memory material so that the cross-section of the shape memory material expands through shape memory effect via the formation of austenite in response to a temperature increase after insertion into the aperture thereby causing a locking-force to be exerted against an inner surface of the aperture, the locking force being sufficient to stabilize the implant in the aperture, wherein at least 70% of the cross-section is occupied by shape memory material."},{"idx":"00002","text":"A femoral stem hip implant for insertion into a surgically created aperture in a femur, the implant comprising:a monolithic femoral stem made of shape memory material, the stem configured to be inserted into the aperture, the stem having a proximal portion and a longitudinal axis, the shape memory material within the proximal portion having a cross-section perpendicular to the longitudinal axis, at least a portion of the shape memory material within the proximal portion being in a compressed state by application of a plurality of compressive forces at a temperature below an austenitic finish temperature of the shape memory material so that the cross-section of the shape memory material expands through shape memory effect via the formation of austenite in response to a temperature increase after insertion into the aperture thereby causing a locking-force to be exerted against an inner surface of the aperture, the locking force being sufficient to stabilize the implant in the aperture, wherein the entirety of the cross-section is occupied by shape memory material."}],"cpc":[],"ipc":[{"class":"61","value":"","source":"H","status":"B","country":"US","section":"A","version":"","subclass":"F","subgroup":"36","main-group":"2","action-date":"2013-03-19","origination":"","symbol-position":"F"}],"document_number":"20120123554","document_published_on":"2012-05-17","document_kind":"","document_country":""},{"number":"6,859,736","artifact":"grant","title":"Method for protein structure alignment","filed_on":"2001-04-02","issued_on":"2005-02-22","published_on":"","abstract":"This invention provides a method for protein structure alignment. More particularly, the present invention provides a method for identification, classification and prediction of protein structures. The present invention involves two key ingredients. First, an energy or cost function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. Second, a minimization of the energy or cost function by an iterative method, where in each iteration (1) a mean field method is employed for the assignment variables and (2) exact rotation and/or translation of atomic coordinates is performed, weighted with the corresponding assignment variables.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application is cross-referenced to and claims priority from provisional U.S. application 60/194,203 filed Apr. 3, 2000 which is incorporated herein by reference.","STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT","This invention was supported in part by grant number DE-AC03-76SF00515 from the U.S. Department of Energy. The U.S. Government has certain rights in the invention.","FIELD OF THE INVENTION","This invention relates generally to protein structure alignment. More particularly, the present invention relates to identification, classification and prediction of protein structures.","BACKGROUND","Proteins fold into a three-dimensional structure. The folding of a protein is determined by the sequence of amino acids and the protein%27s environment. Aligning proteins is a subject of utmost relevance. It enables the study of functional relationship between proteins. It also is very important for homology and threading methods in structure prediction. Furthermore, by grouping protein structures into fold families and subsequent tree reconsideration, ancestry and evolutionary issues may get unrevealed. An example of the importance of identifying protein structures can be illustrated by the comparison of DNA binding homeodomains from two organisms separated by more than 1 billion years of evolution. The yeast α2 protein and the Drosophilla engrailed protein, for example, are both regulatory proteins in the homeodomain family. Because they are identical in only 17 of their 60 amino acid residues, their relationship became certain only when their three-dimensional structures were compared.","Structure alignment amounts to matching two three-dimensional structures such that potential common substrates, e.g. α-helices, have priority. The latter is accomplished by allowing for gaps in either of the chains. Also the possibility of permuting sites within a chain may be beneficial. At first sight, the problem may appear very similar to sequence alignment, as manifested in some of the vocabulary (gap costs, etc.). However, from an algorithmic standpoint there is a major difference since the minimization problem is not trivial due to rigid body constraints. Whereas sequence alignment can be solved within polynomial time using dynamical programming methods (e.g. Needleman S. B . \u0026 Wunsch C. D . (1971) Identification of homologous core structures. Proteins 35:70-79), this is not the case for structure alignment algorithms since rigid bodies are to be matched according to these constraints. Hence, for all structure alignment algorithms the scope is limited to high quality approximate solutions.","Existing methods for structure alignment fall into two broad categories, depending upon whether one (1) directly minimizes the inter-atomic distances between the structures, or (2) minimizes the distance between substructures that are either pre-selected or supplied by an algorithm involving intra-atomic distances.","One approach is an iterative dynamical programming method (e.g. Laurants D.V. et al. (1993) Structural similarity of DNA - binding domains of bacteriophage repressors and the globin core. J. Mol. Biol . 3:141-148%3b and Gerstein M . \u0026 Levitt M . (1996) Using iterative dynamic programming to obtain accurate pairwise and multiple alignments of protein structures. In: Proceedings of the 4 th International Conference on Intelligent Systems in Molecular Biology , Menlo Park, Calif.: AAAI Press). In this approach one first computes a distance matrix between all pairs of atoms (e.g. Cα) forming a similarity matrix, which by dynamical programming methods gives rise to an assignment matrix mimicking the sequence alignment procedure. One of the chains is then moved towards the other by minimizing the distance between assigned pairs. This method does not allow for permutations, since the internal ordering is fixed by construction. In another inter-atomic approach the area rather than the distances between two structures is minimized (e.g. U.S. Pat. No. 5,878,373). In yet another approach, one compares distance matrices within each other of the two structures to be aligned, which provide information about similar structures (e.g. Holm L . \u0026 Sander C . (1993) Protein structure comparison by alignment of distance matrices. J. Mol. Biol . 233:123-138%3b and Lu G . (2000) A new method for protein structure and similarity searches. J. Appl. Cryst . 33:176-183). The similar structures are subsequently matched. In these methods, for instance by Holm \u0026 Sander as well as by Lu, permutations can in principle be dealt with.","However, there are implementation issues shared by both types of methodologies mentioned above. One is structure encoding (Cα and/or Cβ of the chains). For many methodologies Cα appears to be sufficient, whereas in some cases Cβ is needed. Also, the choice of distance metric is a subject of concern in order to avoid the influence of outliers.","The present methods are useful in certain types of problems of protein structure alignment and less useful in others. Some methods only partially explore the space of possible alignments or lack the ability to handle permutations efficiently. In addition, as mentioned above, the minimization problem for protein structure alignment is non-trivial due to the rigid body constraint. Accordingly there is a need to develop a general method that not only provides an acceptable solution for the minimization problem, but also has a high assurance of protein structure alignment and prediction and thereby applicable to a variety of problems.","SUMMARY OF THE INVENTION","This invention relates generally to protein structure alignment. More particularly, the present invention relates to identification, classification and prediction of protein structures. The present invention involves two key ingredients. First, an energy or cost function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. Second, a minimization of the energy or cost function by an iterative method, where in each iteration (1) a mean field method is employed for the assignment variables and (2) exact rotation and/or translation of atomic coordinates is performed, weighted with the corresponding assignment variables.","In accordance with exemplary embodiments of the present invention, a method is provided with a plurality of steps with the purpose of aligning two three-dimensional protein structures. In that respect the method receives a first protein with N 1 atoms and a second protein with N 2 atoms. An initial alignment of the atoms of the first protein to the atoms of the second protein is made. Once the initial alignment is made, all atomic distances between the coordinates of the atoms of the first protein and the atomic coordinates of the atoms of the second protein can be calculated. These distances could be represented in any type of distance matrix using the real-valued atomic coordinates. Subsequently, the present invention provides for a mechanism to define a matrix with a plurality of binary assignment variables wherein each binary assignment variable corresponds to either a match or to a gap (i.e. not a match). Upon defining the binary assignment variables, the present invention defines one or more mean field equations wherein the plurality of binary assignment variables are now replaced by a plurality of continuous mean field variables, whereby each mean field variable has assigned a value between 0 and 1. The mean field equations also include a plurality of forces that are proportional to the atomic distances squared. The present invention provides for the formulism of an energy function wherein four different costs are included. First, the energy function includes a cost for each atomic distance wherein the distance is based on a weighted body transformation using the continuous mean field variables of the first protein while keeping the second protein fixed. Second, the energy function includes a cost λ for each gap that is created by either the first protein or the second protein. Third, the energy function includes a cost 67 for a position-independent consecutive gap that is created. Finally, fourth, the energy function includes a cost for enforcing a constraint to satisfy that each atom of the first protein either aligns with the atom of the second protein or to a gap. In addition, an optional fifth cost could be included in the energy function to discourage any crossed matches. The energy function is minimized by an iterative process wherein the continuous mean field variables are updated using the mean field equations for a decreasing set of temperatures T until convergence to a predefined convergence value is reached. Once the iterative process has been completed, i.e. after convergence, the continuous mean field variables are rounded of to either 0 or 1.","In view of that which is stated above, it is the objective of the present invention to provide for an extensive search of all possible alignments, including those involving arbitrary permutations. It is another objective of the present invention to allow for arbitrary weighting of a selected atom site assignment. It is yet another objective of the present invention to demand a match between selected amino acids in desirable geometric arrangements for certain biological functionality. It is still another objective of the present invention to provide for methods so that by adjusting the gap cost parameters for each site, the method can find matches of selected segments of the protein chains. It is still another objective of the present invention to provide for the inclusion of user prescribed constraints. It is another objective of the present invention to allow for a probabilistic interpretation of the results. The advantage of the present invention over the prior art is that it provides a generic and flexible method which is able to handle protein permutations efficiently.","DETAILED DESCRIPTION OF THE INVENTION","Although the following detailed description contains many specifics for the purposes of illustration, anyone of ordinary skill in the art will readily appreciate that many variations and alterations to the following exemplary details are within the scope of the invention. Accordingly, the following preferred embodiment of the invention is set forth without any loss of generality to, and without imposing limitations upon, the claimed invention.","Algorithm 1","The present invention can be understood according to the following exemplary embodiments in which there are two proteins, protein 1 and protein 2 with respectively N 1 and N 2 atoms, that are to be structurally aligned. In the general sense of the present invention, the structural alignment is accomplished by a series of weighted rigid body transformations of the first chain, keeping the second chain fixed. The atom coordinates of the first and the second chain of protein 1 and 2, respectively, is denoted by x i (i=1, . . . , N 1 ) and y j (j=1, . . . , N 2 ). The word “atom” will be used throughout this description in a generic sense—it could represent individual atoms but also groups of atoms. In the present exemplary embodiment, it could mean Cα atoms along the backbone. It could also mean e.g. center-of-mass of side-chain atoms. A square distance metric between the chain atoms is used according to EQ. 1, for instance d ij 2 =|x i −y j | 2   (1) but the formalism is not confined to this choice. In general, any distance metric could be used as long as it provides a measure for all distances between the atom coordinates of the first and second chain of protein 1 and 2. In the description of the present invention that follows, first the encoding method and energy (or cost) function is discussed using Algorithm 1, including a discussion of the method for minimizing this energy function. In addition, the description will distinguish a gapless case wherein all atoms of the first and second chain are matched with each other versus a gapped case wherein it is allowed to have a gap in either of the chains meaning that an atom in for instance the first chain is not connected to the second chain. Finally, an alternative way for calculating the energy function is provided in Algorithm 2 which is more efficient for alignments where no permutations are expected. Gapless Case","To better illustrate the present invention, the discussion will start off with the gapless case with N 1 =N 2 . First binary assignment variables s ij are defined, such that s ij =1 if atom i in one chain matches j in the other chain and s ij =0 otherwise. Since every atom in one chain must match one atom in the other, the following conditions must be fulfilled: ∑ i = 1 N 1 ⁢ s ij = 1 j = 1 , … ⁢   , N 2 ( 2 ) ∑ j = 1 N 2 ⁢ s ij = 1 i = 1 , … ⁢   , N 1 ( 3 ) ","A suitable energy function to minimize subject to the above constraints (EQS. 2 and 3) is E chain = ∑ i = 1 N 1 ⁢ ∑ j = 1 N 2 ⁢ s ij ⁢ d ij 2 ( 4 ) where the spatial degrees of freedom, x i , are contained in the distance matrix d 2 ij . Thus whenever s ij =1 one adds a penalty d 2 ij to E chain . Note that EQ. 4 is to be minimized both with respect to the binary variables s ij and the real-valued coordinates x i . Gapped Case","Allowing for gaps in either of the chains is implemented by extending s ij to include 0-components in a compact way%3b s i0 =1 and s 0j =1 if an atom (i˜or˜j) in one chain is matched with a gap in the other and vice versa. Hence, gap positions are not represented by individual elements in s ij %3b rather the gap-elements correspond to common sinks. The matrix S, with elements s ij , containing gap-elements is shown in EQ. 5. (         s 0 ⁢ N 2   s 01 s 02     s 10 s 11 s 12 ⋯ s 1 ⁢ N 2       ⋯   s 20 s 21 s 22 ⋯ s 2 ⁢ N 2 ⋮         s N 1 ⁢ 0 s N 1 ⁢ 1 s N 1 ⁢ 2 ⋯ s N 1 ⁢ N 2 ) ( 5 ) Some caution is needed when generalizing EQS. 2 and 3 to host gaps, since the elements of the first row and column (gap-mappings containing the index 0) in EQ. 5 differ from the others in that they need not sum up to 1. Hence EQS. 2 and 3 become ∑ i = 0 N 1 ⁢ s ij = 1 j = 1 ,   ⁢ … ⁢   , N 2 ⁢ ⁢ ∑ j = 0 N 2 ⁢ s ij = 1 i = 1 ,   ⁢ … ⁢   , N 1 ( 6 ) where the first condition can be written as ∑ i = 1 N 1 ⁢ s ij = 1 ⁢   ⁢ or ⁢   ⁢   ⁢ ∑ i = 1 N 1 ⁢ s ij = 0 %3b j = 1 ,   ⁢ … ⁢   , N 2 ( 7 ) ","An illustrative example of the encoding (s ij ) of matches and gaps is shown in FIGS. 1 and 2 . In FIG. 1 , 100 shows two chains, I and J, by respectively 110 and 120 . The first atom in chain I is indicated by 112 as i=1. The first atom in chain J is indicated by 122 as j=1. Analogously, the last atom in chain I is indicated by 114 as i=8, whereas the last atom in chain J is indicated by 124 as j=10. In FIG. 1 , an example of a gapless situation is for instance when atom 112 and 122 are matched in the first position for both atom i and j. In FIG. 1 , an example of a gapped situation is for instance when atom i or j do not match each other as is indicated by 130 . In FIG. 2 , FIG. 1 is now represented as a matrix S as shown by 200 . In FIG. 2 , 210 is the 0-row for chain 110 , i.e. chain I, indicating whether an atom in chain 110 is matched with an atom of chain 120 or matched with a gap%3b i.e. indicated by respectively 0 (match) or a 1 (gap). Similarly, in FIG. 2 , 220 is the 0-column for chain 120 , i.e. chain J, indicating whether an atom in chain 120 is matched with an atom of chain 110 or matched with a gap%3b i.e. indicated by respectively 0 (match) or a 1 (gap).","For instance, s 01 as indicated by 230 is 0 which means that the particular atom (i.e. j=1) in chain J has a match, whereas s 50 as indicated by 240 is 1 which means that the particular atom (i.e. i=5) in chain I is matched with a gap. This latter example is also shown in FIG. 1 by 135 where atom in chain I is not matched with chain J, but matched with a gap.","In FIG. 2 , the binary numbers in the matrix indicated by 250 correspond to which particular atom of I and J match with each other. Here a 0 means that there is no match, and a 1 means a match between the particular atoms in both chains. For instance, 260 shows s 11 as 1 indicating that atom in position i=0 matches atom in position j=1. Another example is given by 270 which shows s 32 as 0 indicating that atom in position i=3 does not match atom in position j=2. On the contrary as shown by 280 , atom in position i=3 matches atom in position j=7 as indicated by a 1.","Assuming a constant penalty per inserted gap one has the error function E = E chain + ∑ i = 1 N 1 ⁢ λ i ( 1 ) ⁢ s i0 + ∑ j = 1 N 2 ⁢ λ j ( 2 ) ⁢ s 0 ⁢ j ( 8 ) where λ i (1) is the cost for matching atom i in the first chain with a gap in the second chain, and similarly for λ j (2) . The position dependence of the gap costs, λ i (1) and λ j (2) , originates from the fact that it is desirable not to break α-helix and β-strand structures.","In EQ. 8 the gap penalties are proportional to gap lengths. In sequence alignment it is conjectured that gap penalties consist of two parts%3b (1) a penalty for opening a gap and then (2) a penalty proportional to the gap length. The present invention includes a similar gap cost philosophy as presented by Gerstein \u0026 Levitt (Gerstein M. \u0026 Levitt M. (1996) Using iterative dynamic programming to obtain accurate pairwise and multiple alignments of protein structures. In: Proceedings of the 4 th International Conference on Intelligent Systems in Molecular Biology , Menlo Park, Calif.: AAAI Press), i.e. λ i (1) and λ j (2) for opening a gap and a position-independent λ per consecutive gap. Hence, EQ. 8 generalizes to E = E chain + ∑ i = 1 N 1 ⁢ λ i ( 1 ) ⁢ s i0 + ∑ j = 1 N 2 ⁢ λ j ( 2 ) ⁢ s 0 ⁢ j + ∑ i = 1 N 1 ⁢ ( δ - λ i ( 1 ) ) ⁢ s i - 1 , 0 ⁢ s i0 + ∑ j = 2 N 2 ⁢ ( δ - λ j ( 2 ) ) ⁢ s 0 ⁢ j - 1 , 0 ⁢ s 0 ⁢ j ( 9 ) where products like s i−1,0 s i0 are 1 if two adjacent atoms are matched to gaps.","In addition, it may also be desirable to discourage “crossed” matches. Cross matches are matches in which i is matched to j, and (i+1) is matched to k, where k\u003cj, or matches in which (i−1) is matched to k, where k\u003ei. This could be accomplished by adding the term according to E crossed = ω ⁢ ∑ i , j ⁢ s i , j ⁢ { ∑ k \u003c j ⁢ s ( i + 1 ) , k + ∑ k \u003e j ⁢ s ( i - 1 ) , k } ( 10 ) where ω is defined as the strength of this penalty term. Minimization","The next aspect that is needed is an efficient procedure for minimizing E with respect to both s ij and x i subject to the constraints in EQS. 6 and 7. As mentioned above, this minimization problem is non-trivial due to the rigid body constraint. Earlier in 1992, Ohlson et al. probed that a mean field approximation could be used for fitting structures with relevance factors in case of track finding problems with a template approach ( Ohlson M., Peterson C . \u0026 Yuille A. L . (1992) Track finding with deformable templates—the elastic arms approach. Comp. Phys. Comm . 71:77-98).","In the present invention, a mean field approximation approach is integrated, however this mean field method is different from any previously mentioned mean field approaches (see e.g. Blankenbecler R . (1994) Deformable templates—revisited and extended—with an OOP implementation. Comp. Phys. Comm . 81:318-344, 1994). In the paper by Blankenbecler (1994), the assignment matrix, S(ij), although as they are also denoted by v(ij) and V(ij), assigns a “hit” (spark) in a particle detector to track a mathematical curve representing the path of the high energy particle. In the present invention, the mean field approach is employed for a protein matching case in which it assigns for instance a carbon alpha (atom) in one chain to a carbon alpha (atom) in another chain. During the iteration/calculation, while the v%27s are not exactly zero or one, they can be interpreted as the “probability” that atom i in one chain is assigned to atom j in the other chain. For an introduction on the mean field approach one could refer to the paper by Peterson C . \u0026 Soderberg B . (1989) A new method for mapping optimization problems onto neural networks, Int. J. Neural. Syst . 1:3-22.","In the formulation of the present invention, the inherent optimization difficulty resides in the binary part (s ij ) of the problem. Hence, minimizing EQ. 9 using a simple updating rule for s ij will very likely yield poor solutions due to local minima. Well known stochastic procedures such as simulated annealing (e.g. Kirkpatrick S., Gelatt C. D . \u0026 Vecchi M. P . (1983) Optimization by simulated annealing. Science 220:671-680) for avoiding these local minima are too costly from a computational standpoint. In the mean field approach of the present invention, the philosophy behind simulated annealing is retained, but the tedious simulations are replaced by an efficient deterministic process. The binary variables s ij are then replaced by continuous mean field variables υ ij , whereby υ ij is a value between 0 and 1, with a dynamics given by iteratively solving the mean field equations for a decreasing set of temperatures T down to T 0 , where most of the υ ij approach either 1 or 0. These continuous mean field variables can evolve in a space not accessible to the original intermediate variables. The intermediate configurations at non-zero T have a natural probabilistic interpretation.","For s ij satisfying EQ. 6, the mean field equations for the corresponding υ ij read υ ij = ⅇ υ ik / T ∑ k = 0 N 2 ⁢ ⅇ υ ik / T %3b   ⁢ i = 1 ,   ⁢ … ⁢   , N 1 ( 11 ) where the force u ij is given by υ ij = - ϑ ⁢   ⁢ E ϑυ ij ( 12 ) and is computed by substituting s ij with v ij in E (EQ. 9). Note that the desired normalization condition, EQ. 6 ∑ j = 0 N 2 ⁢ υ ij = 1 %3b   ⁢ i = 1 ,   ⁢ … ⁢   , N 1 ( 13 ) is fulfilled automatically in EQ. 11. The other condition (EQ. 7) is enforced by adding a penalty term E γ = γ ⁢ ∑ j = 1 N 2 ⁢ [ ( ∑ i = 1 N 1 ⁢ υ ij ) ⁢ ( ∑ k = 1 N 1 ⁢ υ kj - 1 ) ] = γ ⁢ ∑ i = 1 N 1 ⁢ ∑ k ≠ 1 N 1 ⁢ ∑ k = 1 N 2 ⁢ υ ij ⁢ υ kj ( 14 ) where γ is a parameter and the last equality follows from the fact that υ 2 ij =υ ij for T=0.","So far the description only described the assignment part when minimizing the error function. When updating the mean field variables υ ij , using the mean field equations, the distance measure d 2 ij is a fixed quantity. This corresponds to having the chains at fixed positions. However, the present invention also includes the step to minimize the distance between the two chains. Based on the probabilistic nature of the mean field variables, the chain positions are updated using the (probabilistic) assignment matrix V, with elements υ ij . This is done simultaneously with the updating of υ ij . Explicitly, one of the chains will be moved in order to minimize the chain error function E chain (EQ. 4).","The distance measure d 2 ij depends on the translation vector a and the rotation matrix R making a total of six independent variables. Let x′ i be the coordinates of the translated and rotated protein, i.e. x′ i =a+R x i ,then E chain = ∑ i = 1 N 1 ⁢ ∑ j = 1 N 2 ⁢ υ ij ⁡ ( a + R xi - y j ) 2 ( 15 ) ","This minimization problem can be solved exactly with closed-form expressions for R and a that minimizes E chain as was pointed out by Neuman (1937) in a paper entitled “ Some matrix - inequalities and metrization of matric-space” in Tomsk. Univ. Rev. vol . 1 , pp . 286-300. It should be noted that this solution is rotationally invariant (independent of R) for the special case when the atoms in the two chains matches each other with the same weight, i.e. when vij=constant for all i and j, which is the case for high T.","In summary, for a decreasing set of temperatures T, one iterates until convergence: 1. The mean field equations (EQ. 11), and 2. Exact translation and rotation of the chain (EQ. 15) ","It is stressed that in the present invention, step 2, i.e. the translation and rotation of the chain, is done with the probabilistic mean field assignment variables υ ij and not with the binary variables, s ij . After convergence, υ ij are rounded off to 0 or 1 and rms (root-mean-square-distance) is computed for the matching pairs. An exemplary detail of the algorithmic details can be found in the next subsection.","The forces u ij entering EQ. 11 are proportional to d 2 ij (EQS. 4 and 12). It is the ratio d 2 ij /T that counts. Hence, for large temperatures T, υ ij is fairly insensitive to d ij and many potential matching pairs (i,j) contribute fairly evenly. As the temperature is decreased, a few pairs (the ones with small d ij are singled out and finally at the lowest T only one winner remains. One can view the situation as that around each atom i one has a Gaussian domain of attraction, which initially (large T) has a large width, but gradually shrinks to a small finite value.","The probabilistic of the approach is shown in FIG. 3 by 310 , where the evolution of υ ij , as T is lowered, is shown for parts of the first helices of exemplary proteins 1 and 2 that are used for illustrative purposes together with snap-shots of the corresponding chain sections. Protein 1 and 2 are shown in FIG. 3 by respectively 320 and 330 . Evolution of all the 120 υ ij as a function of iteration time τ (T is lowered with τ). At high T all υ ij are similar%3b all potential matches have equal probability. At lower T, several υ ij have approached 0 or 1 and the movable chain is moving in the right direction. At yet lower T, note that a few υ ij converge later than the majority. These are in this example related to the matching of the last atom in one of the chains. This atom has two potential candidates to match resulting in a number of υ ij that converge last.","An illustrative example of the alignment is shown in FIG. 3 by 340 , 350 and 360 for 10 atoms in the first helices in the protein 1 indicated by 320 and protein 2 indicated by 330 . In FIG. 3 , 340 shows the positions of the atoms at τ=1. For high T every atom in a protein feels all the atoms in the other protein and the problem is rotationally invariant. As shown in FIG. 3 by 350 , for τ=12 most of the relevant matchings are forcing the system to move in the right direction. As shown in FIG. 3 by 360 , for τ=50 the final assignments are complete according to a predefined convergence value. The different snapshots in FIG. 3 are presented using different projections. Some υ ij approach 0 or 1 rather late and are indicated in FIG. 3 by 380 . These υ ij are related to the atom at the end of the protein 1. The difficulty is whether to align this atom to the last or second last atom in protein 2.","Algorithm 2","In this section an alternative formulation of the energy function will be described. This alternative algorithm, called Algorithm 2, is more efficient for alignments where no permutations are expected than Algorithm 1. Algorithm 2 can be described as a shortest path algorithm with a varying distance matrix. In that case, the energy function that is to be minimized is now E=Σ i,j D i,j   (16) ","The D i,j elements are referred to as the optimal alignment energy cost elements from point (ij) to the “end” of the protein chain. These elements are computed by the following scheme D i,j =V i,j 1 ( D i,(j+1) +λ j 2 +V i,(j+1) 1 (δ−λ j 2 ))+ V i,j 2 ( D i+1),(j+1) +d i,j 2 )+ V i,j 3 ( D (i+1),j +λ j 1 +V (i+1),j 3 (δ−λ j 1 ))  (17) ","In these EQS. 16 and 17, the various quantities are basically extensions of the parameters introduced and discussed in Algorithm 1 above. The various quantities as in EQ. 17 are defined as"," d i 2 , j square distance between chain atoms λ i 1 energy for matching atom i in protein 1 to a gap λ j 2 energy for matching atom j in protein 2 to a gap δ energy for position-independent con sec utive gap V i,j 1 = “right neuron” = 1 if j matches a gap V i,j 2 = “match neuron” = 1 if j matches i V i,j 3 = “down neuron” = 1 if i matches a gap P i,j = probability of ending up at position (i,j) (see EQ. 20) ","Using the alternative formulation, the mean field variables are now updated by updating equations u i,j 1 =( D i,(j+1) +λ j 2 +V i,(j+1) 1 (δ−λ j 2 )) u ij 2 =( D (i+1),(j+1) +d i,j 2 ) u i,j 3 =( D (i+1),j +λ j 1 +V (i+1),j 3 (δ−λ j 1 ))  (18) ","As will also become clear in the subsequent section where both algorithm 1 and 2 are listed and compared, the Potts mean variables are now updated similar as in Algorithm 1, namely V i , j k = exp ⁡ ( - u i , j k / T ) ∑ l ⁢ - u i , j l / T ( 19 ) and finally, the matching or assignment matrix is given by Matching Matrix=S i,j =P i,j V i,j 2   (20) ","In other words, this means that the probability for matching (ij) is equal to the product of the probability of ending up at position (ij) and the probability of matching that particular pair.","Implementation","The method presented in the present invention can be applied to, but is not limited to, different types of proteins each with its own type of difficulty in terms of structure alignment. For instance, Dihydrofolate Reductases which contain (α- and β-proteins that have mainly parallel beta sheets, Globins that are all-α, Plastocyanin/azurin and Immunoglobulins which are both are proteins that all-β, and Permutated (winged helix fold) proteins. The latter example is a protein group that is considered difficult and where iterative dynamical programming will fail. In the next sections examples are provided for implementation of the algorithm and the parameters involved. This section contains three parts, i.e. parameters, initialization, and iteration steps.","Parameters","In general, two kind of parameters are used%3b the ones related to the encoding of the problem (γ) and iteration dynamics (ε), where ε governs the annealing schedule as shown in the Table 1 below, and the ones specifying gap costs (λ, δ). The same set of parameters can be used for most of the pairs as shown in the Table 1 below. The first protein family shown in Table 1 involves 27 pairs, whereas the others one each. The algorithm is remarkably stable. The value of λ for each carbon alpha site is chosen to reflect the importance of the surrounding substrate structure, such as an (α-helix, β-sheet, and others. Sheet and helix refer to secondary structure assignment for each Cα atom."," TABLE 1 Protein Family ε γ λ λ sheet λ helix δ α, β, all-α 0.8 0.065 0.10 1.5 λ 1.5 λ λ/2 Plastocyanin/azaurin 0.8 0.035 0.10 2.0 λ 2.0 λ λ/5 Immunoglobulins 0.8 0.040 0.15 2.0 λ 2.0 λ λ/5 Winged helix fold 0.8 0.070 0.20 2.0 λ 2.0 λ λ/5 Initialization","An initialization of the chains is made prior to the mean field alignment. First both chains are moved to their common center of mass. For a random initialization, this move is then followed by a random rotation of one of the chains. Most of the times, however, a sequential initialization is used that consists of minimizing EQ. 4 using a band-diagonal assignment matrix S. This corresponds to a situation where, on the average, atom i in one of the chains is matched to atom i in the other.","Iteration Steps","The following describes a preferred way of defining the algorithm steps as shown in FIGS. 4 . However, the algorithm steps could be altered in various ways as long as step 6 through 8 in algorithm 1 and 2 are followed in the order shown in FIGS. 4 by 4060 , 4070 and 4080 . The shortest chain is always chosen as the one that is moved (x i ). The mean field variables υ ij are updated according to EQ. 11 where, in order to improve convergence, the derivatives in EQ. 12 are replaced by finite differences (see e.g. Ohlson M. \u0026 Pi H. (1997) A study of the mean field approach to knapstack problems Neur. Netw . 10:263-271). This update equation accounts for all mean field variables except for the first row of V, which is updated according to υ 0 ⁢ j = 1 - ∑ i = 1 N 1 ⁢ υ ij ⁢   ⁢ j = 1 , … ⁢   , N 2 ( 21 ) ","As shown in FIG. 4 , the updating steps for algorithm 1 could be defined as:","Updating Steps for Algorithm 1"," 1. Initialization, indicated by 4010 in FIG. 4 %3b 2. Rescale coordinates such that the largest distance between atoms within the chains is unity, indicated by 4020 in FIG. 4 %3b 3. Initiate all vij close to 1/max(N 1 , N 2 ) (randomly), indicated by 4030 in FIG. 4 %3b 4. Initiate the temperature (e.g. T=2), indicated by 4040 in FIG. 4 %3b 5. Randomly (without replacement) select one row, say row k, indicated by 4050 in FIG. 4 %3b 6. Update all υ kj , j=0, . . . , N 2 according to EQ. 11, indicated by 4060 in FIG. 4 %3b 7. Repeat items 5-6 N 1 times (such that all rows have been updated once), indicated by 4070 in FIG. 4 %3b 8. Repeat items 5-7 until no changes occur (defined e.g. by 1/(N 1 N 2 )Σ ij |υ ij −υ ij (old) |≦0.0001), indicated by 4080 in FIG. 4 %3b 9. Rotation and translation of the shortest chain using the probabilistic assignment matrix V, indicated by 4090 in FIG. 4 %3b 10. Decrease the temperature T→εT, indicated by 4100 in FIG. 4 %3b ","11. Repeat items 5-10 until all υ ij are close to 1 or 0 (defined e.g. by 1/N 1 Σ ij υ ij 2 ≧0.99), indicated by 4110 in FIG. 4 %3b and 12. Finally, the mean field solution is given by the integer limit of υ ij , i.e. for each row i, i=1, . . . , N, select the column j* such that υ ij * is the largest element for this row. Let s ij *=1 and all other s ij =0 for this row. As indicated by 4120 in FIG. 4 . ","As also shown in FIG. 4 , the updating steps for algorithm 2 could be defined as:","Updating Steps for Algorithm 2"," 1. Initialization, indicated by 4010 in FIG. 4 %3b 2. Rescale coordinates such that the largest distance between atoms within the chains is unity, indicated by 4020 in FIG. 4 %3b 3. Initiate all υ ij close to 1/max(N 1 , N 2 ) (randomly), indicated by 4030 in FIG. 4 %3b 4. Initiate the temperature (e.g. T=2), indicated by 4040 in FIG. 4 %3b 5. Randomly (without replacement) select one row, say row k, indicated by 4050 in FIG. 4 %3b 6. Update all mean field variables V(ij,k) and D(ij), indicated by 4060 in FIG. 4 %3b 7. Repeat items 5-6 N, times (such that all rows have been updated once), indicated by 4070 in FIG. 4 %3b 8. Repeat items 5-7 until no changes occur (defined e.g. by 1/(N 1 N 2 )Σ ij |υ ij −υ ij (old) |≦0.0001), indicated by 4080 in FIG. 4 %3b 9. Compute matching matrix S(ij), move protein 1 and compute new distances d(i,j) 2 , indicated by 4090 in FIG. 4 %3b 10. Decrease the temperature T→εT, indicated by 4100 in FIG. 4 %3b ","11. Repeat items 5-10 until all υ ij are close to 1 or 0 (defined e.g. by 1/N 1 Σ ij υ ij 2 ≧0.99), indicated by 4110 in FIG. 4 %3b and","12. Finally, the mean field solution is given by the integer limit of υ ij i.e. for each row i, i=1, . . . , N 1 select the column j* such that υ ij * is the largest element for this row. Let s ij *=1 and all other s ij =0 for this row. As indicated by 4120 in FIG. 4 .","It is important to note that while the present invention has been described in the context of a fully functional data processing system and method, those skilled in the art will appreciate that the mechanism of the present invention is capable of being distributed in the form of a computer readable medium of instructions in a variety of forms, and that the present invention applies equally regardless of the particular type of signal bearing medium used to actually carry out the distribution. In other words, the present invention is also a program storage device accessible by a computer, tangible embodying a program of instructions or means executable by the computer to perform method steps for protein structure alignments. Examples of computer readable medium include: recordable type media such as floppy disks and CD-ROMS and transmission type media such as digital and analog communication links. In addition, the present invention could be implemented and coded in different programming languages such as, but not limited to, for example C and C ++ programming languages, JAVA or Java script, or DHTML","The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive. Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents"],"drawings":["BRIEF DESCRIPTION OF THE FIGURES","The objectives and advantages of the present invention will be understood by reading the following detailed description in conjunction with the drawings, in which:","FIG. 1 illustrates an example of two exemplary chains%3b","FIG. 2 illustrates an example of the assignment matrix S corresponding to the matching of two exemplary chains%3b","FIG. 3 illustrates the probabilistic nature of the approach and an exemplary alignment process%3b and","FIG. 4 illustrates algorithmic steps."]},"government_interest":"STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was supported in part by grant number DE-AC03-76SF00515 from the U.S. Department of Energy. The U.S. Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/6,859,736","html":"https://www.labpartnering.org/patents/6,859,736","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=6,859,736"},"labs":[{"uuid":"ccdc6a63-c5ce-4ced-bc27-831017b2c08f","name":"Idaho National Laboratory","tto_url":"https://www.inl.gov/inl-initiatives/technology-deployment/","contact_us_email":"td@inl.gov","avatar":"https://www.labpartnering.org/files/labs/9","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/ccdc6a63-c5ce-4ced-bc27-831017b2c08f"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Richard Blankenbecler","location":"Stanford, CA, US"},{"name":"Mattias Ohlsson","location":"Lund, SE, US"},{"name":"Carsten Peterson","location":"Lund, SE, US"},{"name":"Markus Ringner","location":"Lund, SE, US"}],"assignees":[{"name":"The Board of Trustees of the Lealand Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A program storage device accessible by a computer embodying a program of instructions executable by said computer to perform method steps for protein structure alignment, comprising:(a) receiving atomic coordinates of a first protein with N1 atoms%3b (b) receiving atomic coordinates of a second protein with N2 atoms%3b (c) making an initial alignment of said atoms of said first protein to said atoms of said second protein%3b (d) calculating all atomic distances between said atomic coordinates of said atoms of said first protein and said atomic coordinates of said atoms of said second protein%3b (e) defining a matrix with a plurality of binary assignment variables wherein each binary assignment variable corresponding to either a match or to a gap%3b (f) defining one or more mean field equations wherein said plurality of binary assignment variables are replaced by a plurality of continuous mean field variables, whereby said each mean field variable has a value between 0 and 1, and a plurality of forces that are proportional to said atomic distances squared%3b (g) formulating an energy function, wherein:said energy function includes a first cost for each said atomic distance wherein said distance is a weighted body transformation using said continuous mean field variables of said first protein while keeping said second protein fixed, said energy function includes a second cost λ for each said gap by either said first protein or said second protein, said energy function includes a third cost δ for a position-independent consecutive said gap, said energy function includes a fourth cost for enforcing a constraint to satisfy that each said atom of said first protein either aligns with said atom of said second protein or to said gap%3b (h) minimizing by an iterative process of said energy function and updating said continuous mean field variables in said mean field equations for a decreasing set of temperatures T until convergence to a predefined convergence value is reached%3b and (i) after convergence rounding off said continuous mean field variables to either 0 or 1. "},{"idx":"00002","text":"The program storage device as set forth in claim 1, wherein said formulating an energy function further comprises a fifth cost for discouraging crossed matches."},{"idx":"00003","text":"The program storage device as set forth in claim 1, wherein said second cost is a value between 0.01 and 0.5."},{"idx":"00004","text":"The program storage device as set forth in claim 3, wherein said second cost λ for a α-site in a α-helix has a larger said second cost λ by a factor between 0.01 and 0.5 of said second cost λ."},{"idx":"00005","text":"The program storage device as set forth in claim 3, wherein said second cost λ for a β-sheet has a larger said second cost λ by a factor between 0.01 and 0.5 of said second cost λ."},{"idx":"00006","text":"The program storage device as set forth in claim 1, wherein said third cost δ is a function of said second cost λ divided by a value between 1 and 20."},{"idx":"00007","text":"The program storage device as set forth in claim 1, wherein fourth cost includes a parameter γ with a value between 0 and 0.2."},{"idx":"00008","text":"The program storage device as set forth in claim 1, wherein said minimizing by an iterative process includes an iteration parameter ε with a value between 0.5 and 0.95."},{"idx":"00009","text":"The program storage device as set forth in claim 1, wherein said minimizing by an iterative process further comprises the step of initiating said temperature to a value between 1 and 100."},{"idx":"00010","text":"A method of using a mean field approach for protein structure alignment, comprising the steps of:(a) receiving atomic coordinates of a first protein with N1 atoms%3b (b) receiving atomic coordinates of a second protein with N2 atoms%3b (c) making an initial alignment of said atoms of said first protein to said atoms of said second protein%3b (d) calculating all atomic distances between said atomic coordinates of said atoms of said first protein and said atomic coordinates of said atoms of said second protein%3b (e) defining a matrix with a plurality of binary assignment variables wherein each binary assignment variable corresponding to either a match or to a gap%3b (f) defining one or more mean field equations wherein said plurality of binary assignment variables are replaced by a plurality of continuous mean field variables, whereby said each mean field variable has a value between 0 and 1, and a plurality of forces that are proportional to said atomic distances squared%3b (g) formulating an energy function, wherein:said energy function includes a first cost for each said atomic distance wherein said distance is a weighted body transformation using said continuous mean field variables of said first protein while keeping said second protein fixed, said energy function includes a second cost λ for each said gap by either said first protein or said second protein, said energy function includes a third cost δ for a position-independent consecutive said gap, said energy function includes a fourth cost for enforcing a constraint to satisfy that each said atom of said first protein either aligns with said atom of said second protein or to said gap%3b (h) minimizing by an iterative process of said energy function and updating said continuous mean field variables in said mean field equations for a decreasing set of temperatures T until convergence to a predefined convergence value is reached%3b and (i) after convergence rounding off said continuous mean field variables to either 0 or 1. "},{"idx":"00011","text":"The method as set forth in claim 10, wherein said step of formulating an energy function further comprises a fifth cost for discouraging crossed matches."},{"idx":"00012","text":"The method as set forth in claim 10, wherein said second cost λ is a value between 0.01 and 0.5."},{"idx":"00013","text":"The method as set forth in claim 12, wherein said second cost λ for a α-site in a α-helix has a larger said second cost λ by a factor between 0.01 and 0.5 of said second cost λ."},{"idx":"00014","text":"The method as set forth in claim 12, wherein said second cost λ for a β-sheet has a larger said second cost λ by a factor between 0.01 and 0.5 of said second cost λ."},{"idx":"00015","text":"The method as set forth in claim 10, wherein said third cost δ is a function of said second cost λ divided by a value between 1 and 20."},{"idx":"00016","text":"The method as set forth in claim 10, wherein fourth cost includes a parameter γ with a value between 0 and 0.2."},{"idx":"00017","text":"The method as set forth in claim 10, wherein said step of minimizing by an iterative process includes an iteration parameter ε with a value between 0.5 and 0.95."},{"idx":"00018","text":"The method as set forth in claim 10, wherein said step of minimizing by an iterative process further comprises the step of initiating said temperature to a value between 1 and 100."}],"cpc":[],"ipc":[],"document_number":"","document_published_on":"","document_kind":"","document_country":""},{"number":"9,640,851","artifact":"grant","title":"RF waveguide phase-directed power combiners","filed_on":"2015-05-26","issued_on":"2017-05-02","published_on":"2015-11-26","abstract":"High power RF phase-directed power combiners include magic H hybrid and/or superhybrid circuits oriented in orthogonal H-planes and connected using E-plane bends and/or twists to produce compact 3D waveguide circuits, including 8.times.8 and 16.times.16 combiners. Using phase control at the input ports, RF power can be directed to a single output port, enabling fast switching between output ports for applications such as multi-angle radiation therapy.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims priority from U.S. Provisional Patent Application 62/003,002 filed May 26, 2014, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under Contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","FIELD OF THE INVENTION","The present invention relates generally to high power RF waveguide networks. More specifically, it relates to improved phase-directed power combiners and related methods.","BACKGROUND OF THE INVENTION","In certain high power RF applications, pulsed RF power is needed at multiple different loads at different times. For delivery to n loads, this may be implemented using n separate sources and transmission lines, with appropriately coordinated timing. Rather than having each source connected to a single load, another approach is to use phase directed combining to send power from multiple sources to a selected one of the desired loads, allowing power to be sequentially routed to different individual loads by changing the input phases. This approach allows the peak power requirement to be reduced by roughly a factor of n. It may be implemented using a high power RF switching circuit. For example, four-port hybrids may be used for combining power in waveguide by controlling the relative phase of the inputs to selectively direct power out of either output.","As shown in FIG. 1 , a traditional 2×2 waveguide hybrid has a pair of rectangular waveguides joined to allow matched directional coupling. This particular “magic-H” configuration, originated by the inventors, has mitred bends at all four ports and appropriate adjustment of the dual-moded width section to allow combining the input power at the two right ports 102 , 106 to be selectively directed to one of the two left output ports 100 , 104 . Removal of sharp-edged wall apertures, which can be prone to breakdown, makes this geometry eminently suited for use in high power applications. It also avoids the use of posts, common in magic-Ts. The waveguide height of this 2-D design can be raised to further increase power handling. Note that this H-plane geometry can be employed to design couplers with arbitrary power division. The figure shading indicates the electric field strength for a particular example where 9.3 GHz power is directed from the right input ports 102 , 106 to the left output port 104 . The fields at the input ports 102 , 106 are 90° out of phase.","If the port widths are constrained to be half the center width and the mitres 45°, the particular symmetry of the 2×2 hybrid design of FIG. 1 allows it to be merged with three other 2×2 hybrids radially arranged to create an 8-port 4×4 “cross potent” superhybrid waveguide circuit, as shown in FIG. 2 . The resulting 8-port device has four input ports (a pair of ports 200 , 202 on the top and a pair of opposite ports 204 , 206 on the bottom) and four output ports (a pair of ports 208 , 210 on the left and a pair of opposite ports 212 , 214 on the right). RF power input at the four input ports can be combined and directed by proper phase control to any one of the four output ports on the orthogonal arms. This 4×4 design is the equivalent of four hybrids with ports properly joined. For more convenient flange connections and to accommodate maintaining symmetry through the overmoded regions, asymmetric H-plane bend/tapers (e.g., asymmetric H-plane bend taper 216 ) to standard waveguide width are appended to the cross-potent ports in the figure. The figure shading indicates the electric field strength for an example in which RF power from the input ports 200 , 202 , 204 , 206 is directed to the upper left output port 208 through the selection of appropriate phases of the RF signals at the input ports.","Note that the 4×4 design superhybrid, like the 2×2 hybrid design, has its waveguides all in a common plane (the H-plane). A straightforward extension in the plane of this 4×4 8-port device to 8×8 16-port device or 16×16 32-port device, however, leads to increasingly complicated and extensive layouts, requiring many bends and waveguide runs to connect component ports.","SUMMARY OF THE INVENTION","The present invention provides compact and elegant multi-port phase-directed power combiners. A multi-port passive waveguide network according to the invention allows RF power from multiple RF sources to be combined and directed to any of an equal number of output ports through control of the relative phases of the input RF power. These compact waveguide circuits provide an efficient means of instantly switching RF power between the output ports by drive phase manipulation. In another aspect, the devices can also be used in reverse as matched splitters.","Embodiments include 16-port (8×8) design and two 32-port (16×16) design configurations. Both the geometric arrangements and various unique component features of these networks provide advantageous improvements. The networks are symmetric. At the design frequency, each of the input ports is isolated from all of the others and equally coupled, with varying phase, to each of the output ports. These waveguide networks, composed solely of volume enclosed by metal walls, need no active components, dielectrics, ferrites, or any other materials.","In one aspect, the invention provides a high power RF phase-directed power combiner including a first 4×4 superhybrid RF waveguide in a first plane, a second 4×4 superhybrid RF waveguide in a second plane parallel to the first plane, a first RF waveguide circuit in a third plane, a second RF waveguide circuit in a fourth plane parallel to the third plane, where the third and fourth planes are orthogonal to the first and second planes, and E-plane bends connecting the first 4×4 superhybrid RF waveguide to the first RF waveguide circuit and the second RF waveguide circuit and connecting the second 4×4 superhybrid RF waveguide to the first RF waveguide circuit and the second RF waveguide circuit.","The first RF waveguide circuit may be a third 4×4 superhybrid RF waveguide, and the second RF waveguide circuit a fourth 4×4 superhybrid RF waveguide. Four such superhybrids in this arrangement may be duplicated, nested, and joined with interleaving E-plane bends to form a 16×16 combiner. Alternatively, the first RF waveguide circuit may be a first 2×2 magic H hybrid RF waveguide and the second RF waveguide circuit a second 2×2 magic H hybrid RF waveguide, forming an 8×8 combiner.","In another aspect, the invention provides a high power RF directive combining circuit comprising a first set of hybrid waveguides in a first set of multiple parallel planes, a second set of hybrid waveguides in a second set of multiple parallel planes orthogonal to the first set of parallel planes, and a set of waveguide twists connecting ports of the first set of hybrid waveguides to ports of the second set of hybrid waveguides.","DETAILED DESCRIPTION","Embodiments of the present invention provide passive waveguide circuits that have phase-directed switching capability of RF power from multiple inputs to any of multiple outputs using relatively compact geometries. These multi-port waveguide circuits allow agile combining and switching of power from multiple combined sources to any of multiple outputs using phase patterns. Several examples of such circuits are here realized, with different geometrical arrangements and port orientations. Conceptually, these designs are not necessarily bound to the particular sub-components used here for illustrative purposes. For example, the design principles of the combiners of the present invention encompass variations in particulars of hybrid design such as slots or posts, smooth twists, swept bend/tapers, and so on.","A 16-port combiner/splitter according to embodiments of the invention provide compact design by designing the circuit with waveguide components having their H-planes in multiple distinct planes, some of which are orthogonal to others, resulting in a 3D design. FIGS. 3A-B illustrate two such 3D waveguide circuit configurations, each composed of two cross potent superhybrids in parallel planes one above the other, with their output ports turned toward each other (before or after bend/tapers) through E-plane bends to feed into four magic-H hybrids, oriented in parallel planes orthogonal to the superhybrid planes. The design of FIG. 3A , for example, has superhybrids 300 , 302 having their distinct H-planes parallel to each other. A magic-H hybrid 306 with its H-plane perpendicular to that of the superhybrids 300 , 302 joins two arms of the superhybrids 300 , 302 via E-plane bends 304 and 308 , respectively. The superhybrid ports that are not joined serve as inputs, while the magic-H hybrid ports are outputs. Inputs and outputs are indicated in the figure with arrows. The waveguide shading shows RF power entering the 8 ports of superhybrids 300 and 302 being directed to one of the ports in magic-H hybrid 306 . The design of FIG. 3B is analogous to that of FIG. 3A with two superhybrids joined through E-plane bends to four magic-H hybrids. In FIG. 3B , however, the orientation of the hybrids is in a different orthogonal plane than those in FIG. 3A , and the width transitions in FIG. 3A are before the magic-H hybrids, while the transitions in FIG. 3B are after. In the design of FIG. 3B , because the hybrids (e.g., 310 ) reflect the cross-potent interior dimensions, bend/taper transitions (e.g., 312 ) are used at the ports. Note that, though input-output exchange symmetry is not present in these two configurations, they are still functionally interchangeable: eight independent ports couple equally to another eight independent ports. This device contains, as it must, the equivalent of 12 hybrids.","FIGS. 4A-C show a perspective view, side view, and front view, respectively, of a 32-port 16×16 design forming an interleaved, 3-D network device resembling a “crown of thorns.” It is composed of eight cross potent superhybrids, with width-changing H-plane bends on all ports, arranged with a first set of four superhybrids 300 , 302 , 304 , 306 stacked in four distinct parallel planes and a second set of four superhybrids 308 , 310 , 312 , 314 stacked in four distinct parallel planes orthogonal to the first set of planes. The superhybrids are connected by E-plane bend connections (e.g., 316 ) to form an interleaved structure with inner and outer rings. Each cross potent superhybrid couples to both an inner and outer superhybrid on each adjacent perpendicular side. The 16 input ports emerging from the vertical planes couple to the 16 output ports emerging from the horizontal planes. FIG. 4C illustrates the front-facing 8 input ports 434 , 436 , 438 , 440 , 442 , 444 , 446 , 448 , and 8 output ports 418 , 420 , 422 , 424 , 426 , 428 , 430 , 432 . The other 8 input and other 8 output ports face the back. The top view of FIG. 4B shows superhybrid 400 and four orthogonal superhybrids 408 , 410 , 412 , 414 .","By comparison with the compact design of FIGS. 4A-C , FIG. 5 illustrates the conventional design of a 16×16 32-port device using successive combining (top to bottom). From the top down, 2×2 %27s (e.g., 500 ) are connected to make 4×4%27s%3b then 4×4%27s (e.g., 502 ) are connected to make 8×8%27s%3b and then 8×8%27s (e.g., 504 ) are connected to make the 16×16. Note the many line crossings, indicating waveguides which must pass each other, an obstacle to a simple planar solution. This complex and bulky design uses 32 hybrids whose H-planes are in a single common plane, for which 17 of 48 connecting waveguides must leave the plane for 44 cross-overs. The complexity and extent of such a circuit put together in a straightforward manner by simply laying out and connecting hybrids is apparent from this figure.","There are other approaches than merging and encircling to achieving appropriate connections between hybrids in combining circuits. Two such designs are made possible by incorporating either of the additional waveguide components pictured in FIGS. 6A and 6B . The first component, shown in FIG. 6A is a directional coupler of the magic-H type designed for 0 dB, rather than 3 dB, coupling—essentially a “pass through” that allows waveguides to cross in a plane without coupling. The second component, shown in FIG. 6B , is a waveguide twist. In the particular “step twist” design shown, simply orthogonal end segments are connected (with edges rounded) by a short 45° segment of such length that the discontinuity mismatches cancel at the design frequency. This component offers a compact rather than broadband option.","Now, the pass through of FIG. 6A can be used in the middle of a 4-hybrid pattern, such as those that constitute the top two rows of FIG. 5 , to allow the cross-over connection without leaving the plane. This is illustrated in the 8-port 4×4 combining circuit of FIG. 7 , which is composed of four hybrids joined by “pass through” 700 . In this design, the bottom 4 inputs phase combine into any of the top 4 outputs.","As shown in FIG. 8 , an 8-port 4×4 combining circuit composed of four hybrids and four waveguide twists has the outputs of one pair of hybrids connected to the inputs of another by stacking each pair and rotating one 90° with respect to the other such that the ports line up. In particular, hybrids 800 and 802 are in distinct parallel planes, while hybrids 804 and 806 are in distinct parallel planes orthogonal to the first two planes. A twist (e.g., 808 ) such as in FIG. 6B is then used for each connection between the lined up ports to rotate the polarization. The resulting 4×4 combining circuit looks like the simulated model of FIG. 8 , with horizontal inputs and vertical outputs. The shading shows RF power being directed from the four input ports of hybrids 804 and 806 to a single output of hybrid 802 .","An alternate design of a 32-port 16×16 directive combining circuit composed of 32 hybrids, 8 pass throughs and 16 waveguide twists is shown in FIG. 9 . This design combines the latter two concepts, providing another 3-D 16×16 “phased array” combining circuit. This device is composed of two sets of four stacked 4×4 combining circuits of FIG. 7 , a first set 900 , 902 , 904 , 906 in stacked parallel planes, and a second set 908 , 910 , 912 , 914 in stacked parallel planes oriented orthogonal to the first set of parallel planes and arranged such that the 16 ports of one stack line up with the 16 ports of the other stack. The 16 lined up ports of the two sets of stacked circuits are connected by 16 twists (e.g., 916 ) at their lined-up ports. This network is the functional equivalent of the design in FIG. 4 , though the very different geometries offer different port orientations. The shading in the figure illustrates an example in which RF power input to the 16 ports of circuits 908 , 910 , 912 , 914 is directed to a single output port of circuits 900 , 902 , 904 , 906 .","While FIG. 5 illustrates successive binary levels of combining, note that both of the 16×16 circuits are more accurately described by the equivalent 2-D layout of FIG. 10 . The 8×8 stage is avoided by connecting four 4×4 circuits. The number of hybrids, connections and cross-overs in the planar layout is the same.","The RF devices described above may be designed to operate at arbitrary RF frequency, in appropriate waveguide, the pictured examples being for 9.3 GHz in WR112, for several waveguide combining circuits with equal numbers of input and output ports. Properly optimized, each input port is matched, uncoupled from the others, and equally coupled to each of the output ports (and vice versa). With equal power in each input and independent phase control, any combination of output power division, in particular full combining to any one, is possible.","Employing these unique 3D designs as well as unique component designs, embodiments of 8×8 and 16×16 combiners have been described above. Based on the principles of the invention described herein, variations of these designs are also possible. In addition, it may be possible to conceive a next-level 32×32 combiner geometry using the principles of the present invention (though a 4 th dimension is unavailable). Such a device design would incorporate 80 hybrids, or their equivalent.","It should be understood by those skilled in the art that various sub-components of alternate design could be substituted for the components shown in the specific embodiments described herein without departing from the scope of the invention. For example, such alternative components may include a standard waveguide twist, swept bend/taper (curved walls), mitred E-plane bend, slotted hybrid, biplanar coupler, and so on.","Embodiments of the invention advantageously allow the use of smaller RF amplifiers than otherwise required and, more significantly, allow the input power to be combined and selectively directed to any of several different output ports in quick succession by means of applied drive signal phase patterns.","Expressing the port fields in complex notation, where 1, i, −1 and −i represent respectively 0°, 90°, 180° and −90° phases, the scattering matrix of a (lossless) 2×2 hybrid and its directive combining function with appropriate inputs can be represented as follows:"," S = 1 2 ⁢ ( 0 0 1 i 0 0 i 1 1 i 0 0 i 1 0 0 ) ⇒ S ⁡ ( 1 - i 0 0 ) = ( 0 0 2 0 ) , ⁢ S ⁡ ( - i 1 0 0 ) = ( 0 0 0 2 ) ","For the 4×4 superhybrid, the scattering matrix grows to the following:"," S = 1 2 ⁢ ( 0 0 i - 1 0 0 i 1 0 0 1 i 0 0 - 1 i i 1 0 0 i - 1 0 0 - 1 i 0 0 1 i 0 0 0 0 i 1 0 0 i - 1 0 0 - 1 i 0 0 1 i i - 1 0 0 i 1 0 0 1 i 0 0 - 1 i 0 0 ) ","Phase patterns that lead to combining to selective ports for this are shown below."," ⇒ S ⁡ ( 0 0 - i - 1 0 0 - i 1 ) = ( 2 0 0 0 0 0 0 0 ) , S ⁢ ( 0 0 1 - i 0 0 - 1 - i ) = ( 0 2 0 0 0 0 0 0 ) , S ⁢ ( 0 0 - i 1 0 0 - i - 1 ) = ( 0 0 0 0 2 0 0 0 ) , S ⁡ ( 0 0 - 1 - i 0 0 1 - i ) = ( 0 0 0 0 0 2 0 0 ) ","Note that the output power is proportional to the square of the field, so that it is here four times the normalized input powers.","Though unwieldy to display in this text, the extension up to our 16×16 combiners is straight forward. With the factor in front going to ¼, the 32×32 S-matrix, with proper port numbering and phase references, is a symmetric matrix composed of an orthogonal set of column/row vectors, each of which has 16 zeroes and 16 elements of unit amplitude and various phases aligned to the complex axes.","Since the S-matrix inverse is the conjugate transpose, the phase combination needed for combining to a port n can be determined by taking the complex conjugate the n th row, i.e. from:"," SS T * = SS - 1 = ( 1 0 0 0 ⋱ 0 0 0 1 ) ⇒ S ⁡ ( S n ⁢ ⁢ 1 * ⋮ S nN * ) = ( ⋮ 1 ⋮ ) n ","The technology is well established to allow a low-level RF (LLRF) system to control and manipulate the relative phases of the drives to multiple RF amplifiers, with fast switching, from the same phase reference.","One important application of the devices of the present invention is in medical applications where it allows multi-angle irradiation of tumors on a time scale fast compared to bodily movements—thus increasing accuracy and effectiveness while limiting collateral tissue damage—without the unrealistic expense of a 16 times higher power individual RF source for each linac. Specifically, devices of the present invention allow for sequentially powering a set of medical linacs arranged around a patient to provide fast multi-angle radiation therapy without a turning gantry. For example, embodiments of the invention may be used in systems such as that disclosed in U.S. Pat. No. 8,618,521, which is incorporated herein by reference. Other uses are envisioned in areas such as industry and materials detection. With loads on all but one output port, they can be used simply as matched multi-source combiners, or in reverse as 16-way splitters."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 is a top view of an H-plane geometry design and electric field pattern for a 4-port “magic-H” waveguide hybrid device, introduced in 1999.","FIG. 2 is a top H-plane view of planar geometry design and electric field pattern for an 8-port 4×4 “cross potent” superhybrid waveguide circuit.","FIGS. 3A-B are perspective views of the 3D geometry and electric field pattern for two configurations of a 16-port 8×8 combining circuit composed of two cross potents feeding four magic-H%27s, according to embodiments of the present invention.","FIGS. 4A-C show perspective, side, and front views of a 32 port 16×16 cross potent “crown of thorns” combiner, according to embodiments of the present invention.","FIG. 5 is a schematic of an equivalent 2-D layout of the device of FIG. 4A-C .","FIGS. 6A-B illustrate a “pass-through” 0-dB hybrid component and a step twist component, respectively, according to embodiments of the present invention.","FIG. 7 is a top view of a planar 8-port 4×4 combining circuit composed of four hybrids joined by a pass through component, according to embodiments of the present invention.","FIG. 8 is a perspective view of an 8-port 4×4 combining circuit composed of four hybrids and four waveguide twists, according to embodiments of the present invention.","FIG. 9 is a perspective view of a 32-port 16×16 directive combining circuit composed of 32 hybrids, 8 pass throughs and 16 waveguide twists, according to embodiments of the present invention.","FIG. 10 is a schematic of an equivalent 2-D layout of the device of FIG. 9 ."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under Contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,640,851","html":"https://www.labpartnering.org/patents/9,640,851","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,640,851"},"labs":[],"inventors":[{"name":"Christopher D. Nantista","location":"Redwood City, CA, US"},{"name":"Valery A. Dolgashev","location":"San Carlos, CA, US"},{"name":"Sami G. Tantawi","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"An 8 input×8 output high power phase-directed RF power combiner comprising:a first 4×4 (8-port) cross potent superhybrid waveguide circuit%3ba second 4×4 (8-port) cross potent superhybrid waveguide circuit%3bwherein each of the first and the second cross potent superhybrids is an equivalent of four hybrids radially arranged and merged, with waveguides all in a common plane (the H-plane)%3bwherein the first 4×4 (8-port) cross potent superhybrid and the second 4×4 (8-port) cross potent superhybrid are in a first set of parallel planes%3ba first RF waveguide circuit, wherein the first RF waveguide circuit comprises a first pair of magic H 2×2 H-plane waveguide hybrids%3ba second RF waveguide circuit, wherein the second RF waveguide circuit comprises a second pair of magic H 2×2 H-plane waveguide hybrids%3b andwherein the first RF waveguide circuit and the second RF waveguide circuit are in a second set of parallel planes orthogonal to the first set of parallel planes%3beight E-plane waveguide bends, wherein a first four of the eight E-plane bends connect the first 4×4 cross potent superhybrid to each hybrid in the first RF waveguide circuit and to each hybrid in the second RF waveguide circuit, and wherein a second four of the eight E-plane bends connect the second 4×4 cross potent superhybrid RF waveguide to each hybrid in the first RF waveguide circuit and to each hybrid in the second RF waveguide circuit."},{"idx":"00002","text":"A 16 input×16 output high power RF phase-directed power combiner comprising:a first pair of 4×4 (8-port) cross potent superhybrids%3ba second pair of 4×4 (8-port) cross potent superhybrids%3bwherein the first pair of 4×4 (8-port) cross potent superhybrids and the second pair of 4×4 (8-port) cross potent superhybrids are stacked in a first set of parallel planes%3ba third pair of 4×4 (8-port) cross potent superhybrids%3ba fourth pair of 4×4 (8-port) cross potent superhybrids%3bwherein the third pair of 4×4 (8-port) cross potent superhybrids and the fourth pair of 4×4 (8-port) cross potent superhybrids are stacked in a second set of parallel planes orthogonal to the first set of parallel planes%3bsixteen waveguide bends, wherein a first eight of the sixteen waveguide bends connect the first pair of 4×4 (8-port) cross potent superhybrids to the third pair of 4×4 (8-port) cross potent superhybrids and to the fourth pair of 4×4 (8-port) cross potent superhybrids, and wherein a second eight of the sixteen waveguide bends connect the second pair of 4×4 (8-port) cross potent superhybrids to the third pair of 4×4 (8-port) cross potent superhybrids and to the fourth pair of 4×4 (8-port) cross potent superhybrids."},{"idx":"00003","text":"A 4 input×4 output high power phase-directed RF power combiner comprising:a first set of two 2×2 waveguide hybrids stacked in a first set of two distinct parallel planes%3ba second set of two 2×2 waveguide hybrids stacked in a second set of two distinct parallel planes orthogonal to the first set of two parallel planes%3ba set of four waveguide twists connecting four output ports of the first set of two 2×2 hybrid waveguides to four input ports of the second set of two 2×2 waveguide hybrids, wherein the four waveguide twists are rotational twists around a longitudinal waveguide axis."},{"idx":"00004","text":"The 4 input×4 output high power phase-directed RF power combiner of claim 3, wherein the first set of two 2×2 waveguide hybrids and the second set of two 2×2 waveguide hybrids are magic H hybrids."},{"idx":"00005","text":"The 4 input×4 output high power phase-directed RF power combiner of claim 3, wherein each of the waveguide twists comprises simply orthogonal end segments connected with edges rounded by a 45° segment, where a length of the 45° segment is selected such that discontinuity mismatches cancel at a design frequency."},{"idx":"00006","text":"A 16 input×16 output high power phase-directed RF power combiner comprising:a first set of four 4×4 phase directed combining circuits stacked in a first set of distinct parallel planes%3ba second set of four 4×4 phase directed combining circuits stacked in a second set of distinct parallel planes orthogonal to the first set of distinct parallel planes%3ba set of 16 waveguide twists connecting 16 output ports of the first stack to 16 input ports of the second stack, wherein the 16 waveguide twists are rotational twists around a longitudinal waveguide axis%3bwherein each of the four 4×4 phase directed combining circuits in the first and second sets of four 4×4 phase directed combining circuits is composed of four hybrids joined by a magic H passthrough."},{"idx":"00007","text":"The 16 input×16 output high power phase-directed RF power combiner of claim 6 wherein the four hybrids joined by a passthrough comprise four 3-dB hybrids arranged parallel in a 2×2 pattern in a single plane, with a 0 dB coupler located at a center of the pattern in the same plane."},{"idx":"00008","text":"The 16 input×16 output high power phase-directed RF power combiner of claim 6, wherein each of the 16 waveguide twists comprises simply orthogonal end segments connected with edges rounded by a 45° segment, where a length of the 45° segment is selected such that discontinuity mismatches cancel at a design frequency."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"12","main-group":"5","action-date":"2017-05-02","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","P","12","5","2017-05-02","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"20","main-group":"5","action-date":"2017-05-02","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"12","main-group":"5","action-date":"2017-05-02","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"165","main-group":"1","action-date":"2017-05-02","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"12","main-group":"3","action-date":"2017-05-02","origination":"","symbol-position":"L"}],"document_number":"20150340752","document_published_on":"2015-11-26","document_kind":"","document_country":""},{"number":"9,648,713","artifact":"grant","title":"High-gain thompson-scattering X-ray free-electron laser by time-synchronic laterally tilted optical wave","filed_on":"2014-03-14","issued_on":"2017-05-09","published_on":"2016-02-11","abstract":"An improved optical undulator for use in connection with free electron radiation sources is provided. A tilt is introduced between phase fronts of an optical pulse and the pulse front. Two such pulses in a counter-propagating geometry overlap to create a standing wave pattern. A line focus is used to increase the intensity of this standing wave pattern. An electron beam is aligned with the line focus. The relative angle between pulse front and phase fronts is adjusted such that there is a velocity match between the electron beam and the overlapping optical pulses along the line focus. This allows one to provide a long interaction length using short and intense optical pulses, thereby greatly increasing the radiation output from the electron beam as it passes through this optical undulator.","description":{"text":["CROSS REFERENCE TO RELATED APPLICATIONS","This application is 371 of PCT application PCT/US2014/027729 filed on Mar. 14, 2014. PCT application PCT/US2014/027729 filed on Mar. 14, 2014 claims the benefit of U.S. Provisional application 61/792,281 filed on Mar. 15, 2013.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","FIELD OF THE INVENTION","This invention relates to X-ray sources.","BACKGROUND","Free electron lasers (FELs) are useful for various applications, since they can provide intense radiation in various parts of the electromagnetic spectrum, such as X-rays. In a free electron laser, radiation is emitted by the interaction of an electron beam with an undulator. However, conventional free electron lasers tend to be large and complex systems, mainly driven by the complexities of the large-scale magnetic undulator typically employed.","Proposals have been made to provide an undulator suitable for use in a free electron laser using optical techniques. However, these approaches have not yet provided competitive performance relative to traditional FEL approaches.","Accordingly, it would be an advance in the art to provide improved X-ray sources via the interaction of an electron beam with an optical undulator.","SUMMARY","In this work, an improved optical undulator for use in connection with free electron radiation sources is provided. A tilt is introduced between phase fronts of an optical pulse and the pulse front. Two such pulses in a counter-propagating geometry overlap to create a standing wave pattern. A line focus is used to increase the intensity of this standing wave pattern. An electron beam is aligned with the line focus. The relative angle between pulse front and phase fronts is adjusted such that there is a velocity match between the electron beam and the overlapping optical pulses along the line focus. This allows one to provide a long interaction length using short and intense optical pulses, thereby greatly increasing the radiation output from the electron beam as it passes through this optical undulator.","DETAILED DESCRIPTION","A) Introduction","Free-electron lasers (FEL) are the most powerful X-ray radiation sources to support much frontier research%3b however, because of the large-scale magnetic undulator and RF (radio frequency) electron accelerator limit, only a few sources exist worldwide. The optical undulator and laser-plasma accelerators, on the other hand, may provide the potential to significantly reduce the size and cost of these X-ray sources to the university-laboratory scale.","For a nonlinear relativistic Thompson scattering, the magnetic and electric fields of the light have the same effect on the electron motion, and electrons emit X-ray photons through the relativistic motion. The optical wave in the nonlinear Thompson scattering serves as an electromagnetic undulator, whose periods are several orders of magnitude shorter than the conventional undulator that uses an alternating static magnetic field for synchrotron radiation or FEL. There are various applications of such Thompson or Compton X-ray sources including measurement of the plasma parameters in the Z pinch and energy and energy spread of electron beams, imaging of atomic-scale spatial resolution, and biological and medical diagnostic systems.","The conventional method for Thompson scattering using counter propagating lasers with electron beams has con-fronted a bottleneck: the highest yield of X-ray flux was reported at about 2×10 7 photons with several picoseconds duration. The reason is that the interaction time for the close-to-speed-of-light electron beam and the counter propagating laser mainly depends on the laser pulse duration. Thus, a long laser pulse is naturally demanded. For instance, in order to realize FEL in an optical undulator with a 10-20 gain length, i.e., about 3 cm long, an ultra-long 200 ps and ultra-intense Terawatt counter propagating laser pulse is needed, which is hard to realize. For a laser co-propagating with a beam, the electric force and magnetic force on the relativistic electron cancel each other, leading to a very low net field strength. Consequently, only incoherent or weak coherent radiation is emitted. In order to decrease the gain length and enhance the X-ray yield, increasing the beam current or decreasing the electron energy has been proposed. For instance, electron beams with peak current 20 kA, low energy 30 MeV, emittance 0.3 πmm mrad, and relative energy spread 0.4% were proposed%3b however, there is still no experimental demonstration on generating such an ultrahigh current and low energy beam. In other work, an electron beam of low energy 5.88 MeV, current 0.5 kA, and relative energy spread of 0.01% is needed to interact with a Terawatt laser of 1 μm transverse spot size and 20 ps pulse duration to generate a 0.3 MW X-ray. Consequently, how to realize 10 8 photons with femtoseconds duration in a single laser pulse is still a critical problem. In this work, novel methods to significantly increase the coherent X-ray output by several orders with several femtoseconds duration are provided, which may finally realize a tabletop X-ray FEL.","B) Technical Approaches","FIGS. 1A-B show a first exemplary embodiment of the invention. FIG. 1B is a close up side view of the interaction region of FIG. 1A . This example is an apparatus for producing X-rays. It includes at least one source 120 of optical radiation configured to emit pulses of optical radiation. Two such pulses are referenced as 102 a and 102 b . As emitted from the source, these pulses have parallel phase fronts ( 112 a , 112 b ) and pulse fronts (edges of 102 a , 102 b ). Source 120 can be configured as a single source plus an optical splitter, or as two sources appropriately phase and frequency locked to each other such that their outputs can interfere. Focusing optics are configured to bring two counter-propagating pulses of the optical radiation to a common line focus. Here pulses are regarded as counter-propagating if their wave vectors make an angle between about 170 degrees and about 190 degrees with respect to each other. In this example, cylindrical lenses 108 a and 108 b are employed to create a line focus along electron beam path 110 . In this layout 108 a and 108 b could also be cylindrical mirrors, with appropriate modification to beam paths such that the desired line focus is formed.","An electron source 122 is configured to provide an electron beam 116 aligned with the line focus. This line focus is schematically shown by 118 on FIG. 1B . In this example, the electron beam is along beam path 110 (i.e., the Z direction). Electron beam 116 is preferably configured as separated bunches of electrons having as high a repetition rate as possible.","The focusing optics include one or more dispersive optical elements configured to introduce a tilt angle between phase fronts of the counter-propagating pulses and pulse fronts of the counter-propagating pulses. In this example, the dispersive optical elements are gratings 104 a and 104 b , and pulses 106 a and 106 b show the tilt between phase fronts 114 a and 114 b , (which are parallel to the Z-axis) and the pulse fronts (i.e., the edges of pulses 106 a , 106 b , which make a 45 degree angle with respect to the Z-axis). As described in greater detail below, this tilt angle is selected to substantially match a velocity of pulse front propagation along the line focus with an electron velocity of the electron beam along the line focus. Gratings 104 a and 104 b preferably have uniform line spacing.","The standing wave pattern formed by the counter-propagating pulses at the line focus acts as an undulator for emission of X-rays by electrons in the electron beam. Optionally, X-ray mirrors 124 and 126 can be disposed to create an X-ray resonator configured to provide feedback for the emitted X-rays, which provides a free electron laser. In this situation, one would also need to introduce bending magnets (not shown) to bring the electron beam into the X-ray resonator. Further technical details relating to this example follow.","In out first method, after being focused by cylindrical lenses, two counter-propagating laser pulses 106 a , 106 b with equal amplitude, the same vertical electric polarization E y , and identical phase are at normal incidence to the electron-beam path 110 , as illustrated in FIG. 1A . A standing wave along the optical propagation of the x direction is formed, which has a total y-polarized (pointing outward from the page) electric field with the expression of 2E y,m (x,z)×cos(ωt+φ)cos(kx) where ω, k, E y,m (x,z) and φ are, respectively, the angular frequency, the wave number, the amplitude, and the injection phase of the laser, and the z-polarized magnetic field is parallel to the beam motion. The field amplitude of the standing wave at the central plane is strengthened because of the focus effect of the cylindrical lenses 108 a , 108 b . Thus, at the central plane x=0 of the beam channel, electrons undergo an intense transverse electric force 2eE y,m (0,z)cos(ωt+φ) and a negligible magnetic force. In this configuration, the undulator period is λ u =λ, as compared to λ u =λ/2 for a backward wave.","The time-synchronic interaction of the beam and waves is realized by the pulse front tilt, which is created by using an optical diffractive grating element 104 a , 104 b with angular dispersion, as illustrated in FIG. 1A , where γ is the tilt angle between the pulse front and the phase front. The pulses 106 a , 106 b still have their phase front 114 a , 114 b perpendicular to the propagation direction, but the arrival time of the laser pulse at the interaction area is synchronously delayed with the electron beam propagation.","It is illustrated in FIG. 2A that the electron beam 116 moves along the z axis, while the normal-incident laser propagates in the x direction. Configurations referenced as 202 , 204 , and 206 show three snapshots of beam-pulse interaction in order of increasing time. Electron beam 116 propagates in the Z direction (i.e., to the right on FIG. 2 ). Pulse 106 b propagates in the X direction (i.e., up on FIG. 2 ). Overlap of the laser pulse and the electron beam is ensured by proper velocity matching, as shown. It is apparent that the beam always moves inside a diagonal area (actual pulse shape 106 b ) of a rectangular pulse shape 208 . Consequently, the short tilted pulse 106 b is equivalent to a full rectangular pulse 208 as seen by electron beam 116 . Therefore, the interaction length can extend to the entire transverse width of the laser pulse, which can be on the order of several centimeters. This is long enough to realize the FEL exponential growth process, leading to a significantly enhanced coherent radiation.","It should be emphasized that the synchronization between the laser and beam is realized by using pulse front tilt, whose technology has been used in precise synchronization of fast electron diffraction. In our methods, the two lateral lasers could come from the split of a single laser after a single grating structure to avoid the timing jitter between lasers. Moreover, sub-100 as timing jitters between multiple optical pulse trains have been stably generated from mode-locked lasers. The synchronization between the remote optical pulse trains and microwave signal has achieved the rms timing jitter within 1 fs, beneficial for synchronization between laser and beam. Moreover, if the laser power is sufficiently high, a single laser as a lateral traveling wave could avoid the time jitter and realize a more uniform K distribution, while the basic scheme of the synchronous interaction of beam and laser stays the same in the standing wave case.","The necessary pulse front tilt γ is determined by the incidence angle α between the laser and highly relativistic beam: γ=π/2−arctan[cot(α/2)]. For a normal incidence α=π/2, tilt angle is γ=π/4, which can be created by an angular dispersion d∈/dλ from a diffractive grating satisfying γ=arctan[λ 0 (d∈/dλ)]. The angular dispersion d∈/dλ is calculated from the groove spacing d and the incidence angle θ between the laser and the grating, ∈(λ)=arcsin[λ/d-sin(θ)]. For λ 0 =10 μm and θ=45°, a grating of 97 grooves per millimeter is demanded.","The dimensionless strength parameter K=eB eff λ u /(2πmc), where the equivalent magnetic field B eff =2E y,m /c, or we can write K=2eE y,m λ/(2πmc 2 ) for the undulator period λ u =λ. The peak field at the grating elements is limited by its breakdown thresholds, which is about 2 J/cm 2 for an ultrashort laser pulse with τ\u003c1 ps for the commercial high power gratings. The cylindrical lenses located between the grating structure and interaction area further enhance the peak field by focusing the transverse size, while keeping the synchronously delayed time of the laser with the electrons. Thus, K reaches 1 to 2 for laser with wavelength 10 μm at the vacuum interaction area.","The influence of laser intensity on the resonant wavelength is important. Using aspheric lens pairs (not shown on FIGS. 1A-B ), the transverse intensity profile of the laser can be transformed from a Gaussian beam to a flattop beam, whose field E y,m is illustrated in FIG. 2B , and the rms flatness of power intensity for the flattop has been improved to 0.23%. Because of the relation ΔP/P=2ΔE/E, the rms (root-mean square) flatness of electric field has reached 0.12%. We find the requirement on the tolerance of laser intensity temporal uniformity. Due to the fact that the laser temporal electric field is the effective optical undulator strength, the uniformity, one of the important requirements, directly determines the gain of a free-electron laser system. For radiation frequency up to the soft X-ray regime, the rms variation of the laser temporal electric field is preferably less than 0.5% to provide a useful amount of gain, and is more preferably less than 0.15% to provide high gain. These rms time variations are calculated by averaging at times when the pulse is present and excluding times when the pulse is not present.","Another method for enhancing the central electromagnetic field is to design a microstructure, including a central electron-beam vacuum channel and periodic-quadrupole dielectric waveguides, which have periodically varying index of refraction (silicon and vacuum) along the channel. Full-wave 3D electromagnetic simulation HFSS software is used to study the microstructure. The resulting structure is similar to that of FIGS. 1A-B , except that lenses 108 a , 108 b are replaced with a microstructure 302 as shown on FIG. 3 . Crystalline silicon with a high index of refraction is selected as the material of the dielectric waveguides 306 %3b SiO 2 or sapphire with lower refractive index is applied as the substrates 304 . Here W c is the vacuum channel width, and the height and width of the silicon waveguides is H s and W s respectively. Such a microstructure is configured to provide optical resonance of the counter-propagating pulses at the line focus.","Two optical plane waves at normal incidence to the beam channel with the equal amplitude, same polarization, and identical phase are oppositely and laterally coupled into the optical structure of FIG. 3 . The polarized electric fields E y are perpendicular to the central z axis of the channel. When the two incident waves arrive at the central vertical yz plane, the electric fields with the same polarization and identical phase form a resonant standing wave, leading to a significantly enhanced amplitude, and the central yz plane is equivalent to a magnetic boundary by symmetry. In order to further strengthen the central field, a quasiquadrupole structure shown in FIG. 3 is designed, where the bilateral lasers are guided and propagated in the bilateral upper and lower waveguides, which are separated by a substrate layer. The incident phases in the ipsilateral upper and lower waveguides are the same so that the y-directional polarized electric field adds, and there is the strongest field at the center of the quadrupole aperture, as illustrated in FIG. 4 (which shows the modeled complex magnitude field in a quarter of the quadrupole structure 302 ). By symmetry, the horizontal xz plane is equivalent to an electric boundary.","By adjusting the periodic incident phases of the optical waves, a nonzero phase difference Δφ between the adjacent waveguides along the z direction is generated, which results in a traveling wave along the central channel, and a −11 dB reflection loss of incident wave. When the flying direction of the electron beam is opposite to the energy flow, relativistic electrons meet a backward wave, and undergo the sum of electric and magnetic forces.","FIGS. 5A-B show the normalized complex magnitude of the electric field E y /E m along the center line of the Si waveguide in the x direction ( FIG. 5B ) and along the central line of the quadrupole channel in the z direction ( FIG. 5A ). Parameters for these results were W c =1.3λ, H s =0.3λ, W s =0.19λ, L 0 =0.42λ, and Δφ=0.72π. Here E m is the maximum field in the waveguide.","For a channel width W c ˜1.3λ, the optimized center field distribution is shown on FIG. 5A , which implies that the field is distinctly strengthened with the ratio E y,m /E m ˜1.7, corresponding to a total force (E y,m +cB x,m )˜3.4 E m . In work by others, an optical Bragg waveguide with an inner diameter 0.2λ and a corresponding E y,m /E m \u003c0.5 was proposed to enhance the X-ray brightness by two orders since the laser is guided and focused inside the channel. As a comparison, the channel width 1.3λ and E y,m /E m ˜1.7 for our structure are much better than those in the Bragg waveguide. With regard to fabrication, a 3D microstructure with a 3 cm length and detailed size ˜1 μm was demonstrated by others in 1996, so fabrication of such microstructures is within the skill of ordinary workers in micro-fabrication.","The rms opening angle σ of the forward cone of X-ray radiation for undulator periods N=5000, rms K=1, and γ=100 is σ=1.5×10 −4 rad, the transverse width of the radiation cone σL˜4.5 μm for L=3 cm, smaller than the half-channel width. Thus, the dielectric channel walls do not influence the main X-ray radiation.","The electron beam quality has an important influence on FEL performance. Laser-driven plasma accelerators could deliver high-quality electron beams. In recent work by others, the high-brilliant beam was generated with peak current 10 kA, normalized emittance of ∈ n =0.3-0.4 πmm mrad, beam energy 125 MeV, charge 10 pC, and beam size 1 μm. By X-ray spectroscopy measurement, an ultralow ∈ n =0.1 πmm mrad was demonstrated with beam energy 450 MeV, and bunch radius 0.1 μm. Since the beam size 1 μm or even 0.1 μm is much smaller than the CO 2 laser wavelength and laser transverse dimension, the beam mainly sees a uniform field%3b besides, the beam size could be much smaller than the channel width 13 μm.","C) Modeling","We model the above described process of method one as an effective optical undulator. The electron bunch has centroid energy 60 MeV, σ γ =0.06, normalized emittance of ∈ n,x(,y) =0.2 πmm mrad in both the x and y planes, and peak current I pk =3 kA. There is no focusing channel. The initial bunch transverse size is σ x(,y) =10 μm. For this setup, the optical undulator period is λ u =10 μm, assuming a CO 2 laser, and the effective undulator rms parameter K=1.5. With this set of parameters, the FEL Pierce parameter is about ρ=3.0×10 −4 %3b hence, the saturation power at the end of exponential growth is about 140 MW. We double check this analytical calculation against a GENESIS simulation. The GENESIS code has been demonstrated to be correct in an optical undulator, since the analytical theory and the code built for optical undulator were consistent with the GENESIS simulation. The simulated FEL power is shown as the solid curve in FIG. 6A %3b the analytical power with gain length L G =0.7 mm is the dashed curve on FIG. 6A . With a total charge of 50 pC, there are about 1.4×10 10 photons/pulse. By using MHz repetition-rate lasers, this source has the capacity of generating high-repetitive X-ray photons of 10 16 -10 17 /s.","To compare with a hard X-ray source of 6.5 keV as reported in the literature, the centroid energy of electron bunch is 117 MeV, with the same other parameters and conditions as those for the above 1 keV FEL case. The FEL Pierce parameter for this case is about ρ=2.0×10 4 %3b hence, the saturation power is about 50 MW. Similarly, the GENESIS simulated FEL power and analytical power with L G =2.5 mm are shown as the solid and dashed curves in FIG. 6B , where a linear power growth is seen after the exponential growth ceases. With a total charge of 60 pC, there are about 1.0×10 9 photons with a 10 to 20 fs duration, in contrast to 2×10 7 photons in a 3.5 ps pulse reported in the literature.","Besides, if the quality of laser and beam does not support a high-gain FEL, for the spontaneous undulator radiation, the total photon flux in the forward cone is proportional to the square of the undulator periods, i.e., N 2 , and the total flux in the opening angle is proportional to N. Thus, the proposed lateral tilted lasers could significantly improve the total X-ray flux by extending the number of undulator periods by several orders.","D) Conclusions","To restate, by invoking two pulse front tilted lateral lasers, high-gain exponential growth makes possible generation of a FEL-type X-ray source via Thompson scattering. The critical improvement is lengthening the electron-laser synchronic interaction time by several orders%3b cylinder lenses or periodic microstructures are adopted to enhance the central electric field, realizing the high photon number 10 9 to 10 10 with femtoseconds duration, and the brightness enhanced by 4 to 5 orders."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIGS. 1A-B show two views of an embodiment of the invention.","FIG. 2A shows overlap of an electron beam and a pulse having a tilt between the pulse front and the phase front.","FIG. 2B shows a preferred temporal pulse shape.","FIG. 3 shows a microstructure suitable for forming a line focus","FIG. 4 shows a calculated field distribution for the example of FIG. 3 .","FIGS. 5A-B show further calculated field distributions for the example of FIG. 3 .","FIGS. 6A-B show calculated free electron laser output power for several cases."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,648,713","html":"https://www.labpartnering.org/patents/9,648,713","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,648,713"},"labs":[],"inventors":[{"name":"Chao Chang","location":"Beijing, CN, US"},{"name":"Chuanxiang Tang","location":"Beijing, CN, US"},{"name":"Juhao Wu","location":"Palo Alto, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}},{"name":"Tsinghua University","seq":2,"location":{"city":"Beijing","state":" CN","country":" US"}}],"claims":[{"idx":"00001","text":"Apparatus for producing X-rays, the apparatus comprising:at least one source of optical radiation configured to emit pulses of optical radiation%3bfocusing optics configured to bring two counter-propagating pulses of the optical radiation to a common line focus%3ban electron source configured to provide an electron beam aligned with the line focus%3bwherein the focusing optics include one or more dispersive optical elements configured to introduce a tilt angle between phase fronts of the counter-propagating pulses and pulse fronts of the counter-propagating pulses%3bwherein the tilt angle is selected to substantially match a velocity of pulse front propagation along the line focus with an electron velocity of the electron beam along the line focus%3b andwherein a standing wave pattern formed by the counter-propagating pulses at the line focus acts as an undulator for emission of X-rays by electrons in the electron beam."},{"idx":"00002","text":"The apparatus of claim 1, further comprising an X-ray resonator configured to provide feedback for the emitted X-rays, whereby a free electron laser is provided."},{"idx":"00003","text":"The apparatus of claim 1, wherein the dispersive optical elements comprise diffraction gratings having uniform line spacing."},{"idx":"00004","text":"The apparatus of claim 1, wherein the focusing optics comprise cylindrical mirrors."},{"idx":"00005","text":"The apparatus of claim 1, wherein the focusing optics comprise cylindrical lenses."},{"idx":"00006","text":"The apparatus of claim 1, wherein the focusing optics comprise a periodic microstructure configured to provide optical resonance of the counter-propagating pulses at the line focus."},{"idx":"00007","text":"The apparatus of claim 1, wherein the electron beam is configured as separated bunches of electrons."},{"idx":"00008","text":"The apparatus of claim 1, wherein the counter-propagating pulses are obtained by splitting an input pulse with an optical splitter, whereby relative jitter between the counter-propagating pulses is reduced."},{"idx":"00009","text":"The apparatus of claim 1, wherein a root mean square time variation of an electric field of the counter-propagating pulses is less than about 0.5%."}],"cpc":{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"G","subgroup":"00","main-group":"2","action-date":"2017-05-09","origination":"","symbol-position":"F","further":["05","","H","B","US","H","","G","00","2","2017-05-09","","F"]},"ipc":[{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"G","subgroup":"00","main-group":"2","action-date":"2017-05-09","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"S","subgroup":"00","main-group":"4","action-date":"2017-05-09","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"S","subgroup":"09","main-group":"3","action-date":"2017-05-09","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"S","subgroup":"00","main-group":"3","action-date":"2017-05-09","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"S","subgroup":"30","main-group":"3","action-date":"2017-05-09","origination":"","symbol-position":"L"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"04","main-group":"7","action-date":"2017-05-09","origination":"","symbol-position":"L"}],"document_number":"20160044771","document_published_on":"2016-02-11","document_kind":"","document_country":""},{"number":"9,646,074","artifact":"grant","title":"Method for discovering relationships in data by dynamic quantum clustering","filed_on":"2014-09-10","issued_on":"2017-05-09","published_on":"2015-01-29","abstract":"Data clustering is provided according to a dynamical framework based on quantum mechanical time evolution of states corresponding to data points. To expedite computations, we can approximate the time-dependent Hamiltonian formalism by a truncated calculation within a set of Gaussian wave-functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition and/or feature filtering.","description":{"text":["CROSS REFERENCE TO RELATED APPLICATIONS","This application is a continuation of U.S. patent application Ser. No. 12/586,036, filed Sep. 15, 2009, which claims the benefit of U.S. Provisional Patent Application No. 61/198,621, filed Nov. 7, 2008 and titled “Method for Discovering Relationships in Data by Dynamic Quantum Clustering”, the disclosures of which are hereby incorporated by reference in their entirety.","GOVERNMENT SPONSORSHIP","This invention was made with US government support under contract number DE-AC02-76SF00515 awarded by the Department of Energy. The government has certain rights in this invention.","FIELD OF THE INVENTION","This invention relates to data clustering.","BACKGROUND","Clustering of data is a well-known problem of pattern recognition. For our purposes, data clustering can be formulated as follows. Given a set of data-points, one looks for possible structures by sorting out which points are close to each other and, therefore, in some sense belong together. In general, data clustering is often ill-defined in a mathematical sense. Nonetheless, it is a very important problem in many scientific and technological fields of study. Data clustering is a preliminary analysis stage taken before investigating what properties are common to these subsets of the data. Some known approaches for data clustering make use of physical modeling and intuition.","One example of such an approach is known as quantum clustering (as described in US 2004/0117403 and in an article by Horn et al., “Algorithm for Data Clustering in Pattern Recognition Problems Based on Quantum Mechanics”, Phys. Rev. Lett. 88 018702 (2001), both of which are hereby incorporated by reference in their entirety). Briefly, in this approach, the data points are used to define a quantum state (e.g., this state can be composed of a linear combination of Gaussians centered at each data point). A potential function having this state as its ground state is calculated from the time-independent Schrödinger equation. The minima of this potential function provide helpful information for data clustering (e.g., in favorable cases, distinct minima of the potential function can identify the dusters). In this approach, there is a single scale parameter, which determines the scale at which cluster structures are identified.","In some cases, the performance of this quantum clustering approach can have an undesirably high sensitivity to the value of the quantum clustering scale parameter. Accordingly, it would be an advance in the art to provide data clustering having reduced parameter sensitivity. While the quantum wave function (i.e. Parzen function) can be quite sensitive to the choice of scale parameter, the details of the quantum potential are much less sensitive to this choice.","SUMMARY OF THE INVENTION","In the present work, quantum clustering is extended to provide a dynamical approach for data clustering using a time-dependent Schrödinger equation. To expedite computations, we can approximate the time-dependent Hamiltonian formalism by a truncated calculation within a set of Gaussian wave-functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition and/or feature filtering.","A method for data clustering is an embodiment of the invention. First, n data points are provided as an input to the method. Next, n initial states are defined corresponding to the n data points (e.g., each initial state can be centered on its corresponding data point). A potential function is determined such that a quantum mechanical ground state of the potential function is equal to the sum of the initial states. Quantum mechanical time evolution of the initial states in this potential function is calculated. Data point trajectories are determined from this time evolution (e.g., by computing the position expectations of the evolved states). Information (e.g., point positions, point separations etc.) derived from the trajectories is provided as an output. Preferably, this output is provided by way of an interactive color-coded visual display.","To better appreciate the present approach, it is helpful to compare it to diffusion geometry, which is a known dynamical framework for data clustering (e.g., as described in articles by Coifman et al., Proceedings of the National Academy of Sciences, 102(21), 7432-7437, (2005)%3b Lafon et al., IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1393-1403 (2006)%3b Nadler et al., Applied and Computational Harmonic Analysis 21, 113-127, (2006), the entirety of which is hereby incorporated by reference). Diffusion geometry is based on a discrete analog of the heat equation"," i ⁢ ∂ Φ ∂ t = H ⁢ ⁢ Φ , ( 1 ) where H is some operator with positive eigenvalues, guaranteeing that the temporal evolution of Φ({right arrow over (x)}, t) is that of diffusion. Thus, starting out with Φ({right arrow over (x)}, 0), e.g. a Gaussian concentrated around some data point one would expect Φ({right arrow over (x)}, t) to spread over all space that is occupied by the data points. Although dynamic quantum clustering (DQC) and diffusion geometry are both based on models drawn from physics, the underlying physical intuition is quite different in the two cases. Diffusion geometry relies on a random-walk model (i.e., stochastic dynamics), which leads to a diffusion equation for a data point probability density function. In contrast, DQC relies on a quantum-mechanical time evolution (i.e., deterministic dynamics). This can provide deterministic trajectories of data points (e.g., from position expectations).","Data clustering according to the present approach has numerous applications. In biology and medicine, data clustering can provide systematics in plant and animal classifications%3b analysis of high-throughput experiments, such as DNA microarrays for patient and gene classifications%3b search for modules of genes in genetic or metabolic networks%3b and medical image analysis to differentiate types of tissue and blood. In market research and applications, data clustering can provide analysis of multivariate data to determine association of consumer populations and products%3b and creating relevant data presentations on search engine and/or web sites. Other applications include deciphering structures in mathematical chemistry%3b using similarity of geological data to evaluate reservoir properties, relating chemical and biological properties in different environments, and analysis of security information.","DETAILED DESCRIPTION","Introduction","In this work we advocate the use of a Schrödinger Hamiltonian Ĥ that is intimately connected to the data-structure, as defined by the quantum clustering method summarized below. We extend it into a time-dependent Schrödinger equation:"," i ⁢ ∂ ψ ⁡ ( x → , t ) ∂ t = H ^ ⁢ ⁢ ψ ⁡ ( x → , t ) ( 2 ) The ensuing Dynamic Quantum Clustering (DQC) formalism allows us, by varying a few parameters, to study in detail the temporal evolution of wave-functions representing the original data-points. In turn, this dynamical behavior allows us to explore the structure of the quantum potential function defined by the quantum clustering method.","DQC begins by associating each data-point with a state in Hilbert space. The temporal development of the centroids of these states may be viewed in the original data-space as moving images of the original points. Their distances to each other change with time, thus representing associations they form with each other. Convergence of many points onto a common center at some instant of time is a clear manifestation of clustering. Many transitional relationships may occur, revealing substructures in clusters or even more complex associations. For this reason, we propose this approach as a general method for visually and interactively searching for and exploring structures in sets of data.","Quantum Clustering","The quantum clustering approach begins, as does the well-known Parzen-window estimator, by associating to each of n data points {right arrow over (x)} i in a Euclidean space of d dimensions a Gaussian wave-function"," ψ i ⁡ ( x → ) = ⅇ - ( x → - x → i ) 2 2 ⁢ ⁢ σ 2 and then constructing the sum of all these Gaussians,"," ψ ⁡ ( x → ) = ∑ i ⁢ ⅇ - ( x → - x → i ) 2 2 ⁢ ⁢ σ 2 ( 3 ) Conventional scale-space clustering views this function as a probability distribution (up to an overall factor) that could have generated the observed points, and regards therefore its maxima as determining locations of duster centers. Often these maxima are not very prominent and, in order to uncover more of them, one has to reduce a down to low values where the number and location of the maxima depend sensitively upon the choice of σ.","Quantum clustering took a different approach, requiring ψ to be the ground-state of the Hamiltonian"," H ^ ⁢ ⁢ ψ ≡ ( - σ 2 2 ⁢ ∇ 2 ⁢ + V ⁡ ( x → ) ) ⁢ ψ = E 0 ⁢ ψ ( 4 ) By positing this requirement, the potential function V({right arrow over (x)}) has become inextricably bound to the system of data-points, since V({right arrow over (x)}) is determined, up to a constant, by an algebraic inversion of Eq. 4. Moreover, one may expect V to have minima in regions where ψ has maxima and furthermore, that these minima will be more pronounced than the corresponding maxima found in the Parzen estimator. In fact, it frequently turns out that a concentration of data-points will lead to a local minimum in V, even if ψ does not display a local maximum. Thus, by replacing the problem of finding maxima of the Parzen estimator by the problem of locating the minima of the associated potential, V({right arrow over (x)}), we simplify the process of identifying clusters. The effectiveness of quantum clustering has been demonstrated, e.g., as described in the above-cited article by Horn et al. It should be noted that the enhancement of features obtained by applying Eq. 4 comes from the interplay of two effects: attraction of the wave-function to the minima of V and spreading of the wave-function due to the second derivative (kinetic term). This may be viewed as an alternative model to the conventional probabilistic approach, incorporating attraction to cluster-centers and creation of noise, both inferred from—or realized by—the given experimental data.","DQC drops the probabilistic interpretation of ψ and replaces it by that of a probability-amplitude, as customary in Quantum Mechanics. DQC is set up to associate data-points with duster centers in a natural fashion. Whereas in QC this association was done by finding their loci on the slopes of V, here we follow the quantum-mechanical temporal evolvement of states associated with these points. Specifically, we will view each data-point as the expectation value of the position operator in a Gaussian wave-function"," ψ i ⁡ ( x → ) = ⅇ - ( x → - x → i ) 2 2 ⁢ ⁢ σ 2 %3b the temporal development of this state traces the association of the data-point it represents with the minima of V({right arrow over (x)}) and thus, with the other data-points. Dynamic Quantum Clustering (DQC)","As we already noted, the conversion of the static QC method to a full dynamical one, begins by focusing attention on the Gaussian wave-function,"," C ⁢ ⁢ ψ i ⁡ ( x → ) = ⅇ - ( x → - x → i ) 2 2 ⁢ ⁢ σ 2 , associated with the i th data point, where C is the appropriate normalization factor. Thus, by construction, the expectation value of the operator {right arrow over (x)} in this state is simply the coordinates of the original data point%3b i.e., {right arrow over (x)} i = ψ i |{right arrow over (x)}|ψ i =∫d{right arrow over (x)}ψ i *({right arrow over ( x )}) {right arrow over (x)}ψ i ({right arrow over ( x )}).  (5) The dynamical part of the DQC algorithm is that, having constructed the potential function V({right arrow over (x)}), we study the time evolution of each state ψ i ({right arrow over (x)}) as determined by the time dependent Schrödinger equation%3b i.e.,"," i ⁢ ∂ ψ ⁡ ( x → , t ) ∂ t = H ^ ⁢ ⁢ ψ i ⁡ ( x → , t ) = ( - ∇ 2 2 ⁢ ⁢ m + V ⁡ ( x → ) ) ⁢ ψ i ⁡ ( x → , t ) ( 6 ) where m is an arbitrarily chosen mass for a particle moving in d-dimensions. If we set m=1/σ 2 then, by construction, ψ({right arrow over (x)}) of Eq. 3 is the lowest energy eigenstate of the Hamiltonian. If m is chosen to have a different value, then not only does each individual state ψ({right arrow over (x)}) evolve in time, but so does the sum of the states, ψ({right arrow over (x)}).","The important feature of quantum dynamics, which makes the evolution so useful in the clustering problem, is that according to Ehrenfest%27s theorem, the time-dependent expectation value ψ i ( t )| {right arrow over (x)}|ψ i ( t ) =∫ d{right arrow over (x)}ψ i *( {right arrow over (x)},t ) {right arrow over (x)}ψ i ( {right arrow over (x)},t )  (7) satisfies the equation, "," ⅆ 2 ⁢ 〈 x → ⁡ ( t ) 〉 ⅆ t 2 = ⁢ - 1 m ⁢ ∫ ⅆ x → ⁢ ψ i * ⁡ ( x → , t ) ⁢ ∇ → ⁢ V ⁡ ( x → ) ⁢ ψ i ⁡ ( x → , t ) = ⁢ 〈 ψ i ⁡ ( t ) ⁢  ∇ → ⁢ V ⁡ ( x → )  ⁢ ψ i ⁡ ( t ) 〉 ⁢ ( 9 ) ( 8 ) If ψ i ({right arrow over (x)}) is a narrow Gaussian, this is equivalent to saying that the center of each wave-function rolls towards the nearest minimum of the potential according to the classical Newton%27s law of motion. This means we can explore the relation of this data point to the minima of V({right arrow over (x)}) by following the time-dependent trajectory {right arrow over (x)} i ( t ) = ψ i ( t )| {right arrow over (x)}|ψ i ( t ) . Clearly, given Ehrenfest%27s theorem, we expect to see any points located in, or near, the same local minimum of V({right arrow over (x)}) to oscillate about that minimum, coming together and moving apart. In our numerical solutions, we generate animations that display this dynamics for a finite time. This allows us to visually trace the clustering of points associated with each one of the potential minima.","In the above-cited paper by Horn et al., classical gradient descent was successfully used to duster data by moving points (on classical trajectories) to the nearest local minimum of V({right arrow over (x)}). The idea being that points which end up at the same minimum are in the same duster. At first glance, it would seem that DQC replaces the conceptually simple problem of implementing gradient descent with the more difficult one of solving complicated partial differential equations. We will show the difficulty is only apparent. In fact, the solution of the Schrödinger equation can be simplified considerably and allow further insights than the gradient descent method.","The DQC algorithm translates the problem of solving the Schrödinger equation into a matrix form which captures most of the details of the analytic problem, but which involves N×N matrices whose dimension, N, is less than or equal to the number of data points. This reduction is independent of the data-dimension of the original problem. From a computational point of view, there are many advantages to this approach. First, the formulas for constructing the mapping of the original problem to a matrix problem are all analytic and easy to evaluate, thus computing the relevant reduction is fast. Second, the evolution process only involves matrix multiplications, so many data points can be evolved simultaneously and, on a multi-core processor, in parallel. Third the time involved in producing the animations showing how the points move in data space scales linearly with the number of dimensions to be displayed. Finally, by introducing an m that is different from 1/σ 2 we allow ourselves the freedom of employing low a, which introduces large numbers of minima into V, yet also having a low value for m that guarantees efficient tunneling, thus connecting points that may be located in nearby, nearly degenerate potential minima. By using this more general Hamiltonian, we reduce the sensitivity of the calculation to the specific choice of a.","One final point worth making before describing the method of calculation is that the use of Gaussian wave-functions to represent data points allows us to develop a number of flexible strategies for handling very large data sets. This issue will be addressed below.","The Calculation Method","Before discussing how this method works in practice we will give a brief outline of the details of the genera procedure. We begin by assuming that there are n data points that we wish to duster. To these data points we associate n states, |ψ i . These states are n Gaussian wave-functions such that the i th Gaussian is centered on the coordinates of the i th data point. These states form a basis for the vector space within which we calculate the evolution of our model.","Let us denote by N, the n×n matrix formed from the scalar products N i,j = ψ i |ψ j   (10) and by H , the n×n matrix H i,j = ψ i |Ĥ|ψ j   (11) and by {right arrow over (X)} i,j the matrix of expectation values {right arrow over (X)} i,j = ψ i |{right arrow over (x)}|ψ j   (12) ","The calculation process can be described in five steps. First, begin by finding the eigenvectors of the symmetric matrix N which correspond to states having eigenvalues larger than some pre-assigned value%3b e.g., 10 −5 . These vectors are linear combinations of the original Gaussians that form an orthonorrnal set. Second, compute H in this orthonormal basis, H tr . Do the same for {right arrow over (X)} i,j . Fourth, find the eigenvectors and eigenvalues of H tr , construct |ψ i (t) =e −itH tr |ψ , that is the solution to the reduced time dependent Schrödinger problem"," ⅈ ⁢ ∂ ∂ t ❘ ψ i ⁡ ( t ) 〉 = H tr ❘ ψ i ⁡ ( t ) 〉 ( 13 ) such that |ψ i (t=0) =|ψ i . Finally, construct the desired trajectories {right arrow over (x)} i ( t ) = ψ i |e itH tr {right arrow over (X)}e −itH tr |ψ i   (14) by evaluating this expression for a range of t and use them to create an animation. Stop the animation when clustering of points is apparent.","It is clear that restricting attention to the truncated Hamiltonian perforce loses some features of the original problem, however its advantage is that we can derive analytic expressions for all operators involved (see Appendices A and B). As a result, the numerical computations can be done very quickly. Experience has shown that as far as clustering is concerned this approximation causes no difficulties.","EXAMPLE","Ripley%27s Crab Data","To test our method we apply it to a five-dimensional dataset with two hundred entries, used in Ripley%27s text book (B. D. Ripley, “Pattern Recognition and Neural Networks”, Cambridge University Press, Cambridge UK, 1996, hereby incorporated by reference in its entirety). This dataset records five measurements made on male and female crabs that belong to two different species. This dataset has been used in the original paper on quantum clustering by Horn et al. cited above. It is being used here to allow readers to compare the two techniques. Applications to other data sets will be discussed below. Our main motivation is to provide a simple example that exhibits the details of the DQC method. In particular, we wish to show that the simplest computational scheme for implementing the general program captures the essential features of the problem and does as well as one can reasonably expect to do.","The data is stored in a matrix M which has 200 rows and 5 columns. Following an often-used dimensional reduction method, we preprocess our data with a singular-value decomposition M=USV †   (15) where U is a unitary 200×200 matrix and S is the 200×5 matrix of singular values, the latter occurring on the diagonal of its upper 5×5 entries. The sub-matrix of U consisting of the first five columns, the so-called five Principal Components (PCs), can be thought of as assigning to each sample a unique point in a five-dimensional vector space. We may study the problem in the full five-dimensional space or within any subspace by selecting appropriate principal components. In the above cited article by Horn et al., QC was applied to this problem in a 2-dimensional subspace, consisting of PC2 and PC3. In what follows, we will discuss the application of DQC to the 3-dimensional data composed of the first three PCs (although there would be no change in the results if we used all five dimensions).","In order to give the reader some feeling for how the quantum potential associated with the data looks in a simple case, we have included FIG. 1 where we exhibit the original data points with different colors of points correspond to known classes (green 110 , orange 112 , blue 114 , red 116 ), placed upon the associated two-dimensional quantum potential, where the coordinates of the data points are chosen to be given by the second and third principal components. As is apparent from the plot the minima of the potential function do a very good job of capturing the different clusters. Moreover, letting data points roll downhill to the nearest minimum will produce a reasonable separation of the clusters.","Clearly, when we restrict attention to the first three PCs, the rows of the matrix obtained by restricting U to its first three columns are not guaranteed to be normalized to unity. Hence, we employ the conventional approach of projecting all points onto the unit sphere.","In what follows we study the temporal behavior of the curves {right arrow over (x)} i (t) , for all i. Henceforth we will refer to this as the “motion of points”.","FIG. 2 a shows the distribution of the original data points plotted on the unit sphere in three dimensions. This is the configuration before we begin the dynamic quantum evolution. To visually display the quality of the separation we have colored the data according to its known four classes, however this information is not incorporated into our unsupervised method. To begin with, we see that the two species of crabs ((red 216 , blue 214 ) and (orange 212 , green 210 )) are fairly well separated%3b however, separating the sexes in each species is problematic.","FIG. 2 b shows the distribution of the points after a single stage of quantum evolution, stopped at a time when points first cross one another and some convergence into clusters has occurred. It is immediately apparent that the quantum evolution has enhanced the clustering and made it trivial to separate clusters by eye. Once separation is accomplished, extracting the clusters can be performed by eye from the plots or by any conventional technique, e.g. k-means.","FIG. 2 c shows the results of an additional iteration of DQC. In this example, the values of parameters used to construct the Hamiltonian and evolution operator are σ=0.07 and m=0.2. Colors indicate the expert classification of data into four classes, unknown to the clustering algorithm. Note, small modifications of the parameters lead to the same results.","An alternative way of displaying convergence is shown in FIGS. 3 a - c , where we plot the Euclidean distance from the first point in the dataset to each of the other points. FIG. 3 a shows the distances for the initial distribution of points. FIG. 3 b shows the same distances after quantum evolution. FIG. 3 c shows results after another iteration of DQC. The numbering of the data-points is ordered according to the expert classification of these points into four classes (red 316 , blue 314 , orange 312 , green 310 ) containing 50 instances each.","The clusters lie in bands that have approximately the same distance from the first point. It is difficult to get very tight clusters since the points, while moving toward cluster centers, oscillate around them, and arrive at the minima at slightly different times. Given this intuition, it is clear that one way to tighten up the pattern is to stop DQC evolution at a point where the clusters become distinct, and then restart it with the new configuration, but with the points redefined at rest. We refer to this as iterating the DQC evolution. When iterating the DQC evolution, a new potential V is computed based on the current point positions, then DQC evolution is performed in the new potential. FIGS. 2 c and 3 c show what happens when we do this. The second stage of evolution clearly tightens up the clusters significantly, as was expected.","By the end of the second iteration, there can be no question that it is a simple matter to extract the clusters. As is quite evident, clustering does not agree completely with the expert classification, i.e. points with different colors may be grouped together. This is, however, the best one can do by color-blind treatment of the information provided in the data-matrix. As we already noted, the full 5-dimensional study of the crab data-set can proceed in the same manner, although it does not lead to new insights.","Dynamic Distances","The fact that data-points of different classes happen to lie close to each other in the data-matrix can be due to various factors: errors in data measurements, errors in the expert assignment to classes, true proximity of data-points in spite of differences of origin (extreme example would be similarities of phenotypes in spite of differences in genotypes) or—the simplest possibility—the absence of some discriminative features in the feature-space that spans the data measurements. However, there is another important conceptual message to be learned here—clustering and/or classification may not capture all the interesting lessons that may be derived from the data. A similar message is included in the above-described Diffusion Geometry approach that advocates measuring diffusion-distances among points rather than Euclidean ones. Diffusion distances are influenced by the existence of all other points. In our DQC analysis this may be replaced in a straightforward manner by defining dynamic distances among points d i,j ( t )=∥ {right arrow over (x)} i ( t ) − {right arrow over (x)} j ( t ) ∥  (16) with the norm being Euclidean or any other suitable choice.","Clearly d i,j (0) is the geometric distance as given by the original data-matrix or by its reduced form that is being investigated. As DQC evolves with time d i,j (t) changes, and when some semi-perfect clustering is obtained, it will be close to zero for points that belong to the same cluster. FIGS. 3 a - c show this change in time for all d i,1 (t) in the crab-data example studied above. It is apparent that, in addition to the few cases in which clustering disagrees with classification, there are many intermediate steps where different data-points are close to each other in spite of eventually evolving into different clusters and belonging to different classes. Thus a close scrutiny of the dynamic distances matrix d i,j (t) may lead to interesting observations regarding the relationships among individual pairs of points in the original data, a relationship that is brought out by DQC as result of the existing information about all other data-points. It may be used to further investigate the reason for such proximities, along any one of the lines mentioned above, and thus may lead to novel insights regarding the problem at hand.","Analysis of Large Data Sets","There are many scientific and commercial fields, such as cosmology, epidemiology, and risk-management, where the data sets of interest contain many points, often also in large numbers of dimensions. We have already discussed how to overcome the problem of large dimensions. Dealing with large number of points requires yet a new angle. In problems of this sort it is clear from the outset that, especially on a personal computer (PC), diagonalizing matrices which are larger than 2000×2000 is computationally intensive. It is clear that using brute force methods to evolve sets of data having tens of thousands of points simply will not work. The solution to the problem of dealing with sets of data containing tens of thousands of entries each with N features, lies in the fact that the Singular Value Decomposition (SVD) decomposition maps the data into an N-dimensional cube, and the fact that the data points are represented by states in Hilbert space rather than N-tuples of real numbers. Since there is a literature on ways to do SVD decomposition for large sets of data, we will not address this point here. What we do wish to discuss is how to exploit the representation of data points as states in Hilbert space in order to evolve large sets of data.","The trick is to observe that since Gaussian wave-functions whose centers lie within a given cube have non-vanishing overlaps, as one chooses more and more wave-functions one eventually arrives at a situation where the states become what we will refer to as essentially linearly dependent. In other words, we arrive at a stage at which any new wave-function added to the set can, to some predetermined accuracy, be expressed as a linear combination of the wave-functions we already have. Of course, since quantum mechanical time evolution is a linear process, this means that this additional state (which can be regarded as an auxiliary state) can be evolved by expressing it as a linear combination of the previously selected states and evolving them. Since computing the overlap of two Gaussians is done analytically (Appendix B) determining which points determine the set of maximally essentially linearly independent states for the problem is easy. Typically, even for data sets with 35,000 points, this is of the order of 1000 points. This works because, as we have already noted, we do not need high accuracy for DQC evolution. The quality of the clustering degrades very slowly with loss in accuracy. Thus, we can compute the time evolution operator in terms of a well-chosen subset of the data and then apply it to the whole set of points. This is particularly attractive for new multi-core PCs and for computer clusters, since it is possible, even in high-level languages, to write multi-threaded programs that farm the multiplication of large numbers of vectors out to different processors. This means that one can achieve a great improvement in the speed of the computation for very little additional work.","To demonstrate this versatility of DQC we have analyzed a set of 35,213 points in 20 dimensions. We are grateful to JoAnne Hewett and Tom Rizzo for providing us with this example. The points in the plot represent sample super-symmetric models for physics beyond the Standard Model that satisfy all experimental constraints in a parameter space of twenty dimensions. This data-set definitely shows some non-trivial variations in density that can be made apparent by a visual inspection of the data plotted in different dimensional combinations. However, DQC is needed to obtain good visual deciphering of the different structures. Selecting a subset of 1200 points, whose Gaussians we consider to be a set of essentially linearly independent states for the problem, we construct H tr . By expanding the remaining states in terms of these 1200 states we can easily evaluate the DQC evolution of all 35,213 points. The results are displayed in FIGS. 4 a - d. ","More specifically, FIGS. 4 a - d are plots of the first three principal components for this large data-set, before and after DQC evolution. Three stages of DQC development are shown. Thus, FIG. 4 a is the initial configuration, FIG. 4 b is after one iteration of DQC, FIG. 4 c is after 2 iterations of DQC, and FIG. 4 d is after 3 iterations of DQC. The coloring was decided upon by selecting the most apparent clusters from the evolved data and assigning colors to them—light blue 410 , pink 412 , orange 416 , green 418 , red 420 , and gray 422 . The dark blue points 414 correspond to points that were not assigned to dusters. The purpose of coloring is to be able to look at the points in the original data, discern those that belong to common structures, and follow their dynamic distances under DQC evolution.","It seems very clear how the structures develop with DQC. Using the last DQC stage, it is possible to identify the main structures and assign each substructure a different color. One can then examine the colored version of a plot of the individual data points, discern the structures that belong together, and follow the DQC development tracing out dynamic distances between the different points and structures in all dimensions.","Interplay of Feature Selection with DQC","Data exploration involves not only the instances, or data-points, but also the features (coordinates) with which the instances are defined. By performing SVD, and selecting a subset of coordinates, we define superpositions of the original features within which we search for clustering of the instances. In problems with very many features, it is advantageous to also perform some feature filtering, employing a judicious selection of subsets of the original features. Clearly, the effectiveness of preprocessing data using some method for selecting important features is well appreciated. What we wish to show in this discussion is how easily one distinguishes the effects of feature filtering in our visual approach and how easy it is, in problems where one has an expert classification, to see if the unsupervised method used to select important features is working well. Furthermore, we wish to show the power of combining iterations of an SVD based feature filtering algorithm in conjunction with iterations of DQC. To do this we will show what happens when one applies these ideas to the dataset of Golub et al. (Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science 286 531 (1999), hereby incorporated by reference in its entirety).","The Golub et al. dataset contains gene chip measurements on cells from 72 leukemia patients with two different types of Leukemia, ALL and AML. The expert identification of the classes in this data set is based upon dividing the ALL set into two subsets corresponding to T-cell and B-cell Leukemia. The AML set is divided into patients who underwent treatment and those who did not. In total, the apparatus used in this experiment measured the expression of 7129 genes. The feature filtering method we employ is based on SVD-entropy, and is a simple modification of a method introduced by Varshaysky et al. (Novel Unsupervised Feature Filtering of Biological Data, Bioinformatics 22 no, 14 (2006), e507-e513, hereby incorporated by reference in its entirety) and applied to the same data.","The method begins by computing the SVD-based entropy of a dataset M (matrix of n instances by m features of Eq. 15) based on the eigenvalues s j of its diagonal matrix S. Defining normalized relative variance values"," v j = s j 2 ∑ k ⁢ ⁢ s k 2 , the dataset entropy is defined through"," E = - 1 log ⁢ ⁢ r ⁢ ∑ j = 1 r ⁢ ⁢ v j ⁢ log ⁡ ( v j ) ( 17 ) where r is the rank of the data-matrix, typically much smaller than m. Given the dataset entropy of the matrix M, define the contribution of the i th feature to the entropy using a leave-one-out comparison%3b i.e., for each feature we construct the quantity CE i =E ( M (n×m) )− E ( M (n×(m−1)) )  (18) where the second entropy is computed for the matrix with the i th feature removed. Our filtering technique will be to remove all features for which CE i ≦0.","FIG. 5 a displays the raw data for this example in the 3-dimensional space defined by PCs 2 to 4 . FIG. 5 b displays the effect that DQC has on these data, using σ=0.2 and a mass m=0.01. The different classes are shown as blue 510 , red 512 , green 514 and orange 516 . Clearly, without the coloring it would be hard to identify dusters.","In FIGS. 6 a - b we see the result of applying feature filtering to the original data, represented in the same 3 dimensions, followed by DQC evolution. FIG. 6 a is the Golub data after one stage of SVD-entropy based filtering, but before DQC evolution. FIG. 6 b is the same data after DQC evolution. Applying a single stage of filtering has a dramatic effect upon clustering, even before DQC evolution. The latter helps sharpening the duster separation,","FIGS. 7 a - b show the results of three iterations of SVD-entropy, before and after DQC evolution. FIG. 7 a is the data after three stages of SVD-entropy based filtering, but before DQC evolution. FIG. 7 b is the same data after DQC evolution. These plots, especially the after DQC pictures, show dramatic clustering, especially for the blue points 510 . With each stage of filtering, we see that the blue points 510 cluster better and better, in that the single red outlier 512 separates from the cluster and the cluster separates more and more from the other points. The blue points 510 are what we will refer to as a clearly robust cluster that has been identified in early stages of filtering. If one continues iterating past the fifth stage, however, the clear separation of the blue points 512 from the others ( 512 , 514 , 516 ) begins to diminish. Thus, we see that the SVD-entropy based filtering, in trying to enhance the clumping of the red points, starts throwing away those features that make the blue cluster distinct. Since this effect is quite pronounced we would say that features that are important to distinguishing the blue cluster from the others begin to be removed at the sixth and higher iterations of filtering. This is, of course, just what we are looking for, a way of identifying those features that are important to the existing biological clustering. Out of the original 7129 features, we have reduced ourselves to 2766 features by the fifth iteration. In going from step five to step six this gets further reduced to 2488 features, so we could begin searching among the 278 eliminated features to isolate those most responsible for the separation of the blue cluster from the others. Instead, we will take another track and, since it is so robust and easily identified, remove the blue cluster from the original data and repeat the same process without this cluster. The idea here is that now the SVD-entropy based filtering will not be pulled by the blue duster and so it will do a better job of sorting out the red, green, and orange dusters. As we will see, this is in fact the case.","In FIGS. 8 a - b we see plots of what the starting configurations look like if one takes the original data, removes the identified blue duster 510 and re-sorts the reduced data set according to the SVD-entropy based filtering rules. FIG. 8 a is what happens if one filters a single time, removing those features, i, whose one-left-out comparison, CE i , is less than or equal to zero. FIG. 8 b shows what happens if one repeats this procedure two more times, each time removing features for which CE i ≦0. There is no problem seeing that each iteration of the SVD-entropy based filtering step improves the separation of the starting clusters. By the time we have done five SVD-entropy based filtering steps the red 512 , green 514 , and orange 516 clusters are distinct, if not clearly separated.","Finally, to complete our discussion, we show FIGS. 9 a - c . These figures show the results of doing five iterations of the SVD-entropy based filtering and following that with three stages of DQC evolution. FIG. 9 a is what the starting data looks like if one first removes the blue points and does five stages of SVD-entropy based filtering. FIG. 9 b is what happens after one stage of DQC evolution. FIG. 9 c is the final result after iterating the DQC evolution step two more times. At this point, the clusters are trivially extracted.","The dramatic clustering accomplished by DQC evolution makes it easy to extract clusters. Note however, that in FIG. 9 b we see what we have seen throughout, that the red points 512 first form two distinct sub-clusters that only merge after two more stages of DQC evolution. This constant repetition of the same phenomenon, which is only made more apparent by SVD-entropy based filtering, is certainly a real feature of the data. It presumably says that what appears to be a sample of a single type of cell at the biological level is in reality two somewhat different types of cells when one looks at gene expression. A measure of the success of clustering is given by the Jaccard score which, for this result is 0.762, and is higher than the value 0.707 obtained by Varshaysky et al. in the above-cited article. The Jaccard score is evaluated by considering all pairs of data points, and asking if they duster together and if they fit in the same class, as judged by the expert. The Jaccard score is then defined by"," J = tp tp + fp + fn , where tp, fp, and fn, stand for true-positive, false-positive and false-negative, correspondingly.","CONCLUSION AND OUTLOOK","We have proposed a dynamical method for exploring proximity relationships among data-points in large spaces. Starting with the potential function of quantum clustering we have shown how to embed it into a dynamical theory so as to provide a visual exploratory tool. Formulating the theoretical treatment using coherent (Gaussian) states allows us to derive analytic expressions for all necessary calculations of the temporal evolution. This allows us to treat quite complicated data and put them into a visual framework that can be easily manipulated by the user who wishes to search for structures in the data. We have tested the system on random data to make sure that it does not produce unwarranted clustering structures.","Throughout this text, we represent the DQC evolution of the Gaussians associated with the original data-points, by following the centers of the evolving wave-functions. It should be noted that there is more information to be gained from the full wave-function of a data-point: it is expected to expand, at times, and cover a large fraction of the domain of the cluster with which this point is associated. It may also tunnel into neighboring clusters with which the point has small dynamic distances. We expect this notion to be particularly useful when the data may be better described in terms of ‘elongated clusters’, i.e. when cluster cores are not points but lines (e.g. a ring) or higher-dimensional manifolds. Note that our methodology is not confined to potentials that have only well-separated minima.","We have discussed the virtues of combining DQC with some preprocessing tools. The first was SVD, which was used to limit the range of the data values and to allow us to do some dimensional reduction. While dimensional reduction is a must for handling data in very large dimensions, and it helps to remove noise from the data, we wish to point out that DQC can handle a large number of features without much difficulty. The computational complexity of the problem is controlled by the number of data-points, since this defines the size of the matrix to be exponentiated. The computational cost associated with keeping more features is only related to computing the matrices associated with multiplying a wave-function by a given coordinate. This is a one-time cost. The computational cost of computing the values of these operators only grows linearly with the number of features. Clearly it is possible to avoid these costs by keeping a large number of features when constructing the quantum potential, V({right arrow over (x)}), and plotting a much smaller number of features when constructing the animations. Experience has shown that after one stage of DQC evolution, clustering which occurs because of structures in V({right arrow over (x)}) that are only seen in features that are not plotted in the animations becomes readily visible in those plots that we do construct. This aspect of DQC allows us to avoid some of the problems associated with using SVD to strongly reduce the number of dimensions. In addition to dimensional reduction based upon simply making an SVD decomposition of the data, we discussed one scheme for selecting individual features that are judged to be relevant to the data at hand. Since our problem is unsupervised, we employed a feature filtering method that depends on the contribution of the features to SVD-entropy. The examples showed that the visual nature of DQC made it easy to judge the effectiveness of feature filtering, especially after iterative applications of DQC evolution.","We have already noted, that for sets of data containing entries with a very large number of features, DQC has the computational advantage that once one has formed the Hamiltonian of the system, the computational problem is carried out using a matrix which has no more rows and columns than the number of data points. Moreover, we have seen that the simplest reduction of the analytic problem of assigning data points to minima of the multi-dimensional potential function works remarkably well. Going beyond the truncation procedure explained in Appendix B, while easily doable, seems unnecessary for most problems, and this allows us to greatly speed up the computations. In our analysis, we went on to discuss the case of data sets containing large numbers of points. It turns out that, using our Hilbert space representation of data-points, we can naturally select a small set of points whose Gaussians span efficiently the entire Hilbert space. These Gaussians are then used as the basis for calculating the DQC evolvement of all points. It is apparent from the example displayed in FIGS. 4 a - d how well these properties of DQC can be employed to discern structures in the large data-set under consideration.","Finally, we wish to observe that our DQC methods can be easily extended to general classification problems that are usually resolved by supervised machine learning methods. The point is that given a training set, i.e., a data set that has been fully resolved by DQC once the appropriate stages of dimensional reduction and feature filtering has been applied, then one can use this set to classify new data. There are two different ways one can accomplish this task. In the first approach we use the fact that the training set has been successfully clustered to assign distinct colors to points that lie in the training set, so that they may be visually identify in all subsequent studies. Once this has been done, the classification of new data points can be accomplished in two steps. First, reduce the SVD matrix containing both the training set and the new data points (using the previously determined features) to an appropriate dimension, and construct the QC potential for the full data set including the training set. Next, apply DQC In study the evolution of the full system using the new QC potential and see how the new points associate themselves with the points in the training set. Note, as always, both the intermediate dynamics and eventual coalescence of the full set into clusters can give useful information about the full data set. The fact that the old points have been colored according to the original classification scheme makes it possible to see if the SVD reduction of the full data set (training set plus new data) distorts the original classification. If this happens, i.e. if the original points fail to cluster properly, then one can go back and use the tools of feature filtering, etc. to analyze what has changed. This sort of visual identification of aspects of the data that distort clustering was already used in the case of the leukemia data set to see that the existence of a strong cluster can distort the clustering of the remaining data. Once this easily identified cluster was removed from the data set the clustering of the remaining data was significantly improved.","The second approach, which is necessary if the dataset contains many entries and the training set is itself large, is to use only the training set to generate the quantum potential and the exponential of the Hamiltonian. Next, as we already discussed, use this operator to evolve the full dataset, including the training set. In this case, the training set is guaranteed to cluster as before and we can categorize the new points according to how they associate with known clusters in the training data.","The preceding description has been by way of example as opposed to limitation, and many variations of the given examples can also be employed in practicing embodiments of the invention. For example, the quantum-mechanical Schrödinger formalism (i.e., time-dependent states, time-independent operators) has been employed to calculate expected positions. The above development can also be equivalently expressed in the Heisenberg formalism (time-dependent operators, time-independent states), since it is well known in the art that calculated results (i.e., expected positions) do not depend on which of these formalisms is employed.","As another example, it is possible to generalize the quantum mechanical time evolution by including a small diffusion component, so that time evolution is governed by"," i 1 - i ⁢ ⁢ ɛ ⁢ ∂ ψ i ⁡ ( x ⇀ , t ) ∂ t = H ^ ⁢ ⁢ ψ i ⁡ ( x ⇀ , t ) , ( 19 ) where e is the diffusion parameter. In this approach, it is necessary to modify the expectation calculations to properly account for non-unitary time evolution.","APPENDIX A","Useful Operator Identities","Using conventional quantum-mechanical notation we represent the Gaussian wave-function by"," ❘ σ 〉 = ( π ⁢ σ ) - 1 2 ⁢ ⅇ - x 2 / 2 ⁢ σ 2 ( 20 ) where we adopted Dirac%27s bra and ket notation to denote |ψ =ψ( x ) and ψ|=ψ( x )*. Employing the operators x and"," p = 1 i ⁢ ⅆ ⅆ x obeying the commutation relations [x, p]=i, we define the annihilation operator"," A σ = i ⁢ σ 2 ⁢ p + 1 σ ⁢ 2 ⁢ x ( 21 ) obeying A σ |σ =0. its Hermitian adjoint creation operator can be"," A σ † = - i ⁢ σ 2 ⁢ p + 1 σ ⁢ 2 ⁢ x ⁢ ⁢ obeys ⁢ [ A σ , A σ † ] = 1. ","We will need a few identities to derive the matrix elements we have to calculate. First we note the normal ordering identity (meaning rewriting by using the operator commutation relations so that A σ %27s appear to the right of all A σ † %27s): e α(A α † +A σ ) =e α 2 /2 c αA σ † e αA σ   (22) which may be proven by differentiation with respect to α. Next we note that"," ⅇ g ⁡ ( α ) ⁢ A σ † ⁢ A σ ⁢ ⅇ - g ⁡ ( α ) ⁢ A σ † = ∑ n ⁢ ⁢ g ⁡ ( α ) n n ! [ A σ † , [ A σ † , [ ⁢ ⋯ ⁢ , [ A σ † , A σ ] ] ] ⁢ ⁢ ⋯ ⁢ ] n = A σ - g ⁡ ( α ) ( 23 ) which is easily derived by differentiating with respect to g and noting that only the first commutator is non-zero. A similar calculation proves the equally useful result: e α(A α † −A σ ) =e α 2 /2 c αA σ † e −αA σ   (22) ","Now, because the Parzen window estimator is constructed using Gaussian wave-functions centered about points other than x=0, it is convenient to have an operator expression which relates the Gaussian centered about x=0 to the Gaussian centered about x={right arrow over (x)}.","Theorem: |σ, {right arrow over (x)} =e −ip{right arrow over (x)} |σ is a normalized Gaussian wave-function centered at x={right arrow over (x)}%3b i.e."," ❘ σ , x _ 〉 = ( π ⁢ σ ) - 1 2 ⁢ ⅇ - ( x - x _ ) 2 / 2 ⁢ σ 2 ( 25 ) This state is known as a coherent state, obeying A σ |σ,{right arrow over (x)} = {right arrow over (x)}|σ,{right arrow over (x)}   (26) ","The generalization to Gaussians in any number of dimensions is straightforward, since they are just products of Gaussians defined in each one of the different dimensions.","APPENDIX B","Matrix Elements","The states we start out with |σ,{right arrow over (x)} i norm one and are, in general, linearly independent%3b however, they are not orthogonal to one another. In what follows we will need an explicit formula for the scalar product of any such Gaussian with another |σ,{right arrow over (x)} i . This is easily derived given the operator form for the shifted Gaussian derived in Appendix A. Thus we find that σ, {right arrow over (y)}|σ,{right arrow over (x)} = σ|e −ip({right arrow over (x)}−{right arrow over (y)}z |σ =e −({right arrow over (x)}−{right arrow over (y)}) 2 /4σ 2   (27) which is needed for computing the matrix of scalar products N i,j = σ,{right arrow over (x)} i |σ,{right arrow over (x)} j . Similarly, by employing e lp{right arrow over (y)} xe −ip{right arrow over (y)} =x+{right arrow over (y)} we find that"," 〈 σ , y _ ⁢  x  ⁢ σ , x _ 〉 = ( x _ + y _ ) 2 ⁢ ⅇ - ( x _ - y _ ) 2 / 4 ⁢ σ 2 ( 28 ) It is straightforward to generalize this derivation to obtain"," 〈 σ , y _ ⁢  V ⁡ ( x )  ⁢ σ , x _ 〉 = ⅇ - ( x _ - y _ ) 2 / 4 ⁢ σ 2 ⁢ 〈 σ ⁢  V ⁡ ( x + x _ + y _ 2 )  ⁢ σ 〉 ( 29 ) for any function V(x). Note that this expectation value can be evaluated by expanding V in a Taylor series about the point ({right arrow over (x)}+{right arrow over (y)})/2. The leading term is simply"," ⅇ - ( x _ - y _ ) 2 / 4 ⁢ σ 2 ⁢ V ⁡ ( x _ + y _ 2 ) and the remaining terms, involving σ|x n |σ can be evaluated from the identity"," 〈 σ ⁢  ⅇ α ⁢ ⁢ x  ⁢ σ 〉 = ∑ n = 0 ∞ ⁢ ⁢ α n n ! ⁢ 〈 σ ⁢  x n  ⁢ σ 〉 = ∑ p = 0 ∞ ⁢ ⁢ α 2 ⁢ p 4 p ⁢ σ 2 ⁢ p p ! ( 30 ) ","To speed up computations we chose to approximate all expectation values of V(x) by"," V ⁡ ( x _ + y _ 2 ) , the first term in this series. A more accurate approximation to the original problem can be obtained by including additional terms but explicit computation has shown that, for our purposes, this level of accuracy is sufficient.","The final formula we need to derive is that for"," 〈 σ , y _ ⁢  p 2  ⁢ σ , x _ 〉 = 〈 σ ⁢  p 2 ⁢ ⅇ - ⅈ ⁢ ⁢ p ⁡ ( x _ - y _ )  ⁢ σ 〉 = ( x _ - y _ ) 2 2 ⁢ σ 2 ⁢ ⅇ - ( x _ - y _ ) 2 / 4 ⁢ σ 2 ( 31 ) With these preliminaries behind us, it only remains to describe the mechanics of the DQC evolution process, where we evaluate the Hamiltonian truncated to an n×n matrix in the non-orthonormal basis of shifted Gaussians: H i,j = σ,{right arrow over (x)} i |Ĥ|σ,{right arrow over (x)} j   (32) The time evolution of our original states is computed by applying the exponential of the truncated Hamiltonian to the state in question%3b i.e. |σ,{right arrow over ( x )} ( t )= e −iHt |σ,{right arrow over (x)} . Computing the exponential of the truncated operator is quite simple, except for one subtlety: we have defined H by its matrix elements between a non-orthonormal set of states. Hence, to perform the exponentiation, we first find the eigenvectors and eigenvalues of the metric N ij and use them to compute the matrix N i,j −1/2 . If our original set of states is not linearly independent, then N i,j will have some zero eigenvalues. Clearly, we throw their corresponding eigenvectors away when computing N i,j −1/2 . In practice we discard all vectors whose eigenvalue is smaller than a predetermined threshold (e.g., 10 −5 ) selected to balance numerical efficiency and accuracy.","Then we construct the transformed"," H i , j tr = ∑ k , l ⁢ ⁢ N i , k - 1 / 2 ⁢ H k , l ⁢ N l , j - 1 / 2 ( 33 ) Now we can construct the exponential of this operator by simply finding its eigenvectors and eigenvalues. In order to compute the time evolution of one of the original states we simply write them in terms of the orthonormal basis.","The only step which remains is to explain how we compute the expectation values of the operator x as functions of time: we first construct, for each component, the operator X i,j = σ,{right arrow over (x)} i |x|σ,{right arrow over (x)} j   (34) and use N i,j −1/2 to put this into the same basis in which we exponeniate H%3b i.e., construct"," X i , j = ∑ k , l ⁢ ⁢ N i , k - 1 / 2 ⁢ X k , l ⁢ N l , j - 1 / 2 . ( 35 ) "],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 is a plot of a quantum potential function relating to a quantum clustering example.","FIGS. 2 a - c show initial (a), intermediate (b) and final (c) point positions relating to a dynamic quantum clustering example.","FIGS. 3 a - c show initial (a), intermediate (b) and final (c) point separations from the first point relating to a dynamic quantum clustering example.","FIGS. 4 a - d show initial (a), intermediate (b and c) and final (d) point positions relating to a dynamic quantum clustering example of a large and high-dimensional data set.","FIGS. 5 a - b show initial (a) and final (b) point positions relating to a dynamic quantum clustering example.","FIGS. 6 a - b show initial (a) and final (b) point positions relating to a dynamic quantum clustering example.","FIGS. 7 a - b show initial (a) and final (b) point positions relating to a dynamic quantum clustering example.","FIGS. 8 a - b show intermediate (a) and final (b) point positions relating to a SVD-entropy clustering example.","FIGS. 9 a - c show initial (a), intermediate (b) and final (c) point positions relating to a combined DQC and SVD-entropy example."]},"government_interest":"GOVERNMENT SPONSORSHIP This invention was made with US government support under contract number DE-AC02-76SF00515 awarded by the Department of Energy. The government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,646,074","html":"https://www.labpartnering.org/patents/9,646,074","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,646,074"},"labs":[],"inventors":[{"name":"Marvin Weinstein","location":"Palo Alto, CA, US"},{"name":"David Horn","location":"Tel Aviv, IL, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}},{"name":"Ramot at Tel Aviv University Ltd.","seq":2,"location":{"city":"Tel Aviv","state":" IL","country":" US"}}],"claims":[{"idx":"00001","text":"A method for data clustering, comprising:obtaining a set of source data using a dynamic quantum clustering server system, where the set of source data comprises a data dimensionality%3bassigning a subset of the set of source data to a representational space using the dynamic quantum clustering server system, where the representational space allows a distance between pieces of data in the set of source data to be measured%3bconstructing a potential function based on the representational space and the set of source data using the dynamic quantum clustering server system%3bcomputing a frame of animation for the set of source data over a time interval using the dynamic quantum clustering server system, wherein computing the frame of animation includes:associating data points from the set of source data with states, wherein the states include initial wave functions%3bcomputing kinetic and potential energies for each initial wave function%3bdetermining updated wave functions using the time-dependent Schrodinger equation based on the kinetic and potential energies of each initial wave function%3bdetermining at least one trajectory for the time interval based upon the updated wave functions%3b andconstructing the frame of animation based on the at least one trajectory%3bevaluating the computed frame of animation for the set of source data over a time period using the dynamic quantum clustering server system, where the evaluation identifies data clusters comprising a subset of the set of source data within the computed frame of animation%3bgenerating a representation of the computed frame of animation using the dynamic quantum clustering server system%3b andtransmitting the generated representation to a client device configured to display the generated representation by providing an interactive visual animation of point positions at one or more selected times."},{"idx":"00002","text":"The method of claim 1, further comprising labeling the data clusters using the dynamic quantum clustering server system."},{"idx":"00003","text":"The method of claim 2, wherein the data clusters are labeled with color information using the dynamic quantum clustering server system."},{"idx":"00004","text":"The method of claim 1, further comprising preprocessing the set of source data points to reduce the dimensionality of the set of source data using the dynamic quantum clustering server system."},{"idx":"00005","text":"The method of claim 4, wherein the set of source data is preprocessed using singular value decomposition."},{"idx":"00006","text":"The method of claim 4, further comprising generating a matrix representation of the obtained source data using the dynamic quantum clustering server system, where the matrix representation is utilized in place of the obtained source data."},{"idx":"00007","text":"The method of claim 1, wherein the potential function is determined such that a quantum mechanical ground state of the potential function is equal to the sum of the initial states of the potential function."},{"idx":"00008","text":"The method of claim 7, wherein the potential function is constructed as a sum of Gaussian functions centered at each data point in the set of source data."},{"idx":"00009","text":"The method of claim 7, wherein computing the frame of animation comprises computing an expectation value of a quantum mechanical position operator using the dynamic quantum clustering server system."},{"idx":"00010","text":"The method of claim 1, further comprising obtaining labeling data using the dynamic quantum clustering server system, where the labeling data identifies one or more features of the data clusters."},{"idx":"00011","text":"The method of claim 1, wherein the representational space comprises a Hilbert space."},{"idx":"00012","text":"The method of claim 1, wherein the potential function satisfies a time-independent Schrödinger equation."},{"idx":"00013","text":"The method of claim 1, wherein:the potential function comprises a set of initial states%3b andthe cardinality of the set of initial states is based on the number of data points in the set of source data."},{"idx":"00014","text":"The method of claim 1, further comprising:generating filtered data based on the strongly clustered data using the dynamic quantum clustering server system%3b andidentifying features associated with the strongly clustered data using the dynamic quantum clustering server system."},{"idx":"00015","text":"The method of claim 14, further comprising labeling the strongly clustered data based on the identified features using the dynamic quantum clustering server system."},{"idx":"00016","text":"The method of claim 14, further comprising:identifying the points of data in the set of source data that are present in at least one piece of strongly clustered data using the dynamic quantum clustering server system%3bcomputing the distance between each pair of data points in the identified points of data using the dynamic quantum clustering server system%3b andcalculating a success metric based on the computed distances and the set of source data using the dynamic quantum clustering server system."},{"idx":"00017","text":"The method of claim 1, wherein the strongly clustered data is centered around a local minimum in the representational space."},{"idx":"00018","text":"A dynamic quantum clustering server system, comprising:a processor%3b anda memory storing a relationship identification application%3bwherein the relationship identification application directs the processor to:obtain a set of source data, where the set of source data comprises a data dimensionality%3bassign a subset of the set of source data to a representational space, where the representational space allows a distance between pieces of data in the set of source data to be measured%3bconstruct a potential function based on the representational space and the set of source data%3bcompute a frame of animation for the set of source data over a time interval, wherein computing the frame of animation includes:associating data points from the set of source data with states, wherein the states include initial wave functions%3bcomputing kinetic and potential energies for each initial wave function%3bdetermining updated wave functions using the time-dependent Schrodinger equation based on the kinetic and potential energies of each initial wave function%3bdetermining at least one trajectory for the time interval based upon the updated wave functions%3b andconstructing the frame of animation based on the at least one trajectory%3bevaluate the computed frame of animation for the set of source data, where the evaluation identifies data clusters comprising a subset of the set of source data within the computed frame of animation%3bgenerate a representation of the computed frame of animation%3b andtransmit the generated representation to a client device configured to display the generated representation by providing an interactive visual animation of point positions at one or more selected times."}],"cpc":{"class":"06","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"F","subgroup":"30598","main-group":"17","action-date":"2017-05-09","origination":"","symbol-position":"F","further":["06","","H","B","US","G","","F","30598","17","2017-05-09","","F"]},"ipc":[{"class":"06","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"F","subgroup":"60","main-group":"7","action-date":"2017-05-09","origination":"","symbol-position":"F"},{"class":"06","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"F","subgroup":"30","main-group":"17","action-date":"2017-05-09","origination":"","symbol-position":"L"},{"class":"06","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"K","subgroup":"62","main-group":"9","action-date":"2017-05-09","origination":"","symbol-position":"L"}],"document_number":"20150032750","document_published_on":"2015-01-29","document_kind":"","document_country":""},{"number":"9,419,322","artifact":"grant","title":"Compact waveguide circular polarizer","filed_on":"2015-03-09","issued_on":"2016-08-16","published_on":"2015-07-09","abstract":"A multi-port waveguide is provided having a rectangular waveguide that includes a Y-shape structure with first top arm having a first rectangular waveguide port, a second top arm with second rectangular waveguide port, and a base arm with a third rectangular waveguide port for supporting a TE.sub.10 mode and a TE.sub.20 mode, where the end of the third rectangular waveguide port includes rounded edges that are parallel to a z-axis of the waveguide, a circular waveguide having a circular waveguide port for supporting a left hand and a right hand circular polarization TE.sub.11 mode and is coupled to a base arm broad wall, and a matching feature disposed on the base arm broad wall opposite of the circular waveguide for terminating the third rectangular waveguide port, where the first rectangular waveguide port, the second rectangular waveguide port and the circular waveguide port are capable of supporting 4-modes of operation.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application is a continuation-in-part of U.S. patent application Ser. No. 14/530,223 filed Oct. 31, 2014, which is incorporated herein by reference. U.S. patent application Ser. No. 14/530,223 is a continuation of U.S. patent application Ser. No. 14/208,922 filed Mar. 13, 2014, which is incorporated herein by reference. U.S. patent application Ser. No. 14/208,922 filed Mar. 13, 2014 claims priority from U.S. Provisional Patent Application 61/787,730 filed Mar. 15, 2013, which is incorporated herein by reference. U.S. patent application Ser. No. 14/208,922 filed Mar. 13, 2014 claims priority from U.S. Provisional Patent Application 61/952,383 filed Mar. 13, 2014, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under contract no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","FIELD OF THE INVENTION","The present invention relates generally to both lower-power and high-power RF waveguide devices. More specifically, it relates to a 3-dB hybrid device for use in high power RF systems that are also compact and broadband.","BACKGROUND OF THE INVENTION","3-dB hybrids are used in high power RF circuits to realize a verity of components such as distributed loads, pulse compression systems, circulators, phase shifters, variable couplers, etc. Hence the synthesis of planner hybrids, with some times overmoded dimensions for use with ultra-high power applications have been the subject of interest for a long time. 3-dB hybrids are four port devices with a “matched” scattering matrix (diagonal elements are all zeros) representation that couples one port to the other two ports equally and the remaining port is isolated. This is true for all 4 ports. There are many realizations for this device.","What is needed is a 3-dB hybrid device for use in high power RF systems that are also compact and broadband.","SUMMARY OF THE INVENTION","To address the needs in the art, a multi-port waveguide is provided that includes a rectangular waveguide, where the rectangular waveguide includes a Y-shape structure having a first top arm, a second top arm, and a base arm, where the first top arm includes a first rectangular waveguide port, where the second top arm includes a second rectangular waveguide port, where an end of the base arm includes a third rectangular waveguide port that is capable of supporting a TE 10 mode and a TE 20 mode, where the end of the third rectangular waveguide port includes rounded edges that are parallel to a z-axis of the rectangular waveguide, a circular waveguide that includes a circular waveguide port that is capable of supporting a left hand circular polarization TE 11 mode and a right hand circular polarization TE 11 mode, where the circular waveguide is coupled to a broad wall of the base arm of the rectangular waveguide, and a matching feature, where the matching features is disposed on the broad wall of the base arm that is opposite of the circular waveguide, where the matching feature is capable of terminating the third rectangular waveguide port, where the first rectangular waveguide port, the second rectangular waveguide port and the circular waveguide port are capable of supporting 4-modes of operation.","According to one aspect of the invention, the matching feature includes a stub feature that projects outward from the broad wall of the base arm.","In another aspect of the invention, the matching feature includes a capacitive dome that projects inward from the broad wall of the base arm.","In a further aspect of the invention, the matching feature includes a pin feature that projects outward from the broad wall of the base arm.","In yet another aspect of the invention, the circular waveguide is disposed at a pre-defined distance from a junction of the first top arm and the second top arm along the base arm, where the pre-defined distance is according to matching and phase properties of the left hand circular polarization TE 11 mode and the right hand circular polarization TE 11 mode, where a phase difference between the TE 11 mode along the first top arm and the TE 11 mode the second top arm is 90-degrees.","DETAILED DESCRIPTION","The current invention comprises a hybrid 4-port device physically configured as a 3-port device, where two ports are lumped together in one single physical port that have two modes. According to one embodiment, the physical port has a circular cross section and the two modes representing the two ports are the two polarization of the TE 11 mode. Furthermore, the individual polarizations representing the two ports are the left and right hand circular polarizations of the TE 11 mode. This type of device that has three physical ports with 4 modes of operations, two of which are the left handed and right handed circularly polarized mode and has the same representation as a 3-port hybrid is called herein a “polarizer.”","There are many embodiments for these polarizers, but the subject of the current invention is one embodiment that allows the use of this device in high power RF systems. The embodiment is also compact and broadband.","The current invention starts by noticing that a circular waveguide connected at the broad wall of a rectangular waveguide, as shown in FIG. 1 , could have a one to one correspondence between the modes of the rectangular guide and the circular guide. This means that one of the linear polarizations of the circular waveguide will couple to one and only one mode in the rectangular waveguide and the other polarization will couple to a completely different mode in the rectangular waveguide. To be precise, referring to FIG. 1 , the TE 11 mode polarized along the y axis will couple to the TE 10 mode in the rectangular waveguide while the TE 11 mode polarized along the x-axis will couple to the TE 20 mode in the rectangular waveguide. Hence, one has to choose the dimensions of the rectangular waveguide, precisely the broad dimension, to allow for the propagation of the TE 10 and TH 20 modes, and only those two modes. Likewise the diameter of the circular waveguide should allow only the two polarizations of the TE 11 mode to propagate.","The next step of the design is accomplished by noticing that if one put an artificial plane parallel to the Zz-y plane (see FIG. 1 ) along the axis of symmetry of the structure the structure split into to symmetrical parts. If a boundary condition of a perfect electric wall or a perfect magnetic wall is placed along this plane, in other words if one consider either odd or even symmetries of the field in the structure, one would get a perfectly symmetrical three port network, with the circular port in the center of symmetry. Invoking known theories for three port networks, then, there exists a position for a termination (a short circuit), that allow a perfect match between one of the ports and the central port. This means that there exist a position for a short circuit that allow a perfect match for either the TE 10 mode to couple to the TE 11 mode along the y-direction and another position that will match the TE 20 mode to the TE 11 mode along the x-direction. To match both at the same time we recognize that the sort circuit can be achieved at different positions for both modes by shaping the end of the rectangular waveguide, as shown in FIG. 2 .","The next step of the design is to excite the TE 10 mode and the TE 20 modes in the rectangular guide through a “four port” 3-dB hybrid, with two ports being two separate ports and one physical port that contain the TE 10 and the TE 20 mode, as shown in FIG. 3 . This hybrid, typically needing a matching element in the center of the broad waveguide, can eliminate that by perturbing the match of the section containing the circular waveguide. This is accomplished by the choosing the position of the circular port with respect to the rectangular hybrid and the shape of the short circuit termination at the end (see FIG. 3 ).","To create a circular polarization the phase difference between the TE 11 mode along the x and the TE 11 mode along the y need to differ by 90 degrees. This is done also by choosing the phase difference between the TE 10 mode and the TE 20 mode in the rectangular waveguide. This is accomplished also be choosing the distance between the circular port and the rectangular hybrid along the y-axis. Since this distance control both the matching and the phase properties of the two polarizations one need another degree of freedom, this is done by adding either a dome or stub underneath the circular guide. FIGS. 4-6 show some exemplary embodiments of the current invention, where the field patterns are those obtained by finite element simulations.","The polarizer shown in FIGS. 4-6 allows for a verity of applications. First one should notice that a short circuit or a reflection at the circular port results in changing the propagation direction due the reflection of the waves from that port. However, the direction of rotation will not change. This shows that the helicity of the wave has been reversed and hence the reflected power will all go to the isolated rectangular port. With no reflection towards the source placed at the first rectangular port.","If the reflection happens through a lossy material such as stainless steel or something that has less conductivity, a matched load can be constructed by chaining a plurality of these polarizers one after the other, according to one embodiment. In another embodiment, if the reflection happens through a movable short then a phase shifter is constructed. If a reflection happens through a high quality factor cylindrical or spherical cavity a pulse compression system is realized. This would be the most compact pulse compressor constructed to date, according to a further embodiment. Finally if the reflection happens with a piece of ferrite mediatized along the circular waveguide axis one would achieve an isolator, where the power going in one direction between the two rectangular ports would suffer no losses in one direction and would be greatly attenuated in the other direction, according to another embodiment of the invention. To accommodate high power operation one can chain several of these isolators together and hence the losses could be distributed among them, according to further embodiments.","Finally with the embodiment addressing lossy materials, the embodiment could be enhanced by the use of the EH 11 mode in corrugated circular waveguide as part of the termination to increase the losses%3b the EH 11 mode is essentially a surface wave. Also regarding the embodiment incorporating a piece of ferrite mediatized along the circular waveguide axis, the embodiment could be enhanced by the use of the HE 11 mode in corrugated circular waveguide to allow for perfect circular polarizations locally at the ferrite or the garnet surface to minimize spurious loses for the forward direction and to enhance the isolation in the reverse direction.","According to a further embodiment of the invention, a compact and wide-band waveguide dual circular polarizer at Ka-band is presented herein. This compact structure is composed of a three-port polarizing diplexer and a circular polarizer realized by a pair of large grooves. The polarizing diplexer includes two rectangular waveguides with a perpendicular H-plane junction, one circular waveguide coupled in E-plane. A cylindrical step and two pins are used to match this structure. For a left hand circular polarization (LHCP) or right hand circular polarizer (RHCP) wave in the circular port, only one specific rectangular port outputs power and the other one is isolated. The accurate analysis and design of the circular polarizer are conducted by using full-wave electromagnetic simulation tools. The optimized dual circular polarizer has the advantage of compact size with a volume smaller than 1.5λ 3 , broad bandwidth, uncomplicated structure, and is especially suitable for use at high frequencies such as Ka-m, band and above. The prototype of the polarizer has been manufactured and tested, the experimental results are consistent with the theories.","According to one embodiment, the invention applies to large-format focal plane arrays, which could be used in the next generation of cosmic microwave background (CMB) polarization experiments to understand the very early Universe. The detected B-mode polarization is from Ka band to W band, which is received by the antenna array of circular feed horns. There are hundreds of units in the antenna array, thus each unit should be as compact as possible, wideband, and straightforward to mass-produce. The right hand and left hand circular polarized component (RHCP and LHCP) of the B-mode Q±iU include important information, Q and U need to be amplified synchronously rather than separately, thus, before the amplifiers, dual circular polarizer is used to separate the circular polarized Q±iU in two ports with linear polarizations (LP), one of which contains the information of Q+iU, and the other is for Q−iU.","The circular polarizer is usually designed to convert one linearly polarized mode into two orthogonal modes with a 90-degree phase shift by loading the discontinuities of septum, corrugations, and dielectrics. The waveguide septum polarizer has the advantage of compact size with three physical ports, but has a very limited bandwidth due to phase shift of two orthogonal modes%3b the dielectric-loaded polarizer has relative high loss. The polarizer for corrugations, dielectrics, and ridges are two physical ports, and need ortho-mode transducer (OMT) to separate the LHCP and RHCP. The Boifot OMT has broad bandwidth but with very complex matching structure. There are four physical rectangular ports for turnstile OMT, which need two waveguide rings to respectively combine the ports with same polarization. Thus, turnstile OMT is not compact and the two waveguide rings may decrease the final bandwidth. The compact three-port branching OMT composed by two H-plane rectangular waveguides coupled with a common circular waveguide uses two bottle-neck-like irises to match the structure and realize the isolation, whose return loss \u003c−10 dB had a bandwidth \u003c12%, and isolation \u003c−35 dB with a bandwidth \u003e10%. Other kinds of circular polarizers such as microstrip polarizer also have the disadvantage of narrow bandwidth and low efficiency due to losses of conductor, dielectric and surface wave.","As mentioned above, since there are hundreds of units in the antenna array for detecting CMB, the dual circular polarizer have compact size and broad bandwidth. The exemplary embodiment focuses on the Ka-band with frequency from 26 GHz to 36 GHz. Firstly, a compact 3 physical-port polarizing diplexer is provided, which can separate the circular polarized wave Q±iU from a circular port into two separate rectangular ports with linear polarized Q and ±iU. Then, two symmetric grooves are used to form the circular polarizer.","Turning now to the compact polarizing diplexer, the compact three physical-port polarizing diplexer illustrated is shown in FIG. 7 includes two rectangular waveguides with a perpendicular H-plane junction and one circular waveguide coupled in E-plane. This device contains a symmetric diagonal plane, called AA, which decomposes the structure into two equal halves. Because of the symmetry of the structure about AA, the full structure can be optimized by solving just one of the halves. The plane AA is defined to be the XZ plane in 3-dimensional Cartesian coordinates.","When the rectangular port 1 or 3 feeds in a TE 10 mode, a specific TE 11 mode polarized along the incident rectangular waveguide is generated, which can be further decomposed along the X and Y axes. In other words, for a TE 10 mode inserted in port 1 , two orthogonal TE 11 modes with phase difference 0° respectively along X and Y axes are excited, compared with two TE 11 modes with phase difference 180° for incident TE 10 mode from port 3 .","Optimization variables are used to define a central rectangular step as well as one pin on this step and located at the strong electric field region in the ½ structure. Full-wave electromagnetic simulation HFSS software is used to optimize the structure. In order to realize the whole structure matched, no matter for the symmetric plane AA (see FIG. 7 ) is electric or magnetic boundary, there should be a broadband result for the 1/2 structure. First of all, AA plane is assumed to be a perfect electric boundary, as shown in FIG. 8A , and the parameters of the step and one pin are optimized. Then, AA is assumed to be a perfect magnetic boundary, as shown in FIG. 8B , and another pin at the bottom of the waveguide is added in the strong magnetic region, which is far away from the strong electric field region. Consequently, the second pin should have a weak influence on the optimized result for AA as an electric boundary.","It is found that the four pins structure is very difficult to optimize since there are too many parameters to consider, and the optimized S 11 and S 13 is about from −10 dB to −25 dB within the target bandwidth, as shown in FIG. 9 . Thus, a circular step is used instead of the rectangular one and the four pins are replaced by two. Then, the key parameters for matching the structure are the radius R 1 and the height Z 1 of the step, the center position X 1 of the step and the circular waveguide, the radius R 2 , height Z 2 and the location X 2 and Y 2 of the pins.","The optimization module of HFSS software has a strong ability in matching a structure at a single frequency, but is not ideal for optimizing over a large bandwidth. Thus, the influence of the step and pins on the S parameters within the bandwidth is investigated by sweeping the parameters of the structure, while the S parameters at the central frequency (31 GHz) and the edge frequencies (26 GHz and 36 GHz) are monitored. The sweep results for each variable are plotted in separate graphs in FIGS. 10A-10G .","It is shown in FIG. 10A when the center position X 1 of the step and the circular waveguide deviates a little from the coordinate center and moves along the X-axis to the range X 1 ˜0.2 to ˜0.4 mm, the return loss and isolation are significantly decreased. Additionally, when the radius of the step is R 1 ˜2.4-2.5 mm and the height is 0.9-1.2 mm, both S 11 and S 13 are small. The structure is matched well when the pins deviate a little from the center of the step with X 2 ˜0.2-0.4 mm the central distance between the two pins reaches 2Y 2 ˜2*(0.9-1) mm, and the height is Z 2 ˜1.2-1.4 mm. Finally, a smaller R 2 has a higher isolation. It should be emphasized that taking the coordinate satisfying the symmetric plane AA to be the Y Z plane was very important for calculating the optimization results.","Besides, the optimized broadband structure should keep S 11 and S 13 at the boundary frequencies 26 GHz and 36 GHz as low as possible. After sweeping the above multi-parameters of the pins and the step, the researched range of the variables for a matched structure could become smaller. The structure and the optimized S-parameters for the compact broadband polarizing diplexer is shown in FIG. 11A and FIG. 11B . Compared with FIG. 9 , the S parameters of the new structure in FIGS. 11A-11B have much lower return loss and higher isolation. The modes 1 and 2 in port 2 have 0° or 180° phase difference.","Turning now to the design of one embodiment of the dual circular polarizer, a pair of grooves along the symmetric plane AA are used to adjust the phase difference Δφ of the two orthogonal modes reaching 90° and keep the broadband result. A polarizer with single groove was researched. To keep the symmetric of the polarizer in this exemplary embodiment, a pair of large grooves are adopted, which can realized a broad bandwidth because it excites higher order modes, and weakens the frequency dependence of the phase variation βL, where L is the length of the groove and β is the propagation constant. For instance with a depth 2.5 mm and width 1.5 mm, a length L˜λ, is needed to realize Δφ˜90°, smaller grooves, with depth 1 mm and width 1 mm, would need a length of L˜3λ, to reach Δφ˜90° at 31 GHz and the dependence of Δφ on frequency is very sensitive due to a larger phase variation ΔβL compared with a shorter L. By sweeping the height, width, and length of the grooves, the optimized parameters are illustrated in FIGS. 12A-12B .","The results in FIGS. 12A-12B show that the return loss and isolation between the rectangular ports is below −10 dB and the phase differences of the two orthogonal TE 11 modes maintains in the vicinity of 90° within a bandwidth of about 30%, the detailed parameters of the polarizer is shown in Table 1. From FIG. 13 , the isolation between the two orthogonal TE 11 modes is lower −40 dB, and the TE 11 power is equally divided between Port 1 and Port 3 , i.e., S( 2 : 1 %3b 1 )=S( 2 : 2 %3b 1 )=S( 2 : 1 %3b 3 )=S( 2 : 2 %3b 1 )=−3 dB. For the same phase of two TE 11 modes, there are respectively 90° and −90° phase differences between the two modes in Port 1 and Port 2 , i.e., Arg(S( 2 : 1 %3b 1 ))−Arg(S( 2 : 2 %3b 1 ))=90°, and Arg(S( 2 : 1 %3b 3 ))−Arg(S( 2 : 2 %3b 3 ))=−90°. For a LHCP (or RHCP) wave, Arg(S( 2 : 1 %3b 1 ))−Arg(S( 2 : 2 %3b 1 ))=180° (or 0°), and Arg(S( 2 : 1 %3b 3 ))−Arg(S( 2 : 2 %3b 3 ))=0° (or)−180°, thus, only one specific rectangular port outputs power and the other one is isolated.","The transient electric field in FIGS. 14A-14C show that the circular polarized wave from circular waveguide propagates in one rectangular port, and the other rectangular port is isolated. Using only a pair of grooves to realize the broadband circular polarizer has several benefits, including simplification of the design and optimization course, and decreasing the manufacture cost. In addition, this design is suitable for high frequency applications, such as Ka-band and W-band."," TABLE 1 The optimized parameters of the structure (unit in millimeter). Rectangular Circular Cylinder Step waveguide waveguide Radius Height Location Location Width Height Radius R 1 Z 1 X 1 Y 2 7.96 3.455 3.5 2.5 1 −0.15 0 Pin Radius Height Location Location Groove R 2 Z 2 X 2 Y 2 height Depth Width 0.5 1.3 0.275 0.8 9.85 2.51 1.75 ","A couple of dual circular polarizers with the material of brass have been manufactured, and each includes three pieces: one bottom block, and two top left and right blocks. The bottom and top blocks are split along the centerline of the waveguide, and the circular step and the two pins are located at the bottom block%3b the top two blocks split the grooves into two equal halves. This compact circular polarizer has an inner volume smaller than 1.5λ 3 , and the outer metal block is 1 inch 3 .","Agilent E8364B PNA Network Analyzer is used to measure the S parameters. Two polarizers are connected back to back with a circular waveguide, when two coaxial to WR28 waveguide adapters are used to link the inputs of one polarizer with the PNA, and two Ka-band terminations are combined with the inputs of the other polarizer to measure the return loss and isolation. The experimental turn loss and isolation is basically consistent with the simulation result, as illustrated in FIG. 15 . The bandwidth for return loss \u003c−15 dB and isolation \u003c−15 dB is 26%.","When a linear polarizer wave is incident in one rectangular port of the polarizer, a LHCP wave is generated and outputted at the circular port. By placing a short metal plane at the circular port, the polarization of incident LHCP changes to RHCP after reflection, thus, the other rectangular port receives the signal, which shows one method to measure the insertion loss of the polarizer, as shown in FIGS. 16A-16C . Twice of the averaged insertion loss is about −1:2 dB.","In order to measure the circular polarization, two polarizers are jointed back to back with a circular waveguide, one adapter and one load are connected with one polarizer, the output of the LHCP from one polarizer changes to LP after the second polarizer, and further outputs in one rectangular port, with the other rectangular port isolated. Then, by rotating one of the polarizer successively by 0°, 90°, 180°, and 270°, the outputs of one rectangular port are shown in FIG. 16B . The axial ratio (AR) of the polarizer shown in FIG. 16C means the bandwidth for AR\u003c0:5 dB is about 25%.","Before designing this polarizer, a septum dual circular polarizer at W-band was build, whose performance was not very good with a bandwidth \u003c30%, and the limited bandwidth may be came from the non-perfect design. Then, we try to build a more broadband polarizer, although the bandwidth of the new polarizer is not wider than the septum polarizer.","Presented and tested is an embodiment of a dual circular polarizer that is compact, broadband, and easy to manufacture. The total volume of the polarizing diplexer is smaller than 1.52λ 3 and the bandwidth is about 25%. The design uses simple shapes, so it should be easy to manufacture. Due to the compact size and wide bandwidth, this polarizer can be used in a wide range of applications, including detectors of the CMB.","Satellite broadcasting, communicating, and tracking systems generally operate with circular polarization in circular waveguides so as to realize polarization compatibility of reception and transmission, since the received RF signal could be arbitrary linear polarized wave (LP), RHCP and/or LHCP. Thus, a circular polarity converter and a separator are needed, whose crucial design points are to convert the linearly polarized mode into two orthogonal modes with a 90-degree phase shift, and to keep good isolation between two input ports and small return loss. Further, for megawatt power level for medical accelerator and linear accelerators in high-energy research, there is still no compact and high-power capacity phase shifter.","According to further embodiments of the invention, two kinds of for compact waveguide circular polarizers are further presented. One embodiment includes an H-plane T junction of rectangular waveguide, one circular waveguide as an E-plane arm located on top of the junction, the center circular stub, dome or pins are used to isolate the two rectangular ports and match the structure, as well as realizing the mode conversion and 90 deg phase difference of the two orthogonal TE 11 modes together with the T-junction rectangular stub. The optimized polarizer has the advantages of a very compact size with a volume smaller than 0.6λ 3 , low complexity, and high power capacity.","Another embodiment includes two rectangular waveguides with a perpendicular H-plane junction, one circular waveguide coupled in E-plane, and a pair of large grooves in the circular waveguide. A cylindrical step and two pins or domes can be used to isolate the two rectangular ports and match this structure. The dual circular polarizer has a volume smaller than 1.5λ 3 , broad bandwidth ˜20%, high power capacity.","There are several important applications for these two embodiments, firstly, simultaneously receiving and transmitting right-hand and left-hand circularly polarized waves used for communications and polarization transition both for low power and high power microwave domain%3b secondly, by adding an electronic-controlled movable short circuit in the circular waveguide, it becomes the most compact and fast-action waveguide phase shifter and can be used for medical accelerator and most application case for high-power phase shifter.","The embodiments relate to compact microwave circular polarizers for spontaneously receiving and transmitting right hand and left hand circular polarized wave (RHCP and LHCP) both for low power and high power microwave domain.","By adding an electronic-controlled movable short circuit in the circular waveguide and adjusting the plunger position with λ, the dual polarizer becomes the most compact waveguide phase shifter and can be used for medical accelerator and most application case for high-power phase shifter. The phase shifter is much smaller, reduced complexity, and higher capacity compare to the existed high-power phase shifter realized by inserting yttrium-Iron Garnet (YIG) and ferroelectric material and so on.","The structure according to the current embodiments can be adopted in varied frequency from S-band to W-band because of realizable manufacture.","By adding an movable short circuit in the circular waveguide and electronic-controlled adjusting the piston position, the dual polarizer becomes the most compact, and fast-action waveguide phase shifter and can be used for medical accelerator and most application case for high-power phase shifter.","One embodiment of the dual polarizer includes an H-plane T junction of rectangular waveguide, one circular waveguide as an E-plane arm located on top of the junction, the center circular stub, dome or pins are used to isolate the two rectangular ports and match the structure, as well as realizing the mode conversion and 90° phase difference of the two orthogonal TE 11 modes together with the T-junction rectangular stub. The schematic structure is shown in the FIGS. 17A-17B .","Turning now to the design of the S-matrix for the dual circular polarizer:"," S = 2 2 ⁢ ( 0 1 i 0 1 0 0 - 1 i 0 0 i 0 - 1 i 0 ) ","In an example embodiment of a dual polarizer for 30 GHz, the theoretical and experimental S parameters are compared in FIG. 18A .","In order to measure the circular polarization, two polarizers are jointed back to back with a commercial circular waveguide plated by gold, one adapter and one load are connected with one polarizer. The output of the LHCP from one polarizer changes to LP after the second polarizer, and further outputs in one rectangular port, with the other rectangular port isolated. Then, by rotating one of the polarizer successively by 0°, 90°, 180°, and 270°, the outputs of one rectangular port are shown in FIG. 18B representing the circular polarizer wave.","The optimized parameters of the Ka-band septum polarizer are illustrated in Table 2, where standard rectangular waveguide WR28 is used in order to conveniently match and connect with other microwave devices. The circular waveguide has a small radius to cut off TM 01 mode."," TABLE 2 The optimized parameters of the septum polarizer for Ka-band (unit in millimeter). Rectangular Circular waveguide Stub waveguide Cylinder Pins W r H r W s L s R c R 1 Z 1 R 2 Z 2 7.44 3.46 8.05 2.5 3.55 2.02 0.92 0.37 2.85 ","For the dual circular polarizer with three physical ports and four modes, as illustrated in FIG. 17A , its special S-Matrix is disclosed. There is only one symmetric plane for a non-zero stub-arm length. The eigenvectors of the S-matrix of the 4-modes network are denoted by a column vector [a, b, c, d] T , where a, b, c, and d are respectively the amplitudes of the wave in port 1 , 2 : 1 , 2 : 2 , and 3 . The modes Port 2 : 1 and Port 2 : 2 are respectively along Y and X-axis. Due to the electric and magnetic symmetry with regard to the dashed line, the four eigenvectors of the S-matrix can be written as [1, b1, 0, −1] T , [1, b2, 0, −1] T , [1, 0. c1, 1] T , and [1, 0, c2, 1] T . Owing to the orthogonal basis of eigenvectors, the dot product of every two eigenvector should be zero, thus, b1×b2=−2, and c1×c2=−2. It is possible to choose the position of the reference planes in such a way that b1=c1=√{square root over (2)}, and then, b2=c2=−√{square root over (2)}.","The normalized orthogonal Matrix of eigenvectors X is"," X = 1 2 ⁢ ( 1 1 1 1 2 - 2 0 0 0 0 2 - 2 - 1 - 1 1 1 ) ","Since a 4 ×4 S-matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces is 4, or equivalently, if and only if S has 4 linearly independent eigenvectors. Consequently, the S-Matrix of 4-port network can be diagonalizable by the orthogonal eigenvectors Matrix as,"," S = X ⁡ ( λ 1 0 0 0 0 λ 2 0 0 0 0 λ 3 0 0 0 0 λ 4 ) ⁢ X - 1 ","X −1 is the inverse matrix of X, and λ i , i=1, 2, 3, and 4 are the eigenvalues of the S-Matrix. By solving the above equation for S, there is"," S = 1 4 ⁢ ⁢ ( ∑ λ i 2 ⁢ ( λ 1 - λ 2 ) 2 ⁢ ( λ 3 - λ 4 ) - λ 1 - λ 2 + λ 3 + λ 4 2 ⁢ ( λ 1 - λ 2 ) 2 ⁢ ( λ 1 + λ 2 ) 0 2 ⁢ ( λ 2 - λ 1 ) 2 ⁢ ( λ 3 - λ 4 ) 0 2 ⁢ ( λ 3 + λ 4 ) 2 ⁢ ( λ 3 - λ 4 ) - λ 1 - λ 2 + λ 3 + λ 4 2 ⁢ ( λ 2 - λ 1 ) 2 ⁢ ( λ 3 - λ 4 ) ∑ λ i ⁢ ) ","The eigenvalues in the resulting equation for S can be addressed by realizing the function of the dual circular polarizer. For a wave incident with an unit power at Port 1 , a 1 =[ 1 %3b 0 %3b 0%3b 0] T , the output is a circular polarized wave, b 1 =S·a 1 =√{square root over (2)}[0, 1, i, 0]2. Besides, for equal incident power with the same phase from Port 1 and Port 3 , a 2 =√{square root over (2)}[1, 0, 0, 1] T /2, the symmetric plane at Port 2 is equivalent to a magnetic boundary, and only Port 2 : 2 is excited, corresponding to b 2 =S ·a 2 =[0, 0, i, 0] T %3b for equal incident power with 180° phase difference from Port 1 and Port 3 , a 3 =√{square root over (2)}[1, 0, 1, −1] T /2=the symmetric plane at Port 2 is equivalent to a electric boundary, and only Port 2 : 1 is excited, corresponding to b 3 =S·a 3 =[0, 1, 0, 1] T From the three input vector a 1,2,3 , and the corresponding output vector b 1,2,3 , the eigenvalues can be solved in the following equations, Σλ i =0λ 3 +λ 4 −λ 1 −λ 2 =0 λ 1 −λ 2 =2λ 1 +λ 2 =0 λ 3 −λ 4 =2 i λ 3 +λ 4 =0 ","By solving this equation, the eigenvalues for the dual circular polarizer are λ 1 =1, λ 2 =−1, λ 3 =i, and λ4=−i. And the Scattering-Matrix above can be simplified as,"," S = 2 2 ⁢ ( 0 1 i 0 1 0 0 - 1 i 0 0 i 0 - 1 i 0 ) ","This S-matrix is the design goal for the dual circular polarizer, which needs the eigenvalues to satisfy λ 1 =−λ 2 , λ 3 =−λ 4 , and λ 1 =i λ 3 . The three key conditions can be achieved at the same time by tuning the two center pins and the stub. In more detail, by adjusting the height and radius of the dumpy pin and the slim pin, and the length and width of the stub, the polarizer can be obtained. The eigenvalues λ 1 =1 and λ 2 =λ 1 and the corresponding eigenvectors are [1, √{square root over (2)}, 0, −1] T /2 and [1, −√{square root over (2)}, 0, −1] T /2 are equivalent to the condition that the symmetric plane is equivalent to an electric boundary, which means that physically there are equal amplitude field with a 180° phase difference incident at port 1 and port 3 , as illustrated in FIG. 19A . In this situation, the stub is cutoff and there is only evanescent wave in the stub, as shown in FIG. 19B %3b electric field on the slim pin is very small due to the slim pin located very close to the electric boundary, as shown in FIG. 19C . In HFSS simulation, by taking the symmetric plane as electric boundary, a two-physical-port and two-mode network is obtained and optimized, instead of studying the four-port polarizer. Thus, by tuning the dumpy pin, the two-port network is matched, and λ 1 =λ 2 is realized in this situation.","Similarly, the eigenvalues λ 3 =i and λ 4 =−i and the corresponding eigenvectors [1, √{square root over (2)}, 0, 1] T /2 and [1, −√{square root over (2)}, 0, 1] T /2 are equivalent to the symmetric plane as an magnetic boundary, which means that physically there are equal amplitude field with the same phase incident at port 1 and port 3 , as illustrated in FIGS. 20A-20B . In HFSS simulation, by using the magnetic symmetric plane, a two-port network is obtained%3b and by adjusting the slim pin and the width and the length of the stub to realize λ 3 =−λ 4 and λ 1 =i λ 3 , the mode Port 2 : 2 with the equal amplitude of Port 2 : 1 and a 90° phase difference can be realized. Thus, a circular polarizer wave for this structure is generated with the transient surface field shown in FIG. 17B .","In order to increase the bandwidth, the dependence of propagation constant on frequency should be decreased. This can be achieved by broadening the width of the stub since β for a wider waveguide is less sensitive on frequency. Also, the path for exciting TE 11 mode 2 is from Port 1 to the stub and then to Port 2 , which is longer than the path for generating TE 11 mode 1 , thus, it is always sensitive to frequency. Widening the H-plane arm has the benefit of decreasing the path length for TE 11 mode 2 , effectively reducing the difference between the two path lengths. The optimized S parameters of the polarizer given in FIGS. 21A-21B show that the two orthogonal TE 11 modes have relatively equal − 3 B amplitude, the isolation and return loss are respectively below −30 dB and −15 dB, and the phase difference between the two TE 11 modes varies of 60° from 29 GHz to 33 GHz. It should be emphasized that a pure circular wave requires a 90° differential phase between two orthogonal modes. As the frequency increases or decreases from the center frequency, the phase difference moves away from 90° leading to a decrease in the circularly polarized power. When this structure is used in the reverse way, the input RHCP and LHCP in circular Port 2 is respectively transformed into separated linear polarization in the two rectangular Ports 1 and 3 . Thus, this device is a compact dual circular polarizer. Based on the above analysis, finally, the optimized parameter is shown in Table 5, which is also the same data of the manufactured polarizer. Note that the matched stub length L s =2.5 mm is no long 1=4λ g , which is 3 mm for stub width W s =8.05 mm and 3.2 mm for waveguide width W r =7.44 mm.","Regarding manufacture tests, two pieces of dual circular polarizer with the material of brass have been manufactured, and the split-block design has been used to respectively fabricate the bottom and top block. The central circular step and pin are accurately built at the bottom block, and the H-plane arm as well as the rectangular and circular waveguides are located at the top block. This compact circular polarizer has an inner volume smaller than 0.6,3, and the outer metal block is 0.36 inch 3 .","Agilent E8364B PNA Network Analyzer is used to measure the S parameters. In order to measure the return loss and isolation, two matched terminations are connected with the inputs of one polarizer, two coaxial to WR28 waveguide adapters are linked the inputs of the other polarizer with the VNA, and then, two polarizers are connected back to back with a circular waveguide. The experimental return loss and isolation are basically consistent with the simulation results, as illustrated in FIG. 18A .","The second step is to measure the insertion loss of the polarizer. When a linear polarizer wave is incident in Port 1 of the polarizer, a LHCP wave is generated and outputted at the circular Port 2 . By placing a short metal plane at the Port 2 , the polarization of incident LHCP changes to RHCP after reflection, thus, the Port 3 receives the signal, and the transmission coefficient of one polarizer is shown in FIG. 22A , where twice of the averaged insertion loss is about −1 dB.","In order to measure the circular polarization, two polarizers are jointed back to back with a commercial circular waveguide plated by gold, one adapter and one load are connected with one polarizer, the output of the LHCP from one polarizer changes to LP after the second polarizer, and further outputs in one rectangular port, with the other rectangular port isolated. Then, by rotating one of the polarizer successively by 0°, 90°, 180°, and 270°, the outputs of one rectangular port are shown in FIG. 18B representing the circular polarizer wave, and the output in the other port in FIG. 22B represents the cross polarization. It should be emphasized that the outputs in FIG. 18B and FIG. 22B are the results from one polarizer jointed to the other polarizer, for a single polarizer, the bandwidth of the output will be higher than those in FIG. 18B and FIG. 22B .","Turning now to the high power dual polarizer, by replacing the center pins to circular stubs, the high power dual circular polarizer could be realized as shown in FIGS. 23A-23B , and the S parameters for the high power dual polarizer is illustrated in FIG. 21A . For a high power application, the bandwidth of klystron source is very limited, thus, the bandwidth shown in FIG. 21A is enough for most of high power polarizer applications.","Regarding the second embodiment of the dual polarizer, the polarizer includes two rectangular waveguides with a perpendicular H-plane junction, one circular waveguide coupled in E-plane, and a pair of large grooves in the circular waveguide. A cylindrical step and two pins or domes can be used to isolate the two rectangular ports and match this structure. The dual circular polarizer has a volume smaller than 1.5λ 3 , broad bandwidth ˜20%, high power capacity. The transient surface is shown in FIG. 25 .","A couple of dual circular polarizer for central frequency 31 GHz with the material of brass have been manufactured, and each includes three pieces: one bottom block, and two top left and right blocks. The bottom and top blocks are split along the centerline of the waveguide, and the circular step and the two pins are located at the bottom block%3b the top two blocks split the grooves into two equal halves. This compact circular polarizer has an inner volume smaller than 1.5λ 3 , and the outer metal block is 1 inch 3 . The experimental and theoretical turn loss and isolation is basically consistent with each other, as illustrated in FIGS. 26A-26B . The detailed dimension is shown in Table. 3."," TABLE 3 The optimized parameters of the structure (unit in millimeter) for central frequency 31 GHz. Rectangular Circular Cylinder Step waveguide waveguide Radius Height Location Location Width Height Radius R 1 Z 1 X 1 Y 2 7.96 3.455 3.5 2.5 1 −0.15 0 Pin Radius Height Location Location Groove R 2 Z 2 X 2 Y 2 height Depth Width 0.5 1.3 0.275 0.8 9.85 2.51 1.75 ","The current embodiment further includes a phase shifter, where by adding a movable short circuit in the circular waveguide and adjusting the piston position, the dual polarizer becomes the most compact, and, if the position is electronically controlled, fast-acting waveguide phase shifter. It can be used for ultra-high power applications, including but not limited to, microwave linear accelerators. The moving distance for the piston is λ g /2 to realize a full 360° phase shift. The short circuit can be realized in a variety of forms, but most conveniently a chocked plunger with no contact to the walls as shown in FIGS. 27A-27B . The high power polarizer shown in FIGS. 23A-23B and FIG. 24 can be combined with the piston to realize the most compact phase shifter. When the plunger moves up and down, the output phase in the rectangular port of FIGS. 23A-23B will be changed according to the accurate position of the plunger. Of course, the polarizer in FIG. 25 connects with the plunger in FIGS. 27A-27B will become a compact low power phase shifter.","A further embodiment includes a hybrid for a dual mode pulse compressor. Here, this polarizer is essentially a four-port device and its scattering parameters are similar to that of a 90° hybrid. Hence, if one adds a RF spherical or cylindrical cavity at the circular port of FIGS. 23A-23B , two degenerate resonant modes are excited by an input at the first rectangular port. When those two modes are discharged from the cavity the power will flow through the second rectangular port. The discharge can be caused most effectively by changing the phase of the input signal. Hence, the system would act as a pulse compressor.","Turning now to further embodiments of the invention. A novel type of dual circular polarizer for simultaneously receiving and transmitting right-hand and left-hand circularly polarized waves is provided and presented herein. The current embodiment includes an H-plane T junction of rectangular waveguide, one circular waveguide as an E-plane arm located on top of the junction, and two metallic pins used for matching. Provided herein is the theoretical analysis and design of the three-physical-port and four-mode polarizer by solving Scattering-Matrix of the network and using a full-wave electromagnetic simulation tool. The optimized polarizer has the advantages of a very compact size with a volume smaller than 0.6λ 3 , low complexity and manufacturing cost. A couple of the polarizer has been manufactured and tested, and the experimental results are basically consistent with the theories.","The circular polarizer converts a RHCP and/or LHCP into linearly polarized signals of vertically polarized (VP) and/or horizontally polarized (HP) waves, or is used in a reverse way. The transformation of circular polarization with linear polarization is generally realized by loading the discontinuities of a stepped-septum, stepped-corrugations, grooves and loaded dielectrics.","The current embodiment provides a new compact circular polarizer. This work is motivated by the development of instrumentations for the next generation experiments detecting the polarization of the cosmic microwave background (CMB) in order to understand the very early Universe. The incident circularly polarized radiations are received by an array of circular feed horns, converted, and then separated into two rectangular waveguides for respective analysis. In order to build an instrument with hundreds of array elements, each unit needs to be small to allow for close-packing Previous circular polarizers such as microstrip polarizer have the disadvantage of narrow bandwidth and low efficiency due to losses of conductor, dielectric and surface wave.","For a dual circular polarizer, two devices were previously needed, that included a circular polarizer to convert RHCP and LHCP radiation into respective VP and HP waves, and an ortho-mode transducer (OMT) to split the VP and HP waves into two separate waveguide ports. The polarizer together with the OMT forms a sub-system with three physical interface ports, whose total size is relatively large. The current embodiment includes a new more compact dual circular polarizer, whose generation and mechanism is significantly different from those known in the art. According to the current embodiment, the isolation of two rectangular ports and generating the RHCP and LHCP in the circular port are provided by the H-plane stub and two central pins. The network and S-matrix for the present polarizer are provided herein. The designed frequency range of the polarizer is in the Ka-band, and it should be emphasized that this device can be scaled to different frequency bands.","Turning now to analysis and optimization of one embodiment of a turnstile polarizer, consider a symmetric structure shown in FIG. 28 , having a turnstile of rectangular waveguides coupled with a circular waveguide in the E-plane. This structure has five ports (four rectangular ports labeled Port 1 , Port 3 , Port 4 and Port 5 , and one circular labeled Port 2 ) and six modes (identified as Port N:M, where N is the port number and M is the mode number associated with Port N). There are four symmetric planes: diagonal planes A and B, and horizontal and vertical planes C and D. Shown herein, the S-parameter for the OMTs is significantly different from that for the design of the current embodiment. The Scattering-Matrix for the six modes is the following:"," S = 1 2 ⁢ ( 0 2 0 1 1 0 2 0 0 0 0 - 2 0 0 0 2 - 2 0 1 0 2 0 0 1 1 0 - 2 0 0 1 0 - 2 0 1 1 0 ) ","If incident power from only Port 1 , corresponding to a1=[1%3b 0%3b 0%3b 0%3b 0%3b 0] T , the output vector is b 1 =S·a 1 =[0, √{square root over (2)}, 0, 1, 1, 0] T /2. implying that ½ power is excited at Port 2 %3b two TE 10 modes with ¼ equal power and equivalent phase are generated at Ports 3 and 4 %3b and Port 5 is isolated. For input power from four rectangular ports with equal amplitude but with specific incident phases, if line A is an electric boundary and B is a magnetic boundary, then the equivalent input column vector is a 2 =[1, 0, 0, −1, 1, −1] T /2 and the output vector is b 2 =S·a 2 =[0, √{square root over (2)}, √{square root over (2)}, 0, 0, 0] T /2 if line A is an magnetic boundary and B is a electric boundary, then the equivalent input column vector is a 3 =[1, 0, 0, 1, −1, −1] T /2, and the output vector is still b 2 =S·a 3 =[0, √{square root over (2)}, √{square root over (2)}, 0, 0, 0] T /2, which means that there is equal excitation of modes Port 2 : 1 and Port 2 : 2 , and no reflection in any rectangular port. If both A and B are magnetic boundaries, then the input and output vector are either the same a 3 =[1, 0, 0, 1, 1,] T /2, there is no mode excited in the circular waveguide when the higher order mode (i.e., TM 01 ) is cutoff in the circular waveguide. Similarly, there is no mode excited if both A and B are electric boundaries. By assigning A as an electric boundary and B as a magnetic boundary, the turnstile junction is decomposed to four units, and a quarter structure consisting of Port 1 and 1 / 4 of Port 2 is obtained. By using the 3-D electromagnetic simulation tool HFSS, the quarter structure is optimized, whose S parameter can be matched by adding two metallic posts to the center and adjusting their heights and diameters. The matched quarter structure supplies a range of parameters of the pins to help to realize the whole S-Matrix in HFSS simulation. The finally optimized field distribution and S parameters are shown in FIGS. 29A-29B .","FIGS. 29A-29B show that, when the structure (see FIG. 29A ) is matched and fed with unit power in Port 1 , TE 11 mode Port 2 : 1 polarized along the incident rectangular waveguide with −3 dB power is excited in the circular waveguide Port 2 %3b two TE 10 modes with power of −6 dB and equivalent phase are equally generated at the neighbor Ports 3 and 4 %3b the opposite Port 5 is isolated%3b and there is no coupling to the TE 11 mode Port 2 : 2 (S 1,2:2 \u003c−50 dB in the frequencies, and not shown in FIG. 29B ). As a comparison, take an example, the turnstile OMT is as illustrated in FIG. 30A . For an incident wave at Port 1 , one-half power is excited in the circular port, as shown in FIGS. 30B-30C , however, the opposite port is not isolated, there are strong reflection back, and the neighbor ports have \u003c¼ power. The S-parameters for the turnstile OMT are also found to be different from the structure presented here.","Turning now to how the polarizer is enabled. When incident wave E 0 is fed in Port 1 , the excited field E 0 /2 towards Port 3 and Port 4 are the same with equal phases, shown in FIG. 31A . It should be emphasized that the phase of the incident wave at the central area determines the phases of the excited waves in adjacent ports and Port 2 . For instance, the incident wave from Port 3 with 0° phase and field E 0 /2 at the central area excites the neighbor Port 5 and Port 1 with transient electric vector direction out of page and field E 0 /4, and electric vector of mode Port 2 : 2 towards Port 4 with field √{square root over (2)}E 0 /4, shown in FIG. 31B %3b incident wave from Port 4 with 180° phase and field −E 0 /2 at the central area excites the neighbor Port 5 and Port 1 with transient electric vector direction into the page and field −E 0 /4, and electric vector of mode Port 2 : 2 also towards Port 4 with field √{square root over (2)}E 0 /4 illustrated as FIG. 31C . The question is how could the Port 3 and Port 4 have 180° phase difference at the central area? By placing a short on arms 3 and 4 , and adjusting their phase length difference to be equal to (2n+1)λ g /4, where n is an nonnegative integer, when the waves reflected from the shorted Ports of 3 and 4 arrives at the central area, they will have a phase difference of 180°, which means two opposite incident phases. Consequently, the Port 2 : 2 respectively excited by the shorted Ports 3 and 4 are summed to √{square root over (2)}/2E 0 and the TE 10 modes generated towards Port 1 and 5 are fully cancelled. Thus, two orthogonal TE 11 modes with equal amplitude are excited by the structure.","When the phase difference of two orthogonal mode Port 2 : 1 and Port 2 : 2 is 90° or −90°, the turnstile polarizer is realized, and the optimized dimensions are illustrated in Table 4, and the S-parameter is shown in FIG. 32A . A turnstile polarizer was previously researched. However, it did not give any theoretical or experimental S-parameters. Only far field radiation patterns were recorded, and there was no information on its bandwidth. The physics of how the polarizer realized was not explained clearly. Actually, the phase response on frequency influences the bandwidth of the polarizer, which will be shown in the following paragraph."," TABLE 4 The optimized parameter for a turnstile polarizer (in unit of mm). Length difference Circular L arm4 − L arm3 Rectangular waveguide waveguide (2n + 1)λ g /4 Cylinder Pins Width Height Radius L arm3 not Radius Height Radius Height W r H r R c close to zero R 1 Z 1 R 2 Z 2 7.6 3.455 3.6 2.12 1.05 0.48 3.56 ","The phase of the mode Port 2 : 2 depends on the arm lengths L 3 and L 4 of the branches at Ports 3 and 4 . The phases φ 3 and φ 4 of the reflected wave at the entrance of the central area is φ 3,4 ˜2βL 3,4 , where β is the propagation constant. Thus, the phase of excited the mode Port 2 : 2 is varied for different lengths L 3,4 , and the phase difference of two orthogonal mode Port 2 : 1 and Port 2 : 2 is varied with branch lengths, as shown in FIG. 33 . It is found that the slope of the phase difference decreases when the arm length shortens and it reaches the minimum when the arm 3 vanishes and the arm 4 is ¼λ g long. This is because the propagation constant β depends on frequency, φ 3,4 (f, L 3,4 )˜2β(f, L 3,4 , and the longer L 3,4 , the larger the variation range of φ 3,4 for different frequencies. Thus, the slope of phase variation of TE 11 mode 2 decreases with shortening the arm length. Consequently, the profile of the circular polarizer has become an H-type T junction of rectangular waveguide, with a shorted H-plane arm of a ¼λ g long, and one E-plane circular waveguide located on top. However, when the arm 3 trends towards zero and the arm 4 is close to ¼λ g , the evanescent wave excited at port 3 and port 4 will significantly disturb the electric boundary, hence, the center pins used to match the S-Matrix for a Turnstile polarizer becomes mismatched, as illustrated the S parameters in FIG. 32B , compared with the matched one in FIG. 32A . Thus, using the five ports with six modes to analyze the new H-type T junction polarizer is not suitable any more. Consequently, previous device could not make one arm close to zero. FIG. 33 shows variation of phase difference of TE 11 modes 1 and 2 with arm lengths L 3 , according to one embodiment of the invention.","The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive. Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 shows a circular waveguide coupled to a rectangular waveguide from the broad side, according to one embodiment of the invention.","FIG. 2 shows termination of the guide for matching both the TE 10 mode and the TE 20 mode to the circular waveguide TE 11 modes, according to one embodiment of the invention.","FIG. 3 shows a hybrid based on two fundamental mode waveguide and one overmoded waveguide port, according to one embodiment of the invention.","FIG. 4 shows a polarizer with a stub matching, according to one embodiment of the invention.","FIG. 5 shows a polarizer with a capacitive dome matching, according to one embodiment of the invention.","FIG. 6 shows a compact version of the polarizer with a stub matching, according to one embodiment of the invention.","FIG. 7 shows a schematic drawing of the symmetric 3-port polarizing diplexer%3b Port 1 , Port 2 and Port 3 are defined as shown, according to one embodiment of the invention.","FIGS. 8A-8B show electric field vector distributions for the symmetric diagonal plane as ( FIG. 8A ) a perfect electric wall and ( FIG. 8B ) a perfect magnetic wall, where the frequency is 31 GHz, according to one embodiment of the invention.","FIG. 9 shows optimized S-parameters for structure with four pins%3b 2 : 1 represents Port 2 : mode 1 , and 2 : 2 represents Port 2 : mode 2 , according to one embodiment of the invention.","FIGS. 10A-10G show variation of the S parameters with the parameters of ( FIG. 10A ) X 1 , ( FIG. 10B ) Z 1 , ( FIG. 10C ) X 2 , ( FIG. 10D ) Y 2 , ( FIG. 10E ) Z 2 , ( FIG. 10F ) R 1 and ( FIG. 10G ) R 2 , the data of symbol ◯, Δ, □ represent for S 11 at 31 GHz, 26 GHz, and 36 GHz, and *, ⋄%3b and ∇ for S 13 at 31 GHz, 26 GHz, and 36 GHz, according to one embodiment of the invention.","FIGS. 11A-11B show ( FIG. 11A ) the final structure of 3-port compact polarizing diplexer and ( FIG. 11B ) the optimized S parameter, according to one embodiment of the invention.","FIGS. 12A-12B show ( FIG. 12A ) the optimized S parameters and ( FIG. 12B ) the phase differences of the two orthogonal TE 11 modes of the circular polarizer at Port 1 , according to one embodiment of the invention.","FIG. 13 shows the optimized S parameters of the circular polarizer with regard to Port 2 (the solid line S( 2 : 1 %3b 2 : 2 ), the dashed blue S(S( 2 : 2 %3b 2 : 1 )), the dashed-dotted line S(S( 2 : 2 %3b 2 : 2 )), the dotted line S( 2 : 1 %3b 2 : 1 ), the diamond, circular, rectangular, and triangular lines S( 2 : 1 %3b 1 ), S( 2 : 2 %3b 1 ), S( 2 : 1 %3b 3 ), and S( 2 : 2 %3b 1 ), according to one embodiment of the invention.","FIGS. 14A-14C show the snapshot electric field on the surface of the circular polarizer%3b ( FIG. 14A ) 28 GHz, ( FIG. 14B ) 31 GHz and ( FIG. 14C ) 34 GHz, according to one embodiment of the invention.","FIG. 15 shows a comparison of the measured and theoretical return loss S 11 and isolation S 13 , according to one embodiment of the invention.","FIGS. 16A-16C show ( FIG. 16A ) the measured transmission coefficient (twice of the insertion loss) and ( FIG. 16B ) the output of one rectangular port by successively rotating one polarizer with 0°, 90°, 180°, and 270° and ( FIG. 16C ) the axial ratio, according to one embodiment of the invention.","FIGS. 17A-17B show ( FIG. 17A ) a schematic drawing of the dual circular polarizer ( FIG. 17B ) the transient field distribution for the compact dual circular polarizer, according to one embodiment of the invention.","FIGS. 18A-18B show ( FIG. 18A ) a comparison of the measured and theoretical return loss S 11 and isolation S 13 ( FIG. 18B ) the output of one rectangular port for back-to-back jointed polarizers by successively rotating one polarizer with 0°, 90°, 180°, and 270°, according to one embodiment of the invention.","FIGS. 19A-19C show ( FIG. 19A ) the vector electric field and complex magnitude of surface field, ( FIG. 19B ) on top surface, and ( FIG. 19C ) on bottom for the equivalent symmetric electric boundary, according to one embodiment of the invention.","FIGS. 20A-20B show ( FIG. 20A ) the vector electric field and ( FIG. 20B ) complex magnitude on bottom surface for the equivalent symmetric magnetic boundary, according to one embodiment of the invention.","FIGS. 21A-21B show ( FIG. 21A ) S parameters of the dual polarizer%3b S 11 for return loss%3b S 1:2:1 and S 1:2:2 for transition to two orthogonal TE 11 modes%3b S 13 for isolation%3b ( FIG. 21B ) phase difference of two orthogonal TE 11 modes, according to one embodiment of the invention.","FIGS. 22A-22B show ( FIG. 22A ) twice of the insertion loss (see FIG. 18B for the output of one rectangular port), and ( FIG. 22B ) the output of the other rectangular port for back-to-back jointed polarizers by successively rotating one polarizer with 0°, 90°, 180°, and 270°, according to one embodiment of the invention.","FIGS. 23A-23B show ( FIG. 23A ) the structure of the high power polarizer and ( FIG. 23B ) the transient surface field of the high power dual polarizer, according to one embodiment of the invention.","FIG. 24 shows the S parameters for the high power dual polarizer, according to one embodiment of the invention.","FIG. 29 shows the transient field distribution for the broadband dual circular polarizer, according to one embodiment of the invention.","FIGS. 26A-26B show a comparison of the measured and theoretical return loss S 11 and isolation S 13 , according to one embodiment of the invention.","FIGS. 27A-27B show the structure and surface field of the plunger for compact phase shifter, according to one embodiment of the invention.","FIG. 28 shows a symmetric turnstile of rectangular waveguides coupled to a circular waveguide, according to one embodiment of the invention.","FIG. 29A-29B show ( FIG. 29A ) the transient surface electric field and ( FIG. 29B ) S parameters of the 5-port symmetric structure%3b ‘o’ and ‘*’ respectively for S 13 and S 14 (Wave incidence from port 1 with a unit power), according to one embodiment of the invention.","FIGS. 30A-30C show a turnstile OMT structure ( FIG. 30A ) with two posts, ( FIG. 30B ) transient surface field for incident wave at Port 1 and ( FIG. 30C ) S-parameters S 1,2:1 ˜−3 dB, S 13 and S 14 have overlapped curves, S 11 and S 15 have overlapped curves), according to one embodiment of the invention.","FIGS. 31A-31C show excited modes and the corresponding phases for different incident ports, ( FIG. 31A ) Port 1 fed in with 0° wave, ( FIG. 31B ) Port 3 with 0° wave, ( FIG. 31C ) Port 4 fed in with 180° wave, where the circled cross and circled dot symbols respectively represents transient vector of the electric field in and out of the page, according to one embodiment of the invention.","FIG. 32A-32B show S parameters of the turnstile polarizer for the arm 3 length of ( FIG. 32A ) 5.6 mm and ( FIG. 32B ) 0 mm, according to one embodiment of the invention.","FIG. 33 shows variation of phase difference of TE 11 modes 1 and 2 with arm lengths L 3 , according to one embodiment of the invention."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under contract no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,419,322","html":"https://www.labpartnering.org/patents/9,419,322","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,419,322"},"labs":[],"inventors":[{"name":"Sami G. Tantawi","location":"Stanford, CA, US"}],"assignees":[{"name":"The Borad of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A multi-port waveguide, comprising:a. a rectangular waveguide, wherein said rectangular waveguide comprises a Y-shape structure along an, x-y plane, having a first top arm, a second top arm, and a base arm, wherein said first top arm comprises a first rectangular waveguide port, wherein said second top arm comprises a second rectangular waveguide port, wherein an end of said base arm comprises a third rectangular waveguide port that is capable of supporting a TE10 mode and a TE20 mode, wherein said third rectangular waveguide port comprises rounded edges that are parallel to a z-axis relative to said x-y plane of said rectangular waveguide%3bb. a circular waveguide, wherein said circular waveguide comprises a circular waveguide port that is capable of supporting a left hand circular polarization TE11 mode and a right hand circular polarization TE11 mode, wherein said circular waveguide is coupled to a broad wall of said base arm of said rectangular waveguide%3b andc. a matching feature, wherein said matching features is disposed on said broad wall of said base arm that is opposite of said circular waveguide, wherein said matching feature is capable of terminating said third rectangular waveguide port, wherein said first rectangular waveguide port, said second rectangular waveguide port and said circular waveguide port are capable of supporting 4-TE modes."},{"idx":"00002","text":"The multi port waveguide of claim 1, wherein said matching feature comprises a stub feature, wherein said stub feature projects outward from said broad wall of said base arm."},{"idx":"00003","text":"The multi port waveguide of claim 1, wherein said matching feature comprises a capacitive dome, wherein said capacitive dome projects inward from said broad wall of said base arm."},{"idx":"00004","text":"The multi port waveguide of claim 1, wherein said matching feature comprises a pin feature, wherein said pin feature projects outward from said broad wall of said base arm."},{"idx":"00005","text":"The multi port waveguide of claim 1, wherein said circular waveguide is disposed at a pre-defined distance from a junction of said first top arm and said second top arm along said base arm, wherein said pre-defined distance is according to matching and phase properties of said left hand circular polarization TE11 mode and said right hand circular polarization TE11 mode, wherein a phase difference between said TE11 mode along said first top arm and said TE11 mode said second top arm is 90-degrees."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"082","main-group":"5","action-date":"2016-08-16","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","P","082","5","2016-08-16","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"16","main-group":"5","action-date":"2016-08-16","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"08","main-group":"5","action-date":"2016-08-16","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"127","main-group":"3","action-date":"2016-08-16","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"16","main-group":"1","action-date":"2016-08-16","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"20","main-group":"5","action-date":"2016-08-16","origination":"","symbol-position":"L"}],"document_number":"20150194720","document_published_on":"2015-07-09","document_kind":"","document_country":""},{"number":"9,398,681","artifact":"grant","title":"Distributed coupling high efficiency linear accelerator","filed_on":"2014-03-12","issued_on":"2016-07-19","published_on":"2014-07-10","abstract":"A microwave circuit for a linear accelerator includes multiple monolithic metallic cell plates stacked upon each other so that the beam axis passes vertically through a central acceleration cavity of each plate. Each plate has a directional coupler with coupling arms. A first coupling slot couples the directional coupler to an adjacent directional coupler of an adjacent cell plate, and a second coupling slot couples the directional coupler to the central acceleration cavity. Each directional coupler also has an iris protrusion spaced from corners joining the arms, a convex rounded corner at a first corner joining the arms, and a corner protrusion at a second corner joining the arms.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application is a continuation-in-part of U.S. patent application Ser. No. 13/947,043 filed Jul. 20, 2013, which claims priority from U.S. Provisional Patent Application 61/674,262 filed Jul. 20, 2012, both of which are incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under contract DE-AC02-76SF00515 awarded by Department of Energy. The Government has certain rights in this invention.","FIELD OF THE INVENTION","The present invention relates generally to linear accelerators. More specifically, it relates to improved microwave linear accelerators.","BACKGROUND OF THE INVENTION","A linear particle accelerator (linac) accelerates charged particles using a series of oscillating electric potentials generated by RF cells joined together to form a linear beamline. At one end of the linac, the particles from a particle source are injected into the beamline using a high voltage. The typical design process for a linear accelerator requires careful consideration of the coupling parameters between adjacent cells. These structures are fed from one single point or input guide and the power flows from that point to all cells through coupling holes which typically also serve as the beam tunnel for the particles being accelerated. Coupling between cells limits the ability of designers to optimize the cell shape for efficiency (high shunt impedance) and power and gradient handling capability.","SUMMARY OF THE INVENTION","In one aspect, this invention provides a topology for independently feeding each cell, or group of cells, in the accelerator structure. The theoretical idea of feeding each cavity is old%3b however, until now there has been no practical implementation that allows such topology to exist. Meeting this long-standing need, this invention provides a practical implementation of a microwave circuit that is capable of separately feeding individual or multiple cavities. This circuit is designed in such a way that the coupling between cavities is minimized, or nearly minimized. This was previously thought to be impractical due to the required size of the directional couplers, microwave bends and RF loads needed to implement the circuit which all has to fit within the distance between two adjacent cells. This distance is typically less than one half of the RF wavelength.","In one aspect, the present invention provides several new topologies for microwave linear accelerators that allow the optimization of the individual cavities without the constraint usually applied to the coupling between adjacent cavities. This has the benefit of more efficient designs that consumes less RF power, i.e., it allows for an enhanced optimization of the so-called shunt impedance that is the amount of power required for a given accelerator gradient. Hence, the overall cost of building a linear accelerator system for any application is substantially reduced. Furthermore, being able to optimize the accelerator structure shape without the constraint imposed by coupling between the cells allow the optimization process to be geared towards low surface electric and magnetic field and hence more reliable high gradient operation. It has been known for a while that the n-mode structure could be designed with high efficiency. However, this can only work for a small number of cells because of the mode density problems associated with small coupling between cells—a feature required for efficient operation. This problem is currently addressed by the use of bi-periodic structure configurations. In these configurations, an additional set of cavities are inserted either in-line or on the side of the structure to facilitate coupling between cells, ending up with a structure that looks like a π mode from the beam point of view but behaves like a π/2 structure from a circuit point of view. These structures work well but they have a serious drawback: the losses consumed in the in-line cavities or the side cavities reduces the shunt impedance especially in the case of moderate to heavy beam loading. Furthermore, when using the inline cavity configuration the space consumed by the cavity reduces the gradient and reduces the efficiency. In the case of the side coupled cavities the coupling slots associated with each cavity also are expensive and limit the high gradient operation because of the magnetic field enhancement leading to surface fatigue.","Embodiments of this invention allow for the simple realization of the efficient π-mode structure without the drawbacks mentioned above. We eliminate the need for either the types of coupling cavities by, in the first embodiment of this invention feeding each cavity by a compact directional coupler, and in the second embodiment by a symmetrical distribution system. The RF coupling in either case has no resonant structures and hence is highly efficient.","In the first case it also provides an implementation of ideas proposed by one of the inventors, and for which the reflection to the source is eliminated. The second implementation has all the waveguide in the distribution system oriented such that the small dimensions of the waveguide oriented along the accelerator structures radial direction. This orientation minimizes the structure volume and complexity, allowing for lighter and more compact implementation.","According to one embodiment, a microwave circuit is provided having compact, tolerance insensitive, directional couplers, compact E-plane bends, and multiple azimuthal feeds from a single feed.","According to another embodiment, a microwave circuit is provided having a distribution waveguide with its width designed to provide appropriate phase shift between feed arms, where each of the feed arms has two slots feeding two separate short accelerator sections (e.g., each section may have four cavities), where two slots in each feed arm provide a natural 180 degree phase shift between the two fed accelerator section due to the nature of the fundamental mode in the waveguide representing these feed arms. This is ideal for the efficient π-mode accelerator structure. The short circuit length at the end of the feed arm is roughly the guide wavelength divided by four. It is designed this way to maximize the coupling at the slots and hence minimize the size of the slot perturbing the accelerator cavity which contains these slots. Short circuit length at the end of the distribution waveguide designed to make an equal distribution of power between arms.","Any application for a linear accelerator could benefit from this invention because it reduces RF power requirements due to the possibility of optimization of cell shape without undue concern about the coupling between cells, and hence reduces the cost associated with the RF power sources needed for these linacs, and it allows for the implementation of linac structures in a much shorter distance because of the high gradient capabilities of this invention, which is due to the possibility of optimizing the cell shapes for high gradient operation without constraint imposed by cell to cell coupling In particular, embodiments of the invention have commercial application in medical electron accelerators, medical proton accelerators, high energy lepton accelerators for future colliders, high energy hadron accelerators for accelerator driven systems for nuclear fission power stations, future light sources either for compactness or for the capability to operate at high repetition rate efficiently, and accelerator for active interrogation systems for national security.","Accelerators according to the present invention provide a more efficient accelerator structure than others known in the art. Also they are capable of handling high gradient fields which provide compactness of the structures. Both those two features can lead to cost effective systems.","DETAILED DESCRIPTION","FIG. 1 is an illustration of a monolithic metallic linac cell plate according to an embodiment of the invention. A microwave circuit for a linear accelerator may be formed by stacking multiple such cell plates upon each other. The cell has four cross-shaped directional couplers 100 , 102 , 104 , 106 symmetrically oriented around an acceleration cavity 108 that is aligned with a vertical beam axis of the linear accelerator. Each directional coupler 100 , 102 , 104 , 106 has coupling arms. For example, coupler 104 has arms 110 and 112 . Each coupling arm has an in-plane width less than an operational wavelength of the linear accelerator. Each of the cell plates has one or more coupling slots, such as slot 114 , that couples one of the directional couplers in the cell to an adjacent directional coupler of an adjacent cell. Each of the cell plates also has one or more coupling slots, such as slot 116 , that couples the directional coupler to the central acceleration cavity 108 . The cell plate also includes a cavity tuning access hole 118 .","The topology of the cell provides a microwave circuit that allows the implementation of the feeding system within the distance between two adjacent cells. In this figure the H-plane directional couplers are oriented in the plane normal to the acceleration which allows the coupler to be implemented in a distance less than the cell length. Also, the topology allows connecting the different directional couplers that feed the cells through a serpentine E-plane waveguide bend that also fits within the cell length. The fact that all cells are being fed through a directional coupler increases isolation between cavities and the freedom to optimize their shape for higher gradient and shunt impedance.","FIG. 2 is a parameterized model of a directional coupler according to an embodiment of the invention. This compact, tolerance insensitive, H-plane directional coupler has a 2D topology that can be produced in a single machining operation. Preferably, the cell plates are composed of high purity oxygen-free copper. The coupler has four arms 200 , 202 , 204 , 206 . Load arm 202 at the top of the figure is opposite lower arm 206 which couples to the beam tunnel 224 via a taper 226 to match the waveguide to cavity coupling slot and a step 228 in waveguide height to maintain mechanical structural integrity. The two side arms 200 , 204 each have elbow coupling regions 230 , 232 defined by matching irises 234 , 236 formed by protrusions 234 , 236 from the walls. The side arms 200 and 204 have minimum lengths of ½ the waveguide wavelength to eliminate interaction between irises.","The wall of each arm has a protrusion VN 208 , 210 , 212 , 214 forming an iris whose height is selected to minimize reflection and maximize directivity. These protrusions are positioned on alternating sides of the arm walls, and the spacing UN between the protrusions and the corners joining the arms is selected to minimize reflection and maximize directivity. UN and VN are coupled to simultaneously minimize reflection and maximize directivity. The corners joining the arms are of two types. Rounded corners RN 216 , 218 have a convex curvature viewed from inside the cell and are positioned diagonally opposite each other. The other two corners DN 220 , 222 have protrusions into the cell that are selected to set forward the coupling factor. The RN protruding feature and the shifting by UN of the VN protruding feature away from the corners, greatly reduces the sensitivity of the cell to machining tolerances, making it finally practical to build the cell within required tolerances.","The design of the coupler can be characterized by the four parameters: UN, VN, DN, RN. For example, the dimensions of a directional coupler with a coupling factor of 3 dB are UN=21.857 mm, VN=3.418 mm, DN=13.350 mm, RN=3.537 mm, and the dimensions for 4.77 dB are UN=16.320 mm, VN=1.586 mm, DN=14.930 mm, RN=5.143 mm. FIG. 3 shows a Monte-Carlo simulation of the sensitivity of the coupler to random variation of the four design parameters.","FIG. 4 is an isometric view detailing side arms 400 , 402 and corresponding coupling regions 404 , 406 for two stacked directional couplers, implementing an E-plane bend, according to an embodiment of the invention. The different shades depict different electric field intensities, and the coupler is split down the middle of the bend along the beam axis. The dashed line 408 indicates the dividing line between cell plates. Region 410 is the coupling slot between these adjacent plates (corresponding to slot 114 of FIG. 1 ). Protrusion 412 is the matching iris for the elbow. Ends 414 , 416 are output and input arms, respectively, to their respective cells. In contrast with conventional bends that require a 3D machining operation, this implementation of the E-plane bend can be produced by primarily a 2D machining operation.","FIG. 5 is an isometric cut-away view of a stack of multiple cell plates 500 , 502 stacked on a structure plate 504 , according to an embodiment of the invention. The structure includes cooling channels 506 , 508 , 510 , 512 . At the center is the beam tunnel 514 . Also shown are cavity tuning access slot 516 and load arm 518 of one of the directional couplers. This figure illustrates the topology that appears when cells described above in relation to FIGS. 1-4 are combined. The whole structure of each cell can be machined from a single planar block of metal. A stack of these blocks then forms the accelerator with the RF distribution network.","FIG. 6 is a top view of a cell 608 with four coupling arms input ports 600 , 602 , 604 , 606 to minimize RF driven quadrupole moments, according to an embodiment of the invention. Cell 608 has a coupling slot contour to minimize pulse heating and peak magnetic field. This input coupler allows up to four azimuthally distributed parallel fed networks. Although all the figures describe a structure that has four parallel feeds for the cells, the topology presented could be implemented for one, two, three or four parallel feeds, depending on the application. The advantage of the four feed geometry is it cancels both dipole and quadrupole RF field distortion within the cell. This may not be necessary for all applications of a linear accelerator. However, it is described here in its full complexity that would allow any application of a linear accelerator to use this invention.","It should be noted that several sections (i.e., several stacks of cells) with this topology could be connected together with a small offset between the sections to yield a superstructure. The distance between sections then can be adjusted to cancel the reflection to the source. Hence the system would act like a travelling-wave structure from the RF source%27s point of view, and will have all the advantages of a standing wave accelerator structure.","In some embodiments, it is possible to feed the structure every few cells to reduce the cost of the structure. A significant part of the advantage of this structure can be retained while increasing the number of cells per feed arm from every individual cell to multiple cells. Despite an increase in the number of cells fed per feed arm, the shunt impedance would be very high. This is demonstrated in FIGS. 7A and 7B which show an analysis of the shunt impedance versus number of cells being fed. Specifically, FIG. 7A is a graph illustrating shunt impedance as a function of the aperture radius, where the top curve is for a single isolated cavity, and the bottom curve is for the maximum number of cavities that can be fed with one feed. FIG. 7B is a graph illustrating the number of cavities per feed vs. aperture radius. The analysis depicted in these figures assumes that the number of cells that are being fed by a single feed arm is limited by the axial modal density. Hence, the number is determined by the proximity of the π mode to the π−1 mode, and the need for this separation to be more than the band width determined by the quality factor of the π-mode. The analysis is done for cavities operating at 11.424 GHz, but of course can be done at any other frequency as well to yield similar results.","It should be noted that this design can be used for injector sections where the particle speed is less than the speed of light. This will provide an ideal topology for these sections. Furthermore, this will work with heavy particle such as protons and ions.","In some embodiments, the distribution between cavities can be provided with a tap-off instead of directional couplers, hence simplifying the system further. In this case the cavities will be coupled, and this needs to be taken into account in the design. One possible implementation of these tap-offs is shown in FIGS. 8A and 8B , which illustrate a compact RF distribution waveguide 806 with feed arms 800 , 802 , 804 , each feeding two accelerator sections simultaneously with π-phase shift between them. The arms are all fed by a parallel waveguide 806 that provides appropriate phase shift between feed arms and distributes the power equally between all the arms. Indeed it is always possible to achieve this equal distribution of power between arms using a translationally symmetric distribution%3b i.e., each arm of the distribution system is coupled to the distribution wave guide with the same coupling features and with the same coupling coefficient. The distance between the arms 800 , 802 , 804 , would allow for either equal phases or alternating phases with 180 degree phase shift between arms. This will allow for a great flexibility in the design. The input 808 is shown at one end of waveguide 806 . Finally, the position of the short circuit 810 at the opposite end of the distribution waveguide 806 is adjusted and placed to create the appropriate standing wave pattern allowing for this equal coupling with the appropriate phase shift and equal distribution of power between arms. The short circuit length at the end of the feed arm is roughly the guide wavelength divided by four. It is designed this way to maximize the coupling at the slots and hence minimize the size of the slot perturbing the accelerator cavity which contains these slots. The feed arms 800 , 802 , 804 may be implemented as symmetrical pairs to eliminate dipole field components. A feed arm with two slots feeds two separate short accelerator sections (each section comprises four cavities in this particular example). Note that due to the nature of the fundamental mode in the feed arm waveguide there is a natural 180 degree phase shift between the two fed accelerator sections 812 , 814 . This is ideal for the efficient π-mode accelerator structure.","This design uses a waveguide with its narrow wall along the radial direction of the structure, which allows for compact mechanical structure. Then a dual tap-off from each side allow followed by an E-plane bend provide the feed to two sections of the accelerator structure simultaneously through two coupling slots. Note that the feeding waveguide field has an odd symmetry around the two coupling slot, and hence its perfectly aligned to feed the π-mode of a standing wave accelerator structure. This way one can feed a number of accelerator structure sections with only series of tap-offs that are half that number of sections fed%3b thus reducing the mechanical complexity of the overall structure. Note also that it is possible to design the overall tap-off network from identical tap-offs separated by an integer number of free space wavelength. At the same time the amplitude of the output signal at each tap off is equal and the phases of the output of the tap-offs are equal. Just as well one could have designed the system with a π-phase shift between outputs to feed every odd number of cavities rather than even, the case shown in FIG. 8B . Finally note that the position of the short-circuit at the end of the distribution system plays a crucial role in the design and have to be chosen carefully to achieve this performance.","Since the structures are applicable to devices at different frequencies, dimensions of the cavities, couplers and plates are determined relative to the operational wavelength or frequency. Cavities have a length of approximately one half wavelength and a diameter of approximately 4.2 c/2λf, where c is the speed of light and f is the frequency. The coupling arms that form the coupler preferably have a width W such that λ/2\u003cW\u003cλ, where λ is the wavelength. The plates preferably have a thickness equal to the cavity length."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 is an illustration of a linear accelerator RF cell with four directional coupler feeds according to an embodiment of the invention.","FIG. 2 is an illustration of a directional coupler according to an embodiment of the invention.","FIG. 3 is a graph of frequency of occurrence vs. difference from design value resulting from a Monte-Carlo simulation of the sensitivity of the coupler to the four design parameters according to an embodiment of the invention.","FIG. 4 is an illustration of an E-plane bend where the different shades depict different electric field intensities, and where the coupler is split down middle of bend along beam axis, and the dashed line indicates second half of coupler on following plate, according to an embodiment of the invention.","FIG. 5 illustrates a stack of cell plates split in half along beam axis, according to an embodiment of the invention.","FIG. 6 illustrates a cell with four coupling arms to minimize RF driven quadrupole moments, according to an embodiment of the invention.","FIG. 7A is a graph illustrating shunt impedance as a function of the aperture radius, where the top curve is for a single isolated cavity, and the bottom curve is for the maximum number of cavities that can be fed with one feed, according to an embodiment of the invention.","FIG. 7B is a graph illustrating the number of cavities vs. aperture radius, according to an embodiment of the invention.","FIGS. 8A and 8B illustrate a compact RF distribution system with feed arms, each feeding two accelerator sections simultaneously with π-phase shift between them, according to an embodiment of the invention."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under contract DE-AC02-76SF00515 awarded by Department of Energy. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,398,681","html":"https://www.labpartnering.org/patents/9,398,681","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,398,681"},"labs":[],"inventors":[{"name":"Sami G. Tantawi","location":"Stanford, CA, US"},{"name":"Jeffrey Neilson","location":"Redwood City, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A microwave circuit for a linear accelerator, the microwave circuit comprising multiple monolithic metallic cell plates, a distribution waveguide, and a sequence of feed arms%3bwherein the cell plates are stacked upon each other and grouped to form a sequence of cell sections%3bwherein each of the feed arms has two slots coupled symmetrically on opposite sides of the distribution waveguide, wherein the two slots are coupled to adjacent cell sections."},{"idx":"00002","text":"The microwave circuit of claim 1 wherein each of the feed arms is designed to provide equal power and appropriately correlated phases to the adjacent cell sections."},{"idx":"00003","text":"The microwave circuit of claim 1 wherein each of the feed arms has a short circuit length equal to a quarter of a waveguide wavelength."},{"idx":"00004","text":"The microwave circuit of claim 1 wherein each of the cell sections has four cells."},{"idx":"00005","text":"A microwave circuit for a linear accelerator, the microwave circuit comprising multiple monolithic metallic cell plates, a distribution waveguide, and a sequence of feed arms%3bwherein the cell plates are stacked upon each other and grouped to form a sequence of cell sections%3bwherein each of the feed arms has a short circuit length equal to a quarter of a waveguide wavelength%3bwherein each of the feed arms has two slots coupled symmetrically on opposite sides of the distribution waveguide, wherein the two slots are coupled to adjacent cell sections."}],"cpc":{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"04","main-group":"9","action-date":"2016-07-19","origination":"","symbol-position":"F","further":["05","","H","B","US","H","","H","04","9","2016-07-19","","F"]},"ipc":[{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"04","main-group":"9","action-date":"2016-07-19","origination":"","symbol-position":"F"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"7","action-date":"2016-07-19","origination":"","symbol-position":"L"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"18","main-group":"7","action-date":"2016-07-19","origination":"","symbol-position":"L"}],"document_number":"20140191654","document_published_on":"2014-07-10","document_kind":"","document_country":""},{"number":"9,386,682","artifact":"grant","title":"Distributed coupling and multi-frequency microwave accelerators","filed_on":"2015-07-09","issued_on":"2016-07-05","published_on":"2016-01-14","abstract":"A microwave circuit for a linear accelerator has multiple metallic cell sections, a pair of distribution waveguide manifolds, and a sequence of feed arms connecting the manifolds to the cell sections. The distribution waveguide manifolds are connected to the cell sections so that alternating pairs of cell sections are connected to opposite distribution waveguide manifolds. The distribution waveguide manifolds have concave modifications of their walls opposite the feed arms, and the feed arms have portions of two distinct widths. In some embodiments, the distribution waveguide manifolds are connected to the cell sections by two different types of junctions adapted to allow two frequency operation. The microwave circuit may be manufactured by making two quasi-identical parts, and joining the two parts to form the microwave circuit, thereby allowing for many manufacturing techniques including electron beam welding, and thereby allowing the use of un-annealled copper alloys, and hence greater tolerance to high gradient operation.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims priority from U.S. Provisional Patent Application 62/022,469 filed Jul. 9, 2014, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under grant (or contract) no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","FIELD OF THE INVENTION","The present invention relates generally to linear accelerators. More specifically, it relates to improved microwave linear accelerators.","BACKGROUND OF THE INVENTION","A linear particle accelerator (linac) accelerates charged particles using a series of oscillating electric potentials generated by RF cells joined together to form a linear beamline. At one end of the linac, the particles from a particle source are injected into the beamline using a high voltage. The typical design process for a linear accelerator requires careful consideration of the coupling parameters between adjacent cells. These structures are fed from one single point or input guide and the power flows from that point to all cells through coupling holes which typically also serve as the beam tunnel for the particles being accelerated. Coupling between cells limits the ability of designers to optimize the cell shape for efficiency (high shunt impedance) and power and gradient handling capability.","Commonly owned U.S. Pat. Appl. Pub. 20140191654 entitled “Distributed Coupling High Efficiency Linear Accelerator”, which is incorporated herein by reference, describes a practical implementation of a microwave circuit that is capable of separately feeding multiple cavities while minimizing the coupling between cavities. This design, however, has a somewhat complicated structure in the case of coupling to each cavity. In the case of coupling to every few cavities, it has a simple structure but at the expense of a reduced efficiency. Accordingly, there remains a need for further improvement in efficient linac design.","SUMMARY OF THE INVENTION","Improving on the earlier work described in U.S. Pat. Appl. Pub. 20140191654 as discussed above, the present invention simultaneously provides a simple design that couples to each cavity while also attaining a maximum efficiency. The simplicity of the design is thus less expensive to manufacture and also provides superior performance. This improvement can benefit various applications of linacs, including scientific research, national security, and medical, and industrial applications.","In one aspect, this invention presents a new topology for microwave accelerators that optimizes their efficiency. It allows linear accelerators to operate with much less power for a given acceleration gradient than existing accelerators. This design allows the structure to be highly efficient and also allows the structure to be built economically because of the smaller number of parts. It allows the structure to operate at even higher efficiency if one uses two frequencies and two modes. It allows for extremely high gradient operation, especially in the two-modes, two-frequency topology because the fields from the two modes do not add simultaneously on the surface. It allows high repetition rate because the losses on the wall is minimized. If this design is implemented in superconducting linac it allows the dynamic losses, which impact the needed refrigeration power, to be reduced by more than a factor of 2. For superconducting machines the structure could be optimized to maximize the gradient by minimizing the magnetic field, hence the maximum gradient attained by superconducting accelerators could be extended substantially. With this design, a 65 MV/m accelerator at L-band may be realized.","Innovative features include one or more of the following: The design provides coupling to each cell in the structure. It has a simple and very low loss distribution network. It provides the highest possible shunt impedance for a given set of cells. Because of the topology of the distribution system, it allows the manufacturing of the accelerator structure from only two blocks. This is in contrast to typical structures that are manufactured from 10%27s of cells brazed together. It leaves room for two distribution systems, and hence one can feed the structure at two different frequencies allowing for even better shunt impedance and ever lower power for a given gradient.","In one aspect, the invention provides a microwave circuit for a linear accelerator. The circuit includes multiple metallic cell sections, a pair of distribution waveguide manifolds, and a sequence of feed arms connecting the manifolds to the cell sections. The distribution waveguide manifolds are connected to the cell sections so that alternating pairs of cell sections are connected to opposite distribution waveguide manifolds. The distribution waveguide manifolds have concave modifications of their walls opposite the feed arms, and the feed arms have portions of two distinct widths. The coupling geometry to each cell section is preferably implemented with a three port network adapted such that a dependence of the accelerator cavity design on a distribution manifold circuit parameter is minimized. The three port network is an E-plane junction, and the waveguide manifolds and three-port network are formed from two parts joined along the E-plane. In some embodiments, the distribution waveguide manifolds are connected to the cell sections by two different types of junctions adapted to allow two frequency operation. Each distribution waveguide manifold may be composed of identical units, whereby power may be distributed evenly between accelerator structures. The distribution waveguide preferably matches a set of standing wave accelerator structures and allows for reflected power be output to external loads.","In another aspect, the invention provides a method of manufacturing a microwave circuit for a linear accelerator by making two quasi-identical parts, and joining the two parts to form the microwave circuit, where the microwave circuit comprises multiple metallic cell sections, a pair of distribution waveguide manifolds, and a sequence of feed arms connecting the manifolds to the cell sections, where the distribution waveguide manifolds are connected to the cell sections so that alternating pairs of cell sections are connected to opposite distribution waveguide manifolds, thereby allowing for many manufacturing techniques including electron beam welding, and thereby allowing the use of un-annealled copper alloys, and hence greater tolerance to high gradient operation. The distribution waveguide manifolds preferably have concave modifications of their walls opposite the feed arms, and wherein the feed arms have portions of two distinct widths.","DETAILED DESCRIPTION","Preferred embodiments of the invention will now be described in relation to the figures. For specific examples, for purposes of illustration only, the dimensions are based on an operating frequency of 11.424 GHz. Based on the teachings provided herein, the design methodology can be extended to any other band, as will be shown by specific calculations for other bands later in the description.","The topology of one embodiment of an accelerator structure according to the invention is shown in FIGS. 1A-C . Two manifolds 100 , 102 are feeding the structure cavities in pairs, where the two cavities in each pair are adjacent to each other and where the pairs alternately couple to one or the other of the two manifolds. Every cavity is coupled to one of the manifolds. In this embodiment, the distance between feeding points at the feeding waveguide manifold is larger than the periodic distance or the spacing between the centers of the adjacent cavities. Hence, if one operates at the pi mode, the required distance between the feeding points should be ˜½ of a guide wavelength, which is always greater than the distance between the centers of the cavity, which is a ½ a free space wavelength. This way, with only two manifolds, one can feed every cavity in the system. Note that the π mode is not a necessity but it turns out that it is very close to being optimal.","Each accelerator cavity is coupled to a manifold by a junction. For example, cavity 104 is coupled to manifold 100 by junction 108 . The cavity 104 has a coupling iris 110 whose corners are preferably rounded.","Another aspect of this embodiment is the design of the manifold junction. The optimal design of the manifold junction should achieve a minimal standing wave within the manifold waveguide. To this end, each three port network representing the manifold with a feed point, as shown in FIG. 2 , has the following scattering matrix:"," S = ( 1 - 1 - 2 ⁢ n - 1 + 1 1 + 2 ⁢ n - 2 ⁢ ⅇ ⅈ ⁢ ⁢ σ ⁢ n 1 + 2 ⁢ n - 1 + 1 1 + 2 ⁢ n 1 - 1 - 2 ⁢ n 2 ⁢ ⅇ ⅈσ ⁢ n 1 + 2 ⁢ n - 2 ⁢ ⅇ ⅈ ⁢ ⁢ σ ⁢ n 1 + 2 ⁢ n 2 ⁢ ⅇ ⅈ ⁢ ⁢ σ ⁢ n 1 + 2 ⁢ n ⅇ 2 ⁢ ⅈ ⁢ ⁢ σ ⁡ ( - 1 + 2 1 + 2 ⁢ n ) ) , where n is the number of cavities feed by a single manifold. This would guarantee attaining a minimal VSWR along the manifold. To achieve this matrix, one modifies the shape of the waveguide around the manifold 200 , as shown in FIG. 2 . A feature 202 is a protrusion on the wall of the waveguide opposite to the wall with the feed 204 of the junction. Another feature 204 is widening of the feed from a narrow portion 204 to a wider portion 206 . With these features shown in FIG. 2 , the manifold exerts minimal influence on the cavity, for which the coupling could be adjusted separately and hence the design is insensitive to the distance between the manifold and the cavities. This is a very important feature of this design which allows the system to be tunable and could be manufactured with lower tolerances. The accelerator structure with these features is shown in FIGS. 3A-B , which show a waveguide manifold 300 with protrusion 302 opposite feed with narrow portion 304 and wide portion 306 . The feed couples manifold 300 to cavity 308 . Other cavities, feeds, and protrusions are similarly designed, forming a periodic accelerator structure. The simulation of the fields in the structure is shown in FIG. 4 , which shows two parallel manifold waveguides 400 and 402 coupled to a series of 20 cavities by coupling junctions. The shading represents the intensity of the E field in the structure, where the field intensity in the manifolds is reduced compared to that near the center of the cavities where the beamline is positioned.","Each segment of the accelerator structure can be manufactured from two blocks as shown in FIGS. 5A-B for an accelerator divided into four segments with 20 cells each. Both the manifolds and the cavities have no currents crossing the plane which splits the manifold in half along the long dimension of the manifold cross section. This allows the structure to be built out of just two blocks. This reduces the complexity of manufacturing the structure and provides logical places for both the cooling manifolds and the tuning holes. FIG. 5A is a cut-away view of braze assembly including inconel spring pin (nickel ‘superalloy’) 500 , miter bend 502 , tuning pin (two per cell) 504 , and feed waveguide 506 . FIG. 5B shows a circuit ‘half’ including accelerator cell 508 , feed waveguide 510 , precision alignment holes 512 , coupling hole 514 , and axial coolant holes 516 . The circuit halves are aligned with an elastic averaging technique. Improved accuracy is derived from the averaging of error over a large number of contacting surfaces.","Although the designs of the structures shown in the above figures are done for a structure operating at 11.424 GHz, we now show the advantages of using this type of structures at other bands. The shunt impedance for an optimized design at different aperture opening and different frequency bands is shown in FIG. 6 . This shows great gains, i.e., improved shunt impedance for all bands.","Finally, this type of topology allows the structure to be fed at more than one frequency. In FIG. 7 the structure is optimized to operate at the first two modes at two different frequencies, realizing multi-frequency acceleration. FIG. 7A is a cross-sectional view for operation at a first frequency of 11.424 GHz, where Rs is 181 MΩ/m. FIG. 7B is a cross-sectional view for operation at a second frequency of 18.309 GHz, where Rs is 63 MΩ/m. The common sub-harmonic is 300 MHz and total shunt impedance is 244 MΩ/m. The shading in the figures represents the E field intensity.","This design provides a practical realization of multi-frequency operation. Conventional proposals for multi-frequency design insist on harmonically related frequencies. This, however, is not optimal. If one insists on harmonically related frequencies, the efficiency of the structure is degraded from that of a single frequency accelerator. However, here we break free from this idea and assume a single bunch operation. Hence we are able to use frequencies that simply have a common sub-harmonic. To implement the feeding for this structure we use two manifolds for each mode at a different frequency. The coupler for a two mode cavity pair is shown in FIGS. 8A-B , and the whole two-mode, two-frequency structure is shown in FIG. 9 . Note that the coupling from the manifold 800 to the cavity 804 for the lower frequency mode is done at the center of the cavity with a bent waveguide 802 . This allows coupling to this mode without disturbing the higher frequency mode. The coupling from the second manifold 808 for the higher frequency mode is achieved with a junction 806 whose design is similar to that of FIG. 3A-B by coupling on the side of the cavity 804 at the peak magnetic field point at which the coupling hole will be small enough to prevent distortion to the lower frequency mode. FIG. 9 shows the whole accelerator structure with manifolds 900 , 902 , 904 , 906 feeding the cavity pairs.","Finally one has to iterate that the principles of the present invention are not limited to normal conducting accelerator structures but are very well applicable to superconducting accelerator structures."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIGS. 1A-C show cut-away and cross-sectional views of two manifolds for feeding every cell in a pi mode accelerator structure, according to an embodiment of the invention.","FIG. 2 is a perspective view of a three port network used for each tap-off of an accelerator structure, according to an embodiment of the invention.","FIGS. 3A-B show schematic and cut-away views of coupling details for an accelerator structure, according to an embodiment of the invention.","FIG. 4 is a cut-away view of an accelerator structure, where E-field intensity is indicated by shading, according to an embodiment of the invention.","FIGS. 5A-B are perspective cut-away views of an accelerator section, where the split plane is orthogonal to feed waveguide, according to an embodiment of the invention.","FIG. 6 is a graph of shunt impedance vs. beam aperture for several bands, illustrating frequency choice for highly optimized standing-wave structure with distributed feeding, according to an embodiment of the invention.","FIGS. 7A-B are cross-sectional diagrams of accelerator structures, where shading indicates E-field intensity, for multi-Frequency acceleration, according to an embodiment of the invention.","FIGS. 8A-B show perspective and cut-away views of a coupler for a two mode cavity pair, according to an embodiment of the invention.","FIG. 9 is a perspective view of a two-mode, two-frequency accelerator structure, according to an embodiment of the invention."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under grant (or contract) no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,386,682","html":"https://www.labpartnering.org/patents/9,386,682","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,386,682"},"labs":[],"inventors":[{"name":"Sami G. Tantawi","location":"Stanford, CA, US"},{"name":"Zenghai Li","location":"Sunnyvale, CA, US"},{"name":"Philipp Borchard","location":"San Francisco, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A microwave circuit for a linear accelerator, the microwave circuit comprising multiple metallic cell sections,a pair of distribution waveguide manifolds, anda sequence of feed arms connecting the manifolds to the cell sections%3bwherein the distribution waveguide manifolds are connected to the cell sections so that alternating pairs of cell sections are connected to opposite distribution waveguide manifolds, wherein the distribution waveguide manifolds have concave modifications of their walls opposite the feed arms, and wherein the feed arms have portions of two distinct widths."},{"idx":"00002","text":"The microwave circuit of claim 1 wherein coupling geometry to each cell section is implemented with a three port network, wherein the three port network is adapted such that a dependence of the accelerator cavity design on a distribution manifold circuit parameter is minimized."},{"idx":"00003","text":"The microwave circuit of claim 2 wherein the three port network is an E-plane junction, and wherein the waveguide manifolds and three-port network are formed from two parts joined along the E-plane."},{"idx":"00004","text":"The microwave circuit of claim 1 wherein the distribution waveguide manifolds are connected to the cell sections by two different types of junctions adapted to allow two frequency operation."},{"idx":"00005","text":"The microwave circuit of claim 1 wherein each distribution waveguide manifold is composed of identical units, whereby power may be distributed evenly between accelerator structures."},{"idx":"00006","text":"The microwave circuit of claim 1 wherein the distribution waveguide matches a set of standing wave accelerator structures and allows for reflected power be output to external loads."},{"idx":"00007","text":"A method of manufacturing a microwave circuit for a linear accelerator, the method comprising making two quasi-identical parts, and joining the two parts to form the microwave circuit, wherein the microwave circuit comprises multiple metallic cell sections, a pair of distribution waveguide manifolds, and a sequence of feed arms connecting the manifolds to the cell sections%3b wherein the distribution waveguide manifolds are connected to the cell sections so that alternating pairs of cell sections are connected to opposite distribution waveguide manifolds, thereby allowing for many manufacturing techniques including electron beam welding, and thereby allowing the use of un-annealled copper alloys, and hence greater tolerance to high gradient operation."},{"idx":"00008","text":"The method of claim 7 wherein the distribution waveguide manifolds have concave modifications of their walls opposite the feed arms, and wherein the feed arms have portions of two distinct widths."}],"cpc":{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"7","action-date":"2016-07-05","origination":"","symbol-position":"F","further":["05","","H","B","US","H","","H","02","7","2016-07-05","","F"]},"ipc":[{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"9","action-date":"2016-07-05","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"12","main-group":"3","action-date":"2016-07-05","origination":"","symbol-position":"L"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"00","main-group":"9","action-date":"2016-07-05","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"00","main-group":"11","action-date":"2016-07-05","origination":"","symbol-position":"L"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"7","action-date":"2016-07-05","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"P","subgroup":"207","main-group":"1","action-date":"2016-07-05","origination":"","symbol-position":"L"}],"document_number":"20160014876","document_published_on":"2016-01-14","document_kind":"","document_country":""},{"number":"9,335,466","artifact":"grant","title":"Waveguide apparatuses and methods","filed_on":"2013-12-17","issued_on":"2016-05-10","published_on":"2014-06-26","abstract":"Optical fiber waveguides and related approaches are implemented to facilitate communication. As may be implemented in accordance with one or more embodiments, a waveguide has a substrate including a lattice structure having a plurality of lattice regions with a dielectric constant that is different than that of the substrate, a defect in the lattice, and one or more deviations from the lattice. The defect acts with trapped transverse modes (e.g., magnetic and/or electric modes) and facilitates wave propagation along a longitudinal direction while confining the wave transversely. The deviation(s) from the lattice produces additional modes and/or coupling effects.","description":{"text":["FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT","This invention was made with Government support under contracts DE-FG02-12ER86510 and DE-AC02-76SF00515 awarded by the Department of Energy. The U.S. Government has certain rights in the invention.","FIELD","Aspects of the present disclosure relate to apparatuses, devices, and methods involving waveguides.","BACKGROUND","Confinement of electromagnetic energy as it propagates along a fiber is useful for a variety of technologies including, but not limited to, communications, detectors, sensors and experimentation. One mechanism uses total internal reflection to confine the electromagnetic waves to the fiber. Total internal reflection can be accomplished by using materials with different kinds of refractive indices. In particular, a central portion of the fiber can be constructed out of a material with a higher index of refraction (“index”) than a surrounding material (or cladding material). The electromagnetic energy is reflected at the boundary between these two materials. These and other matters have presented challenges to guiding waves, as may be implemented for a variety of applications.","SUMMARY","Various example embodiments are directed to waveguides and their implementation. Certain embodiments are directed to photonic bandgap (PBG) fibers, and more particularly to the control and use of electromagnetic modes by the introduction of inserts or breaks in the periodic structure of a PBG crystal.","In accordance with an example embodiment, an optical fiber waveguide includes a substrate having a first dielectric constant, a lattice, a longitudinally-extending defect, and a set of one or more deviations. The lattice includes a plurality of lattice regions having a second, different dielectric constant. The longitudinally-extending defect is in the lattice, and acts with trapped transverse modes including at least one of a magnetic mode and an electric mode. The defect facilitates wave propagation along the longitudinal direction while confining the wave transversely, in which a corresponding phase velocity equals the speed of light (TM SOL ). The set of deviations produce additional modes and/or coupling options for the waveguide, with the deviations having physical properties that are bounded by a figure of merit.","Another embodiment is directed to a waveguide apparatus having a substrate with a first dielectric constant, a plurality of lattice regions in the substrate, a defect region in the substrate and a deviation region. The lattice regions include holes in the substrate and have a second dielectric constant that is different than the first dielectric constant. The defect region extends in a longitudinal direction and facilitates propagation of waves using a trapped transverse mode, with the waves propagating along the longitudinal direction while being confined transversely. The deviation region includes a deviation in the lattice regions and provides an additional surface-based propagation mode for the propagation of the waves. In some implementations, the lattice regions provide a photonic crystal fiber in which modes exist in frequency passbands separated by band gaps. Waves having a frequency in one of the band gaps are confined to propagation via the defect region in the trapped transverse mode.","Another embodiment is directed to a method in which waves are propagated via a waveguide including a substrate having a first dielectric constant, and a lattice that includes a plurality of lattice regions in the substrate and having a second, different dielectric constant. Waves are propagated along a longitudinal direction and confined transversely, with a corresponding phase velocity of the speed of light (TM SOL ), using a longitudinally-extending defect in the lattice to provide trapped transverse modes. These modes include one or more of a magnetic mode and an electric mode. A set of one or more deviations from the lattice is used to produce at least one of additional modes and coupling options for the waveguide, with the deviations having physical properties that are bounded by a figure of merit. In some implementations, the set of one or more deviations from the lattice are used to produce at least one of additional modes and coupling options by producing additional modes that are predominantly surface type modes. In other implementations, data bandwidth is increased by communicating or transporting data or particles using different wavelengths of light for the surface type modes, and using different defects having different characteristics for the respective different wavelengths of light to produce additional modes.","The above discussion/summary is not intended to describe each embodiment or every implementation of the present disclosure. The figures and detailed description that follow also exemplify various embodiments.","While various embodiments discussed herein are amenable to modifications and alternative forms, aspects thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the disclosure to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the disclosure including aspects defined in the claims. In addition, the term “example” as used throughout this application is only by way of illustration, and not limitation.","DETAILED DESCRIPTION","Aspects of the present disclosure are believed to be applicable to a variety of different types of apparatuses, systems and methods involving photonic bandgap (PBG) materials for accelerator structures and for communications. While not necessarily so limited, various aspects may be appreciated through a discussion of examples using this context.","Various embodiments include a fiber having a central defect surrounded by a periodic structure. The periodic structure can include an array of variations in the fiber material. These variations can run the length of the fiber (“capillaries”) and have a different dielectric constant relative to the fiber material. The particular configuration for these variations helps to determine the PBG wavelengths. Consistent with various embodiments discussed herein, the PBG material can be constructed using a hexagonal array of capillaries. Other array patterns are also possible including, for example, shapes with more or less sides than a hexagon (e.g., a square).","Particular embodiments of the present disclosure are directed toward the strategic use of modification to the periodic structure. Somewhat surprisingly, it has been discovered that such modifications can be used while maintaining the confinement of the desired wavelength. This is true despite the complexity and unpredictability of assessing the effect of modifications to a fiber that is designed to take advantage of surface modes.","For accelerator structures, such as those based on TM-like modes in PBG fibers, the surface modes can be relevant to the effectiveness of the structure for use in communication or as a particle accelerator but with very different figures of merit. The PBG fibers can be subject to a variety of (manufacturing) errors that may render them less, or even completely, ineffective. Aspects of the present disclosure are directed toward methods and structures useful for facilitating rapid prototyping of variant structures to help account for such errors. Such techniques can be useful for a variety of other purposes including, but not limited to, creating matched structures for injection, extraction or beam containment insertions in accelerators. Such modifications can be useful for a wide variety of accelerators and they can all be related to the basic accelerator mode.","Transverse magnetic (TM) modes are used for particle acceleration and are so named because they have a longitudinal electric field on the accelerator axis and no longitudinal magnetic field on axis. To achieve particle acceleration in the absence of conducting boundaries, a dielectric structure must be designed to: support a TM mode with a uniform longitudinal electric field, slow the accelerating wave%27s phase velocity to be synchronous with the relativistic particle (v_c), and confine the field energy near the particle beam. The refractive index of dielectrics like (SiO2) is greater than one and will naturally reduce the wave phase velocity v p =c/n eff =ω/k z . Here c is the speed of light, n eff is the mode%27s effective index, k z is the propagation constant (wave number) in the material, ω=ck 0 =2πc/λ is the frequency, and λ is the freespace wavelength. Silica is highly resistant to radiation damage, has a damage threshold of about 2 GV/m for picosecond pulse lengths, and is highly transmissive from about 0.2 to 2 μm and above, making this the natural wavelength range for an optical particle accelerator.","Consistent with embodiments of the present disclosure, field confinement without metal boundaries can be achieved by optical interference through the creation of a dielectric structure arranged in aperiodic geometry (e.g., a photonic crystal). Solutions to the Maxwell equations in aperiodic system exhibit the symmetry of the periodic array, and allowed modes are those which scatter coherently from the distributed inclusions. Light waves travel as Bloch waves, characterized as a product of a periodic function and a plane wave with characteristic wave vector. These Bloch waves have a dispersion relation similar to free photons, but modified by the Fourier components of the variation of the dielectric structure, particularly near the Brillouin zone boundaries (given by half of the unit reciprocal lattice vectors). This results in frequency passbands and stop bands, or photonic bandgaps, through constructive and destructive interference. The frequencies in the bandgap correspond to modes with periodicity unmatched to the lattice and unable to propagate. The photonic bandgap (PBG) structure acts like a perfectly reflecting mirror at these frequencies. Trapped modes, also referred to as defect modes in optics terminology, can be obtained by breaking the symmetry with the introduction of a defect into the lattice. These modes cannot propagate in the crystal and are spatially confined to the defect, becoming evanescent in the extended crystal.","As used herein, the discussed insertions can relate to techniques for producing or modifying thin wafers of PBG crystals. These thin wafers can be used in separate ways, such as: 1) to achieve basic design goals, e.g., to optimize a design, 2) to make a design better, e.g., by integrating previously disparate or independent elements into the overall system and 3) to develop capabilities beyond the original design goals or to implement very significant improvements, as well as for rapid prototyping of variant structures to test new ideas such as the tolerance of the basic design to errors or perturbations such as aperiodic inclusions in a lattice.","For example, it is useful to be able to effectively drill or etch a new capillary or to change the size or shape of an existing capillary. To demonstrate the generality of this to other modes and applications, one can increase the throughput or bandwidth of a PBG crystal by developing an array of defects either by increasing the number of single defect lattices in a wafer or increasing the number of defects in a single lattice and/or by increasing the number of usable bandgaps in a single defect lattice or any combination of these. In certain instances, it can be useful to reduce the size of a capillary, e.g., via a coating technique such as CVD. The ability to effect changes to the lattice can be complicated by the effects of the complex geometry of the refractive index n(x,y,z) of these PBG fibers. For example, one implication is that there are no exact global solutions for their modal fields. Thus, the term “TM01-like” represents the lack of an exact solution. This complicates attempts to couple into fibers for such modes and also presents associated problems with efficiency. Somewhat surprisingly, the present disclosure presents modifications to basic PBG lattices that can be useful for improving characteristics of the fiber, such as aperiodic inclusions. The discussion of these modifications sometimes assumes cylindrical symmetry for simplicity of presentation and calculation because they do not vary with distance z along the fiber%3b however, the present disclosure is not necessarily so limited. For instance, the modifications can include twists under certain constraints which allow the fields to be expressed in separable form (transverse and longitudinal). This is the basis of many of the calculations shown, e.g., with the CUDOS code. Thus, having an approximate numerical solution, perturbations can be applied in a variety of ways to obtain and to understand many important results without doing damage to their generality.","Various embodiments are directed toward the addition of either periodic or non-periodic inclusions in the form of capillaries and/or defects into the basic photonic crystal lattice. Of particular interest are additional defects disposed in an alternative symmetry to that of the original lattice. Somewhat surprisingly, capillary inclusions can enhance the accelerating gradient in accelerator applications considerably through eliminating hot spots in the material of the lattice. Other modifications relate to the inverse effect of changing the index of a capillary or even eliminating it by filling it with the same or different material. This can be useful for incorporating lasers or, for example, to shift the phase between the particle and laser beams in an accelerator application.","Other possibilities include ways to manipulate such insertions in a dynamic way, e.g., via the equivalent of a cassette exchanger or possibly a mechanism for rotating them where a Geneva mechanism could be used to make accurate, discrete angular steps. Similarly, it is useful to be able to effectively drill or etch a capillary to change its size or shape.","Relative to other modes and applications, the throughput or bandwidth of a PBG crystal can be increased by developing an array of defects by increasing the number of single defect lattices in a wafer or by increasing the number of defects in a single lattice and/or by increasing the number of usable bandgaps in a single defect lattice or any combination of these.","Another mechanism uses photonic bandgap (PBG) structures/fibers to confine propagating electromagnetic energy to the fiber. For instance, a fiber can be constructed with a periodic structure that exhibits a photonic bandgap over an extended wavelength range. A central defect in the periodic structure can facilitate the propagation of electromagnetic energy at the desired wavelength, while the surrounding PBG structure confines the electromagnetic energy to the central defect.","As discussed herein, fibers and devices can be constructed to make use of defect/surface modes that are not confined to the central defect. These modes can be particularly useful for contributing to the performance of the PBG fiber and associated application, whether the application relates to data communications or particle acceleration.","Because of electrical breakdown of metals in the presence of high electric fields, particle accelerators that use metal cavities driven by high-power microwaves operate with accelerating fields of 20 to 40 megavolts per meter (MV/m). Charged particle devices can be large and expensive due to the accelerator length and total stored energy needed to achieve high energy. Size and cost reductions are required for many applications. By comparison, the maximum surface fields of dielectric materials exposed to pulsed laser light are fluence limited to the order of a joule/cm2 below two picosecond pulse lengths and are expected to exceed 10E9 volts/meter (gigavolt/meter (GV/m)). These fields are an order of magnitude above metallic structures, making a laser-powered, dielectric waveguide, and are implemented for particle acceleration, in accordance with one or more embodiments.","In accordance with another example embodiment, an optical fiber waveguide includes a substrate having a lattice with a plurality of lattice regions, in which the lattice regions and the substrate have different dielectric constants. In some implementations, the lattice regions include capillaries extending longitudinally. A longitudinally-extending defect in the lattice acts with trapped transverse modes including at least one of a magnetic mode and an electric mode. The defect facilitates wave propagation along the longitudinal direction while confining the wave transversely, in which a corresponding phase velocity equals the speed of light (TM SOL ). One or more deviations from the lattice produce additional modes (e.g., predominantly surface-type modes) and/or coupling options for the waveguide, with the deviations having physical properties that are bounded by a figure of merit. Such a figure of merit may include, for example, one or more of a radius of the defect, a radius of the lattice regions, a lattice spacing between the lattice regions, a damage factor (DF), lattice symmetry, Poynting flux loss (a) and wave dispersion.","The deviations from the lattice are implemented using one or more of a variety of approaches. In some embodiments, the additional modes increase bandwidth by communicating or transporting data or particles using different wavelengths of light via the additional surface type modes. In some implementations, different wavelengths of light reside (e.g., are propagated) in different defects. In certain embodiments, the deviations include one or more of: additional regions having a different dielectric constant than the substrate%27s dielectric constant and extend longitudinally%3b relative size variations in the lattice regions%3b different spacing between the lattice regions%3b one or more of the lattice regions having a dielectric constant that is different than the dielectric constants of both the substrate and the lattice regions%3b and deviations that increase the transmission of power via the defect for at least one of optical and particle transmission.","In various embodiments, the deviations include additional lattice regions extending longitudinally, having a dielectric constant that is different than the substrate%27s dielectric constant, and that reduce hotspots in the substrate. In some implementations, the additional lattice regions include dielectric material that have a higher breakdown field than the substrate and that act both as a strong field attractor and as an enhancer of the figure of merit.","The waveguide as discussed herein is implemented in a variety of manners to suit different embodiments. In some embodiments, the waveguide operates as an accelerator and/or a transport channel in which a phase velocity of a propagating wave therein equals the speed of light. In certain embodiments, the defect is sized to provide a trapped transverse magnetic-like mode in a bandgap by way of a dispersion relation that crosses a line that corresponds to a phase velocity equaling the speed of light.","FIG. 1 shows a system diagram for providing high bandwidth communications using photonic bandgap crystals with propagating fields outside of a central defect, consistent with embodiments of the present disclosure. As discussed in more detail herein, a photonic bandgap crystal can be used to transmit data using multiple different carrier frequencies. This ability can be realized by introducing inserts or breaks in the periodic structure of a photonic bandgap crystal. This can facilitate the use of bundled photonic bandgap crystals that are designed with different bandgaps for corresponding carrier frequencies. In some embodiments, a single crystal structure surrounding a central defect can be designed to have multiple modes thereby facilitating the use of multiple carrier frequencies.","FIG. 2 shows a cross section of a photonic bandgap fiber bundle with multiple central defect regions, consistent with embodiments of the present disclosure, in which each central defect and corresponding periodic structure can be designed independently. This can include enlarging one or more of the capillaries surrounding the central defect. The capillaries can also be reduced in size and/or filled with a different material. Further possible modifications include changing the spacing between capillaries and/or adding new capillaries. These modifications can be used alone or in combination and are not necessarily limiting.","As discussed in more detail herein, limitations on the extent and type of modifications can be defined according to a relevant figure of merit. A particular figure of merit is the damage factor (DF). Other figures of merit can also be used for assessing the viability of the modifications.","FIG. 3 shows a graph of bandgaps of an experimental photonic bandgap fiber as related to speed of light (SOL) modes, consistent with embodiments of the present disclosure. The experimental photonic bandgap fiber is consistent with various experimental disclosures discussed in more detail herein, and by way of example refers to an ET3509 fiber structure. One mode comes very close to the speed-of-light line in the center of the bandgap in the lowest bandgap here that intersects the light line near k o a=8.17. Other gaps of interest to study are those centered near 9.84 and 11.78. These lie in the range of Ti:Sa and He:Ne lasers when the lattice period is adjusted to allow the use of a Nd:YAG laser for the lowest bandgap at 8.17.","FIG. 4 shows a cross section of a photonic bandgap fiber with a central defect that is subject to hotspots, consistent with embodiments of the present disclosure. These hotspots represent points at which the DF value can be assessed. As discussed in more detail herein, various modifications can be undertaken to lessen the impact of such hotspots. FIG. 5 shows an example of the disposition of hotspots.","As discussed in more detail herein, both end and side coupling can be dominated by the basic crystal symmetry, but this can be broken by imposing a minor array of defects such as shown in FIG. 6 . FIG. 6 shows a new mode whose local distributions closely parallel those shown in the previous Figure and those shown in FIGS. 30A-B , consistent with discussions herein. FIG. 7 shows the Re[E z ] dominated by the constructive interference between the radiative losses from the three defects excited by the same longitudinal accelerating mode as in FIGS. 30A-B . The radiation pattern no longer has a hexagonal symmetry%3b the perturbations shown above can improve this by removing the two vertex capillaries and adding external rings.","New types of accelerator structures such as those based on TM modes in photonic bandgap (PBG) crystals rely on modern technology for their production and can be expected to have a variety of errors that may render them ineffective before the final production process is fully debugged. Even when processes are debugged, they are seldom optimal so that modifications to the as-built structures are often useful. While essential in some form for rapid prototyping of variant structures, such techniques are useful for many other purposes, e.g., to make matched structures for injection or extraction or beam containment insertions. Such insertions are extremely important for any practically usable accelerator and they are all closely related to the basic mode of the accelerator.","Aspects of the present disclosure are directed toward a wide variety of PBG crystals. Particular aspects are directed toward applications using surface modes as opposed to the so-called core modes familiar in the telecom field where much of the work and study on PBG crystals has been focused. Further, due to the very different and much simpler character of those modes none of these techniques seem necessary, but can provide some very real benefits.","Insertions make possible an integrally new system so these techniques are useful in at least three or more separate ways: 1) to achieve basic design goals, e.g., to optimize a design, 2) to make a design better, e.g., by integrating previously disparate or independent elements into the overall system and 3) to develop totally new capabilities beyond the original design goals or to implement very significant improvements to it, as well as for rapid prototyping of variant structures to test new ideas such as the tolerance of the basic design to aperiodic inclusions.","Before providing a few illustrative examples of insertions and some techniques to produce them, it is useful to comment on the effects of the complex geometry of the refractive index n(x,y,z) of these PBG fibers. For example, one implication is that there are no exact global solutions for their modal fields which explains the use of the term “TM01-like.” This also helps to explain why so little has been done on the coupling problem for such modes into these fibers and the associated questions of efficiency. Many modifications to the basic PBG lattices of interest here that improve certain characteristics of the fiber, such as aperiodic inclusions, assume cylindrical symmetry for simplicity of presentation because they do not vary with distance z along the fiber. Note that this does not exclude twists under certain constraints and this allows the fields to be expressed in separable (transverse and longitudinal) form. This is the basis of many of the calculations shown here, e.g., with the CUDOS code (B. Kuhlmey, “ CUDOS Utilities for Micro - Structured Optical Fibers ,” Univ. of Sydney, Australia., which is fully incorporated herein by reference). Thus, with an approximate numerical solution, perturbations can be made in a variety of ways to obtain and to understand many important results without doing damage to their generality.","Examples of techniques and how they apply to each of these items include the addition of either periodic or non-periodic inclusions in the form of capillaries and/or defects in the basic photonic crystal lattice. Of particular interest are additional defects disposed in an alternative symmetry to that of the original lattice. We have shown that capillary inclusions can enhance the accelerating gradient considerably through eliminating hot spots in the material of the lattice. Other techniques address the inverse effect of changing the index of a capillary or effectively eliminating it by filling it with the same or different material than the lattice. This can be effective in shifting the phase between particle and laser beams as particles are accelerated.","Similarly, it is useful to be able to effectively drill or etch a capillary to change its size or shape. To demonstrate the generality of this to other modes and applications, one can increase the throughput or bandwidth of a PBG crystal by developing an array of defects. For instance, the number of single defect lattices in a wafer may be increased, the number of defects in a single lattice may be increased, the number of usable bandgaps in a single defect lattice may be increased, or two or more of these approaches may be employed together. In some instances, a capillary size can be enlarged (e.g., by drilling or etching) or reduced (e.g., by coating techniques).","Aspects of the present disclosure are directed toward the use of using dry, fused quartz or pure silica as well as other possible techniques to optimize the damage factor (DF) for these PBG crystals based on what one can take as their primary Figure-of-Merit (FoM) that is discussed in more detail. Various aspects relate to the effects of crystal symmetry and its perturbations or breaking to achieve or optimize various goals—including an improved DF. Of particular interest are the effects of symmetry perturbation, breaking and mixing, e.g., between distinctly different symmetry types when they coexist in the same PBG crystal and especially when they share capillaries in common. Non-limiting examples are provided for perturbations of interest for a matrix accelerator showing the viability of this idea when the basic symmetry is only perturbed. This provides a better understanding of this type of accelerator, how it can operate and, a chance to observe and determine viability. Various calculations are provided for mode characteristics and for the type and size of crystal that can be used. The use of filler materials in certain capillaries is studied in some detail, e.g., showing it has the effect of emphasizing a defect so that it acts very much as though it is a strong attractor for the fields. The conditions for this are discussed as well.","FIG. 8 shows a test setup used to obtain the following transmission data on three samples: PBG crystals ET3509 and ET3516 and a glass slide of comparable thickness made from the same capillary glass that was used for the crystals. This setup can be varied in several ways to accommodate a variety of targets from a small cross-sectional area to large or from thick or thin samples where the main limitations come not from the bandwidth of the PbSe detector (at least 1-4.5 μm), but from its sensitive area which is only 2×2 mm. Because of this limitation the incident beam size was limited to the target which is attached to a circular collimator having a 3.5 mm OD.","FIG. 9 shows a plot of un-normalized transmission data taken in 25 nm steps (typical) on the Incom wafer ET3509 having included defects. The OPA was setup to provide a small focal spot on the crystal that was less than the size of a single-defect hexagonal lattice having eleven rings. The dotted lines show the one sigma, statistical error bars.","FIG. 10 shows a plot of un-normalized transmission data taken in 25 nm steps (typical) on an Incom PBG wafer ET3516. This PBG wafer has similar characteristic dimensions to ET3509, but has no included defects. The OPA was setup to provide a “small” focal spot on the crystal that was less than the basic single defect hexagonal lattice with eleven rings. The dotted lines give the one sigma, statistical error bars. The structure observed around 1.4, 1.65, 1.9, 2.3 and 2.5 microns will be discussed later.","In contrast to the previous case (wafer ET3509), the only characteristic dimension or aperture in this lattice is the capillary radius (r=1.46 μm was measured for ET3509).","FIG. 11 shows a plot of un-normalized transmission data for a glass slide made from the same glass that was used for the ET series of Incom wafers. This data was taken in 25 nm steps (typical) with the OPA. It shows a distinctly different spectrum with structure at wavelengths near 1.4, 1.6, 1.9, 2.1, 2.24 and 2.5 microns where the additional structure evident at 2.1 microns was not as obvious in the previous data for the crystals. Notice, however, that the regions near 1.6 and 2.1 microns were crossover points for the OPA, e.g., between the signal and idler.","This amount of structure in an unstructured glass slide seems surprising especially since the samples were kept in a portable desiccator the whole time except when in use. This provides another argument for using dry fused quartz or silica that is as free of contaminants as practicable. The reasons for this are especially clear in this example because the excitations of some of these “dopants” (contaminants) in the glass line up with some of the bandgaps in the crystals. This makes it necessary but difficult to unfold the two even when the contaminants come from known water groups with their well-known lines. Further, there is no guarantee that these or their effects are the same in the two samples because of their very different fabrication methods. At the same time, the many binary and ternary molecules such as BO and OH that are comparatively light and thereby lower the temperatures of many phase transitions make “bad” glass good by making it easier to work.","Further, there are questions of capillary or tubing availability and its costs including the draw tower required. Nonetheless, one needs to remember how these same characteristics contribute to radiation damage in such crystals. Thus, while there are the inevitable trade-offs, it is also safe to say that this has proven to be a good prototyping material with cost advantages, but very serious limitations for some applications. The next figure shows the problems encountered when trying to separate the different contributions to each resonance.","FIG. 12 shows a plot of the normalized data for the ET3509 wafer, the first plot (black lines) of this sequence, is normalized by the data for the glass slide just shown. The transmission for the slide is about 90% based on our FTIR data over most of this range. It appears that we need to normalize these two sets of data individually, e.g., near 1.7 or 2.4 μm and then subtract them to unfold the bandgap strengths in the ET3509 and ET3516 wafers. The red line is the combined error for ET3509N and the blue is for the subtraction of the two data sets after normalizing them at 1.7 μm. It is interesting to compare the resonance lines now, e.g., at 1.39, 1.6, 1.7, 1.9, 2.1, 2.22, 2.38 and 2.56 microns. Also, one can argue there are 2 lines near 1.3 and 1.9 microns. These may come from different nearly degenerate sources.","It has been shown that there was radiation damage induced when ET3133 was used as a collimator—even under very low doses. This was observed visually as darkening in the crystal at visible wavelengths and it was shown to be even worse in the NIR and MIR using the FTIR. Together with the data above this suggests that better glass such as dry fused silica would be beneficial. These are some of the new results that have been demonstrated here (and not simply surmised) during this Phase 2 study. It appears to be a valid application to use such good (patterned) glass as protective collimating inserts or reticles in conjunction with any of the more expensive components to fabricate or to test, especially the accelerating “cavities.” Further, these components themselves should be fabricated using fused quartz or silica.","In the next set of figures a transition is made to study the ET3861 crystal and to explore the etching of such structures for various purposes, e.g., to modify small errors in the fabricated lattices in order to optimize them.","FIG. 13 shows a basic lattice on which the subsequent calculations for the ET3861 crystal were based. It has a good accelerating mode with a good damage factor DF=0.492 and most of the characteristics desired for an accelerator lattice. As the structure was successively modified, some interesting changes are observed, e.g., the good central mode is lost because of the breaking of the basic hexagonal symmetry of the lattice and the subsequent coupling to new modes. In this case, the index of refraction (RI) is n=1.003676+4.8173E-6(i) and the wavelength of the mode is λ=1.995 μm.","FIG. 14 shows the lattice with the central defect filled with glass of the same kind, i.e., RI. FIG. 14 has the look of a whispering gallery mode with a nonzero field in the center, but very much lower than the peripheral fields as one goes outward toward the defect%27s wall. The RI for this mode is n=1.01817+7.218E-5(i) with a damage factor that is DF=1.0E-5 or essentially zero even though the meaning of this term is ambiguous here. This is due to the field%27s strong concentration in the glass-filled defect. The only other mode that was found was another surface mode that was zero in the center, but even higher in strength and much more uniform around the periphery while still being confined almost solely inside the defect and therefore with an even smaller DF.","In the following calculations, 5 rings separated the defects rather than 4, to simplify tracking changes and to reduce coupling effects even though it extends the calculations somewhat. Six or more rings could also have been used.","A good DF factor can be used as an important figure-of-merit for any future applications of this type of surface-mode PBG crystal, and is important for the TM01-like accelerating mode of interest for high energy physics. Generally speaking, the higher the DF, the higher the achievable gradient and therefore the higher beam energy per unit length or cost. This might allow the possibility of building a new linear collider, which may be an important step of “proving” the existence of super-symmetry.","To obtain high DF values, the structures can be created using dry, fused silica or quartz because this material can tolerate lower DF values resulting from the “as-built” structures as opposed to the “as-designed.” Also, under ideal conditions, one might expect nearly an order of magnitude improvement from using good glass over Si, even with the latter%27s many fabrication advantages, because the bandgap differential for pure silica is approaching and, in some cases, exceeding the ionization potential for a number of solids and gases.","FIG. 15 shows 5 rings of capillary separating the central defect from two peripheral defects. Even with this separation there is still noticeable coupling between defects that reduces the strength of the central accelerating mode by more than 6%. Further, the peripheral modes are not good accelerating modes because they are distorted by their nearness to the outer boundaries and have strengths some 10% of the central defect even though this is not obvious from the figure. However, these defects have strong radial fields approaching 40% of the central defect%27s accelerating mode. Further, the radial fields are the dominant contribution to determining DF=0.48 or a 2.2% drop. The similarity of this distribution to the previous distribution is believed to be due to lattice%27s index of n=1.00310+3.7496E-5(i), i.e., an imaginary component that is nearly eight times larger due to the coupling(small) and the proximity of these defects to the edge. However, this lattice does not break the hexagonal symmetry so that the overall mode structure around the central defect remains nearly identical to the previous structure.","Various embodiments are directed toward increasing the number of rings as well as the separation between defects. Increasing the number of rings can make later symmetry calculations easier, with some 6 rings or more between defects showing the perturbative effect of adding rings.","FIG. 16 shows a lattice with glass in the peripheral defects. This case shows the effects of loading the two outer defects with glass. Although their fields increase dramatically, it is small in their peripheral regions directly outside the defects in strong contrast to previous cases. While it is a hard calculation to make accurately, the DF goes to \u003c0.1% over the very short distance of 100 μm due to the lack of total confinement of the mode in the glass defect and the mode itself. This is a potentially important effect to enhance the DF because of how well the central defect%27s mode can be maintained while improving DF using such schemes. The RI is quite good compared to the previous figure with n=1.00362+7.1174E-6. Further, the central field strength is reduced by only 0.22% from the base case so one can conclude that the effect of adding the glass is to shield and confine the diffractive losses without doing damage to the central accelerating mode. Notice that the central mode structure remains comparable to the previous cases. Also, in talking about DF values, it is assumed that the load material has a higher breakdown field than the glass.","While this barbell line defect perturbs the symmetry, it is only a minor perturbation. Further, it is necessary to note that this effect compliments our technique of adding capillaries at the hot spots to improve the DF. Likewise, it is important to keep in mind that the effectiveness of this technique is strongly tied to the number of rings separating the effective defects in the lattice.","FIG. 17 shows a radically modified lattice where the radii of a number of lattice capillary have been increased and each of these has been loaded or filled with glass while leaving the original central defect empty. A good accelerating mode remains, whose strength is within 1% of the basic single defect case and an improved DF=0.516 for a 5% improvement. The mode distribution is very similar to the above and the RI for this case is n=1.004190+3.35624E-5.","While it is apparent that the underlying hexagonal symmetry of the crystal has been broken, it has not had a significant effect on the mode because the basic crystal symmetry has not been broken inside the surrounding hex ring of glass that shields the central defect from the outer horizontal line defects. The next figure opens this protective hexagonal glass fence and thereby allows strong coupling to the line defects which effectively ruins the good central accelerating mode.","In FIG. 18 , the solid glass capillaries in the hex ring between its glass vertices have been replaced with the normal, but larger, open capillaries. It has many modes reflecting the underlying symmetries of the crystal. The two horizontal rows of large capillary outside the hex ring are still loaded with glass. While not apparent, there is still a reasonably uniform accelerating mode in the central defect but only 55% of the one seen in the basic lattice because of the stronger coupling to the horizontal glass defect vertices. Thus, there is not a pure dipole mode here, contrary to appearances. The RI is n=1.000766+5.3269E-5 and the DF is essentially zero.","It should be noted that this is the only example where there was more than one or at most two modes found whereas this lattice had more than twelve based on the two linear strings and the hex “ring” of 6 solid glass capillaries at the vertices.","FIG. 19 has a different RI from the previous mode, i.e., n=1.006203+4.0441E-4. The fields in the outer glass vertex capillaries are two orders higher than in the central defect. This and the fact that the glass line defects provide a path to the outside helps to explain the higher imaginary index. This mode is shown to illustrate that while this lattice shows a mixed or broken hexagonal symmetry, it may be said to have three distinct symmetries even though it is difficult to find modes fully reflective of these symmetries, e.g., the strong central accelerating field, the dipole or the hex ring.","Further, this is especially hard to observe when these different symmetries share common capillaries. In this case, there is mixing between the dipole and hex ring modes. A completely different example is shown next for contrast.","FIG. 20 has the same fundamental mode structure with an RI n=1.002993+3.95262E-5(i). The field strength decreases by 8%, but the DF increases by 6% to DF=0.52 giving only a small net loss which is somewhat surprising. This is due in part to replacing the large dipole capillaries with the conventional lattice capillaries. The next figure compares these numbers to one with a larger ring count.","FIG. 21 shows an example where the surrounding ring count is increased to 13 giving an RI of n=1.002993+8.2871E-6 with a field strength that is slightly better than the previous 11 ring case, but still decreases by 8% from the original 11 ring, single defect base case while DF increases to DF=0.53 or an increase of 7.3%. As such, there is still an overall net loss but it is small, and the mode structure remains the same.","The next figures help to explain the advantages of a somewhat larger separation between defects and also show that the optimal separation is \u003e6 rings or so rather than five. They help demonstrate the viability of the matrix accelerator in a comparatively simple, single hex lattice.","In the lattice of FIG. 22 , which is the same as the previous one, another eigenmode is shown where the imaginary index increases considerably because of proximity of the mode%27s strength to the outer boundary. Note that the structure of the accelerating mode in the outer defects is very similar except for leakage on the sides nearest to the closest boundary where diffractive losses are largest. RI is n=1.004782+2.4456E-5. Another orthogonal eigenmode is shown next that is useful to allow one to excite all of the possible accelerating channels as a linear combination of these eigenmodes in this lattice. It is to be noted that this is not a unique combination for this task but simply demonstrates the theoretical basis for the matrix linac. It is believed that this demonstrates a better use of the term “linear” accelerator than previous usage.","FIG. 23 shows an eigenmode, with the same mode structure in the excited defects, but perturbed by the nearness of the other defects and the closest boundaries. The RI here is n=1.000709+5.13077E-5. The difference with the previous mode is a result of the different symmetry of this mode relative to the underlying crystal symmetry. It is possible to excite this mode alone by using two synchronized laser pulses coming in on either side of the two horizontal vertex capillaries nearest the excited defects. The DF here is only weaker than the original single defect case by 1%.","There are various manners in which modes can be excited, and there can be several ways to excite modes simultaneously. For instance, one could use two laser pulses, e.g., coming in along the horizontal axis and phased differently depending on what defects one wants to excite. To excite the central mode alone one could couple them in through the outer defects and adjust their phases to interfere in the center. This is also excitable by end coupling as are the others. By eliminating one of the outer defects, one can excite the central defect with a single laser pulse. However, this pulse has a different structure from the previous double pulse example which is not unique either in that one need not couple through the adjacent defect. Similarly, the outer defects can be excited either singly or together, although the distribution of the input laser pulses will differ.","FIG. 24 shows another example of a 3 defect accelerator matrix in a single PBG crystal lattice having 11 rings of capillary. In this example, one could excite either the left or right defects alone by using only two laser pulses or one as for the central defect and therefore by extension, one can excite any single defect or any combination here.","This case can be thought of as an effective “5-defect” matrix in a single PBG lattice where the missing capillaries near the end of the horizontal vertices represent an asymmetric extension of the line defect in that these effective vertex defects are separated by only 3 capillaries from their nearest neighboring defects rather than 5. Also, the surrounding ring of solid glass capillaries has been moved outwards from the peripheral defects by 2 layers but without intercepting the horizontal, linear defect chains.","FIG. 25 shows how the modes are tied to the underlying lattice structure as a whole that may be said to be “just waiting” for defects to appear. This shows a different structure with no central defect but accelerating modes with the same general structure as before except for the perturbing effects from the diffractive losses at the nearby boundaries.","Tests using a 60 MEV electron linac, the NLCTA at SLAC, have been applied to a variety of structures that have been fabricated based on simulations, but the measurement results suggest mismatches in scale between an RF structure and the “THz” regimes of the accelerator and the PBG structures of interest. Thus it can be difficult to overcome a fundamental scale limitation that is “built-in” and seems to manifest itself in many aspects of such tests according to the various tolerances that go as some power of the frequency scaling of more than three orders of magnitude between the RF and THz. A broader definition of “defect” is given as well as a demonstration of the close relationship between the modes of a crystal to its underlying crystal symmetry.","Related to this, FIG. 26 shows an example relevant to the interplay between the underlying lattice symmetry (hexagonal) and the defect symmetries (line (open) and ring (solid)) where the surrounding ring is displaced outwards by one ring so that it does not overlap the line defects anywhere, i.e., share any common capillary locations. FIG. 26 shows the accelerating mode. This case corresponds to a good accelerating mode within 4-5% of the original single defect strength and a DF that is 2% better with DF=0.500. The next two modes are examples of ring and line defect modes.","FIG. 27 shows a defect mode excited in the upper and lower lines of glass capillaries in the ring of glass capillary surrounding the central defect.","FIG. 28 shows a mode that is associated with the ring defect structure. There are several variants of this ring mode related to various closures or lack thereof of these modes around the glass ring. This ring mode clearly traces out the glass loaded capillaries that define this defect structure, but is complicated by the nearness of the external boundaries that vary as you go around the ring. This can be improved by adding rings on the outside and adding the missing capillaries back along the horizontal.","A number of examples have been given that demonstrate some new ways to modify and control the properties of PBG crystals. The emphasis has been on hexagonal lattices with TM01-like modes for acceleration since these and other related modes seem to have the most obvious applications ranging from basic science to Homeland Security. Further emphasis has been on the symmetry of the defect arrangement within the single hexagonal lattice where the proximity of the defects to one another plays an important role, especially in the matrix accelerator where typically one wants to have the same mode excited with the same strength and distribution in every defect. At the same time, one would like to be able to adjust both their strength and distribution because these characteristics are clearly affected by their different local relation to one another and to their nearest boundaries wherever they happen to be in the lattice, especially when they are near to the circumference of the crystal and the defect array symmetry differs from the basic crystal symmetry. At the same time, it is important to realize that these characteristics provide further potentially useful tools to change or modify a mode.","Other reasons to change or modify a distribution include the effects of space charge of one bunch on its nearest neighbors. Of course, none of this is important if efficiency is not at issue except under special conditions, e.g., when one wants to combine the matrix of bunches into a smaller number or set of reduced matrices to build up the bunch charge to achieve higher luminosity in a collider scenario or to shape a combined bunch either longitudinally or transversely without losing the improved phase space density that accrues from the matrix production and transport scheme that was our original justification for this approach.","A relevant characteristic for TM01-like modes is the field strength and corresponding DF. Improvements can be made by optimizing the lattice parameters as just discussed, e.g., increasing the number of capillary rings. However, one can also improve DF by adding unloaded, auxiliary capillary at strategic hotspots in the lattice or by adding loaded defects that act as what may be called “field attractors.” The following discussion identifies a few non-limiting examples of techniques that can improve the central field strength and, at the same time, improve the DF and/or other characteristics.","The general importance of DF to surface modes was given but especially to the field of High Energy Physics (HEP). Note, the general relevance follows almost by definition from the form of surface modes. The importance of contaminants in the glass and how it affects things was discussed, e.g., in unfolding the strength of bandgaps from other resonance sources that can be nearly degenerate as demonstrated. Techniques to unfold overlapping resonances from different sources were discussed beyond various model or curve fitting techniques.","Such subjects suggest the development and use of much more complex materials, especially amorphous ones, where induced resonance lines can be introduced for various purposes including the study of short range order and/or long and intermediate range interactions. However, very pure or “good” glass has been shown to be particularly useful.","As opposed to including small glass capillaries or defects for various purposes such as mediating “hot spots” in lattices a discussion was given of the use of a their “duals” i.e., loaded, aperiodic capillaries that can act as field attractors depending on their sizes compared to that of the defects in the lattice.","A major discussion was provided regarding the role of symmetries in most of the above cases, e.g., coupling effects based on the separation of nearest neighbor defects and/or proximity of the defects to the bounding surface of a crystal and its underlying symmetry, or whether that surface was distorted in some way, e.g., to provide an effective defect. In this same area, a discussion was given on the importance of the relative size of any defects compared to the smaller lattice capillaries and whether such defects were loaded or not. The use of defects to couple laser pulses into a lattice to excite modes in various ways was discussed as were different coupling schemes, such as the relation of “conventional” end-coupling to the cleaved end face side-coupling that can be derived from it. Scale mismatch between the test accelerator and the new accelerator under test is also a relevant consideration.","Consistent with various experimental embodiments and tests, the following discussion describes additional and complementary embodiments of the present disclosure.","FIG. 29A shows the ET3509 wafer manufactured by Incom Inc. with the hexagonal structure that is ˜1 mm OD composed of an array of smaller hexagonal cells. Each of these smaller hex arrays of capillaries has a single, central defect surrounded by 11 rings of capillaries, as shown in FIG. 29B (using greater magnification). The individual defects here have diameters of 4 microns and the surrounding capillaries have diameters of 2 microns.","FIG. 29A shows a wafer with an (approximately) 21×21 matrix of single defect lattices each having 11 rings of capillaries per defect. Each defect, shown in more detail in FIG. 29B , has accelerating modes with λ=2.1 μm (shown in FIG. 30A ) and λ=1.6 μm (shown in FIG. 30B ) associated with different bandgaps. Scaling this structure down to allow one to use Nd:YAG at 1 μm for the 2.1 μm mode suggests the use of a Ti:Sapphire laser at 0.76 μm for the scaled 1.6 μm mode.","Translating such a possibility as demonstrated here for a single defect, multiple bandgap fiber to the telecom field would allow a greatly increased bandwidth for very little increase in costs compared to such current techniques as wavelength division multiplexing that requires very low dispersion. The dispersion here is easily tailored by the perturbation techniques to be discussed but is already near zero in both cases (see FIGS. 30A-B ) because the modes are roughly centered in their respective bandgaps.","FIG. 30A shows an accelerating mode with wavelength λ=2.1 μm that has a damage factor DF=0.45 and an effective index n=(1.00664, 1.537E-3). This corresponds to the Incom, Inc. fiber ET3509. While it has a variety of perturbations to the ideal lattice, it still has the characteristic pattern for an accelerating mode and is testable now using a Tm:YAG laser at this wavelength. See FIG. 3 for the bandgap diagram where one sees that this mode falls in the lowest bandgap that crosses the light line.","FIG. 30B shows an accelerating mode with wavelength λ=1.6 μm as discussed above on the basis of the as-built parameters for ET3509 shown in FIG. 29 . This also has a damage factor DF=0.45 and an effective index n=(1.0002, 6.986E-5). As above, it has a variety of significant perturbations to the ideal lattice but it still has the characteristic pattern for an accelerating mode and is presumably testable now with an Er-doped laser.","FIGS. 29A-B and 30 A-B show examples of how to increase the throughput or bandwidth using the single defect lattice mentioned above. FIG. 3 shows the bandgap diagram for the structure shown in FIGS. 29-30 that helps one understand how this comes about where the gaps are broad near their intersections with the speed of light (SOL) line and the modes are near the centers of their respective bandgaps.","To demonstrate some perturbations to the structure shown above and how they relate to coupling the base structure, the unperturbed case is shown in FIG. 4 a having the primary characteristics just shown in FIGS. 29-30 . A few differences here are the uniform size and placement of the lattice capillaries. Since the symmetry is not perturbed yet, a hexagonal radiation pattern is expected around the external boundary in FIG. 4 b as demonstrated for end coupling. In FIG. 4 a , the central field strength is reduced by less than 0.2% by removing the vertex capillaries as shown in FIG. 4 c while n imag is increased by 62% to n=(1.001437,3.42173E-4) while n real changes by less than 0.003%. The resulting pattern is more directed and stronger in FIG. 4 c and could be enhanced further by additional changes near the vertices such as eliminating another capillary along the symmetry lines and perturbing the adjacent capillaries on either side of this line. Not shown is the Poynting vector in FIG. 4 , but only one component of it for an improved view.","FIGS. 4-5 show photonic bandgap micro-capillary arrays with a) the uniform field accelerating mode |E z | in the defect, and b) a diffuse, hexagonal pattern of radiative loss around the vertices and in c) a more directed pattern obtained by eliminating a single capillary at each vertex.","FIG. 5 shows the effects of reducing the number of capillary rings to enhance the side coupling efficiency. A hexagonal radiation pattern is expected, although it may be more diffuse. The central field strength is reduced by less than 2.5% by removing the vertex capillaries while n imag is increased by 158% to n=(1.0022956,3.22418E-3) but n real changes by less than 0.07%. The radiation strength is clearly increased compared to that in FIG. 4 .","For both end and side coupling the symmetry of the radiation pattern (and by inference, the coupling symmetry) is that of the underlying photonic crystal which presents some challenges. First, it is very different from that encountered in the telecom field and it is definitely not easier. Further, the surface character of these modes, as opposed to the core modes of telecom, implies the designs are essentially dual to one another. This has many implications. Still, there are advantages, e.g., the possibility of integrating the laser drive system into this hollow core fiber in a natural way. The hollow core allows for passage of the electron beam without undue degradation of its properties such as its emittance or energy spread.","For the laser, existing capillary and/or newly included ones (as above) near the defect could be filled with doped laser material such as suggested in the captions for FIGS. 30A-B . When the material is not doped, e.g., pure YAG crystal, the effect may provide both a phase delay and/or an increase in the achievable gradient as shown in FIG. 31 where a ring of six small, open capillaries were added and a ring of six hotspots were eliminated from FIG. 4 and FIG. 30A providing the possibility of increasing the drive laser field before breakdown occurs in the material. Being close to the defect, these “inclusions” perturb the field distribution so it may be necessary to make further adjustments.","FIG. 31 shows a PBG crystal with six extra, very small, unloaded capillaries added as well as with a reduced radius for the first, innermost ring. While not necessarily optimized, the extra capillaries eliminate six hot spots. No attempts were made to optimize the central field strength or damage factor.","When these or other capillaries are loaded other possibilities arise including rejuvenation of the laser pulse or the possibility of phase shifting the laser pulse (relative to the electron pulse). It should be noted that when the included material has a higher breakdown field than the lattice material these other possibilities can be pursued simultaneously with the improvement of the gradient. As noted above, multiple bandgaps exist that can be driven at different laser frequencies. How one excites the modes in these different bandgaps becomes much more interesting and should provide further applications including coupled systems such as OPOs, OPAs and various pump-probe experiments. A particularly interesting possibility is one that does not actually insert a laser gain medium although the relevant capillaries might be coated with some gain material. Instead, it may be desirable to retain the hotspot or at least some residual enhanced field at those locations to act as a pump for whatever material is located there because this typically determines the gain. The breakdown field for the doped material can usually be considered (if known). For fused silica the molecular vibration frequencies correspond to the 1.5-1.6 μm wavelength so that it can be important to map the bandgap width and the frequency of the mode shown in FIG. 30B in the actual PBG crystal. The structure can then be perturbed in such a way as to optimize it, e.g., to bring it to the optimal transmission band around 1.55 μm for silica as well as for Er-doped lasers.","Such a distributed (Raman) system has a number of advantages if it could be realized, but typically the pump can be at a shorter wavelength to initiate gain (excite vibrations) and the produced wavelength must also couple into the defect. If one attempts to run a waveguide(s) for the shorter wavelength pump into the hotspot(s) to insure some degree of coupling, there is the possible perturbation of the fundamental mode from the waveguide(s) depending on how one does this. Thus, embodiments relate to bringing them in only as far as one must to achieve acceptable coupling, but avoid perturbing the fundamental too much while trying to minimize the dissipation of either the injected or produced power into lattice modes.","Other means to couple power into a defect using doped capillaries include polished ends with at least the downstream end having partially transmitting end surfaces on the actively doped capillaries in combination with subsequent chamfers to refract the transmitted laser light into a downstream defect. The disposition of the doped capillaries depends on the symmetry of the crystal but this appears to provide a simpler mechanism to achieve end coupling in such PBG crystals. Other coupling schemes are associated with the defects themselves that may or may not be doped, but act as coupled defects to the original defect. Of particular interest here is that this presents another important simplification when the symmetry of the defect pattern differs from that of the lattice. In that case, fewer incident laser pulses are required to achieve high coupling efficiency and this should also have a higher degree of success not to mention safety. Since this option is less apparent and can be more complicated, it is discussed further herein.","If one wants other frequencies than mentioned above, other materials are required, e.g., in the single defect, multiple bandgap structure of FIGS. 29-30 , the defect could be coated or doped or loaded in some way with other material (e.g. air) that can be driven by the coexisting 1.6 μm mode to enhance the 2.1 μm mode or others in the higher bandgaps (see FIG. 3 ).","For the possibility of disk phase shifters, there are again several options to consider. What is referred to as a “disk phase shifter” is an insert that has the basic fiber structure that supports an accelerating mode, but is perturbed in such a way as to increase or decrease the local effective index in the vicinity of the defect. This can be done in several ways, e.g., by introducing additional capillaries close to the defect or by changing the material there, e.g., by loading some of the existing capillary with material. The greater the change in optical properties in the vicinity of the defect, the greater the effect that is expected where the limit is determined by what the acceptable change to the fundamental or unperturbed mode might be based on the materials available for this purpose.","To see how this works, let β represent the longitudinal propagation constant, possibly complex, for the unperturbed solution where the phase velocity is v p =ω/β=c/n eff . It can be shown that the perturbed propagation constant is then | =βkηδn(x,y,z) where k is the free space wavenumber of the mode and η is the overlap efficiency between the power density of the unperturbed case (Poynting vector) and the index perturbation. There are simplifying limitations for the index perturbation δn(x,y,z) that are imposed and that are extensible. Because n eff is usually complex, a loss coefficient can be defined as α=2k Im(n eff ) that defines the exponential decay of the Poynting flux with distance. If a mode%27s wavenumber in the fiber is k z then one has k z =k n eff and the group velocity is: V g =dω/dk z =c /( n eff +ωdn eff /d ω). ","To maximize the mode%27s group velocity for a better match to that of relativistic particles, one wants to minimize both n eff and its derivative, e.g., by reducing the fractional amount of glass in the lattice and also making the dispersion (proportional to the second derivative) zero. Since the PBG group velocities in our examples are v g /c˜0.6, this is matched to an electron kinetic energy of only 128 keV. While there are many important applications lying below this energy such as SEMs it may be desirable to phase slip the two beams relative to one another quite often for accelerators. The refractive index versus wavelength is shown in FIG. 32 with several variants based on loading the extra, small capillaries in FIG. 31 with different materials, e.g., gases at variable pressures and/or mixtures.","FIG. 32 shows refractive indices for the PBG crystal with six extra, very small capillaries shown in FIG. 31 . The index at STP for dry air is 1.008 for the base (non-optimized) structure without extra capillaries is n=1.01952 and this structure was not changed except for using the different materials as indicated. Note that doped Nd:YAG cylinders are available down to a hundred microns in lengths of a mm or more.","FIG. 33 shows the normalized group velocity for different cases of loading the small capillaries in FIG. 31 . n=1.0 is the unloaded case (shown in green) and the blue squares are for silica w/o the holes. Because of the two terms in the denominator and their differing variations with type of material it can be difficult to make simple predictions as shown by the material for n=1.35 that is scaled from YAG.","While it has been shown that both end and side coupling are dominated by the basic crystal symmetry, it can be broken by imposing a minor array of defects such as shown in FIG. 6 . FIG. 6 shows a new mode whose local distributions closely parallel those shown in FIGS. 30A-B . FIG. 7 shows the Re[E z ] dominated by the constructive interference between the radiative losses from the three defects excited by the same longitudinal accelerating mode as in FIGS. 30A-B . Notice that the radiation pattern no longer has a hexagonal symmetry and that the perturbations shown above can improve this by removing the two vertex capillaries and adding external rings.","The various embodiments discussed herein can be used alone and in combination. Moreover, aspects can be understood in connection with embodiments discussed in the appendix filed as part of the underlying provisional application, and which is fully incorporated herein by reference. For further details regarding data communications or particle acceleration, reference can be made to C. K. Ng et al., “ Transmission and Radiation of an Accelerating Mode in PBG ”, PRSTAB 13, 121301 (2010) and J. England et al., “ Coupler Studies for PBG Fiber Accelerators ”, PAC11, New York, N.Y., March 28 (2011), each of which are fully incorporated herein by reference for all they contain.","Based upon the above discussion and illustrations, those skilled in the art will readily recognize that various modifications and changes may be made to the various embodiments without strictly following the exemplary embodiments and applications illustrated and described herein. For instance, various ones of the disclosed structures and techniques for reducing and or balancing parasitic coupling may be permutations in almost unlimited numbers in various combinations. Such modifications do not depart from the true spirit and scope of various aspects of the disclosure, including aspects set forth in the claims."],"drawings":["DESCRIPTION OF THE FIGURES","Various example embodiments may be more completely understood in consideration of the following detailed description in connection with the accompanying drawings, in which:","FIG. 1 shows a system diagram for providing high bandwidth communications using photonic bandgap crystals with propagating fields outside of a central defect, consistent with embodiments of the present disclosure%3b","FIG. 2 shows a cross section of a photonic bandgap fiber bundle with multiple central defect regions, consistent with embodiments of the present disclosure%3b","FIG. 3 shows a graph of bandgaps of an experimental photonic bandgap fiber as related to speed of light (SOL) modes, consistent with embodiments of the present disclosure%3b","FIG. 4 shows a cross section of a photonic bandgap fiber with a central defect that is subject to hotspots, consistent with embodiments of the present disclosure%3b","FIG. 5 shows the effects of reducing the number of capillary rings to enhance the side coupling efficiency, consistent with embodiments of the present disclosure%3b","FIG. 6 shows a new mode whose local distributions closely parallel those shown in FIG. 5 and those shown in FIGS. 30A-B , consistent with embodiments of the present disclosure%3b","FIG. 7 shows the Re[E z ] dominated by the constructive interference between the radiative losses from the three defects excited by the same longitudinal accelerating mode, consistent with embodiments of the present disclosure%3b","FIG. 8 shows a test setup used to obtain the following transmission data on three samples, consistent with embodiments of the present disclosure%3b","FIG. 9 shows a plot of un-normalized transmission data taken in 25 nm steps on a wafer having included defects, consistent with embodiments of the present disclosure%3b","FIG. 10 shows another plot of un-normalized transmission data taken in 25 nm steps on a wafer having no included defects, consistent with embodiments of the present disclosure%3b","FIG. 11 shows a plot of un-normalized transmission data for a glass slide made of the same glass as used for the capillaries in FIGS. 9-10 , consistent with embodiments of the present disclosure%3b","FIG. 12 shows a plot of the normalized data for the ET3509 wafer, consistent with embodiments of the present disclosure%3b","FIG. 13 shows a basic lattice, consistent with embodiments of the present disclosure%3b","FIG. 14 shows the lattice with the central defect filled with glass, consistent with embodiments of the present disclosure%3b","FIG. 15 shows 5 rings of capillary separating the central defect from two peripheral defects, consistent with embodiments of the present disclosure%3b","FIG. 16 shows a lattice with glass in the peripheral defects, consistent with embodiments of the present disclosure%3b","FIG. 17 shows a lattice which has increased a number of capillary radii in comparison to the first, single defect array and with glass in these defects, consistent with embodiments of the present disclosure%3b","FIG. 18 shows the lattice of FIG. 17 , but with the solid glass capillaries between the vertices of the enclosing solid hex ring now open, consistent with embodiments of the present disclosure%3b","FIG. 19 has the same lattice as used for FIG. 18 but the mode that is shown has a significantly different RI, consistent with embodiments of the present disclosure%3b","FIG. 20 shows a significantly different configuration of defects but still has the same fundamental mode structure with an RI n=1.002993+3.95262E-5(i), consistent with embodiments of the present disclosure%3b","FIG. 21 shows an example where the surrounding ring count is increased to 13, consistent with embodiments of the present disclosure%3b","FIG. 22 shows another eigenmode where the imaginary index increases considerably because of the proximity of the mode%27s strength to the outer boundary, consistent with embodiments of the present disclosure%3b","FIG. 23 shows an eigenmode, with the same local mode structure in the excited defects but perturbed by the nearness of the other defects and the closest boundaries, consistent with embodiments of the present disclosure%3b","FIG. 24 shows an example of a ⅗ defect accelerator matrix in a single PBG crystal lattice having 11 rings of capillary, consistent with embodiments of the present disclosure%3b","FIG. 25 shows how the modes are tied to the underlying lattice structure as a whole and may be said to be “just waiting” for defects to appear, consistent with embodiments of the present disclosure%3b","FIG. 26 shows interplay between the underlying lattice symmetry (hexagonal) and the defect symmetries (line (open) and ring (solid)), consistent with embodiments of the present disclosure%3b","FIG. 27 shows a defect mode excited in the upper and lower lines of glass capillaries in the ring of glass capillary surrounding the central defect, consistent with embodiments of the present disclosure%3b","FIG. 28 shows a mode that is associated with the ring defect structure, consistent with embodiments of the present disclosure%3b","FIGS. 29A-29B show a wafer with an (approximately) 21×21 matrix of single defect lattices each having 11 rings of capillaries per defect, consistent with embodiments of the present disclosure%3b","FIG. 30A shows an accelerating mode with wavelength λ=2.1 μm that has a damage factor DF=0.45 and an effective index n=(1.00664, 1.537E-3), consistent with embodiments of the present disclosure%3b","FIG. 30B shows an accelerating mode with wavelength λ=1.6 μm, consistent with embodiments of the present disclosure%3b","FIG. 31 shows a PBG crystal with six extra, very small, unloaded capillaries added as well as with a reduced radius for the first, innermost ring, consistent with embodiments of the present disclosure%3b","FIG. 32 shows refractive indices for the PBG crystal with six extra, very small capillaries, consistent with embodiments of the present disclosure%3b and","FIG. 33 shows the normalized group velocity for different cases of loading the small capillaries, consistent with embodiments of the present disclosure."]},"government_interest":"FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT This invention was made with Government support under contracts DE-FG02-12ER86510 and DE-AC02-76SF00515 awarded by the Department of Energy. The U.S. Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,335,466","html":"https://www.labpartnering.org/patents/9,335,466","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,335,466"},"labs":[{"uuid":"facca896-d97c-4a47-8260-7e75539f4010","name":"Ames Laboratory","tto_url":"https://www.ameslab.gov/techtransfer","contact_us_email":"ameslps@ameslab.gov","avatar":"https://www.labpartnering.org/files/labs/16","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/facca896-d97c-4a47-8260-7e75539f4010"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"James E. Spencer","location":"Menlo Park, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"An optical fiber waveguide comprising:a substrate having a first dielectric constant and that includesa lattice that includes a plurality of lattice regions having a second, different dielectric constant%3ba longitudinally-extending defect in the lattice that acts with trapped transverse modes including at least one of a magnetic mode and an electric mode, the defect being configured and arranged to facilitate wave propagation along the longitudinal direction while confining the wave transversely and in which a corresponding phase velocity equals the speed of light (TMSOL)%3b anda set of one or more deviations from the lattice configured and arranged to produce at least one of additional modes and coupling options for the waveguide, the deviations having physical properties that are bounded by a figure of merit."},{"idx":"00002","text":"The waveguide of claim 1, wherein longitudinally-extending defect acts with transverse electric modes."},{"idx":"00003","text":"The waveguide of claim 1, wherein the additional modes are predominantly surface type modes."},{"idx":"00004","text":"The waveguide of claim 3, wherein the additional modes are configured and arranged to communicate or transport data or particles using different wavelengths of light for the additional surface type modes, thereby increasing data bandwidth."},{"idx":"00005","text":"The waveguide of claim 4, wherein the different wavelengths of light reside in different defects."},{"idx":"00006","text":"The waveguide of claim 1, wherein the figure of merit includes at least one of a radius of the defect, a radius of the lattice regions, a lattice spacing between the lattice regions, a damage factor (DF), lattice symmetry, Poynting flux loss (a) and wave dispersion."},{"idx":"00007","text":"The waveguide of claim 1, wherein the deviations include additional regions having a different dielectric constant than the first dielectric constant and extend longitudinally."},{"idx":"00008","text":"The waveguide of claim 1, wherein the deviations include at least one of the lattice regions that has a smaller size, relative to other ones of the lattice regions."},{"idx":"00009","text":"The waveguide of claim 1, wherein the deviations include at least one of the lattice regions that has a larger size, relative to other ones of the lattice regions."},{"idx":"00010","text":"The waveguide of claim 1, wherein the deviations include at least two of the lattice regions having a spacing that is different than a spacing of at least two other ones of the lattice regions."},{"idx":"00011","text":"The waveguide of claim 1, wherein the deviations include at least one of the lattice regions that has a third dielectric constant that is different than the first and second dielectric constants."},{"idx":"00012","text":"The waveguide of claim 1, wherein waveguide is configured and arranged to operate as at least one of an accelerator and a transport channel, in which a phase velocity of a propagating wave therein equals the speed of light."},{"idx":"00013","text":"The waveguide of claim 1, wherein the defect is configured and arranged with a size that provides a trapped transverse magnetic-like mode in a bandgap for the waveguide by way of a dispersion relation that crosses a line that corresponds to a phase velocity equaling the speed of light."},{"idx":"00014","text":"The waveguide of claim 1, wherein the deviations include additional lattice regions that are configured and arranged to reduce hotspots in the substrate, the additional lattice regions extending longitudinally and having a dielectric constant that is different than the first dielectric constant."},{"idx":"00015","text":"The waveguide of claim 14, wherein the additional lattice regions include dielectric material having a higher breakdown field than the substrate and configured and arranged to act as a strong field attractor and enhance the figure of merit."},{"idx":"00016","text":"The waveguide of claim 1, wherein the deviations are configured and arranged to increase the transmission of power via the defect for at least one of optical and particle transmission."},{"idx":"00017","text":"The waveguide of claim 1, wherein the lattice regions include capillaries extending longitudinally."},{"idx":"00018","text":"A waveguide apparatus comprising:a substrate having a first dielectric constant%3ba plurality of lattice regions in the substrate, the lattice regions including holes in the substrate and having a second dielectric constant that is different than the first dielectric constant%3ba defect region in the substrate and extending along a longitudinal direction, the defect region being configured and arranged to facilitate propagation of waves, using a trapped transverse mode, along the longitudinal direction while confining the waves transversely%3b andat least one deviation region of the lattice regions, configured and arranged to provide at least one additional surface-based propagation mode for the propagation of the waves."},{"idx":"00019","text":"The apparatus of claim 18, wherein the defect region is configured and arranged to facilitate the propagation of the waves along the longitudinal direction with a phase velocity of the speed of light using trapped transverse modes that include at least one of a magnetic mode and an electric mode."},{"idx":"00020","text":"The apparatus of claim 18, wherein the lattice regions are configured and arranged with the substrate to provide a photonic crystal fiber in which modes exist in frequency passbands separated by band gaps, and to confine the propagation of the waves by confining waves having a frequency in one of the band gaps to propagation via the defect region in the trapped transverse mode."},{"idx":"00021","text":"For use in propagating waves via a waveguide including substrate having a first dielectric constant and that includes a lattice that includes a plurality of lattice regions having a second, different dielectric constant, a method comprising:facilitating wave propagation along a longitudinal direction while confining the wave transversely in which a corresponding phase velocity equals the speed of light (TMSOL), by using a longitudinally-extending defect in the lattice to provide trapped transverse modes including at least one of a magnetic mode and an electric mode%3b andusing a set of one or more deviations from the lattice to produce at least one of additional modes and coupling options for the waveguide, the deviations having physical properties that are bounded by a figure of merit."},{"idx":"00022","text":"The method of claim 21, wherein using the set of one or more deviations from the lattice to produce at least one of additional modes and coupling options includes producing additional modes that are predominantly surface type modes."},{"idx":"00023","text":"The method of claim 22, wherein producing additional modes includes increasing data bandwidth by communicating or transporting data or particles using different wavelengths of light for the surface type modes, using different defects having different characteristics for the respective different wavelengths of light."}],"cpc":{"class":"02","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"B","subgroup":"02042","main-group":"6","action-date":"2016-05-10","origination":"","symbol-position":"F","further":["02","","H","B","US","G","","B","02042","6","2016-05-10","","F"]},"ipc":[{"class":"02","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"B","subgroup":"02","main-group":"6","action-date":"2016-05-10","origination":"","symbol-position":"F"}],"document_number":"20140178022","document_published_on":"2014-06-26","document_kind":"","document_country":""},{"number":"7,228,534","artifact":"grant","title":"Optimizing performance of a program or a computer system","filed_on":"2003-06-14","issued_on":"2007-06-05","published_on":"2004-12-16","abstract":"A function may be a portion of software code. A first function having a known optimization and a second function may be executed. The first function may provide a first trace, and the second function may provide a second trace. The first trace and the second trace may be analyzed to determine an optimization of the second function. The optimization of the second function may indicate how efficiently the second function may be executed.","description":{"text":["BACKGROUND","This invention relates generally to software code optimization and performance analysis.","Software program developers face the challenge of maintaining stability of programs by analyzing performance data and refining the program code to resolve problems revealed by the data. Performance data is typically used to describe performance properties, which are characterizations of performance behaviors, such as cache misses or load imbalances, in the program.","Performance tools are often used to measure and analyze performance data to provide statistics relating to the historical behavior of a program. Although a performance problem may be determined subjectively, most program developers use at least one performance tool to assist in such a determination. For example, the performance tool may indicate a performance problem when the severity of an issue exceeds some defined threshold. The severity of a problem indicates the importance of the problem. A review of problem severities, therefore, may allow the program developer to focus efforts on the more critical problems of the program. The issue having the highest severity is generally referred to as the bottleneck of the program. The bottleneck is frequently addressed before other issues, provided its severity is high enough to render it a performance problem.","Performance statistics of a program may be compared to those of a previous version of the program to determine whether changes in the program have resulted in improved performance. Using the statistics, the program developer may predict future performance problems, as well as resolving existing performance problems.","Although performance tools have proven very helpful in allowing program developers to improve the performance of programs, the tools are often limited in their applicability. For example, performance tools are often platform-dependent and/or language-dependent. Even if a tool is capable of supporting performance analyses of a variety of program paradigms and architectures, such a tool is generally incapable of correlating performance data gathered at lower levels with higher-level programming paradigms.","Thus, there is a need for an improved way of optimizing the performance of software or a computer system.","DETAILED DESCRIPTION","Referring to FIG. 1 , a performance tree 100 may provide a way to visualize the performance of a software program. The performance tree 100 may include event statistics 110 to provide information regarding the execution of different portions of the software program. An event statistic may be defined as a representation of the number of times portions of the software program satisfy certain conditions 130 . The performance of different portions of the software program may be analyzed, with the results being provided by the event statistics 110 . For example, if execution of different portions of the software program satisfies condition 130 a , information regarding those portions may be combined within event statistics 110 b . If portions of the software program that satisfy condition 130 a also satisfy condition 130 a , for example, information regarding those portions may be combined within event statistics 110 d. ","In some embodiments, the event statistics 110 may be organized into levels 140 . Event statistics 110 at a particular level 140 are generally associated with a certain action that may occur during execution of a portion of the software program. For example, the event statistics 110 b at level 140 a may be associated with accessing a cache memory. For instance, satisfaction of condition 130 a may require at least a certain percentage of cache memory access attempts to be successful. In some embodiments, if execution of the portion of the software program does not satisfy the condition 130 a , information regarding the portion may not be included in the event statistics 110 b. ","In some embodiments, if information regarding a certain portion of the software program is not included in event statistics 110 at a particular level 140 , information regarding that portion may not be included in event statistics 110 at levels 140 below the particular level 140 . For example, if event statistics 110 b at level 140 a do not include information regarding a portion of the software program, event statistics 110 c–h at levels 140 b–d may not include information regarding the portion.","Referring to FIG. 2 , a performance tree 100 may provide a way to visualize event statistics 110 of a source training data set, for example. Executing a function, which is a portion of software code, may cause certain events to occur. An event may be defined as an action performed in response to instructions included in a function. An event ratio 120 may indicate the number of times or the frequency with which an event occurs during execution of the software code.","In FIG. 2 , the event ratios 120 may be processor ratios, such as “first level cache load hit rate” 120 a , “machine clear count performance impact” 120 b , “TC delivery rate” 120 c , or “first level cache load miss performance impact” 120 d , to give some examples. For example, a “first level cache load miss rate” event ratio 120 a may equal the number of times the first level cache is not successfully accessed, divided by the number of memory access instructions executed. A “machine clear count performance impact” event ratio 120 b may equal the number of times the processor had to stop processing, divided by the number of clock cycles that occur during execution of the software code. A “TC delivery rate” event ratio 120 c may equal the number of times an instruction from the trace cache is delivered, divided by the number of clock cycles that occur during execution of the software code. A “first level cache load miss performance impact” event ratio 120 d may equal the number of times the first level cache is not successfully accessed, divided by the number of clock cycles that occur during execution of the software code.","A collection of event ratios 120 may be defined as a trace. A trace may be provided by executing a function on a processor, for example. Each function may provide a different trace when executed. However, different traces need not necessarily include different event ratios 120 . An event ratio 120 is generally included in a trace if the event associated with the event ratio 120 is performed during execution of the function associated with the trace. For example, the “first level cache load miss rate” event ratio 120 a may be included in a trace if the first level cache is not successfully accessed during execution of a function from which the trace is provided.","Event statistics 110 may indicate whether traces that include a certain event ratio 120 satisfy a particular condition 130 . A condition 130 may indicate that an event ratio 120 may equal a particular value or fall within a particular range of values. For those traces that satisfy the particular condition 130 , the event statistics 110 may indicate the number or percentage of traces provided from functions having a certain configuration. For instance, event statistics 110 b in FIG. 2 indicate that, of the 670 traces that have a “first level cache load hit rate” event ratio 120 a greater than or equal to 96.394, 424 traces have a first configuration and 246 traces have a second configuration.","The source training data set may be defined as a collection of traces. In some embodiments, the source training data set may be compared to another trace to determine an optimization of the function from which the other trace is provided, for example. In FIG. 2 , the source training data set may include 2078 traces, as indicated in event statistics 110 a . Of those 2078 traces, 979 traces may correspond to a first code configuration, and 1099 traces may correspond to a second code configuration. For example, the event statistics 110 a may indicate that 47.11% of the traces that include the “first level cache load hit rate” event ratio 120 a correspond to the first code configuration, and 52.89% of the traces that include the “first level cache load hit rate” event ratio 120 a correspond to the second code configuration.","In some embodiments, the source training data set may be used to train an expert system. An expert system may use a knowledge base of human expertise to solve a problem. For example, the expert system may be used to analyze another trace and determine an optimization of a function associated with the trace.","In some embodiments, the optimization of a function may be inferred by the event statistics 110 associated with a trace provided by the function. An optimization is generally a numerical representation of the efficiency with which a set of instructions may be executed. The optimization is generally a floating point value from 0 to 1. For example, in some embodiments, a value of 1 may indicate that the set of instructions is written to execute as efficiently as possible on a particular processor. A value less than 1 may indicate that changes to the set of instructions may allow it to execute more efficiently.","For example, in FIG. 2 , event statistics 110 b indicate that 63.28% of the traces that satisfy condition 130 a may be provided by functions having a first code configuration, and 36.72% of the traces may be provided by functions having a second code configuration. It may be inferred that, if a trace satisfies condition 130 a , the function from which the trace is provided has a 63.28% probability of having a first code configuration and a 36.72% probability of having a second code configuration. For example, if the function having the second code configuration is written to execute as efficiently as possible on a particular processor, the optimization of the function may be inferred to be 36.72%, or 0.3672.","A set of instructions included in a function may operate according to a certain specification, for example, such as calculating an output variable based on an input. Although multiple sets of instructions may each operate according to the same specification(s), the different functions may have different execution times. An execution time is the time to execute a set of instructions. The execution time may be a processor-specific measure. For example, a first set of instructions may run faster than a second set of instructions on one type of processor, but slower on another. In some embodiments, the set of instructions may be obtained from a C/C++ source code using a compiler. For example, a compiler may construct a set of instructions in a certain configuration that does not rely substantially on processor-specific instructions. Such a set of instructions is generally not highly optimized with respect to a particular processor. On the other hand, a compiler or a software engineer may generate a set of instructions in another configuration to operate as quickly as possible on a particular processor.","An event ratio 120 may be a low-level characterization of how efficiently software code is executed on a processor. An event ratio 120 differs from an optimization in that the event ratio 120 may indicate the number of times an event occurs during execution of a certain number of functions%3b whereas, the optimization may indicate the probability that an executed function has a particular configuration. An event may be accessing a first level cache, stopping the execution of an instruction, or delivering a particular type of data, to give some examples. The event ratio 120 may be normalized to indicate the frequency with which the event occurs with respect to another value. For example, the number of times the event occurs may be divided by the total number of functions executed. In some embodiments, a software engineer may be able to increase the performance of software code by analyzing the event ratios 120 associated with a particular function.","In some embodiments, a performance impact may be a type of event ratio 120 in which the number of times an event occurs is divided by the number of clock cycles that occur during execution of the software code. For example, a “first level cache load miss performance impact” event ratio 120 d may equal the number of first level cache misses divided by the total number of clock cycles. For example, a “machine clear count performance impact” event ratio 120 b may equal the number of times the processor had to stop, divided by the total number of clock cycles.","In some embodiments, a hit rate may be a type of event ratio 120 in which the number of times an event occurs is divided by the total number of actions associated with the event. The hit rate may differ from the performance impact in that the divisor for the hit rate may be the total number of actions associated with the event, rather than the number of clock cycles. For example, a “first level cache load miss rate” event ratio may equal the number of first level cache misses divided by the total number of memory access instructions executed. The “first level cache load hit rate” event ratio 120 a may equal 100% minus the “first level cache load miss rate” event ratio. In another example, a “machine clear count miss rate” event ratio may equal the number of times the processor had to stop, divided by the total number of instructions executed. The “machine clear count hit rate” event ratio may equal 100% minus the “machine clear count miss rate” event ratio.","Referring to FIG. 3 , a processor-based system 200 may be any processor-based system, including a desktop computer, a server, or a computer network, to mention a few examples. The system 200 may include a processor 210 coupled over a bus, for example, to an input/output (“I/O”) device 220 , a display 230 , and a memory 240 . In some embodiments, the I/O device 220 may be any device that allows the user to make selections from a user interface 250 that may be stored in the memory 240 .","The user interface 250 may be a graphical user interface that displays text or symbols to enable the user to make selections of events to be included in a source training data set. Generally, a user may use the I/O device 220 to select a source training data set from the user interface 250 . In accordance with one embodiment of the present invention, a source training data set may be stored so as to be accessed through the user interface 250 . A function may be executed on the processor 210 to provide event statistics. The event statistics may be collected using an event sampling feature of a software application, such as VTune™, which is owned by Intel Corporation, 2200 Mission College Boulevard, Santa Clara, Calif. 95052-8119. The event statistics may be stored in the memory 240 and may be displayed on the display 230 in the form of a performance tree 100 (see FIG. 2 ), for example.","Referring to FIGS. 4A and 4B , an optimization routine 300 may estimate an optimization of a function using traces of a source training data set, for example. In some embodiments, a function may be modified by the optimization routine 300 , so that the function may execute more efficiently on a particular processor 210 (see FIG. 3 ), for example. In some embodiments, the optimization routine 300 may determine the function that executes most inefficiently. The optimization routine 300 may be stored in a memory 240 (see FIG. 3 ), for example.","The optimization routine 300 may include executing a first function to provide a first trace, as indicated at block 305 . In some embodiments, a second function may be executed at block 310 to provide a second trace. For example, the first trace and/or the second trace may include event ratios 120 (see FIG. 2 ).","In some embodiments, the first function may be an optimized function, and the second function may be an un-optimized function. A function may be optimized when the function is written to execute efficiently on a particular processor 210 . In some embodiments, the optimized function may be written to execute as efficiently as possible on the particular processor 210 . An un-optimized function may be written such that changes to the function may allow the function to execute more efficiently.","In some embodiments, executing an optimized function and an un-optimized function may provide a way to estimate an optimization of another function. A third function may be executed at block 315 to provide a third trace. In some embodiments, the third trace may include the event ratios 120 . For example, in some embodiments, the optimization of the third function may be interpolated or extrapolated using the optimizations of the first and second functions.","In some embodiments, the first trace and the second trace may be selected to be included in a source training data set. In some embodiments, the first trace and/or the second trace may be randomly selected, as indicated at block 320 . For example, in some embodiments, random selection may provide a more robust source training data set than deliberate selection of the traces.","The traces may include event statistics 110 (see FIG. 2 ), such as the number of times an event occurs during execution of the first and second functions. In some embodiments, the number of times the event occurs may be normalized at block 325 . For instance, an event statistic 110 may equal the number of times an event occurs divided by the number of clock cycles within a particular period of time. In some embodiments, normalizing an event may enable a statistic associated with the event to become less dependent upon the input data size.","The source training data set may be used to train an expert system, for example, at block 330 . In some embodiments, the expert system may be a partition tree system, such as a Classification and Regression Trees™ (“CART”) system, registered to California Statistical Software, Inc., 961 Yorkshire Ct., Lafayette, Calif. 94549-4623. In some embodiments, the expert system may be a gradient boosted tree system, such as a Multiple Additive Regression Trees™ (“MART”) system, developed by Jerome H. Friedman, Department of Statistics and Stanford Linear Accelerator Center, Stanford University, Stanford, Calif. 94305. The expert system may be stored in memory 240 (see FIG. 3 ), for example. In some embodiments, functions having different optimizations may be used to provide traces that are included in the source training data set. In such cases, particular traces may be associated with particular optimizations.","Traces of the source training data set may be analyzed at block 335 , along with the third trace, to determine the optimization of the third function, as indicated at block 340 . For example, if the optimization is determined to be a value close to 1, then the third function may be close to optimal in terms of low-level execution. In another example, an optimization close to 0 may indicate that performance of the third function may be significantly improved.","An issue may be defined as inefficiency in a program. For example, execution of a function may provide a trace for which an event statistic 110 may equal zero. The issue in this example may be that the event did not occur during execution of the function. For example, if an issue arises with respect to the third function, as determined at diamond 345 , the severity of the issue may be determined at block 350 . For example, issues of different types may be assigned different severity values, though some types of issues may be assigned the same severity value. In some embodiments, the severity of an issue may indicate the importance of its resolution. In some embodiments, a threshold may be established. For example, a severity above the threshold, as determined at diamond 355 , may indicate that the issue is a performance problem. In some embodiments, issues that do not qualify as performance problems may not be resolved.","For example, if no other performance problems have a higher severity than the performance problem regarding the third function, as determined at diamond 360 , a set of instructions included in the third function may be modified to resolve the performance problem regarding the third function, as indicated at block 365 . If another performance problem has a higher severity than the performance problem regarding the third function, as determined at diamond 360 , the performance problem having the highest severity may be determined at block 370 . In such a case, a set of instructions included in a function associated with the performance problem having the highest severity may be modified to resolve the performance problem having the highest severity, as indicated at block 375 .","While the present invention has been described with respect to a limited number of embodiments, those skilled in the art will appreciate numerous modifications and variations therefrom. It is intended that the appended claims cover all such modifications and variations as fall within the true spirit and scope of this present invention."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 is a conceptualized representation of a performance tree according to an embodiment of the present invention%3b","FIG. 2 is an example of a performance tree according to an embodiment of the present invention%3b","FIG. 3 is a system according to an embodiment of the present invention%3b and","FIGS. 4A and 4B are a flow chart for software that may be utilized by the system shown in FIG. 3 according to an embodiment of the present invention."]},"government_interest":"","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/7,228,534","html":"https://www.labpartnering.org/patents/7,228,534","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=7,228,534"},"labs":[{"uuid":"d498ff5c-39fd-417e-8f3b-b086894fb6ce","name":"Fermi National Accelerator Laboratory","tto_url":"http://partnerships.fnal.gov/","contact_us_email":"optt@fnal.gov","avatar":"https://www.labpartnering.org/files/labs/17","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/d498ff5c-39fd-417e-8f3b-b086894fb6ce"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Victor L. Eruhimov","location":"Nizhny Novgorod, RU, US"},{"name":"Igor V. Chikalov","location":"Nizhny Novgorod, RU, US"}],"assignees":[{"name":"Intel Corporation","seq":1,"location":{"city":"Santa Clara","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A method comprising:executing a first function having a known optimization and a second function, the first function to provide a first trace and the second function to provide a second trace%3b andanalyzing the first trace and the second trace to determine an optimization of the second function."},{"idx":"00002","text":"The method of claim 1 further including randomly selecting the first trace to determine the optimization of the second function."},{"idx":"00003","text":"The method of claim 1 further including normalizing a number of times an event occurs during execution of the first function."},{"idx":"00004","text":"The method of claim 1 including training an expert system using the first trace and analyzing the second trace using the expert system."},{"idx":"00005","text":"The method of claim 1 including training a partition tree system using the first trace and analyzing the second trace using the partition tree system."},{"idx":"00006","text":"The method of claim 1 including training a gradient boosted tree system using the first trace and analyzing the second trace using the gradient boosted tree system."},{"idx":"00007","text":"The method of claim 1 further including executing a third function having a known optimization, the third function to provide a third trace, and analyzing the first trace and the second trace includes analyzing the third trace."},{"idx":"00008","text":"The method of claim 7 including executing a first function that is optimized and executing a third function that is un-optimized."},{"idx":"00009","text":"An article comprising a medium storing instructions that, if executed, enable a processor-based system to:execute a first function having a known optimization and a second function, the first function to provide a first trace and the second function to provide a second trace%3b andanalyze the first trace and the second trace to determine an optimization of the second function."},{"idx":"00010","text":"The article of claim 9 further storing instructions that, if executed, enable the system to randomly select the first trace to determine the optimization of the second function."},{"idx":"00011","text":"The article of claim 9 further storing instructions that, if executed, enable the system to normalize a number of times an event occurs during execution of the first function."},{"idx":"00012","text":"The article of claim 9 storing instructions that, if executed, enable the system to train an expert system using the first trace and to analyze the second trace using the expert system."},{"idx":"00013","text":"The article of claim 9 storing instructions that, if executed, enable the system to train a partition tree system using the first trace and to analyze the second trace using the partition tree system."},{"idx":"00014","text":"The article of claim 9 storing instructions that, if executed, enable the system to train a gradient boosted tree system using the first trace and to analyze the second trace using the gradient boosted tree system."},{"idx":"00015","text":"The article of claim 9 further storing instructions that, if executed, enable the system to execute a third function having a known optimization, the third function to provide a third trace, and to analyze the third trace."},{"idx":"00016","text":"The article of claim 15 storing instructions that, if executed, enable the system to execute a first function that is optimized and to execute a third function that is un-optimized."},{"idx":"00017","text":"A system comprising: a processor-based device%3b and a storage coupled to said device storing instructions that, if executed, enable the processor-based device to enable a: Means for executing a first function having a known optimization and Means for executing a second function, the first function to provide a first trace and the second function to provide a second trace, and a Means for analyzing the first trace and the second trace to determine an optimization of the second function."},{"idx":"00018","text":"The system of claim 17 further storing instructions that, if executed, enable the processor-based device to randomly select the first trace to determine the optimization of the second function."},{"idx":"00019","text":"The system of claim 17 further storing instructions that, if executed, enable the processor-based device to normalize a number of times an event occurs during execution of the first function."},{"idx":"00020","text":"The system of claim 17 storing instructions that, if executed, enable the processor-based device to train an expert system using the first trace and to analyze the second trace using the expert system."},{"idx":"00021","text":"The system of claim 17 storing instructions that, if executed, enable the processor-based device to train a partition tree system using the first trace and to analyze the second trace using the partition tree system."},{"idx":"00022","text":"The system of claim 17 storing instructions that, if executed, enable the processor-based device to train a gradient boosted tree system using the first trace and to analyze the second trace using the gradient boosted tree system."},{"idx":"00023","text":"The system of claim 17 further storing instructions that, if executed, enable the processor-based device to execute a third function having a known optimization, the third function to provide a third trace, and to analyze the third trace."},{"idx":"00024","text":"The system of claim 23 storing instructions that, if executed, enable the processor-based device to execute a first function that is optimized and to execute a third function that is un-optimized."}],"cpc":[],"ipc":[{"class":"06","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"F","subgroup":"45","main-group":"9","action-date":"2007-06-05","origination":"","symbol-position":"F"}],"document_number":"20040255282","document_published_on":"2004-12-16","document_kind":"","document_country":""},{"number":"9,380,695","artifact":"grant","title":"Traveling wave linear accelerator with RF power flow outside of accelerating cavities","filed_on":"2015-06-04","issued_on":"2016-06-28","published_on":"2015-12-10","abstract":"A high power RF traveling wave accelerator structure includes a symmetric RF feed, an input matching cell coupled to the symmetric RF feed, a sequence of regular accelerating cavities coupled to the input matching cell at an input beam pipe end of the sequence, one or more waveguides parallel to and coupled to the sequence of regular accelerating cavities, an output matching cell coupled to the sequence of regular accelerating cavities at an output beam pipe end of the sequence, and output waveguide circuit or RF loads coupled to the output matching cell. Each of the regular accelerating cavities has a nose cone that cuts off field propagating into the beam pipe and therefore all power flows in a traveling wave along the structure in the waveguide.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims priority from U.S. Provisional Patent Application 62/007,817 filed Jun. 4, 2014, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under grant (or contract) no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","FIELD OF THE INVENTION","The present invention relates generally to high power RF devices. More specifically, it relates to accelerating waveguide structures for linear accelerators.","BACKGROUND OF THE INVENTION","An accelerating structure is a critical component of particle accelerators for medical, security, industrial and scientific applications. Standing-wave side-coupled accelerating structures are used where available RF power is at a premium, while average current is high and average power lost in the structure is high. These structures are expensive to manufacture and typically require a circulator%3b a device that diverts structure-reflected power away from RF source, klystron or magnetron.","SUMMARY OF THE INVENTION","In one aspect, the invention provides a traveling wave accelerating structure that advantageously combines simplicity of tuning and manufacturing of traveling wave waveguide with high shunt impedance of side-coupled standing wave accelerating structure. This improves efficiency while reducing cost and enhancing operational flexibility of particle accelerators for medical, security and industrial applications. In addition, the traveling wave structure is matched to the RF source so no circulator is needed.","A traveling wave waveguide according to the invention may be used to accelerate charged particles such as electrons and protons. Embodiments of the invention use a traveling wave in combination with accelerating cavities which could be isolated at the beam pipe. This design improves efficiency while reducing cost and improving operational flexibility of particle accelerators. Although advantages of this invention are evident when the accelerating cavities are not coupled thorough the beam pipe, some coupling through the beam pipe is allowed, which provides additional possible applications.","The structure includes one or more parallel waveguides which are loaded by accelerating cavities. This circuit allows configurations where no RF power is flowing through the accelerating cavity while maintaining a traveling RF wave through the cross-section of the accelerating structure. The cavities have a so-called beam pipe that allows the accelerated particles to cross the accelerating cavity without being intercepted by the cavity walls. This absence of the power flow through the accelerating cavity allows configurations where no power flows through the beam pipe.","The design is cost efficient, easier to manufacture and tune then the existing high-efficiency accelerating structures. It enhances operational and design flexibility, and it does not need circulator to operate.","The practical high shunt impedance traveling wave structures of the present invention are an improvement over both existing traveling wave and standing wave accelerating structures. Conventional traveling wave structures typically use coupling RF power through the beam hole. This requirement constrains its shunt impedance to relatively small values. Embodiments of the present invention are free from this limitation.","Side-coupled standing wave structures have similar shunt impedance to embodiments of this invention but they more complex to manufacture and tune. Plus they require expensive power isolators to operate. Embodiments of the present invention are free from this limitation.","The present invention also provides structures with flexible profile of RF losses along structure, which is impractical in the state of the art traveling wave structures.","In existing standing and traveling wave structures, RF power flows through the accelerating cells. This power flow increases the probability of faults, or vacuum RF breakdowns. With embodiments of the present invention, absence of power flow through the cavities is beneficial for fault-free operation of the accelerator.","There are existing standing-wave accelerating structures in which power is coupled into an accelerating cell or a set of accelerating cells using an outside waveguide. In contrast to these, embodiments of the present invention provide traveling wave accelerating structures that are practical in construction, tuning, and do not need a circulator to operate.","Embodiments of the invention may be designed for use at arbitrary RF frequency. They could have different numbers of power coupling waveguides. The accelerating cavity may be shaped according to requirements of a specific accelerator. The power couplers that match impedance of this structure to RF feeding waveguides could have different configurations, depending on requirements.","Since no power flow through the beam hole is needed, focusing elements could be placed between the accelerating cavities.","Embodiments of the invention could be used to accelerate electrons, protons, or other charged particles in scientific, industrial, security and medical particle accelerators. It could be used in accelerators where RF power is premium: Compact accelerators for radiation therapy, compact and high repetition rate accelerators for security and imaging applications, and compact, high dose industrial accelerators for sterilization.","In one aspect, the invention provides a traveling wave accelerator structure including a symmetric RF feed%3b this symmetric feed eliminates transverse fields that deflect the accelerated beam which is of importance especially at low energies%3b an input matching cell coupled to the symmetric RF feed, this matching cell (or set of matching cells) transforms field of the rectangular waveguide into traveling wave in the waveguide loaded by the accelerating cavities%3b a waveguide loaded by a sequence of regular accelerating cells coupled to the input matching cell at an input beam pipe end of the sequence%3b a waveguide parallel to and loaded by the sequence of regular accelerating cells, an output matching cell (or set of matching cells) coupled to the sequence of regular cells at an output beam pipe end of the sequence, this matching cells transforms traveling wave of the waveguide loaded with the accelerating cells into field of a rectangular waveguide for further extraction out of the structure%3b and output waveguide circuit or RF loads coupled to the output matching cell or cells. In a possible configuration each of the regular accelerating cells has a nose cone. This nose cone increases accelerating efficiency or shunt impedance of the accelerating cell. While increasing the shunt impedance, this nose cone cuts-off field propagating into the beam pipe whereby all power flows along the structure in the waveguide. A main feature of this invention which differentiates it from side-coupled standing-wave structures that also use nose cones is that in the side-coupled-standing-wave-structure the RF power flows through the accelerating cavities and in embodiments of this invention power flows through the outside waveguide or waveguides.","The symmetric RF feed is preferably an input waveguide circuit comprising an input waveguide, matched splitter, two matched H-plane bends, and a matched E-plane bend. The structure may include multiple input matching cells coupled to the symmetric RF feed. The matching cells will have few critical dimensions such as internal cavity diameter and size of the hole coupling the cavity to the outside waveguide which are different from that of the regular accelerating cavities. This difference is determined during the RF design, where the dimensions are optimized to transform all power coming from input waveguide into power of the wave traveling in the periodic structure made of the waveguide loaded by regular accelerating cavities. The dimensions of the output matching cells are determined by similar optimization.","The regular cells may have different lengths from input to output to facilitate bunching of the beam and to match velocity of the beam when accelerated from low energies.","DETAILED DESCRIPTION","To better appreciate the present invention, consider first a typical side-coupled standing wave (SW) accelerating structure. As shown in FIGS. 1A-1B , a cell of a typical side-coupled standing wave accelerating structure has a central accelerator cavity 100 with beam pipe 106 , nose cone 108 , and two coupling cavities 102 and 104 . This accelerating structure is a bi-periodic system that works at π/2 resonant mode. In the working mode, most of electro-magnetic fields are in the accelerating cells. The cavities are coupled magnetically with the coupling slots located near the outer diameter of the accelerating cavity. Surface fields are normalized to 100 MV/m accelerating gradient. The shading in FIG. 1A is indicative of magnetic fields with peak magnitude of ˜1.5 MA/m, while the shading in FIG. 1B is indicative of electric fields with peak magnitude ˜550 MV/m. Further details of this design are contained, for example, in U.S. Pat. Nos. 6,316,876 and 5,039,910. This type of accelerator is widely used in medical, industrial and security applications because it offers very high shunt impedance and operational stability. For example, this high shunt impedance permits positioning of the complete accelerator on arm of a robot for radio-surgery, such as in devices manufactured by Accuray Incorporated.","The coupling slots in the side-coupled SW structure are located asymmetrically with respect to the axis where electrons or other charged particles are accelerated. This asymmetry as well as power flow through the accelerating cell creates electric and magnetic fields deflecting the beam off its axis. This deflection distorts the beam, especially during initial stages of acceleration, increasing beam losses and creating an uneven pattern on the x-ray target thus reducing the performance of the system.","The side-coupled SW structures are typically brazed in pieces, where each piece includes one half of accelerating cavity and one half of coupling cell. When joined, two such pieces create the cavity shown in FIGS. 1A-B . The complexity of the joint%27s surface complicates the brazing so each accelerating cavity and each coupling cell has to be tuned. The tuning is done to insure the desired field profile and make the frequencies of coupling and accelerating cells the same. The tuning is made difficult by the small fields in the coupling cell. This low field prevents tuning of this cell while in working configuration, so the cell typically has a hole to insert a probe or perturb the cavity volume. This complexity both increases manufacturing and tuning cost and makes it difficult to evaluate the quality of the tuned structure.","By its nature of being a resonant cavity, a standing-wave structure absorbs RF signals in a narrow frequency band. For higher efficiency, the RF loss in the structure has to be as small as practical. The lower the RF losses, the smaller the frequency span of the structure. During initial transient, when such a narrow-band structure is filled with RF power, most of the power is reflected. If this reflected power does propagate back to the RF source, it will degrade its performance or may damage it. To protect the RF source, a waveguide isolator (typically a circulator) is installed between the SW accelerating structure and RF source. The isolator, however, attenuates precious RF power in the forward direction, and it increases complexity and cost of the linac.","There is an alternative solution to this problem of narrow-band reflection. Several standing-wave structures could be connected using a waveguide hybrid so the combined reflection is directed away from the RF source toward an RF load. This solution, however, also increases complexity and cost of the system: one will need at least two accelerating structures, a waveguide hybrid and an additional set of waveguides.","During operation of an accelerating structure, vacuum arcs or RF breakdowns degrade and disrupt the structure performance. There is overwhelming experimental evidence that increased RF power flow increases the probability of RF breakdowns. In the side-coupled SW structure the power flows through both accelerating and coupling cells. If the breakdown occurs near an input coupler of the structure, almost half of input RF power could reach the breakdown site. The inventors envision that limiting the RF power available to the RF breakdown will improve its performance.","Next, consider conventional traveling wave (TW) structures, such as used at SLAC National Accelerator Laboratory. These are typically axisymmetric, so they do not deflect the accelerated beam (assuming they use input couplers with symmetrized fields). All accelerating cells are filled with electromagnetic fields, so their tuning process is simpler than tuning of side-coupled SW structures. Traveling wave structures are matched to the RF source, and so they do not need a waveguide isolator or circulator.","Despite all these advantages, the TW structures are not used in compact linacs because they have low shunt impedance. The increase of the shunt impedance is limited by the fact that RF power flows through each cell of the structure. To sustain this flow, coupling apertures cannot be reduced below a certain size. At the same time, the reduction of the aperture increases shunt impedance. As a result, the shunt impedance of TW structures is 30-50% lower than that of side coupled standing-wave structures.","Another disadvantage of the TW structures is related to the RF power flow. The whole power passes through the first accelerating cell. The higher the power flow, the higher the probability of RF breakdowns.","To improve performance of standing wave and traveling wave structures, accelerating structures with parallel coupled cavities were developed. Specifically, this approach eliminates power flow through the accelerating cell in order to decrease RF breakdown probability. However, these structures are significantly more complex in construction and tuning in comparison with both traveling-wave structures and side coupled standing-wave structures.","Similar to side-coupled SW structures, the field inside the asymmetric accelerating cells deflects the particle beam, and, as with other standing wave structures, they need a waveguide isolator or additional waveguide components to protect the RF power source.","Because of the above disadvantages of known designs, there is a need in the art for a linear accelerator having improved characteristics compared to compact side-coupled standing wave accelerators.","FIG. 2 shows a schematic view of a vacuum region of a TW accelerating structure with power flow outside of accelerating cavities according to an embodiment of the present invention. This accelerating structure combines high shunt impedance of the side-coupled SW accelerating structure with the beneficial properties of a traveling wave structure. An upper left part of the structure is cut away to show internal geometry. The scale is for 9.3 GHz, 2π/3 phase advance structure. Input RF power 200 enters%3b input waveguide 202 and passes through matched 3 dB splitter 204 and matched H plane bends 206 , 208 followed by matched E-pane bend 210 coupled to the side of input matching cavity 212 at the input beam pipe 214 positioned around the longitudinal axis along which electron beam 216 travels. Adjacent to input matching cavity 212 along the axis is a first regular accelerating cavity 218 and subsequent set of cells arranged sequentially along the axis, terminating with output matching cavity 220 at output beam pipe 222 . The power propagates from input to output through the side-coupled waveguide loaded with the accelerating cavities 224 , so RF power travels through output waveguide assembly 226 and exits as output RF power 228 .","The structure shown in FIG. 2 illustrates one possible concrete instantiation of the principles of the invention, and it is by no means the only possible implementation. Possible modifications within the scope of the invention include scaling to any operational frequency%3b replacing the input waveguide circuit with any other symmetric feed%3b or replacing the output circuit with two RF loads. A structure built according to this method could be designed with a field profile that accelerates electrons from low energy of ˜10 keV to serve as a drop-in replacement for a side-coupled standing wave structure. The sequence of cavities connected to outside waveguides forms a periodic structure. One period of the structure is shown in more detail in FIGS. 3A-B . The cell has an accelerating cavity 300 coupled to a waveguide 302 that transmits RF power 306 between the accelerating cells. Cavity 300 has nose cone 308 . The figure shows a cut-away view of a quarter-cell finite element model of the traveling wave accelerating structure. Surface electric fields are normalized to 100 MV/m accelerating gradient. FIG. 3A has shading indicative of magnetic fields with peak magnitude of 0.71 MA/m, while FIG. 3B has shading indicative of electric fields with peak magnitude ˜325 MV/m. Beam pipe 304 is positioned along the longitudinal axis of the device.","The accelerating cell has a nose cone 308 in order to increase the shunt impedance. This nose cone 308 increases shunt impedance of the cell but cuts-off field propagating into the beam pipe and therefore all power flows along the structure in the outside waveguide 302 .","The structure is symmetric with respect to the beam axis, so it has no dipole field component deflecting the beam. Remaining quadruple components could either be used to focus the beam or eliminated by slightly distorting accelerating cell shape.","A key distinction between this structure and either side-coupled, on-axis coupled or parallel-coupled SW structures it that the wave travels in it with significant group velocity. In this property it is similar to traditional on-axis-coupled TW accelerating structures, but without the drawback of low shunt impedance or increased RF breakdown probability due to RF power flow through accelerating cavity.","An important property of a traveling wave structure is the absence of parasitic modes, propagating at working frequency. Parasitic modes make electrical design of the input coupler complicated and tighten manufacturing tolerances to satisfy requirements on the working mode stability. Simulations by the inventor show that this TW structure is single moded, as seen in FIGS. 4A-B , where the dispersion diagram is shown for one cell of the TW structure shown in FIGS. 3A-B . Specifically, FIG. 4A is a graph of frequency vs. phase advance per cell showing full frequency span with two lowest brunches%3b FIG. 4B is a graph of frequency vs. phase advance per cell showing 400 MHz frequency span. As seen in FIG. 4B , at the working point (2π/3 phase advance per cell), only the operating mode is propagating.","Table 1 shows a comparison between parameters for the traveling-wave structure of an embodiment of the invention and those of a typical side-coupled standing wave structure. The structures were simulated using HFSS."," TABLE 1 TW with outside SW, Parameter power flow side-coupled Cell length [mm] 10.745 16.104 Aperture radius “a” [mm] 1.14 1.14 a/lambda 0.035 0.035 Frequency [GHz] 9.3 9.3 Q-value 6802 7917 Phase Advance per Cell [deg.] 120 180 Group Velocity [speed of light] 0.013 0 Attenuation Length [m] 0.47 — Shunt Impedance [MOhm/m] 144 143 R/Q [kOhm/m] 21.2 18.1 Accelerating Gradient [MV/m] 100 100 RF Power Flow [MW] 32.25 — Peak Electric Field [MV/m] 325 550 Peak Magnetic Field [kA/m] 710 1500 Emax/Eacc 3.25 5.5 Hmax*Z0/Eacc 2.7 5.7 RF Losses per Cell [MW] 0.74 1.12 Stored Energy per Cell [mJ] 87 152 ","Table 1 illustrates a quantitative comparison between a typical side-coupled standing wave structure and the proposed traveling wave structure shown in FIGS. 3A-B . Both structures will accelerate an ultra-relativistic beam moving with close-to-speed of light velocity. As seen in the table, both structures have practically identical shunt impedance. At the same time, the TW structure of the present invention has lower peak surface electric and magnetic fields, lower stored energy and power lost per cell. The inventors envision that with other advantages brought by use of traveling wave and symmetric feed, linacs build with this type of accelerating structure will have superior performance to both commonly used side-coupled standing wave structures and to the parallel-coupled standing wave structures.","In conclusion, the traveling wave accelerating structure of the present invention has high shunt impedance similar to that of side-coupled standing-wave accelerating structure, but without its drawbacks. It does not need a waveguide isolator, has no deflecting on-axis fields or power flow through the accelerating cell, it is simple to tune and characterize electrically. Possible uses of the structure are compact, high repetition rate medical or industrial accelerators."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIGS. 1A and 1B are perspective views of a finite element model of a half-cell of a conventional side-coupled standing wave accelerating structure.","FIG. 2 is a perspective view of a vacuum region of a TW accelerating structure according to an embodiment of the invention.","FIGS. 3A and 3B are perspective views of a quarter-cell finite element model of a traveling wave accelerating structure according to an embodiment of the invention.","FIGS. 4A and 4B are dispersion diagrams for one cell of the TW structure shown in FIGS. 3A-B showing a full frequency span with two lowest brunches and 400 MHz frequency span, respectively."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under grant (or contract) no. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,380,695","html":"https://www.labpartnering.org/patents/9,380,695","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,380,695"},"labs":[{"uuid":"9b75b728-64aa-45c3-8624-704df2161e15","name":"Princeton Plasma Physics Laboratory","tto_url":"https://www.pppl.gov/organization/technology-transfer","contact_us_email":"contactus@pppl.gov","avatar":"https://www.labpartnering.org/files/labs/18","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/9b75b728-64aa-45c3-8624-704df2161e15"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Valery A. Dolgashev","location":"San Carlos, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A traveling wave accelerator structure comprising: a symmetric RF feed%3b an input matching cell coupled to the symmetric RF feed%3b a sequence of regular accelerating cavities coupled to the input matching cell at an input beam pipe end of the sequence%3b a waveguide parallel to the sequence of regular accelerating cavities, an output matching cell coupled to the sequence of regular accelerating cavities at an output beam pipe end of the sequence of regular accelerating cavities%3b and output waveguide circuit or RF loads coupled to the output matching cell, wherein the waveguide is coupled at an input end to the symmetric RF feed, coupled at an output end to the output waveguide circuit or RF loads, coupled to the input matching cell, coupled to the output matching cell, and coupled to each of the cavities in the sequence of regular accelerating cavities, wherein each of the regular accelerating cavities has a nose cone that cuts-off field propagating into the beam pipe such that all power flows in a traveling wave along the structure in the waveguide."},{"idx":"00002","text":"The traveling wave accelerator structure of claim 1 wherein the symmetric RF feed is an input waveguide circuit comprising an input waveguide, matched splitter, two matched H-plane bends, and a matched E-plane bend."},{"idx":"00003","text":"The traveling wave accelerator structure of claim 1 comprising multiple input matching cells coupled to the waveguide and to the symmetric RF feed."},{"idx":"00004","text":"The traveling wave accelerator structure of claim 1 wherein the regular accelerating cavities have different length from input to output to facilitate bunching of the beam and to match velocity of the beam when accelerated from low energies."}],"cpc":{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"7","action-date":"2016-06-28","origination":"","symbol-position":"F","further":["05","","H","B","US","H","","H","02","7","2016-06-28","","F"]},"ipc":[{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"00","main-group":"9","action-date":"2016-06-28","origination":"","symbol-position":"F"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"7","action-date":"2016-06-28","origination":"","symbol-position":"L"},{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"02","main-group":"9","action-date":"2016-06-28","origination":"","symbol-position":"L"}],"document_number":"20150359080","document_published_on":"2015-12-10","document_kind":"","document_country":""},{"number":"9,559,388","artifact":"grant","title":"Electrochemical systems configured to harvest heat energy","filed_on":"2014-06-18","issued_on":"2017-01-31","published_on":"2015-04-09","abstract":"Electrochemical systems for harvesting heat energy, and associated electrochemical cells and methods, are generally described. The electrochemical cells can be configured, in certain cases, such that at least a portion of the regeneration of the first electrochemically active material is driven by a change in temperature of the electrochemical cell. The electrochemical cells can be configured to include a first electrochemically active material and a second electrochemically active material, and, in some cases, the absolute value of the difference between the first thermogalvanic coefficient of the first electrochemically active material and the second thermogalvanic coefficient of the second electrochemically active material is at least about 0.5 millivolts/Kelvin.","description":{"text":["RELATED APPLICATIONS","This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application Ser. No. 61/836,593, filed Jun. 18, 2013, and entitled “An Electrochemical System for Highly Efficient Harvesting of Low-Grade Heat Energy”%3b U.S. Provisional Patent Application Ser. No. 61/847,025, filed Jul. 16, 2013, and entitled “Electrochemical Systems and Methods for Harvesting Heat Energy”%3b U.S. Provisional Patent Application Ser. No. 61/864,056, filed Aug. 9, 2013, and entitled “Electrochemical Systems and Methods for Harvesting Heat Energy”%3b and U.S. Provisional Patent Application Ser. No. 61/883,125, filed Sep. 26, 2013, and entitled “Electrochemical Systems and Methods for Harvesting Heat Energy,” each of which is incorporated herein by reference in its entirety for all purposes.","STATEMENT OF GOVERNMENT SUPPORT","This invention was made with government support under Contract Nos. DE-SC0001299, DE-FG02-09ER46577, DE-EE0005806, and DE-AC02-76SF00515 awarded by the U.S. Department of Energy and under Contract No. FA9550-11-1-0174 awarded by the Air Force Office of Scientific Research. The government has certain rights in the invention.","TECHNICAL FIELD","Electrochemical systems for harvesting heat energy, and associated electrochemical cells and methods, are generally described.","BACKGROUND","Thermally regenerative electrochemical systems (TRES) are systems in which heat is converted into electricity in an electrochemical heat engine. The heat recovery strategy in TRES is based on the temperature dependence of the electrochemical potential of the system components. For the half reaction, A+n e − →B, the thermogalvanic coefficient α is defined as:"," α = ∂ V ∂ T = Δ ⁢ ⁢ S A , B n ⁢ ⁢ F ( 1 ) where V is the electrode potential, T is temperature, n is the number of electrons transferred in the reaction, F is Faraday%27s constant, and ΔS A,B is the partial molar entropy change for the half cell reaction at isothermal conditions. For the full cell reaction, A+B→C+D (discharge), the thermogalvanic coefficient α is defined as:"," α = ∂ E ∂ T = - 1 n ⁢ ⁢ F ⁢ ∂ Δ ⁢ ⁢ G ∂ T = Δ ⁢ ⁢ S n ⁢ ⁢ F ( 2 ) where E is the full cell voltage and ΔG and ΔS are the change of partial molar Gibbs free energy and partial molar entropy, respectively, in the full cell reaction.","Generally, the voltage of the electrochemical cell depends on temperature%3b thus, a thermodynamic cycle can be constructed by discharging the electrochemical cell at T 1 and charging the electrochemical cell at T 2 . If the charging voltage at T 2 is lower than the discharging voltage at T 1 , net energy is produced by the voltage difference, similar to a thermomechanical engine whose theoretical efficiency is limited by Carnot efficiency.","Traditional TRES are often impractical, as such systems must often be operated at conditions that are incompatible with many processes in which heat recovery would be useful. Improved systems and associated methods would be desirable.","SUMMARY","Electrochemical cells, electrochemical systems, and electrochemical methods for harvesting heat energy are generally described. Certain embodiments relate to electrochemically harvesting low-grade heat energy using electrochemical cells and related electrochemical systems. The subject matter of the present invention involves, in some cases, interrelated products, alternative solutions to a particular problem, and/or a plurality of different uses of one or more systems and/or articles.","Certain embodiments relate to electrochemical cells comprising a first electrode comprising a first electrochemically active material and a second electrode comprising a second electrochemically active material.","In some embodiments, the electrochemical cell is configured to be discharged at a discharge voltage and at a discharge temperature at or below about 200° C. such that the first electrochemically active material is at least partially electrochemically consumed. In some embodiments, the electrochemical cell is configured to regenerate electrochemically active material from a product of at least a portion of electrochemically active material consumed during discharge at a regeneration voltage that is at least about 5 mV lower than the discharge voltage and at a regeneration temperature that is different than the discharge temperature and at or below about 200° C. In certain cases, at least one of the first and second electrodes comprises an electrochemically active material that is in a solid phase in both a reduced state and an oxidized state.","In some embodiments, the electrochemical cell is configured to be discharged at a discharge temperature such that the first electrochemically active material is at least partially electrochemically consumed. In some cases, the electrochemical cell is configured to regenerate electrochemically active material from a product of at least a portion of electrochemically active material consumed during discharge via a non-chemical-reaction regeneration pathway at a temperature different than the discharge temperature, such that at least a portion of the regeneration of the electrochemically active material is not driven by the application of electrical current external to the electrochemical cell.","In some embodiments, methods are described. One method comprises, in some embodiments, discharging an electrochemical cell at a discharge voltage and a discharge temperature at or below about 200° C. In some embodiments, the method further comprises electrochemically regenerating electrochemically active material from a product of at least a portion of electrochemically active material consumed during discharge, at a regeneration voltage that is at least about 5 mV lower than the discharge voltage and a regeneration temperature that is different than the discharge temperature and at or below about 200° C. In certain embodiments, the electrochemical cell comprises at least one electrode comprising an electrochemically active material that is in a solid phase in both a reduced state and an oxidized state.","Some methods comprise, in certain embodiments, discharging an electrochemical cell at a discharge temperature such that an electrochemically active material within the electrochemical cell is at least partially electrochemically consumed. In some embodiments, the methods further comprise electrochemically regenerating electrochemically active material from a product of at least a portion of electrochemically active material consumed during discharge via a non-chemical-reaction regeneration pathway at a temperature different than the discharge temperature, such that at least a portion of the regeneration of the electrochemically active material is not driven by the application of electrical current external to the electrochemical cell.","In some embodiments, methods of transferring heat from a first set of electrochemical cells to a second set of electrochemical cells are described. In certain embodiments, the methods comprise transferring heat from a first electrochemical cell at a first temperature to a second electrochemical cell at a second temperature lower than the first temperature. In some cases, the methods further comprise, after transferring heat from the first electrochemical cell to the second electrochemical cell, transferring heat from the first electrochemical cell to a third electrochemical cell at a temperature lower than the first temperature. In certain embodiments, the methods further comprise, after transferring heat from the first electrochemical cell to the second electrochemical cell, transferring heat from a fourth electrochemical cell to the second electrochemical cell.","Certain embodiments relate to methods of transferring heat from a first electrochemical cell to a second electrochemical cell. In some embodiments, the methods comprise flowing a first fluid at a first temperature through a first heat exchanger, wherein the temperature of the first fluid is reduced to a second temperature lower than the first temperature. In some embodiments, the methods further comprise flowing the first fluid at the second temperature through a first electrochemical cell, wherein the temperature of the first fluid is increased to a third temperature higher than the second temperature. In certain cases, the methods further comprise flowing a second fluid at a fourth temperature through the first heat exchanger, wherein the temperature of the second fluid is increased to a fifth temperature higher than the fourth temperature. In some embodiments, the methods further comprise flowing the second fluid at the fifth temperature through a second electrochemical cell, wherein the temperature of the second fluid is reduced to a sixth temperature lower than the fifth temperature.","In some embodiments, methods of transferring heat from a first electrochemical cell to a second electrochemical cell are described. The methods, in certain cases, comprise flowing a first electrolyte for a first electrochemical cell at a first temperature through a heat exchanger. In some cases, the methods further comprise flowing a second electrolyte for the second electrochemical cell at a second temperature through the heat exchanger. In some cases, the first temperature is higher than the second temperature. In certain embodiments, the heat exchanger places the first electrolyte in thermal communication with the second electrolyte. The methods, in some embodiments, further comprise flowing the first electrolyte from the heat exchanger to the first electrochemical cell. In some embodiments, the methods further comprise flowing the second electrolyte from the heat exchanger to the second electrochemical cell.","Other advantages and novel features of the present invention will become apparent from the following detailed description of various non-limiting embodiments of the invention when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and/or inconsistent disclosure, the present specification shall control.","DETAILED DESCRIPTION","Electrochemical systems for harvesting heat energy, and associated electrochemical cells and methods, are generally described. Certain embodiments relate to electrochemical systems in which the cell voltage varies as a function of temperature. It has been discovered that the operating voltage of electrochemical cells can be efficiently altered in a desired fashion by employing at least one electrode comprising an electrochemically active material that is in solid phase during both discharge and regeneration. Without wishing to be bound by any particular theory, it is believed that such solid electrode materials have relatively low heat capacities, compared to liquid and gaseous electrodes. Accordingly, the temperatures of such electrodes can be changed relatively rapidly, reducing the amount of heat lost from the system. In some embodiments, such properties can be useful in operating electrochemical cells in thermally regenerative electrochemical systems (TRES). In addition, in some embodiments, the use of such electrode materials can be particularly useful in electrochemical cells that are operated at discharge and/or regeneration temperatures at or below about 200° C. For example, such materials may be useful in electrochemical systems (including certain TRES systems) used to capture low-grade thermal energy.","In some embodiments, certain of the electrochemical cells described herein can be discharged and regenerated spontaneously. That is to say, certain of the electrochemical cells described herein can be both discharged and regenerated without the application of an external electrical current. In some such embodiments, the temperature at which the cell is operated can be altered to achieve spontaneous operation. For example, in some embodiments, the electrochemical cell can be discharged at a first temperature at which discharge of the electrochemical cell is thermodynamically favored. Subsequently, in some embodiments, the electrochemical cell can be heated or cooled to a second temperature at which a reverse electrochemical reaction is thermodynamically favored. In this way, the heat that is input to the electrochemical cell to alter its temperature is effectively converted to electricity.","Still further embodiments relate to inventive methods for transferring heat to and from electrochemical cells within a multi-cell system. In some such embodiments, a plurality of hot electrochemical cells and a plurality of cold electrochemical cells are provided. In certain embodiments, the heat from the hot cells can be used to raise the temperature of one or more of the cold cells to a temperature that is greater than the temperature that could be achieved if all hot cells were simultaneously thermally connected to all of the cold cells.","FIGS. 1A-1B are exemplary cross-sectional schematic diagrams illustrating the arrangement and operation of certain of the inventive electrochemical cells described herein. In some embodiments, the electrochemical cell comprises a first electrode comprising a first electrochemically active material and a second electrode comprising a second electrochemically active material. For example, referring to FIGS. 1A-1B , electrochemical cell 100 comprises first electrode 101 and second electrode 104 . Those of ordinary skill in the art are familiar with electrochemically active materials, which generally refer to materials that participate in oxidation and/or reduction reactions within an electrochemical cell. One of ordinary skill in the art would be capable of discerning an electrochemically active material (which participates in electrochemical reactions) from, for example, a current collector (which generally facilitates transfer of electrons from electrochemically active materials to an external circuit, but does not itself participate in electrochemical reactions). Referring to FIGS. 1A-1B , first electrode 101 comprises a first electrochemically active material, and second electrode 104 comprises a second electrochemically active material. In addition, current collector 102 is in electrical contact with electrode 101 , as illustrated in FIG. 1A .","In some embodiments, at least one of the electrodes may comprise a solid electrochemically active material. In some such embodiments, the solid electrochemically active material is in a solid phase in both its discharged and its regenerated states. For example, referring to FIGS. 1A-1B , second electrode 104 can comprise an electrochemically active material that is in solid phase in both its regenerated state (as shown in FIG. 1A ) and its discharged state (as shown in FIG. 1B ). A variety of electrochemically active materials that are in a solid phase during both discharged and regenerated states may be used, including Prussian Blue (KFe II Fe III (CN) 6 ), copper hexacyanoferrate (CuHCF, KCu II Fe III (CN) 6 ), nickel hexacyanoferrate (NiHCF, KNi II Fe III (CN) 6 ), and others, as described in more detail below.","In contrast, in FIGS. 1A-1B , first electrode 101 comprises an electrochemically active material that is in a solid phase in its regenerated state (as shown in FIG. 1A ) but is in solution in its discharged state (as shown in FIG. 1B ). A variety of electrochemically active materials that are not in a solid state during both discharged and regenerated states may be used, including for example Cu/Cu 2+ , Ag/AgCl, and/or Fe(CN) 6 3−/4− among others, as described in more detail below.","In some embodiments, one of the electrodes may be referred to as the anode and the other electrode may be referred to as the cathode. Those of ordinary skill in the art will be familiar with the terms anode and cathode. Generally, an anode refers to a negative electrode%3b typically, oxidation reactions occur at the anode in discharge. A cathode generally refers to a positive electrode typically, reduction reactions occur at the cathode in discharge. For example, in FIGS. 1A-1B , for the particular non-limiting example wherein electrode 101 comprises Cu/Cu 2+ and electrode 104 comprises copper hexacyanoferrate, electrode 101 may be referred to as the anode, and electrode 104 may be referred to as the cathode.","In some embodiments, the electrochemical cell may comprise one or more electrolytes. For example, referring to FIGS. 1A-1B , first electrode 101 is at least partially immersed in first electrolyte 107 . In addition, second electrode 104 is at least partially immersed in second electrolyte 108 . Generally, an electrolyte can be configured to conduct one or more electrochemically active ions. Non-limiting examples of electrochemically active ions include Li + , Na + , K + , Cu 2+ , and Zn 2+ . In certain embodiments, the electrolyte can be configured to be substantially electronically insulating. By configuring the electrolyte such that it does not substantially conduct electrons, an electrical short circuit between the electrodes of the electrochemical cell during operation may be prevented.","An electrochemical cell may additionally comprise an optional separator (e.g., in the form of a membrane, such as an ion-exchange membrane) that electronically separates the electrodes but permits transfer of ions (e.g., electrochemically active ions) across the separator. For example, referring back to FIGS. 1A-1B , first electrode 101 is separated from second electrode 104 by separator 106 . In some embodiments, the separator (e.g., separator 106 ) is an ion-selective membrane. The ion-selective membrane may advantageously be selected to prevent transfer of certain ions (e.g., to prevent side reactions). For example, in the non-limiting case in which the cathode comprises CuHCF and the anode comprises Cu/Cu 2+ , an ion-selective membrane may be selected that prevents transfer of Cu 2+ ions to avoid side reactions between CuHCF and Cu 2+ . In certain embodiments, the ion-selective membrane is a Nafion membrane (e.g., a Nafion 115 membrane). In some embodiments, an ion-selective membrane is not necessary. For example, if ions involved in the anode and the cathode do not have side reactions with each other and/or with other materials associated with the anode or cathode (e.g., an ion involved in the anode does not have side reactions with any materials of the cathode, or an ion involved in the cathode does not have side reactions with any materials of the anode), an ion-selective membrane may not be needed. In some cases, not using an ion-selective membrane may advantageously reduce the costs associated with an electrochemical cell. In certain cases, not using an ion-selective membrane may advantageously improve long-term operation of an electrochemical cell. In cases where an ion-selective membrane is not needed, any porous separator may be used. A non-limiting example of a porous separator is a glass fiber filter. It should be understood that separator 106 is an optional component, and in certain embodiments, separator 106 may be absent. For example, separator 106 may be absent in some embodiments in which the electrodes are exposed to a single electrolyte that is substantially electronically insulating.","In some embodiments, the electrochemical cell may be configured to be discharged. Those of ordinary skill in the art are familiar with the concept of discharge, which generally refers to a process in which an electrochemical reaction proceeds such that net electrical current is generated. In certain embodiments, an electrical circuit connecting the two electrodes may be formed by one or more electrolytes configured to conduct one or more electronically active ions and an external element configured to conduct electrons. In some embodiments, as the electrochemical reaction proceeds, electrons released at one electrode travel through the external element to the other electrode, resulting in an electrical current.","During discharge, at least one of the electrochemically active materials may be at least partially electrochemically consumed. Two half-cell reactions typically occur during discharge of an electrochemical cell. In some embodiments, electrons may be emitted at one electrode as a result of oxidation of the electrochemically active material of the electrode. Those of ordinary skill in the art are familiar with oxidation, which generally refers to a process in which electrons are lost by the oxidized material, leading to an increase in oxidation state of the material that is being oxidized. In some embodiments, one of the electrodes may absorb electrons. For example, electrons may be absorbed at an electrode as a result of reduction of the electrochemically active material of the electrode. Those of ordinary skill in the art are familiar with reduction, which generally refers to a process in which electrons are gained by the reduced material, leading to a decrease in oxidation state of the material that is being reduced. During electrochemical cycling of an electrochemical cell, an electrode may be both oxidized and reduced. For example, in certain embodiments, an electrode may be oxidized during discharge and reduced during regeneration. Alternatively, an electrode may be reduced during discharge and oxidized during regeneration. In general, those of ordinary skill in the art understand electrochemical consumption to refer to oxidation or reduction of an electrochemically active material, thereby causing the material to become depleted.","In some embodiments, the two half-cell reactions that occur during discharge are both spontaneous. Generally, a reaction is spontaneous when the change in the Gibbs free energy associated with the reaction (ΔG) is less than zero. Gibbs free energy can be expressed mathematically as ΔG=ΔH−TΔS, where H is enthalpy, T is temperature, and S is entropy. It may be advantageous, in some cases, for a reaction to be spontaneous, because a spontaneous reaction generally does not require application of an external source of energy to proceed. For example, in some instances, it may be advantageous for an electrochemical reaction to be spontaneous because such spontaneous reactions generally do not require application of an external electrical current to proceed.","In some cases, the electrochemical cell may be configured to regenerate electrochemically active material from a product of at least a portion of electrochemically active material consumed during discharge. As used herein, regeneration refers to a process in which the reverse reactions of the electrochemical reactions that occur during discharge proceed. For example, in one particular non-limiting example of the system in FIGS. 1A-1B in which the electrochemically active material of first electrode 101 comprises copper metal (Cu), and the electrochemically active material of second electrode 104 comprises copper hexacyanoferrate, the two half-cell reactions that occur at the two electrodes can be expressed as: Na 0.71 Cu[Fe III (CN) 6 ] 0.72 +a (Na + +e − )⇄Na 0.71+a Cu[Fe III (CN) 6 ] 0.72−a [Fe II (CN) 6 ] 0.72+a and: Cu⇄Cu 2+ +2 e − In another non-limiting example of the system in FIGS. 1A-1B , the electrochemically active material of first electrode 101 comprises silver chloride, and the electrochemically active material of second electrode 104 comprises nickel hexacyanoferrate. The two half-cell reactions that occur at the two electrodes can be expressed as: KNi II Fe III (CN) 6 +K + +e − ⇄K 2 Ni II Fe III (CN) 6 and: Ag+Cl − ⇄AgCl+ e − During discharge, these reactions proceed in the forward direction (i.e., from left to right as written above), and during regeneration, these reactions proceed in the reverse direction (i.e., from right to left as written above).","In certain embodiments, the electrochemical cell is configured to regenerate at least a portion of the consumed electrochemically active material via a non-chemical-reaction regeneration pathway. A chemical reaction regeneration pathway generally refers to a pathway in which regeneration occurs by contacting discharged components such that regeneration occurs via a chemical reaction between the discharged components. For example, in a system comprising Cr 3+ and Sn, contacting the discharged components Cr 2+ and Sn 2+ can result in a chemical reaction that regenerates Cr 3+ and Sn. In some embodiments, regeneration may occur by transporting electrons via external electrical circuitry. This can be achieved, for example, by applying an external electrical current to supply electrons. In some embodiments, the electrons may be provided spontaneously, for example, by altering the temperature of the system such that ΔG becomes negative, and electrons are exchanged between discharged components spontaneously. In some embodiments, regeneration is achieved by initiating electrochemical reactions that are the reverse of those that occur during discharge. At least a portion of the regeneration of the electrochemically active material may be driven by heating and cooling the electrochemical cell. In certain embodiments, regeneration of the electrochemically active material is driven only by heating and cooling the electrochemical cell.","Generally, electrochemical cells are discharged at a discharge voltage. Similarly, electrochemical cells are generally regenerated at a regeneration voltage. As used herein, discharge voltage refers to the open-circuit voltage of the electrochemical cell when discharge begins. Regeneration voltage, as used herein, refers to the open-circuit voltage of the electrochemical cell when regeneration begins. Those of ordinary skill in the art are familiar with the concept of open-circuit voltage, which generally corresponds to the difference in electrode potential between two electrodes when disconnected from a circuit.","Electrochemical cells are generally discharged at a discharge temperature (T D ), which corresponds to the temperature at which the electrochemical cell is discharged. Electrochemical cells are also generally regenerated at a regeneration temperature (T R ), which corresponds to the temperature at which the electrochemical cell is regenerated. Discharge and regeneration temperatures can be calculated by determining the mass-averaged average temperature of each electrode within the electrochemical cell during operation (e.g., during discharge or during regeneration) and averaging the two average electrode temperatures. In certain of the embodiments described herein, the electrochemical cell is substantially isothermal. That is to say, the temperature of the first electrode is substantially the same as the temperature of the second electrode. In some embodiments, the temperature of the first electrode is within about 10° C., within about 5° C., within about 2° C., or within about 1° C. of the temperature of the second electrode.","In some embodiments, the discharge and/or regeneration voltage of the electrochemical cell varies with temperature. One material property reflecting the voltage response of an electrochemically active material to change in temperature is the thermogalvanic coefficient. Those of ordinary skill in the art are familiar with the thermogalvanic coefficient (α) of an electrochemically active material, which generally refers to the change in electrode potential with change in temperature. The thermogalvanic coefficient of a particular material can be expressed mathematically as:"," α = ∂ V ∂ T ( 3 ) where V is electrode potential and T is temperature. The thermogalvanic coefficient of an electrode may be determined experimentally, for example, by measuring voltage across an electrochemical cell having a counter electrode with known thermogalvanic behavior at various temperatures. Generally, the thermogalvanic coefficient of a full electrochemical cell corresponds to the difference between the thermogalvanic coefficient of the two electrodes, and can be calculated by subtracting the thermogalvanic coefficient of the anode from the thermogalvanic coefficient of the cathode.","In certain embodiments, the first electrode comprises an electrochemically active material having a first thermogalvanic coefficient and the second electrode comprises an electrochemically active material having a second thermogalvanic coefficient. The absolute value of the difference between the first and second thermogalvanic coefficients may be, in some cases, relatively large. The use of electrode material pairs in which the difference in thermogalvanic coefficients, and thus the thermogalvanic coefficient for the full electrochemical cell, is relatively large, may be advantageous in certain instances because a relatively modest change in temperature can be accompanied by a relatively large change in voltage. In some cases, the difference between the first and second thermogalvanic coefficients is at least about 0.5 millivolts/Kelvin, at least about 1 mV/K, or at least about 2 mV/K (and/or, in certain embodiments, up to about 10 mV/K, or more).","In certain embodiments, the electrochemical cell can be configured to be operated such that the regeneration temperature T R is different from the discharge temperature T D . In some embodiments, as temperature changes from T D to T R , the open-circuit voltage of the electrochemical cell changes from discharge voltage V D to regeneration voltage V R . For example, one or more electrodes of the electrochemical cell may have a thermogalvanic coefficient that has a relatively high absolute value, causing a relatively large change in potential as a function of temperature. In some embodiments, the electrochemical cell can be configured such that regeneration voltage is lower than the discharge voltage. In some embodiments, the regeneration voltage is at least about 1 mV, at least about 5 mV, at least about 10 mV, at least about 20 mV, at least about 50 mV, at least about 100 mV, at least about 200 mV, or at least about 500 mV (and/or, in some embodiments, up to about 1 V, or more) lower than the discharge voltage.","As described in detail below, it may be advantageous, in certain embodiments (although not required), for regeneration voltage to be lower than discharge voltage. For example, in certain systems in which the regeneration voltage is lower than the discharge voltage, the amount of electrical current required to perform the regeneration step can be smaller than the amount of current required to perform the discharge step, resulting in net electrical current.","Additionally, it may be advantageous, in certain embodiments, for regeneration voltage to be reduced due to change in temperature. For example, in certain systems in which the regeneration voltage is lower than the discharge voltage, the amount of electrical current required to perform the regeneration step can be smaller than the amount of current that would be required were the regeneration voltage not lowered. By reducing the amount of electrical current required to perform the regeneration step, the net amount of electrical current extracted from the electrochemical cell (calculated by subtracting the current input during the regeneration step from the current produced during the discharge step) can be increased.","Thus, in some embodiments, the electrochemical cell is heated and/or cooled to obtain net energy. For example, in some embodiments, the electrochemical cell(s) may be heated or cooled between discharge and regeneration steps to alter the discharge and/or regeneration voltage which can, in certain embodiments, increase the amount of net electricity extracted from the electrochemical cell. Such operation is schematically illustrated, for example, in FIG. 2 . FIG. 2 is an exemplary temperature-entropy diagram depicting a thermodynamic cycle an electrochemical cell may undergo to generate net work from input heat. In FIG. 2 , an electrochemical cell may be discharged at discharge temperature T D via pathway 201 . In some embodiments, the electrochemical cell is subsequently heated from T D to regeneration temperature T R , for example, via pathway 202 in FIG. 2 . In some embodiments, after the electrochemical cell has been heated to T D , the electrochemical cell can be regenerated at T R , for example, via pathway 203 in FIG. 2 . In some embodiments, heating the electrochemical cell such that the regeneration temperature is higher than the discharge temperature can lower the regeneration voltage of the electrochemical cell, relative to the regeneration voltage that would have been observed were the electrochemical cell maintained at the discharge temperature (and, in certain embodiments, lower than the discharge voltage). In some such embodiments, lowering the regeneration voltage in this manner can reduce the amount of electrical current needed to complete the regeneration process, thus increasing the net electrical current extracted from the electrochemical cell. Referring back to FIG. 2 , after regenerating the electrochemical cell, the electrochemical cell may be cooled to discharge temperature T D via pathway 204 .","In some embodiments, T D and T R are less than about 200° C. Many previous thermally regenerated electrochemical systems relied on input of a large amount of heat at high temperature (typically greater than 300° C., and often above 1000° C.). It was unexpectedly found, according to certain aspects of the present invention, that highly efficient systems may be formed with discharge and regeneration temperatures of less than about 200° C. A thermally-regenerated electrochemical cell with relatively low discharge and regeneration temperatures may be advantageous, according to certain embodiments, because it can allow for generation of electrical energy with input from low temperature waste heat, including certain waste heat which is abundantly available from industrial processes, solar-thermal energy, and geothermal energy. Although low-temperature thermal energy is abundant, it has generally been difficult to convert such energy into electricity using traditional methods. In certain embodiments described herein, waste heat from an industrial or other process is used to heat an electrochemical cell to its regeneration temperature, at which point the cell is discharged at a regeneration voltage that is lower than the discharge voltage.","In some embodiments, the electrochemical cell has a negative thermogalvanic coefficient. That is, when the temperature of the electrochemical cell is increased, the voltage of the electrochemical cell is decreased. In some such embodiments, the regeneration temperature may be at least about 5° C. higher, at least about 10° C. higher, or at least about 20° C. higher than the discharge temperature (and/or, in certain embodiments, up to about 100° C. higher, up to about 200° C. higher, or more than the discharge temperature).","In some embodiments, regeneration temperature T R and/or discharge temperature T D may be at or below about 200° C., at or below about 150° C., at or below about 100° C., or at or below about 50° C. (and/or, in certain embodiments, down to −100° C. or lower). In some embodiments, the discharge temperature may be within about 5° C., within about 2° C., or within about 1° C. of the temperature of the ambient environment. In some cases, the discharge temperature may be substantially the same as the temperature of the ambient environment. For example, in some embodiments, the discharge temperature may be about 24° C.","In some embodiments, the electrochemical cell has a positive thermogalvanic coefficient. For such a cell, voltage would increase with an increase in temperature. In order for net energy to be extracted, the electrochemical cell may be discharged at high temperature (high voltage) and regenerated at low temperature (low voltage). In some such embodiments, the regeneration temperature may be at least about 5° C. lower, at least about 10° C. lower, or at least about 20° C. lower than the discharge temperature (and/or, in certain embodiments, up to about 100° C. lower, up to about 200° C. lower, or more than the discharge temperature). In some embodiments, regeneration temperature T R may be within about 5° C., within about 2° C., or within about 1° C. of the temperature of the ambient environment. In some cases, the regeneration temperature may be substantially the same as the temperature of the ambient environment. For example, in some embodiments, the regeneration temperature may be about 24° C.","In some embodiments, a change in temperature from T D to T R results in a regeneration voltage V R that is negative. The impact of altering the temperature on operating voltages is illustrated for two exemplary systems in the voltage-capacity diagrams of FIGS. 3A-3B . FIG. 3A shows an exemplary voltage-capacity diagram for a thermally regenerative electrochemical system in which temperature change results in a regeneration voltage that is smaller than the discharge voltage but is still positive. In FIG. 3A , as the cycle progresses from point 301 to point 302 , the electrochemical cell discharges at temperature T D , with voltage decreasing from voltage V 301 to voltage V 302 , and electricity is produced in this process. Discharge voltage is V 301 , the voltage at the beginning of the discharge process. As the cycle progresses from point 302 to point 303 , the cell is disconnected, and the temperature changes from T D to regeneration temperature T R . As the cycle progresses from point 303 to point 304 , the electrochemical cell regenerates (i.e., a process that is the reverse of the discharging electrochemical process occurs) at T R , with voltage increasing from V 303 to V 304 . The regeneration voltage is V 303 , the voltage of the electrochemical cell at the beginning of the regeneration process. In the exemplary system illustrated in FIG. 3A , the net electricity generated within the system may be greater than the net electricity that would have been generated were the temperature kept constant because the regeneration voltage V R is less than the discharge voltage V D . However, in the example of FIG. 3A , application of an external electrical current is still needed to drive the system from point 303 to point 304 .","FIG. 3B shows an exemplary voltage-capacity diagram for a thermally regenerative electrochemical system in which temperature change results in a regeneration voltage that is less than zero. As the cycle progresses from point 301 to point 302 , the pathway is substantially identical to the pathway from 301 to 302 in FIG. 3A , with the electrochemical cell discharging at temperature T D and voltage decreasing from V 301 to V 302 . As the cycle progresses from point 302 to point 305 , temperature changes from discharge temperature T D to regeneration temperature T R . Unlike the voltage at point 303 in FIG. 3A , however, the voltage at point 305 in FIG. 3B is negative. As the cycle progresses from point 305 to point 306 , the absolute value of the voltage decreases. As a result, the process from point 305 to point 306 is spontaneous and does not require external electrical current to proceed. Unlike in FIG. 3A , electricity is produced during the pathway from 305 to 306 in FIG. 3B as well. The cycle illustrated in FIG. 3B therefore does not require application of an external electrical current, and electricity is produced during both discharge and regeneration. In some such embodiments, such electricity generation may be driven only by the heating and cooling of the electrochemical cell.","An electrochemical cell that requires only external heat as input may be advantageous, in some instances. Certain embodiments in which both T D and T R are below 200° C. may be especially advantageous, since low-grade waste heat can be used to generate electricity in some such instances. Such embodiments may be particularly advantageous for off-grid applications, especially in remote areas where external electrical sources are not accessible.","In some embodiments, the electrochemical cell may be highly efficient. The efficiency of a thermally regenerative electrochemical cycle may be mathematically expressed as:"," η = W Q H + Q HX ( 4 ) where W is the net work output in one cycle, Q H is the heat absorbed at T H , and Q HX is the external energy needed to heat the system. In some embodiments, the efficiency is at least about 0.25%, at least about 0.5%, at least about 1%, at least about 1.5%, at least about 1.9%, at least about 2%, at least about 3.5%, at least about 5%, at least about 6%, at least about 6.5%, at least about 10% (and/or, in certain embodiments, up to about 15%, up to about 25%, or higher).","In some embodiments, at least one of the first and second electrodes comprises an insoluble solid in both oxidized and reduced states. Use of solids in an electrode may be advantageous due to their low heat capacity and high charge capacity compared to, for example, liquid electrode materials. Low heat capacity may be important in certain instances because less heat is required to obtain the desired temperature change during operation of the electrochemical cell. For example, as described above, operation of the electrochemical systems of FIGS. 2 and 3A-3B involve heating and cooling the electrochemical cell. In certain instances in which low heat capacity materials are employed in the electrode, less heat is required to be input into the cell to achieve the desired temperatures. Less heat input results in less wasted energy, yielding a more efficient system. The use of materials with high charge capacities may also be advantageous, in certain embodiments, because more energy can be stored and obtained from the system when such materials are used.","In some embodiments, the electrodes described herein can have relatively low specific heat capacities. Those of ordinary skill in the art are familiar with the concept of specific heat capacity, which generally refers to the amount of energy (generally in the form of heat) required to change the temperature of a material by a given amount per unit mass. The specific heat capacity of a particular material may be measured, for example, by differential scanning calorimetry (DSC). In some embodiments, the specific heat capacity of at least one of the first electrode and the second electrode may be less than about 5 J/g K, less than about 4 J/g K, less than about 3 J/g K, less than about 2 J/g K, less than about 1 J/g K, or less than about 0.5 J/g K (and/or, in certain embodiments, down to about 0.1 J/g, or lower). However, it should be understood that the electroactive materials of the electrodes are not limited to electrode materials having the above specific heat capacities, and in other embodiments, electrode materials having higher heat capacities than those outlined above could be used.","In certain embodiments, the materials from which certain of the electrodes described herein are made have a relatively high specific charge capacity. Those of ordinary skill in the art are familiar with specific charge capacity, which generally refers to the amount of charge per unit mass of electroactive material. Generally, it is advantageous for the specific charge capacity of a particular electrode material to be as high as possible. In certain cases, the specific charge capacity of at least one of the first electrode and second electrode may be greater than about 10 mAh/g, greater than about 20 mAh/g, greater than about 30 mAh/g, greater than about 40 mAh/g, greater than about 50 mAh/g, greater than about 200 mAh/g, greater than about 1000 mAh/g, or greater than about 4000 mAh/g (and/or in some embodiments, up to about 100 mAh/g, up to about 10,000 mAh/g, or greater). It should be understood that the electroactive materials of the electrodes are not limited to electrode materials having the above specific charge capacities, and in other embodiments, electrode materials having smaller specific charge capacities could be used.","In some embodiments, a material figure of merit Y is used to assess efficiency of an electrochemical system. Y may be mathematically expressed as:"," Y = α ⁢ ⁢ q c p ( 5 ) where α is the thermogalvanic coefficient, q is the specific charge capacity, and c p is the specific heat capacity. It may be advantageous, in some embodiments, for the absolute value of Y to be as large as possible. In certain of the electrochemical cells and systems described herein, the value of Y of at least one of the electrodes may be at least about 0.01, at least about 0.05, at least about 0.1, at least about 0.2, at least about 0.5, at least about 1, or at least about 5 (and/or, in certain embodiments, up to about 10, up to about 20, or more).","In certain embodiments in which solid electrochemically active materials are used, the solid electrochemically active material can be of a variety of suitable shapes and sizes. In some embodiments, the solid electrochemically active material may comprise particles. In certain cases, the solid electrochemically active material may comprise nanoparticles. The average nanoparticle diameter may be, in some embodiments, less than about 1 micron, less than about 500 nm, less than about 200 nm, less than about 100 nm, or less than about 50 nm (and/or, in certain embodiments, as low as 1 nm, or less). Without wishing to be bound by any particular theory, the use of nanoparticulate electrode active material may be advantageous due to an increase in surface area, which can provide for enhanced electronic conductivity. The use of particulate electrochemically active material is not required, however, and in some embodiments, the electrochemically active material can be in another form factor (e.g., in the form of a slab, block, or any other suitable form).","In some embodiments in which an electrochemically active material is in a solid phase, particles (e.g., nanoparticles) of the electrochemically active material are suspended in a fluid. The fluid may be an electrolyte (e.g., a liquid electrolyte). In some cases, an electrode comprising the solid electrochemically active material particles suspended in the fluid is a flowable electrode (e.g., the electrode is substantially fluid or easily deformed). For example, the electrode may have measurable viscosity and/or may tend to flow and to conform to the outline of its container.","In some embodiments, the solid electrochemically active material may comprise an intercalation compound. Intercalation compounds may be considered to be those that can be oxidized and/or reduced by the insertion and/or extraction of ions. Intercalation compounds include, but are not limited to, metal oxides, metal chalcogenides, Prussian Blue and its analogues, and graphitic compounds. Exemplary, non-limiting examples of Prussian Blue analogues include transition metal hexacyanoferrates, such as copper hexacyanoferrate (CuHCF) and nickel hexacyanoferrate (NiHCF). Examples of suitable transition metal hexacyanoferrates include, but are not limited to, hexacyanoferrates of transition metals selected from the group consisting of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. Oxidation of CuHCF and/or NiHCF may include intercalation of, for example, Na + ions and/or K + ions from an electrolyte. Chalcogenides may pertain to compounds that contain one or more of the elements of oxygen, sulfur, and selenium. Examples of suitable transition metal chalcogenides include, but are not limited to, the electroactive oxides, sulfides, and selenides of transition metals selected from the group consisting of Mn, V, Cr, Ti, Fe, Co, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Os, and Ir.","In some embodiments, the solid electrochemically active material may be capable of undergoing a conversion reaction. In some embodiments, the material comprises a metal salt that stores an alkali ion by undergoing a displacement or conversion reaction. Examples of such compounds include metal oxides such as CoO, Co 3 O 4 , NiO, CuO, MnO.","In some cases, the electrochemically active material of an electrode may comprise a metal (e.g., in the form of an elemental metal, a metal alloy, or in another form). Examples of suitable metals include, but are not limited to, silicon, germanium, tin, lead, silver, nickel, cadmium, and/or lithium. In some embodiments, the electrochemically active material of an electrode may comprise PbO 2 , PbSO 4 , and/or metal hydrides (e.g., Ni-metal hydrides (Ni(OH) 2 )).","In some embodiments, the electrochemically active material of an electrode is not in solid phase in both the discharged and regenerated states. For example, the electrochemically active material may be in a solid phase in a first state (e.g., a regenerated state) and in a liquid phase in a second state (e.g., a discharged state). Examples of suitable electrochemically active materials that are not in solid state during in both the discharged and regenerated states include, but are not limited to, Cu/Cu 2+ , Zn/Zn 2+ , Ni/Ni 2+ , Ag/AgCl, and/or Fe(CN) 6 3−/4− . In some embodiments, when the electrode is part of an electrochemical cell comprising another electrode (e.g., an electrode having an electrochemically active material in solid phase in both the discharged and regenerated states), the ions that participate in the half-cell reaction of the electrode may not react (e.g., engage in a side reaction) with the electrochemically active material of the other electrode.","In certain embodiments, the electrochemically active material in one or both electrodes of certain of the electrochemical cells described herein is non-radioactive. A radioactive material generally refers to a material that has sufficient spontaneous radioactive decay such that the decay products can be detected above the background radiation of the earth. Additionally, a radioactive material generally has a half-life of less than about one million years. Examples of radioactive materials include, but are not limited to, UF 6 and UF 5 . Radioactive materials generally pose hazards to human health if not managed properly. Thus, in certain applications, it may be advantageous for electrodes to be formed from non-radioactive materials.","In certain embodiments, the electrochemically active material in one or both electrodes of certain of the electrochemical cells described herein is non-toxic to humans. Non-toxic materials include materials with median lethal doses (LD 50 ) of greater than 90 g/kg. Toxic materials generally pose a danger to human health if not managed properly. Thus, in certain instances, it may be advantageous for electrodes to be formed from non-toxic materials.","In some embodiments, the electrochemically active material in one or both electrodes of certain of the electrochemical cells described herein is Earth-abundant. Earth-abundant elements include elements that are higher in elemental abundance than Pt-group metals. Examples of Earth-abundant elements include, but are not limited to, first row transition metals, silicon, oxygen, carbon, and sulfur. Earth-abundant materials are typically low in cost. Thus, for certain applications, it may be advantageous to form electrodes from Earth-abundant materials.","In some cases, certain of the electrodes described herein are stable over at least about 100 cycles, at least about 200 cycles, at least about 250 cycles, at least about 300 cycles, at least about 400 cycles (and/or, in certain embodiments, up to about 500 cycles, or more). In certain embodiments, the initial specific charge capacity of an electrode decreases by less than about 5 mAh/g or less than about 2 mAh/g (and/or, in certain embodiments, down to about 1 mAh/g, or lower) after 30 cycles. In some cases, the change in specific charge capacity is less than about 5 mAh/g after about 30 cycles, about 50 cycles, about 100 cycles, about 150 cycles, about 200 cycles, about 250 cycles, about 300 cycles, about 350 cycles, about 400 cycles (and/or, in certain embodiments, about 500 cycles, or more). Generally, each cycle has two steps, a discharge step and a regeneration step, one at a first temperature and one at a second, different temperature. After 500 cycles, decaying of specific charge capacity may be less than about 30%, less than about 20%, less than about 15%, less than about 10%, or less than about 5% (and/or, in certain embodiments, down to about 1%, or lower).","In some embodiments, a system comprises a plurality of electrochemical cells. In one embodiment, the system comprises a second electrochemical cell to which heat is transferred from the first electrochemical cell. The second electrochemical cell, in some embodiments, may be configured to be regenerated while the first electrochemical cell is discharged. The temperature of the second electrochemical cell during regeneration may be different than (e.g., less than or higher than) the temperature of the first electrochemical cell during discharge. In some embodiments, the first electrochemical cell is in direct thermal contact with at least the second electrochemical cell.","In some embodiments, one or more heat exchangers may be used to harvest heat rejected during the cooling process. Use of such heat exchangers may be advantageous, in some embodiments, because less external energy is required to cycle the electrochemical cell.","FIG. 4 is an exemplary schematic illustration of a system 400 comprising a plurality of electrochemical cells between which heat is exchanged during operation. In FIG. 4 , heat exchanger 403 can be used to transfer heat between cell 401 at regeneration temperature T R and cell 402 at discharge temperature T D , where T R is different than T D . In the set of embodiments illustrated in FIG. 4 , T R is larger than T D , although in other embodiments, T R could be smaller than T D . In FIG. 4 , after cell 401 has been regenerated and cell 402 has been discharged, some portion of heat 404 is transferred from cell 401 to cell 402 . Because the efficiency of the heat exchanger in FIG. 4 is not 100%, a portion of heat 405 is expelled to the environment. In order to fully heat cell 402 to regeneration temperature T R , external energy is generally used. At the end of the heat transfer process, cell 401 is at discharge temperature T D , and cell 402 is at regeneration temperature T R . As the cells continue to proceed through the thermodynamic cycle shown in FIG. 2 , cell 401 is discharged at temperature T D , and cell 402 is regenerated at temperature T R . Heat is then transferred from cell 402 to cell 401 . Eventually, additional heat may be input into the system such that cell 401 is at temperature T R and cell 402 is at temperature T D . Subsequently, cell 401 may be regenerated at temperature T R and cell 402 may be discharged at temperature T D , completing the cycle. This cycle may be repeated any number of times.","Heat may be transferred between electrochemical cells using any suitable method. In some embodiments, heat may be transferred between electrochemical cells by configuring the first and second electrochemical cells such that they are in direct thermal contact. Generally, two electrochemical cells are in direct thermal contact when one may trace at least one spatial pathway from the outer boundary of the first electrochemical cell to the outer boundary of the second electrochemical cell without passing through a fluid. In some embodiments, two electrochemical cells in direct thermal contact may share at least a portion of at least one wall. In some embodiments, heat may be transferred between two electrochemical cells using a heat transfer fluid, as described in more detail below.","In certain embodiments, more than two electrochemical cells may be used in an electrochemical system to generate electrical current. In some such embodiments, heat is exchanged between one hot cell with more than one cold cell in sequence, and subsequently, heat is exchanged between another hot cell with more than cold cell in sequence.","FIG. 5A is an exemplary schematic illustration of system 500 comprising multiple hot and multiple cold electrochemical cells, configured such that heat is exchanged among the cells during operation. FIG. 5A includes two hot cells 501 -A and 501 -B. In other embodiments, three, four, or more hot cells (e.g., as many as 10, 20, 50, 100, or more hot cells), up to n total hot cells (with the n th hot cell shown as hot cell 501 - n in FIG. 5A ), could be included. In addition, system 500 includes two cold cells 502 -A and 502 -B. In other embodiments, three, four, or more cold cells (e.g., as many as 10, 20, 50, 100, or more cold cells), up to m total cold cells (with the m th cold cell shown as cold cell 502 - m in FIG. 5A ), could be included.","In certain embodiments, heat can be transferred from a first electrochemical cell at a first temperature to a second electrochemical cell at a second temperature lower than the first temperature. For example, referring back to FIG. 5A , heat can be transferred from first hot cell 501 -A to first cold cell 502 -A, for example, as illustrated by arrow 503 -A in FIG. 5A .","In some embodiments, after transferring heat from the first electrochemical cell to the second electrochemical cell, heat can be transferred from the first electrochemical cell to a third electrochemical cell at a temperature lower than the first temperature. For example, referring to FIG. 5A , after heat is transferred from cell 501 -A to cell 502 -A, heat can be transferred from cell 501 -A to cell 502 -B, as illustrated via arrow 503 -B in FIG. 5A .","In certain embodiments, after transferring heat from the first electrochemical cell to the second electrochemical cell, heat can be transferred from a fourth electrochemical cell to the second electrochemical cell. For example, referring to FIG. 5A , after heat is transferred from cell 501 -A to cell 502 -A, heat can be transferred from cell 501 -B to cell 502 -A, as illustrated via dashed arrow 504 -A in FIG. 5A . In some embodiments, the transfer of heat from the fourth cell to the second cell (e.g., from cell 501 -B to cell 502 -A in FIG. 5A ) can occur before, during, and/or after the transfer of heat from the first cell to the second cell (e.g., from cell 501 -A to cell 502 -A in FIG. 5A ).","In some embodiments, after transferring heat from the first electrochemical cell to the second electrochemical cell, heat can be transferred from the fourth electrochemical cell to the third electrochemical cell. For example, referring to FIG. 5A , after heat is transferred from cell 501 -A to cell 502 -A, heat can be transferred from cell 501 -B to cell 502 -B, as illustrated via dashed arrow 504 -B in FIG. 5A .","In certain embodiments, fifth, sixth, seventh, eighth, and/or additional cells may be present within the electrochemical system. For example, FIG. 5B is a schematic illustration of system 550 , comprising six electrochemical cells. System 550 comprises three hot cells 501 -A, 501 -B, and 501 -C. In addition, system 550 comprises three cold cells 502 -A, 502 -B, and 502 -C. System 550 can be operated in a similar fashion as system 500 in FIG. 5A . In some embodiments, however, after heat has been transferred from hot cell 501 -A to cold cell 502 -A and from hot cell 501 -A to cold cell 502 -B, heat can be transferred from first cell 501 -A to cold cell 502 -C. Similarly, after heat has been transferred from hot cell 501 -B to cold cells 502 -A and 502 -B, heat can be transferred from hot cell 501 -B to cold cell 502 C. In addition, in some embodiments, after heat has been transferred from hot cell 501 -A to cold cells 502 -A, 502 -B, and/or 502 -C and/or after heat has been transferred from hot cell 501 -B to cold cells 502 -A, 502 -B, and/or 502 -C, heat can be transferred from hot cell 501 -C to cold cell 502 -A, 502 -B, and/or 502 -C.","A specific example of the operation of system 550 of FIG. 5B is now described. In this example, cold cells 502 -A, 502 -B, and 502 -C are initially at 0° C., and hot cells 501 -A, 501 -B, and 501 -C are initially at 100° C. During the heat exchange process, hot cell 501 -A first transfers heat to first cold cell 502 -A. Assuming that substantially perfect heat exchange occurs through direct contact, with no thermal losses, hot cell 501 -A is reduced in temperature to 50° C. and cold cell 502 -A is raised to 50° C. Subsequently, hot cell 501 -A transfers heat to second cold cell 502 -B. Again, assuming substantially perfect heat exchange, hot cell- 501 -A is reduced to 25° C. and cold cell 502 -B is raised to 25° C. Finally, hot cell 501 -A transfers heat to cold cell 502 -C, after which both hot cell 501 -A and cold cell 502 -C are at 12.5° C. In some such embodiments, after heat has been transferred from hot cell 501 -A to cold cells 502 -A, 502 -B, and/or 502 -C, hot cell 501 -B transfers heat to cold cell 502 -A, after which hot cell 501 -B and cold cell 502 -A are at 75° C. Next, hot cell 501 -B transfers heat to cold cell 502 -B, after which hot cell 501 -B and cold cell 502 -B are at 50° C. Finally, hot cell 501 -B transfers heat to cold cell 502 -C, after which hot cell 501 -B and cold cell 502 -C are at 31.25° C. Subsequently, hot cell 501 -C can be contacted with cold cell 502 -A, and the temperatures of hot cell 501 -C and cold cell 502 -A become 87.5° C. Next, heat can be transferred from hot cell 501 -C to cold cell 502 -B, such that the temperatures of hot cell 501 -C and cold cell 502 -B become 68.75° C. Finally, heat can be transferred from hot cell 501 -C to cold cell 502 -C such that the temperatures of hot cell 501 -C and cold cell 502 -C each become 50° C. After this heat exchange step has been performed, the temperature of the initially “hot” cells can be as follows: cell 501 -A=12.5° C.%3b cell 501 -B=31.25°%3b and cell 501 -C=50° C. In addition, the temperature of the initially “cold” cells can be as follows: cell 502 -A=87.5° C.%3b cell 502 -B=68.75° C., and cell 502 -C=50° C. As a result of the serial heat exchange process described above, the initially “hot” cells (which one desired to cool) are able to achieve lower temperatures than would have been possible if all hot cells had been directly contacted in parallel with all cold cells. In addition, by using the serial heat exchange process described above, the initially “cold” cells (which one desires to heat) are able to achieve higher temperatures than would have been possible if all hot cells had been directly contacted in parallel with all cold cells. Although only three hot cells and three cold cells are shown in FIG. 5B , it should be understood that heat can be exchanged between any number of hot cells and any number of cold cells. In some embodiments, increasing the number of cells will further increase efficiency.","While FIG. 5B illustrates an example in which the electrochemical cells between which heat is transferred are in direct contact, heat may also be exchanged between electrochemical cells using heat transfer fluid. FIG. 6A provides an exemplary schematic of cells 601 and 602 in heating process, cells 603 and 604 in cooling process, and heat exchangers 605 and 606 used to assist the heat transfer process. FIG. 6B provides a corresponding diagram of temperature as a function of heat duty for the system illustrated in FIG. 6A , where heat duty generally refers to the amount of heat transferred to a heat transfer fluid. In the example of FIG. 6A , heat exchanger 605 is at temperature T 1 , and heat exchanger 606 is at temperature T 6 , where T 1 is greater than T 6 . Heat transfer fluid with a temperature of T 1 can be introduced in heat exchanger 605 , and its temperature at the outlet can be reduced by ΔT HX . The heat transfer fluid can then be guided through cell 601 , and its temperature can be increased by ΔT HTF . The heat transfer fluid can then flow through heat exchanger 606 , and its temperature can be reduced by ΔT HX . The heat transfer fluid can then flow into cell 602 , and its temperature can be increased by ΔT HTF . Flowing in the opposite direction through the system, heat transfer fluid with a temperature of T 6 can be introduced in heat exchanger 606 and can absorb thermal energy from the hot stream, increasing the temperature by ΔT HX . The heat transfer fluid can then be transported through cell 603 , transferring some of its thermal energy to the cell. The temperature of the fluid at the outlet of cell 603 can drop by ΔT HTF . The heat transfer fluid can then flow to heat exchanger 605 , and the temperature of the heat transfer fluid can increase by ΔT HX . The fluid can subsequently flow to cell 604 , and its temperature can decrease by ΔT HTF . Heat transfer between electrochemical cells may be achieved using any suitable heat transfer fluid known to those of ordinary skill in the art. Heat transfer fluids generally refer to fluids that are capable of transferring heat in the range of temperatures at which the electrochemical cell is operated. The heat transfer fluid may be a liquid or a gas. Suitable heat transfer fluids may have a specific heat capacity of at least about 1 J/g·K or at least about 2 J/g·K (and/or, in certain embodiments, up to about 3 J/g·K, or more). In some embodiments, the heat transfer fluid comprises a fluid external to the electrochemical cells. Non-limiting examples of suitable heat transfer fluids include fluids comprising water, one or more oils, one or more alcohols, one or more polyalkylene glycols, one or more refrigerants, or any combination thereof.","In some embodiments, heat transfer between one or more electrochemical cells may be achieved using a heat transfer fluid that is internal to at least one of the electrochemical cells. In certain cases, a heat transfer fluid may be used to transfer heat between a first electrochemical cell at a first temperature (e.g., a hot cell) and a second electrochemical cell at a second temperature (e.g., a cold cell). The heat transfer fluid may comprise an electrolyte of one or more of the electrochemical cells between which heat is being transferred. In some embodiments, the heat transfer fluid may comprise a liquid electrolyte. In some embodiments, the heat transfer fluid may consist essentially of a liquid electrolyte. The heat transfer fluid, in certain cases, may comprise a solid electrochemically active material (e.g., particles of a solid electrochemically active material) suspended in a liquid electrolyte. The solid electrochemically active material may be electrochemically active material of the first electrochemical cell and/or the second electrochemical cell. In some cases, the use of an internal heat transfer fluid may advantageously increase heat transfer efficiency. It should be noted that an electrochemical cell may comprise two or more electrolytes, each of which may be used as a heat transfer fluid.","In some embodiments, a method of transferring heat from a first electrochemical cell to a second electrochemical cell comprises flowing a first electrolyte for the first electrochemical cell to a heat exchanger. The first electrolyte may be at a first temperature. In certain embodiments, the method further comprises flowing a second electrolyte for the second electrochemical cell to the heat exchanger. The second electrolyte may be at a second temperature, where the first temperature is higher than the second temperature. The heat exchanger may place the first electrolyte and the second electrolyte in thermal communication. In some embodiments, heat may thereby be transferred from the first electrolyte to the second electrolyte. The first electrolyte may then be flowed to the first electrochemical cell, and the second electrolyte may be flowed to the second electrochemical cell.","An exemplary system in which heat is transferred between two electrochemical cells using internal fluids is shown in FIG. 7 . In FIG. 7 , system 700 comprises a first electrochemical cell 710 , a second electrochemical cell 720 , and a heat exchanger 730 . As shown in FIG. 7 , first electrochemical cell 710 is in fluid communication with heat exchanger 730 , and second electrochemical cell 720 is in fluid communication with heat exchanger 730 . First electrochemical cell 710 may comprise a first electrode comprising a first electrochemically active material and a second electrode comprising a second electrochemically active material. In some embodiments, first electrochemical cell 710 further comprises a first electrolyte. The first electrolyte may, in some cases, comprise a liquid. In some cases, the first electrolyte consists essentially of a liquid. In certain embodiments, solid particles of the first electrochemically active material and/or the second electrochemically active material are suspended in the first electrolyte (e.g., a liquid electrolyte). In some embodiments, the first electrode and/or second electrode are flowable electrodes.","Second electrochemical cell 720 may comprise a third electrode comprising a third electrochemically active material and a fourth electrode comprising a fourth electrochemically active material. Second electrochemical cell 720 may, in some embodiments, further comprise a second electrolyte. In some cases, the second electrolyte comprises a liquid. In some cases, the second electrolyte consists essentially of a liquid. In certain embodiments, solid particles of the third electrochemically active material and/or the fourth electrochemically active material are suspended in the second electrolyte (e.g., a liquid electrolyte). In some embodiments, the third electrode and/or fourth electrode are flowable electrodes.","In operation, first electrochemical cell 710 may be at a first temperature, and second electrochemical cell 720 may be at a second temperature. In some cases, the first temperature may be higher than the second temperature. The first temperature may be at least about 5° C., at least about 10° C., at least about 20° C., at least about 50° C., at least about 100° C. (and/or, in certain embodiments, up to about 200° C., or more) higher than the second temperature.","In some embodiments, first electrochemical cell 710 is configured such that a first electrochemical reaction is thermodynamically favored at the first temperature. For example, the first electrochemical cell may be configured to discharge at a first discharge voltage (e.g., such that the first and/or second electrochemically active material is at least partially electrochemically consumed) or to regenerate at a first regeneration voltage (e.g., such that electrochemically active material is regenerated from a product of at least a portion of the electrochemically active material consumed during discharge) at the first temperature. First electrochemical cell 710 may have a first polarity at the first temperature. In some embodiments, second electrochemical cell 720 is configured such that a second electrochemical reaction is thermodynamically favored at the second temperature. For example, the second electrochemical cell may be configured to discharge at a second discharge voltage (e.g., such that the third and/or fourth electrochemically active material is at least partially electrochemically consumed) or regenerate at a second regeneration voltage at the second temperature. Second electrochemical cell 720 may have a second polarity at the second temperature.","A first fluid may be flowed from first electrochemical cell 710 to heat exchanger 730 . In some embodiments, the first fluid comprises the first electrolyte. In some embodiments, the first fluid consists essentially of the first electrolyte. In some embodiments, the first fluid comprises solid particles of the first and/or second electrochemically active material suspended in the first electrolyte. The first fluid may be at the first temperature at an inlet to heat exchanger 730 . In heat exchanger 730 , the first fluid may be cooled, such that the first fluid may be at a third temperature at an outlet to heat exchanger 730 , where the third temperature is lower than the first temperature. The first fluid at the third temperature may be flowed back to first electrochemical cell 710 . As a result, the temperature of first electrochemical cell 710 may decrease to a fourth temperature (e.g., a temperature that is lower than the first temperature and higher than the third temperature). In some cases, the reverse of the electrochemical reaction favored at the first temperature may be favored at the fourth temperature. For example, if discharge was thermodynamically favored at the first temperature, regeneration may be thermodynamically favored at the fourth temperature. If regeneration was thermodynamically favored at the first temperature, discharge may be thermodynamically favored at the fourth temperature. The polarity of the first electrochemical cell at the fourth temperature may be the opposite of the polarity at the first temperature. In some cases, the first electrochemical cell may be further cooled (e.g., by any suitable external cooling device) to a fifth temperature that is lower than the fourth temperature. This may be advantageous because, for example, the heat exchanger generally will not have 100% heat recuperation efficiency. In some cases, the reverse of the electrochemical reaction favored at the first temperature may be favored at the fifth temperature. The polarity of the first electrochemical cell at the fifth temperature may be the opposite of the polarity at the first temperature.","A second fluid may be flowed from second electrochemical cell 720 to heat exchanger 730 . In some embodiments, the second fluid comprises the second electrolyte. In some embodiments, the second fluid consists essentially of a liquid electrolyte. In some embodiments, the second fluid comprises solid particles of the third and/or fourth electrochemically active material suspended in the liquid electrolyte. The second fluid may be at the second temperature at an inlet to heat exchanger 730 . In heat exchanger 730 , heat may be transferred from the first fluid to the second fluid, such that the temperature of the second fluid is at a sixth temperature at an outlet to heat exchanger 730 , where the sixth temperature is higher than the second temperature. The second fluid at the sixth temperature may be flowed back to second electrochemical cell 720 . As a result, the temperature of second electrochemical cell 720 may increase to a seventh temperature (e.g., a temperature higher than the second temperature and lower than the sixth temperature). In some cases, the reverse of the electrochemical reaction favored at the second temperature may be favored at the seventh temperature. For example, if regeneration was thermodynamically favored at the second temperature, discharge may be thermodynamically favored at the seventh temperature. If discharge was thermodynamically favored at the first temperature, regeneration may be thermodynamically favored at the seventh temperature. In some cases, the second electrochemical cell may be further heated (e.g., by any suitable external heating device) to an eighth temperature that is higher than the seventh temperature. In some cases, the reverse of the electrochemical reaction favored at the second temperature may be favored at the eighth temperature. The polarity of the second electrochemical cell at the eighth temperature may be the opposite of the polarity at the second temperature.","In some embodiments, the first fluid at the fourth temperature may be flowed to heat exchanger 730 . In heat exchanger 730 , heat may be transferred from the second fluid to the first fluid, and the first fluid may be heated such that the first fluid is at a ninth temperature at an outlet to heat exchanger 730 , where the ninth temperature is higher than the fourth temperature. The first fluid at the ninth temperature may be flowed back to first electrochemical cell 710 . As a result, the temperature of the first electrochemical cell may increase to a tenth temperature (e.g., a temperature that is higher than the fourth temperature and lower than the ninth temperature). In some embodiments, the electrochemical reaction favored at the first temperature may be favored at the tenth temperature. The polarity of the first electrochemical cell at the first temperature may be the same as the polarity at the tenth temperature. In some embodiments, the tenth temperature may be substantially the same as the first temperature. For example, the difference between the tenth temperature and the first temperature may be less than about 20° C., less than about 10° C., less than about 5° C. (and/or, in certain embodiments, less than about 1° C., or less). In some embodiments, the tenth temperature may be substantially different from the first temperature. In certain cases, the electrochemical cell may be further heated (e.g., by any suitable external heating device) to an eleventh temperature. In some embodiments, the electrochemical reaction favored at the first temperature may be favored at the eleventh temperature. The polarity of the first electrochemical cell at the first temperature may be the same as the polarity at the eleventh temperature. The eleventh temperature may be substantially the same as the first temperature. For example, the difference between the eleventh temperature and the first temperature may be less than about 20° C., less than about 10° C., less than about 5° C. (and/or, in certain embodiments, less than about 1° C., or less). In some embodiments, the eleventh temperature may be substantially different from the first temperature. It should be noted that although flow of the first fluid at the fourth temperature to heat exchanger 730 is described, the first fluid may, alternatively, be at the fifth temperature when it is flowed to heat exchanger 730 .","In some embodiments, the second fluid at the seventh temperature may be flowed to heat exchanger 730 . In heat exchanger 730 , heat may be transferred from the second fluid to the first fluid, and the second fluid may be cooled such that the second fluid is at a twelfth temperature at an outlet to heat exchanger 730 , where the twelfth temperature is lower than the seventh temperature. The second fluid at the twelfth temperature may be flowed back to second electrochemical cell 720 . As a result, the temperature of the second electrochemical cell may decrease to a thirteenth temperature (e.g., a temperature that is lower than the seventh temperature and higher than the twelfth temperature). In some embodiments, the electrochemical reaction favored at the second temperature may be favored at the thirteenth temperature. The polarity of the second electrochemical cell at the second temperature may be the same as the polarity at the thirteenth temperature. In some embodiments, the thirteenth temperature may be substantially the same as the second temperature. For example, the difference between the thirteenth temperature and the second temperature may be less than about 20° C., less than about 10° C., less than about 5° C. (and/or, in certain embodiments, less than about 1° C., or less). In some embodiments, the thirteenth temperature may be substantially different from the second temperature. In certain cases, the electrochemical cell may be further cooled (e.g., by any suitable external cooling device) to a fourteenth temperature. In some embodiments, the electrochemical reaction favored at the second temperature may be favored at the fourteenth temperature. The polarity of the second electrochemical cell at the second temperature may be the same as the polarity at the fourteenth temperature. The fourteenth temperature may be substantially the same as the second temperature. For example, the difference between the fourteenth temperature and the second temperature may be less than about 20° C., less than about 10° C., less than about 5° C. (and/or, in certain embodiments, less than about 1° C., or less). In some embodiments, the fourteenth temperature may be substantially different from the second temperature. It should be noted that although flow of the second fluid at the seventh temperature to heat exchanger 730 is described, the second fluid may, alternatively, be at the eighth temperature when it is flowed to heat exchanger 730 .","In some embodiments, the electrochemical cell comprises a current collector. The current collector can be electronically conductive and should generally be electrochemically inactive under the operation conditions of the electrochemical cell. Typical materials from which current collectors can be made include metals including, but not limited to, copper, aluminum, titanium, and the like. The current collector may be in the form of, for example, a sheet, a mesh, or any other configuration in which the current collector is distributed in the electrolyte and permits fluid flow. Selection of current collector materials is well-known to those skilled in the art.","Also as noted above, in some embodiments, the electrochemical cell comprises an electrolyte. The electrolyte may be a liquid in certain cases. In some embodiments, the electrolyte may be aqueous-based. In other embodiments, the electrolyte may be non-aqueous-based. In some cases, the electrolyte may be a gel. In some cases, the electrolyte may be a solid. The electrolytes used in certain of the electrochemical cells described herein can function as a medium for the storage and transport of ions, and in the special case of solid electrolytes and gel electrolytes, these materials may additionally function as a separator between the anode and the cathode. Any liquid, solid, or gel material capable of storing and transporting ions may be used, so long as the material is electrochemically and chemically unreactive with respect to the anode and the cathode, and the material facilitates the transport of electrochemical ions between the anode and the cathode. The electrolyte may be electronically non-conductive to prevent short circuiting between the anode and the cathode.","Those of ordinary skill in the art would be capable of selecting appropriate electrolyte materials (including electrolyte salts, electrolyte solvents, and separator materials) for use in an electrochemical cell. Generally, such materials are selected based at least in part upon the electrodes and the electrochemical half cell reactions being employed in the electrochemical cell.","The electrolyte can comprise one or more ionic electrolyte salts to provide ionic conductivity and one or more liquid electrolyte solvents, gel polymer materials, or polymer materials. Suitable non-aqueous electrolytes may include organic electrolytes comprising one or more materials selected from the group consisting of liquid electrolytes, gel polymer electrolytes, and solid polymer electrolytes.","The electrolyte might also, in certain embodiments, include a solvent, for example, in which the ionic electrolyte salt is dissolved. Examples of useful non-aqueous liquid electrolyte solvents include, but are not limited to, non-aqueous organic solvents, such as, for example, N-methyl acetamide, acetonitrile, acetals, ketals, esters, carbonates, sulfones, sulfites, sulfolanes, aliphatic ethers, cyclic ethers, glymes, polyethers, phosphate esters, siloxanes, dioxolanes, N-alkylpyrrolidones, substituted forms of the foregoing, and blends thereof. Fluorinated derivatives of the foregoing could also be used as liquid electrolyte solvents. In some cases, aqueous solvents can be used as electrolytes. Aqueous solvents can include water, which can contain other components such as ionic salts.","The following examples are intended to illustrate certain embodiments of the present invention, but do not exemplify the full scope of the invention.","Example 1","This example describes a high-efficiency thermally regenerative electrochemical cycle (TREC) for harvesting low-grade heat energy by employing solid copper hexacyanoferrate (CuHCF) as a positive electrode and Cu/Cu 2+ as a negative electrode in an aqueous electrolyte. The fast kinetics, high charge capacity, high thermogalvanic coefficient (α), and low heat capacity of these materials allowed the system to operate with excellent efficiency. As illustrated in FIG. 8A , to harvest thermal energy, the entire device underwent a thermal cycle containing four processes: heating up, charging at high temperature, cooling down, and discharging at low temperature. FIG. 8B is a plot of this cycle on a temperature-entropy (T-S) diagram to clarify the thermodynamics. In process 1, the cell was in the discharged state and heated from T L (low temperature) to T H (high temperature) at open circuit. Since CuHCF has a negative α and Cu/Cu 2+ has a positive α, the open circuit voltage (OCV) of the full cell decreased during this process. The cell was then charged at a low voltage at temperature T H in process 2, and the entropy of the cell increased through heat absorption during the electrochemical reaction. In process 3, the cell was disconnected and cooled from T H to T L , and thus the OCV was increased. In the final process, the cell was discharged at a higher voltage at temperature T L , and the entropy of the cell decreased through the ejection of heat into the environment. After the cycle, the system returned to the original discharged state at T L . Since the charging voltage was lower than the discharging voltage, net work (W) was extracted as the difference between charging and discharging energy. The theoretical energy gained over one cycle was the area of the loop determined by the temperature difference and entropy change. This was the opposite of the consumption of energy due to electrochemical hysteresis during a typical charge/discharge cycle of a battery, since the charging energy here was partially provided by heat (see FIG. 9 ).","FIG. 9 shows an exemplary schematic plot of voltage as a function of charge for an electrochemical cell. As shown for a cold temperature, typically the charging (dashed line) and discharging (solid line) voltage curves at a given temperature form a closed loop, the area of which means energy loss during a cycle. In the example shown in FIG. 9 , the negative thermogalvanic coefficient of the cell shifted down the charging curve at a high temperature (labeled as charging (hot)), below the voltage curve for discharging at a low temperature. The area of the closed loop between charging at the high temperature and discharging at the low temperature was the theoretical energy obtained during the cycle.","The efficiency of the system (η) was calculated as the net work (W) divided by the energy input. If the enthalpy change ΔH and the entropy change ΔS were the same at T H and T L , which was a good approximation when ΔT=(T H −T L ) was small, then the maximum W was ΔTΔS (see FIG. 8B ). The energy input to complete the cycle included two parts: the heat absorbed at T H (Q H =T H ΔS) and the external heat required to raise the temperature of the system (Q HX ). As part of heat rejected from the cooling process could be used for heating up through heat exchangers, Q HX =(1−η HX )C p ΔT, where C p was the total heat capacity of the electrochemical cell, and η HX was the effectiveness of the heat exchanger (see FIG. 10 ). Consequently η could be expressed as:"," η = W Q H + Q HX = Δ ⁢ ⁢ T ⁢ ⁢ Δ ⁢ ⁢ S - E loss T H ⁢ Δ ⁢ ⁢ S + ( 1 - η HX ) ⁢ C p ⁢ Δ ⁢ ⁢ T ( 6 ) where E loss was the energy loss due to the cell resistance. Note that ΔTΔS=αQΔT, where Q was the charge capacity of the battery and a was the thermogalvanic coefficient of the electrochemical cell. The efficiency could be written as:"," η = η c ⁢ 1 - I ⁡ ( R H + R L ) /  α  ⁢ Q ⁢ ⁢ Δ ⁢ ⁢ T 1 + η c ⁡ ( 1 - η HX ) /  Y  ( 7 ) where I was the current used in discharging and charging. R H and R L were the internal resistance at T H and T L , respectively. Y=αQ/C p , was a dimensionless parameter to describe the features of the system that can be used for high efficiency. If only the contributions of the electrode materials were considered, and it was assumed that both electrodes had the same properties except opposite signs of the thermogalvanic coefficient, Y=αq/c p and it was defined as the figure of merit of an electrode material for TREC. Here, q was the specific charge capacity and c p was the specific heat capacity. Consequently, it was clear that a higher thermogalvanic coefficient (α), a higher specific charge capacity (q), and a smaller heat capacity (c p ) led to higher efficiency for heat-to-electricity conversion. In addition, low voltage polarization and a high-efficiency heat exchanger could also improve the efficiency.","Considering these requirements, solid copper hexacyanoferrate (CuHCF) was selected as the positive electrode for the TREC because of its negative thermogalvanic coefficient (−0.36 mV K −1 ), high specific charge capacity (60 mAh g −1 ) compared to redox couples in solution, relatively low heat capacity (1.07 J K −1 g −1 ), and ultra-low voltage hysteresis. The corresponding figure of merit Y was −0.073, almost three times that of the Fe(CN) 6 3−/4− redox pair in solution (−0.026), commonly used in thermogalvanic cells. For the negative electrode, a copper metal immersed in 3M Cu(NO 3 ) 2 aqueous solution was selected because of the high positive thermogalvanic coefficient (0.83 mV K −1 ) of Cu/Cu 2+ and its large specific charge capacity (118 mAh g −1 ) due to the high solubility of Cu(NO 3 ) 2 in water. The corresponding Y was as high as 0.107.","The electrochemical cell for TREC was assembled with the CuHCF and Cu/Cu 2+ electrodes in a flooded beaker cell containing an anion exchange membrane, as shown in FIG. 11 . The relevant redox reactions at each electrode were Na 0.71 Cu[Fe III (CN) 6 ] 0.72 +a (Na + +e − )=Na 0.71+a Cu[Fe III (CN) 6 ] 0.72−a [Fe II (CN) 6 ] 0.72+a and: Cu 2+ +2 e − =Cu. ","The thermogalvanic coefficient of each electrode was tested by measuring the open-circuit voltage while varying temperature from 10 to 70° C. FIG. 12A shows the OCV change of the CuHCF electrode (50% state of charge), the Cu/Cu 2+ (3M) electrode, and the full cell for each 10° C. increment when the voltage was set at 0 V at 10° C. The potentials of both electrodes exhibited a linear dependence on temperature, indicating a constant α in the temperature window tested. The measured thermogalvanic coefficients of CuHCF, Cu/Cu 2+ , and the full cell were −0.36, 0.83, and −1.20 mV K −1 , respectively. These experimental values matched the expected ones.","FIG. 12B shows the voltage vs. time plot of the full cell over one thermal cycle between 10 and 60° C. when the specific current density was 7.2 mA g −1 with respect to active materials (all current, energy, and power densities were based on the mass of active materials at charged state, including CuHCF, electrolyte for Na + , copper, and water for Cu 2+ in this example). The temperature of each process is shown by the dotted line, which is artificially superimposed for clarity. In process 1, the open-circuit voltage of the cell decreased from 0.406 to 0.337 V as the temperature increased from 10 to 60° C. Then the cell was charged for 250 min at 60° C. in process 2, and the voltage gradually increased. In process 3, the OCV of the cell increased from 0.613 to 0.679 V as the temperature was decreased back to 10° C. The cell was discharged in process 4 at 10° C. until the voltage reached the initial voltage of the discharged state at the beginning of process 1. The corresponding plot of voltage against specific charge capacity is shown in FIG. 12C . The average charging voltage was 59.0 mV lower than the average discharging voltage, and thus, electrical energy was generated with a net energy density of 5.2 J g −1 . The voltage spikes at the beginning of each process were electrochemical in nature and were due to overpotential and internal resistance. At the end of process 4, the discharging curve formed a nearly perfect closed loop with only a tiny loss of electric charges. The Coulombic efficiency for this cycle was adequately high, at about 98.6%.","The efficiency of the cycle was estimated based on Equation (6). The effects of internal resistance and coulombic efficiency were both taken into account. FIG. 13A is a plot of the cycle efficiency vs. the effectiveness of the heat exchanger when cycled between 10 and 60° C. The current density was 7.2 mA g −1 . Dotted lines represent the efficiencies for each equivalent figure of merit (ZT) value, where the equivalent ZT value refers to that of a thermoelectric device with the same efficiency working between the same cold and hot sources. When a heat exchanger was not used, the cycle efficiency was 3.51%. As the effectiveness of the heat exchanger was enhanced, the cycle efficiency increased since the dominant energy loss due to heat capacity decreased. When the effectiveness of the heat exchanger reached 50% to 70%, the corresponding cycle efficiencies were 5.28% and 6.62%, respectively. 50% effectiveness represents the limit of direct contact of the cold and hot cells, and 70% is a reasonable value when heat exchangers are employed. If the effectiveness of the heat exchanger is 100%, the efficiency of the cycle is close to the theoretical Carnot efficiency. FIG. 13B shows the efficiency at various cycling conditions with T H varying between 40° C. and 70° C. and T L fixed at 10° C. Dotted lines represent the efficiencies for each ZT value. At a current density of 7.2 mA g −1 , the efficiencies when including a heat exchanger with 70% effectiveness in the calculations were 3.24% for T H =40° C., 5.54% for T H =50° C., 6.62% for T H =60° C., and 6.55% for T H =70° C. Without wishing to be bound by any particular theory, it is believed that the efficiency became higher as T H increased because of larger voltage differences between the charging and discharging curves and faster kinetics at higher temperature. Without wishing to be bound by any particular theory, it is believed that the change in this correlation between a T H of 60 and 70° C. was due to a decrease in the Coulombic efficiency that began at these temperatures (see FIG. 13 ). When the current density increased to 17.9 mA g −1 for higher power output, the efficiencies (again, assuming a heat exchanger with an effectiveness of 70% was employed) were still as high as 2.17% for T H =40° C., 3.63% for T H =50° C., 5.85% for T H =60° C., and 6.40% for T H =70° C. despite the larger overpotential.","The galvanostatic cycling performance of a CuHCF half cell at temperatures ranging from 10 to 90° C. is shown in FIGS. 13A-13B . FIG. 14A is an exemplary plot of voltage (vs. standard hydrogen electrode (SHE)) as a function of specific charge capacity for a CuHCF half cell with an activated carbon counter electrode as a sodium ion sink at 10, 40, and 70° C. In the example shown in FIG. 14A , cycling rate was 5C, which took about 24 minutes for charging and discharging. The curves for different temperatures have similar shapes, but they exhibit shifting due to the thermogalvanic effect. FIG. 14B is an exemplary plot of specific charge capacity and coulomb efficiency of three cycles at each temperature. As shown in FIG. 14B , specific charge capacity increased as temperature increased until 60° C. For temperatures higher than 60° C., specific charge capacity decreased as temperature increased. Coulomb efficiency decreased slightly with increasing temperature, and its slope got stiffer with increasing temperature.","The cycling performance of the thermal energy harvesting system is shown in FIG. 15A . T H and T L were set to 50 and 20° C., respectively, to represent widely accessible temperatures of waste heat and room temperature. The current density was 17.9 mA g −1 . The energy density reached 1.26 J g −1 in the initial cycle with an efficiency of 2.01%. The average efficiency was 1.91%, supposing 70% effectiveness of a heat exchanger. The asterisk denotes changing of the electrolyte because of severe drying after the 24 th cycle. FIG. 15B compares the full cell voltage vs. specific capacity of CuHCF for the 1 st (dotted line) and 40 th (solid line) cycles. A slight shift of the loop was observed, but there was no significant change in the overall shape. In addition, the cycling performance of CuHCF at higher temperature was confirmed by long-term galvanostatic cycling of a CuHCF electrode at 70° C. At this temperature, the capacity decay was only 9.1% over 500 cycles. (see FIG. 16 ). This result signified that this TREC for thermal energy harvesting was expected to have stable cycling with further optimization.","FIG. 16A is an exemplary plot of voltage (vs. SHE) as a function of specific charge capacity for long-term galvanostatic cycling of a thermogalvanic cell with a CuHCF electrode. While the shapes of the curves after 250 and 500 cycles did not significantly change compared to the curve of the first cycle, decaying of specific capacity was observed. FIG. 16B is an exemplary plot of specific charge capacity and coulomb efficiency as a function of number of cycles. After 500 cycles, 9.1% decaying of specific capacity was observed, and coulomb efficiency saturated at 99.5%.","Example 2","This example describes a charging-free thermally regenerative electrochemical system (TRES) comprising a Fe(CN) 6 3−/4− positive electrode and a Prussian blue negative electrode.","The electrochemically active material could be discharged at a low temperature. At a higher temperature, the cell voltage decreased to a negative value such that the electrochemically active material could be regenerated (via a process that was the reverse of the discharging process) spontaneously (essentially corresponding to a discharge process rather than a charge process) (see FIG. 17 ). FIGS. 17A-17B show exemplary schematics of electrochemical cells that are and are not charging free. For example, FIG. 17A is an exemplary schematic diagram for an electrically-assisted thermally regenerative system. Net energy is generated as the regeneration voltage is smaller than the discharge voltage, but external charging is needed in each cycle. FIG. 17B , however, presents an exemplary schematic diagram for a charge free electrochemical cell. For the cell of FIG. 17B , the voltage shift due to temperature change is large enough such that the full cell voltage at second temperature T 2 is negative. The electrochemical process to return to the initial state (A+B) at T 2 is still discharge, regenerating the cell. Consequently, the system can be cycled without the input of electricity, which can simplify system design and lower cost. The heat-to-electricity efficiency of the system can reach 1.9% when a heat exchanger is used. Even without a heat exchanger, the efficiency is three times higher than that of previous thermogalvanic cells. Furthermore, the system can be configured to use only Earth-abundant materials, making it even more attractive for harvesting waste heat and renewable thermal energy.","At room temperature, the positive and negative electrodes of the charging-free cell were 0.3 M K 3 Fe(CN) 6 /0.5 M K 4 Fe(CN) 6 aqueous solution and half-discharged Prussian blue nanoparticle (KFe II Fe III (CN) 6 , PB), respectively. All chemicals described in this example were purchased from Sigma Aldrich.","PB nanoparticles were synthesized using a simple solution approach. To synthesize PB, 40 mL of 50 mM FeCl 2 was added to 40 mL of 25 mM K 3 Fe(CN) 6 under strong stirring at room temperature, producing nanoparticles with an average particle size of about 100 nm. The precipitation was centrifuged and dried at 70° C. overnight. The PB electrode was prepared by mixing 70 wt % PB nanoparticles, 20 wt % Super P carbon black, and 10% polyvinylidene fluoride (PVDF) in N-Methyl-2-pyrrolidone (NMP) and drop casting onto a carbon cloth disc electrode (Fuel Cell Store) at 90° C. The carbon cloth disc had a diameter of 1.27 cm and the mass loading was about 5 mg PB cm −2 . The PB electrode was pre-cycled in 1 M KNO 3 aqueous electrolyte for 10 cycles to convert it from the so called “insoluble” phase to “soluble phase”. Then it was discharged to the midpoint of the voltage curve before assembling the full cell. 0.5 M K 4 Fe 4 (CN) 6 /0.3 M K 3 Fe 3 (CN) 6 catholyte was prepared by dissolving corresponding chemicals in deionized water. The concentration was chosen to be close to the solubility limit. A carbon cloth electrode disc with diameter of 1.27 cm served as a current collector for the catholyte. A Nafion 115 membrane was used to separate the liquid catholyte from the anode. The membrane was pretreated with concentrated sulfuric acid for two hours and stored in 0.5 M KNO 3 aqueous solution before use.","Measurements on the thermogalvanic coefficient of electrodes were performed against a calibrated Ag/AgCl/4 M KCl reference electrode (Fisher Scientific) in a three neck flask. The thermogalvanic coefficient of the reference electrode was measured to be 0.12±0.02 mV/K. A home-made plastic cell was used for all measurements of the full cell. The PB electrode and the cathode current collector were first attached to 50 μm thick stainless steel strips. Subsequently, the electrodes were inserted into the home-made plastic cell and separated by the Nafion 115 membrane. Then the Fe(CN) 6 3−/4− catholyte and the KNO 3 electrolyte were injected into each side through holes on top of the plastic cell. The cycling tests of full cells were performed through loading the plastic cell in and out of a gravity convection oven (MTI) with temperature measured by a thermocouple. For high temperature cycling of the PB electrode, Ag/AgCl was used as the reference electrode, and another piece of PB electrode with three times the density of active materials was used as the counter electrode. High temperature cycling of Fe(CN) 6 3−/4− catholyte was done in a symmetric configuration by injecting the solution to both sides of the plastic cell. All electrochemical measurements were done with a Bio-Logic VSP300 tester.","As shown in FIG. 18A , the positive electrode had a negative thermogalvanic coefficient of −1.46±0.02 mV/K while the potential of the PB electrode showed a very weak dependence on temperature (0.00±0.03 mV/K) from room temperature to 60° C. The cell voltage showed a thermogalvanic coefficient of 1.43±0.03 mV/K, which was consistent with the difference between the thermogalvanic coefficients of the two electrodes. The thermogalvanic coefficient also slightly depended on the state of charge (SOC). The temperature dependence of the PB electrode and the full cell were measured when PB was discharged to the midpoint of the voltage curve. In the full cell, the voltage polarity is reversed at low and high temperatures, suggesting that the cell can operate in both charging and discharging states. The electrochemical process of the electrodes and the full cell in a thermal cycle between 24° C. and 60° C. is illustrated in FIG. 18B . At the low temperature (T L ), the cell was discharged to 0 mV (illustrated as the voltage curve moving from left to right), producing electricity. Then the cell was disconnected and heated. The electrochemical potential of the Fe(CN) 6 3−/4− electrode shifted down due to its negative thermogalvanic coefficient while the potential of the PB electrode remained almost unchanged. This led to a negative full cell voltage at the beginning of the high temperature process (right end in the scheme of T H ). In the reverse process at the high temperature (T H ) (moving from right to left in FIG. 18B ), the absolute value of the full cell voltage decreased to 0 mV. Hence, during this process, the cell was discharged (instead of charged), and the current ran in the opposite direction. The last process was to cool the cell down to T L to complete the cycle. The minimum energy input in the cycle was the heat absorbed at T H . Consequently, the theoretical efficiency of this charging-free electrochemical system is Carnot efficiency. Details on the efficiency calculation are discussed later in this example.","FIG. 18C is a plot of the experimentally determined full cell voltage as a function of time. The cell was cycled between room temperature (24° C.) and 60° C., and electricity was generated at both temperatures. The open-circuit voltage (OCV) at 24° C. was 41 mV, and the cell was discharged to 0 mV. After current stopped, the voltage increased to 4-5 mV due to relaxation. This small overpotential indicated that the system had fast kinetics. Then the cell was moved to an oven preheated to 60° C. When heated, the OCV became more negative and finally saturated at −52 mV. The cell was then discharged at 60° C. After the voltage reached 0 mV again, the cell was cooled down and returned to its initial state at 24° C. Without wishing to be bound by any particular theory, it is believed that the difference between the OCV at 24° C. and the OCV at 60° C. arose from the thermogalvanic coefficient%27s dependence on SOC. During the cooling and heating process, the cell was at different SOCs, and the cell thermogalvanic coefficients were different. It is believed that this led to different magnitudes of voltage change in cooling and heating. The current rate in both discharges was 60 mA g −1 , based on the mass of the PB electrode. The constant current discharge was followed by a short period of constant voltage discharge at 0 mV until the current was reduced to 30 mA g −1 . The data was also plotted as voltage versus specific capacity ( FIG. 18D ). It was clear that the voltage curve at both 24° C. and 60° C. had the same shape and the thermogalvanic effect simply shifted the curve down without affecting the nature of the electrochemical reactions. The plot also showed that the specific capacity was only about ¼-⅓ of the theoretical capacity of PB (60 mAh g −1 ). This was because the potential difference between the two electrodes must be less than αΔT, the voltage change due to the thermogalvanic effect. Otherwise, the cell would need a charging process at either T H or T L .","FIG. 19A illustrates the cycling performance of this charging-free system with respect to specific capacity and specific energy. The volume of Fe(CN) 6 3−/4− and the mass of PB are about 100 μL and 5-6 mg, respectively. Discharges at both temperatures were done with a current rate of 60 mA g −1 to 0 mV followed by constant voltage discharge with a cut-off of 30 mA g −1 . Results on cycles between 55° C./24° C. and 60° C./24° C. in air are plotted. Each cycle had two steps, one at high temperature and one at low temperature. For 60° C./24° C., the initial specific capacity based on the mass of PB was 15.2 mAh g −1 and dropped slightly to 13.8 mAh g −1 after 30 steps. The capacity between 55° C. and 24° C. was slightly lower. This demonstrates that the reaction was reversible and the system had a reasonable cycle life. The corresponding data on specific energy vs. step number is plotted in FIG. 19B . Although T H only changed by 5° C., the energy of the cell cycled between 24° C. and 60° C. was almost twice that of the cell cycled between 24° C. and 55° C. Without wishing to be bound by any particular theory, it is believed that this was because the higher temperature not only increased the full cell voltage, but also extended the capacity range and lowered the internal resistance at high temperature. It is believed that these three effects doubled the energy output of the electrochemical system.","PB electrodes show excellent cycling performance at room temperature and Fe(CN) 6 3−/4− is highly reversible, but there have been few studies of their high temperature performance, which is generally thought to be worse. To test the long term stability of the system, the cycle life of both electrodes was examined at 60° C. Both electrodes showed stable cycling over 200 cycles. For the PB electrode, oxygen dissolved in water significantly impacts cycle life, so the test was performed in a N 2 environment. Since only about 20 mAh g −1 of the full capacity could be used in real operation, the electrode was cycled between 360 and 190 mV vs. Ag/AgCl at a current rate of 300 mA g −1 , which corresponded to a specific capacity of about 30 mAh g −1 . The capacity was chosen to be higher than that in real operation to estimate the lower boundary of cycle life. Substantially no decay was observed over 250 cycles ( FIG. 19C ) and the coulomb efficiency was as high as 99.94%. The Fe(CN) 6 3−/4− electrode was tested in constant capacity cycling mode in air. The current was 10 mA. The voltage gap between charge and discharge even became slightly smaller than the first cycle as more surface of the carbon cloth electrode became activated ( FIG. 19D ). These observations support that the electrode material was stable under cycling and the system is promising for long term operation.","The efficiency for heat-to-electricity conversion (η) was calculated for the cycle between 24° C. and 60° C. and was based on the theory discussed in Example 1:"," η = W Q H + Q HX where W was the total electrical work in one cycle or the total amount of discharged energy at both low and high temperatures, Q H was the heat absorbed at high temperature, and Q HX was the energy loss in the heat exchanging process. The absolute efficiency was a function of the ratio (φ) of Fe(CN) 6 3−/4− volume to PB mass ( FIG. 20A ). The cell operated with a maximum efficiency of 1.9% at φ of about 1-2, assuming a heat exchanger effectiveness of 70% and no overpotential. The latter assumption was theoretically achievable at small currents or by minimizing the internal cell resistance with the use of a high surface current collector and nano-sized materials. The theoretical results, however, could be matched with the experiments (unconnected dots in FIG. 20A ) by introducing an overpotential of 10 mV (lower curve in FIG. 20A ). It is believed that there were two competing effects responsible for the cell efficiency maximum. When a large amount of Fe(CN) 6 3−/4− catholyte was used, the catholyte%27s contribution to the change of the full cell voltage was negligible and thus, a larger charge capacity and output energy could be obtained. However, this happened at the cost of a larger heat capacity of the full cell requiring a larger heat input leading to a decrease in the overall efficiency. When a 10 mV overpotential was considered, the maximum efficiency was 1.3. This was lower than the efficiency of the TRES based on copper hexacyanoferrate (CuHCF) and Cu/Cu 2+ electrodes described in Example 1. It is believed that there are two reasons for this: 1) Fe(CN) 6 3−/4− has a low solubility in water which limits the charge capacity and 2) only about ⅓ of the theoretical capacity can be used due to the charging-free characteristic. However, the efficiency is still much higher than thermogalvanic cells, another strategy based on the thermogalvanic effect but with the same architecture as thermoelectric devices. It is believed that the highest reported efficiency in thermogalvanic cells is 0.24% with hot side at 65° C. and cold side at 5° C. The efficiency of the same device working between 24° C. and 60° C. is estimated to be about 0.16% as the temperature difference is less.","The conversion efficiency of this charging-free electrochemical system depended on the effectiveness of the heat exchanger ( FIG. 20B ). If effectiveness of 85% was considered, the heat-to-electricity conversion efficiency could reach 3.2% and 2.3% for 0 and 10 mV overpotential, respectively. If no heat exchanger was used, which simplified the design, efficiency was still around 0.5% and it was about a threefold over that of alternatives such as thermogalvanic cells. It is interesting to compare the efficiencies above with thermoelectric devices. For a cycle between 60° C. and 24° C., efficiencies of 1.9% and 1.3% would requires an ideal thermoelectric device with average ZT of 0.97 and 0.58, respectively, while efficiencies of 3.2% and 2.3% led to equivalent ZT of 2.3 and 1.3 for ideal thermoelectric devices. It is believed that further improvement in efficiency and power rate could be realized by reducing the internal resistance of electrodes and by using materials with high positive thermogalvanic coefficients and figures of merit (Y).","Example 3","This example describes the conceptual design and experimental validation of a heat recuperation scheme with high efficiency.","The efficiency of heat recuperation can be an important factor in TREC system efficiency. However, in certain instances in which low temperature differentials between the hot and cold cells, and constant temperature operation at the charge and discharge states of the thermodynamic cycle are used, it is not immediately apparent how to achieve highly efficient heat recuperation. This example describes a simple contact experiment showing a heat recuperation efficiency of 43.5% and a design capable of achieving higher efficiency (60-70%). Tests on key components to validate the design are also described.","Direct Contact Heat Recuperation","One example of a heat recuperation configuration is to directly contact the hot and the cold cell, which can lead to a theoretical heat recuperation efficiency of 50%. In this example, a commercial Motorola Li-ion battery pack with a capacity of 1130 mAh and a mass of 23.2 grams was used. Its temperature was monitored by thin thermocouple wires attached to its surface. The experimental process is illustrated in FIG. 21A . First, both batteries were covered with the same amount of thermal paste (0.7 gram). FIG. 21B shows photographic images of a commercial Li-ion battery with and without thermal paste. One battery was placed in an oven set to 50° C. for 2 hours to equilibrate with the environment. The hot cell was subsequently removed from the oven and pressed onto the cold cell. The two cells were surrounded by fiberglass insulation during heat exchange. The temperature of the cold cell was calculated as the average of temperatures at the top (T m ) and bottom surfaces (T b ) of the cold cell.","The experimental results, showing temperature change when a hot cell and a cold cell contact each other, are shown in FIG. 22 . T t , T m and T b are the temperatures at the top of the hot cell, between the two cells, and at the bottom surface of the cold cell, respectively. The highest average temperature between T m and T b was 35.95° C. in the experiment. The temperatures of the cold cell (T C ) and the hot cell (T H ) before contact were 25.0 and 50.2° C., respectively. Consequently, the heat recuperation efficiency was (35.95−25.0)/(50.2−25.0)=43.5%.","The results indicated that heat recuperation efficiency of about 40% could be achieved.","Step-Wise Heat Recuperation: Concept","It is believed that the direct contact scheme is generally limited to 50% recuperation efficiency. Higher efficiency can be achieved with more sophisticated designs. Here, the use of a liquid, such as water, as a heat carrier to transfer heat from hot TREC cells to cold TREC cells can be considered. Ideally, hot cells would be cooled to the ambient temperature, and energy rejected from hot cells would be used to heat cold cells to the desired high operational temperature. In certain cases, temperature inversion happens: the original hot cells become cooler than the original cold cells, and heat rejected from the originally hot cell cannot be transferred to the originally cold cell after this temperature inversion.","To overcome this challenge, a step-wise process was developed. In this scheme, hot cells are cooled by multiple thermal reservoirs from high to low temperature in sequence, then the reservoirs transfer absorbed energy to cold cells step by step from low temperature to high temperature. This ensures that the heat transfer between hot cells and cold cells happens at a small temperature difference with high effectiveness.","The design of such a system is illustrated in FIG. 23 . In this exemplary system, the hot cell is initially at 60° C., and the cold cell is initially at 26° C. (room temperature). In the exemplary system, the reservoir at 26° C. is the ambient reservoir, and the reservoir at 60° C. is the external heat source. The hot cell can be cooled down and the cold cell can be heated up step by step using intermediate hot and cold reservoirs containing a heat transfer fluid (HTF, water for example) at different temperatures (51.5, 43, and 34.5° C. in FIG. 23 ). The reservoirs may be connected to the hot and cold cells with tubing, which is not shown in FIG. 23 . In this exemplary system, reservoirs were used to explain the step-wise heat recuperation concept. These hot and cold reservoirs can be replaced by heat exchangers in practical systems. The cooling of the hot cell originally at 60° C. can be done by four steps using HTF at 51.5, 43, 34.5, and 26° C., respectively. In each step, the HTF temperature increases slightly, absorbing heat from the hot cell. The heated HTFs at 34.5, 43 and 51.5° C. can be diverted to cold cells in sequence ( FIG. 23B ) to transfer the gained heat to the cold cell. If the effectiveness of heat exchange between the cell and HTFs is 1 (as demonstrated experimentally), there is no energy loss for reservoirs at 34.5, 43 and 51.5° C., since all heat received from the hot cell is transferred to the cold cell. The only extra energy needed is the last step in heating, warming the cold cell to 60° C. using an external reservoir at 60° C., which is C c *8.5 K with C c the heat capacity of the cell in the unit of J K −1 . Consequently the heat recuperation efficiency (η HX ) is 1−C c *8.5K/C c *(60° C.−26° C.)=75% In general, if there are n+1 reservoirs at T L , T L +ΔT, T L +2 Δ T, . . . and T H (Δ T=(T H −T L )/n),"," η HX = n - 1 n ( 8 ) Experimental Validation of the Step-Wise Heat Recuperation System","To validate the step-wise heat recuperation approach, a prototype system was built as shown in FIGS. 23A-B . For each heat exchange step, water was pumped from reservoir 1 (1.5 L) at a flow rate of 2.3 liters per minute. The flow rate was controlled by a valve and a flowmeter. The pumped water flowed through a plastic chamber with a stainless steel dummy battery inside and drained to the other empty reservoir (reservoir 2). After each step of heat exchange, reservoirs 1 and 2 were replaced by another set of reservoirs at a different temperature for the next step. Water flowed to reservoir 2 in the heating process was used in the cooling process. A dummy cell made of 304 stainless steel, which has a thermal diffusivity (4×10 −6 m 2 s −1 ) similar to batteries (10 −6 to 10 −5 m 2 s −1 ), was used. The size of the dummy battery was 3.3 cm×7 cm×0.6 cm. In comparison, a typical phone battery has a size of 3 cm×5 cm×0.5 cm (Motorola). To calculate the heat exchanged between water and the cell, temperatures at the inlet, cell, and outlet were measured with K-type thermocouples (TCs) and recorded with a data acquisition (DAQ) board at a frequency of 10 Hz. The cell temperature was measured with a thermocouple embedded in a hole drilled in the center of the cell ( FIG. 24B ).","FIG. 25 shows the measured temperature at the inlet (T in ), cell (T cell ), and outlet (T out ) during heating and cooling. In the experiment, heating ( FIG. 23B ) was performed before cooling ( FIG. 23A ). This switch did not affect any results relating to efficiency, as cells in real systems go through cyclic processes. T in behaved like a step function as the temperature of the reservoirs changed from 26° C. to 60° C. and decreased back to 34.5° C. step by step. The last step in cooling (34.5→26° C.) was not performed, as heat harvested in this step cannot be used for heating in following cycles and thus was not used in any calculations. T cell and T out gradually responded to T in due to the heat capacity of the dummy cell. The highest temperature T cell and T out reached was 59.6° C. at the end of heating. The fast and efficient heat exchange between cell and water was reflected by the small difference between T cell and T out . Based on the small temperature difference between T cell and T out , an effectiveness of 1 for the heat exchange between the cell and the HTF can be assumed. The gap between T in and T out indicated heat rejected from or lost to the cell.","Based on equation (8), the theoretical efficiency of the procedure above is (4−1)/4=75%. The experimental heat recuperation efficiency can be expressed as"," η ex = Heat ⁢ ⁢ rejected ⁢ ⁢ from ⁢ ⁢ the ⁢ ⁢ hot ⁢ ⁢ cell ⁢ ⁢ to reser ⁢ ⁢ voirs ⁢ ⁢ at ⁢ ⁢ 51.5 , 43 , and ⁢ ⁢ 34.5 ⁢ ° ⁢ ⁢ C . ⁢ Heat ⁢ ⁢ absorbed ⁢ ⁢ by ⁢ ⁢ the ⁢ ⁢ cold ⁢ ⁢ cell ⁢ ⁢ from reser ⁢ ⁢ voirs ⁢ ⁢ at ⁢ ⁢ 34.5 , 43 , 51.5 , and ⁢ ⁢ 60 ⁢ ° ⁢ ⁢ C . ( 9 ) In the i th step, heat rejected to the reservoir (Q i ) is: Q i =∫{dot over (m)}C water ΔTdt   (10) where {dot over (m)} is the volumetric flow rate of water in the unit of m 3 s −1 , C water is the heat capacity of water in the unit of J m −3 K −1 , and ΔT=T out −T in . Q i is positive for the cooling process and negative for the heating process.","In experiments, the flow rate {dot over (m)} was kept constant by the flowmeter and valve. C water was nearly constant between 26 and 60° C. (about 0.1% difference). Thus, based on FIG. 25 and equations (9) and (10):"," η ex = ⁢ - ∑ cooling ⁢ ⁢ with ⁢ ⁢ reservoirs ⁢ ⁢ at ⁢ ⁢ 51.5 , 43 , and ⁢ ⁢ 34.5 ⁢ ° ⁢ ⁢ C . ∫ Δ ⁢ ⁢ T ⁢ ⅆ t ∑ heating ⁢ ⁢ with ⁢ ⁢ reservoirs ⁢ ⁢ at ⁢ ⁢ 34.5 , 43 , 51.5 , and ⁢ ⁢ 60 ⁢ ° ⁢ ⁢ C . ∫ Δ ⁢ ⁢ T ⁢ ⅆ t = ⁢ - - 225.5 ⁢ Ks 329.5 ⁢ Ks = ⁢ 0.684 ( 11 ) The achieved experimental efficiency (68.4%) was close to the theoretical value (75%). One reason for the difference may be heat loss through walls of the container. More detailed analysis showed that the heat dissipation loss became negligible (about 1%) when the system dimension increased to about one meter, suggesting that the experimental efficiency could reach about 74%. It is believed that by further increasing the number of reservoirs, heat recuperation efficiency could exceed 80%. Step-Wise Design with Heat Exchangers Instead of Thermal Reservoirs","The design and experiments above demonstrate that heat recuperation efficiency of 70% may be reasonable. Thermal reservoirs at different temperatures can be made through mixing hot water and water at ambient temperature with different ratios. This method does not result in any energy loss. However, it may be more practical and compact to use heat exchangers to create HTFs at different temperatures for heat exchange with TREC cells. In the following part, the heat recuperation efficiency of a system with heat exchangers instead of thermal reservoirs at intermediate temperatures is analyzed. Although the overall efficiency becomes lower as extra loss exists due to effectiveness of heat exchangers, the analysis shows that the design is capable of achieving efficiency of 60-70%.","The system structure is presented in FIG. 26 . This figure shows the case with eight TREC cells and four heat exchangers (HXs, n=4), although systems may use any number of additional cells and HXs to increase efficiency. In this design, two HTF streams are utilized to transport thermal energy from hot cells to cold cells. Each cell in this configuration undergoes a transient heat transfer with the HTF.","In this design, each cell is cooled/heated by multiple steps with HTFs at the outlet of the HXs, which act as the thermal reservoirs described above. Cells 1-4 are in the cooling process, and Cells 5-8 are in the heating process. Two reservoirs, one at high temperature (T 1 ) and one at ambient temperature (T 10 ), are utilized to assist the heat transfer process.","Starting from left to right, in this example, an HTF with the temperature of T 1 is introduced in HX1, and its temperature at the outlet is reduced by ΔT HX (e.g. T 1 −T 2 ). In this exemplary arrangement, the HTF exchanges heat with Cell 1, and its temperature is increased by ΔT HTF (e.g. T 3 −T 2 ) to recuperate some of the thermal energy of Cell 1. Subsequently, the HTF flows through other HXs and cells in sequence, going through the same heat transfer processes at lower temperatures before exiting the recuperation step at a temperature of T 9 . On the other side, in this example, the HTF with the inlet temperature of T 10 is introduced in HX4, absorbs thermal energy and then flows through cell (5) transferring some of its thermal energy to the cell. The temperature of the HTF drops by ΔT HTF in this process. Then, it flows through other HXs and cells in sequence, undergoing the same heat transfer processes at higher temperatures. The corresponding pinch diagram is shown in FIG. 26B . At the end of this step, the temperatures of the cells become the same as that of the HTFs. The temperatures of cells 1-4 are T 3 , T 5 , T 7 and T 9 , while the temperatures of cells 5-8 are T 12 , T 14 , T 16 and T 18 . In this way, heat exchange happens between cells with small temperature difference (e.g. cell 3 and 5), and thus higher recuperation efficiency is realized. After this step, cells are disconnected from that stream and connected to another HX for the next recuperation step. Connection and disconnection are realized by automatic valves in the practical system.","This heat recuperation method can be further developed to a practical continuous procedure that contains all four steps (discharge, heating, charge and cooling) in the cycle, which will be explained below.","Heat recuperation efficiency can be defined as:"," η HX = Heat ⁢ ⁢ absorbed ⁢ ⁢ by ⁢ ⁢ the ⁢ ⁢ n ⁢ ⁢ cold ⁢ ⁢ cells - Energy ⁢ ⁢ extracted ⁢ ⁢ from ⁢ ⁢ the ⁢ ⁢ hot ⁢ ⁢ reservoir ⁢ Heat ⁢ ⁢ rejected ⁢ ⁢ in ⁢ ⁢ cooling ⁢ ⁢ the ⁢ ⁢ n ⁢ ⁢ hot ⁢ ⁢ cells ( 12 ) As heat recuperation is a cyclic process, the system can be analyzed by considering only energy change in a certain step. Assuming all cells and the temperature difference between cells are identical, the efficiency is written as:"," η HX = n ⁢ ∫ MC cell ⁢ ⅆ T cell - ∫ m . ⁢ C HTF ⁡ ( T 1 - T 18 ) ⁢ ⅆ t n ⁢ ∫ m . ⁢ ⁢ C HTF ⁢ Δ ⁢ ⁢ T HTF ⁢ ⅆ t ( 13 ) where T 18 is the temperature of THF flowing into the hot reservoir. M is the mass of a cell and C cell is the specific heat of a cell (J Kg −1 K −1 ). T cell is the temperature of a cell. {dot over (m)} is the flow rate of HTF in the unit of kg s −1 . C HTF is the specific heat of the HTF (J Kg −1 K −1 ). ΔT HTF is the temperature difference of HTF before and after heat exchange with the cell. The integral is from the beginning to the end of one step. If the effectiveness of heat exchange between cells and HTFs is 1: ∫ MC cell dT cell =∫{dot over (m)}C HTF ΔT HTF dt   (14) From FIG. 26B , T 1 −T 18 =T p +ΔT HTF   (15) Suppose that {dot over (m)} and C cell are constant during heat recuperation. Applying formula (14) and (15) to (13) results in:"," η HX = ∫ [ ( n - 1 ) ⁢ Δ ⁢ ⁢ T HTF - T p ] ⁢ ⅆ t ∫ n ⁢ ⁢ Δ ⁢ ⁢ T HTF ⁢ ⅆ t = ( n - 1 ) ⁢ Δ ⁢ ⁢ T HTF _ - T p _ n ⁢ ⁢ Δ ⁢ ⁢ T HTF _ ( 16 ) where ΔT HTF and T p are the time-averaged value of corresponding integrals. This equation illustrates that the system efficiency is"," η HX = n - 1 n with ideal HXs (T p =0), which converges to the configuration with thermal reservoirs, since HTFs at outlets of HXs act as thermal reservoirs and there is no loss within HXs. In the ideal case, the two lines shown in FIG. 26B would be superpositioned. The effectiveness of a heat exchanger is defined as"," ɛ = q . q . max = Δ ⁢ ⁢ T HX Δ ⁢ ⁢ T HX + T p ≈ Δ ⁢ ⁢ T HX Δ ⁢ ⁢ T HX + T p _ ( 17 ) Thus, the pinch temperature difference can be expressed in terms of the effectiveness and replaced in the recuperation efficiency,"," η HX = ( n - 1 ) ⁢ Δ ⁢ ⁢ T HTF _ - Δ ⁢ ⁢ T HX ⁡ ( 1 - ɛ ɛ ) n ⁢ ⁢ Δ ⁢ ⁢ T HTF _ ( 18 ) If the temperature difference between the hot and the cold source is defined as ΔT=T 1 −T 10 =T p +nΔT HX −(n−1) ΔT HTF , then"," Δ ⁢ ⁢ T HX = ( Δ ⁢ ⁢ T n ) + n - 1 n ⁢ Δ ⁢ ⁢ T HTF _ 1 + 1 - ɛ n ⁢ ⁢ ɛ ( 19 ) Thus, η HX is only a function of the given parameters ΔT, n, ε, and ΔT HTF . The effectiveness of heat exchange between the HTF and the cell is assumed 1 as demonstrated experimentally in the previous section.","The dependence of η HX on the number of heat exchangers is plotted in FIG. 27 at two different heat exchanger effectiveness values (an effectiveness of 0.9 and an effectiveness of 0.85) that are available for commercial heat exchangers. This figure shows that over 50% heat recuperation efficiency can be achieved with n larger or equal to 4 and that 80% heat recuperation efficiency is achievable.","Continuous Operation","To realize a continuous process with heat exchangers, all cells in the system can be divided into four groups: discharge at T L , heating, charge at T H , and cooling. At each moment, a certain number of cells can be operated in each group, and each cell can undergo all four groups in a full cycle. For example, Table 1 shows the procedure for a system with two-step heating/cooling, where charge/discharge time is the same as cooling/heating time. In this procedure, each cell operates through the four steps with a time offset so that the whole process is continuous. Cool 1 represents the cooling process from T H to (T H +T L )/2, and Cool 2 is from (T H +T L )/2 to T L . Heat 1 is from T L to (T H +T L )/2, and Heat 2 is from (T H +T L )/2 to T H . C and DC represent charge and discharge, respectively. For each cell, the switch between different cooling steps and heating steps is realized by opening and closing valves between cells and heat exchangers."," TABLE 1 The procedure for two steps in heating/cooling and heating/cooling time the same as charge/discharge time Time Cell No. Period 1 2 3 4 5 6 1 Cool 1 Cool 2 DC at T L Heat 1 Heat 2 C at T H 2 Cool 2 DC at T L Heat 1 Heat 2 C at T H Cool 1 3 DC at T L Heat 1 Heat 2 C at T H Cool 1 Cool 2 4 Heat 1 Heat 2 C at T H Cool 1 Cool 2 DC at T L 5 Heat 2 C at T H Cool 1 Cool 2 DC at T L Heat 1 6 C at T H Cool 1 Cool 2 DC at T L Heat 1 Heat 2 7 (same Cool 1 Cool 2 DC at T L Heat 1 Heat 2 C at T H as 1) In general, if the step number for heating/cooling is n, and the ratio of discharge/charge time to cooling/heating time of each step is m, then n cells are in heating and cooling, respectively, while m cells are in discharge and charge, respectively.","Example 4","This example describes an ion-selective-membrane-free electrochemical system comprising a nickel hexacynoferrate cathode and a silver/silver chloride anode.","In TREC systems such as CuHCF//Cu 2+ /Cu, an ion-selective membrane is typically used to avoid side reactions between CuHCF and Cu 2+ . Ion-selective membranes may be expensive, and it may be difficult to completely block penetration of ions such as Cu 2+ during long-term operation. As described in this example, an ion-selective-membrane-free electrochemical system comprising a nickel hexacyanoferrate (NiHCF, KNi II Fe III (CN) 6 ) cathode and a silver/silver chloride anode was developed. The reactions of the two half cells were: Cathode: KNi II Fe III (CN) 6 +K + +e − →K 2 Ni II Fe II (CN) 6 Anode: AgCl+ e − →Ag+Cl − In this system, ions involved in each electrode did not have side reactions with each other, so the ion-selective membrane was unnecessary and could be replaced by an inexpensive porous separator. The full cell had a thermogalvanic coefficient of −0.74±0.05 mV K −1 and a heat-to-electricity conversion efficiency of 2.6% and 3.5% when cycled between 15° C. and 55° C. at a current rate of C/2 (20 mA g −1 ) with assumed heat recuperation efficiency of 50% and 70%, respectively.","All chemicals for synthesis of nickel hexacyanoferrate (NiHCF) were purchased from Sigma Aldrich. NiHCF nanoparticles were synthesized using a simple solution approach by dropping 40 mL of 50 mM Ni(NO 3 ) 2 aqueous solution into 40 mL of 25 mM K 3 Fe(CN) 6 aqueous solution under strong stirring at 50° C. at a speed of about one drop per second. The precipitation was centrifuged and dried at 70° C. overnight. The average size of as-synthesized particles was about 50 nm.","The NiHCF electrode was prepared by mixing 70 wt % NiHCF nanoparticles, 20 wt % Super P carbon black, and 10% polyvinylidene fluoride (PVDF, Kynar) in N-Methyl-2-pyrrolidone (NMP) and drop casting onto a carbon cloth disc electrode (Fuel Cell Store) at 90° C. The carbon cloth disc had a diameter of 1 cm, and the mass loading was about 3 mg NiHCF cm −2 .","An aqueous KCl solution was used as the electrolyte. As discussed in further detail below, the KCl concentration was selected to be 3 M. 0.2 M Ni(NO 3 ) 2 was added to stabilize NiHCF at high temperature based on the common ion effect. To optimize the performance of NiHCF, the pH of the electrolyte was tuned to 2 by adding HNO 3 .","The NiHCF electrode, an Ag/AgCl reference electrode made by precharging a silver rod in 1 M KCl solution, an Ag film, and the electrolyte were assembled in a pouch cell configuration, as shown in FIG. 28 . Typically, about 500 μl of electrolyte was used in the cell. A glass fiber filter (Whatman) was used as a separator. The Ag film, which had a thickness of about 25 μm and a size of 2 cm by 2 cm, was partially charged inside the pouch cell to form an Ag/AgCl anode with a high porous surface area. Specifically, the Ag film was charged to 1 mAh and then discharged back by 0.5 mAh. The in situ formed Ag/AgCl film electrode then acted as the anode. Pt foil was used as the current collector for the cathode, and Ag foil was used as the current collector for the anode. The typical thickness of the pouch cell was 1-1.5 mm.","Temperature-dependent electrochemical characteristics were measured with a home-made temperature cycler. Thermocouples were attached to both sides of the pouch cell, and the temperatures of the thermocouples were acquired by a data acquisition board and controlled with fluctuations of less than about 0.1° C. The compact design allowed the temperature to be switched in less than three minutes so that other effects, such as self-discharge and dissolved oxygen, could be minimized.","Using the temperature cycler, electrode potentials of the NiHCF and Ag/AgCl electrodes were measured at different temperatures. The pouch cell configuration described above was used, and the potential of each electrode was measured using the reference Ag/AgCl electrode exposed to the same electrolyte in the pouch. The temperature was changed in the sequence of 55° C., 15° C., 45° C., 25° C., 35° C., and 15° C. Each temperature step lasted for eight minutes, and the voltage became steady after three minutes in each step, indicating that the system quickly reached equilibrium and that there was no obvious effect due to self-discharge. For thermal cycling between 55 and 15° C., the current acquired by the EC-lab software for the VMP3 tester was monitored. Once a step (charge or discharge) was finished as current became zero, the temperature was switched accordingly.","The dependence of full cell voltage on temperature was investigated for different states of charge (SOC) for a 3 M KCl cell. For specific charge capacities of 5, 15, 25, 35, 45, and 55 mAh g −1 , where 0 mAh g −1 represented the fully discharged state, it was found that full cell voltage was linearly related to temperature in the range of 15 to 55° C., indicating that thermogalvanic coefficient α was constant in that temperature range.","The dependence of thermogalvanic coefficient α (mV K −1 ) of the full cell on specific charge capacity (mAh g −1 ) at KCl concentrations ([KCl]) of 1 M, 2 M, 3 M, and 4 M was also investigated. For all KCl concentrations, it was found that α showed an inverse bell shape against specific charge capacity. α was flat for specific charge capacities in the range of 10-50 mAh g −1 , but its absolute value became smaller when the system approached a fully charged or a fully discharged state. Moreover, it was found that lower KCl concentrations led to more negative temperature coefficients for all specific charge capacities, which may have been a result of changes in K + and Cl − activity.","For example, the dependence of thermogalvanic coefficient α at 50% SOC on [KCl] was investigated and found to show a trend consistent with the derivation of a from the Nernst equation:"," E = E 0 + RT F ⁢ ln ⁡ ( [ K + ] ⁡ [ Cl - ] ) ( 20 ) α = ⁢ α 0 + R F ⁢ ln ⁡ ( [ K + ] ⁡ [ Cl - ] ) = ⁢ α 0 + 0.0862 ⁢ ⁢ mV ⁢ ⁢ K - 1 ⁢ ln ⁡ ( [ K + ] ⁡ [ Cl - ] ) ( 21 ) where E was the electrode potential, R was the ideal gas constant, and F was the Faraday constant (96485 C mol −1 ). E 0 and α 0 were the electrode potential and thermogalvanic coefficient with unit activity of ions for a certain SOC. The activities of the solid phases, which were assumed to be 1, were not shown in the equations. The activity coefficients of the ions were assumed to be 1, so the activities of the ions were replaced by concentration. While the experimental dependence of α on [KCl] appeared to generally be consistent with the dependence α on [KCl] derived from the Nernst equation, some deviation may have arisen from the activity coefficient and influence of Ni 2+ , which could also be inserted into NiHCF. The thermogalvanic coefficient mainly came from the half cell of NiHCF, as previous studies showed that the thermogalvanic coefficient of Ag/AgCl was 0.22-0.26 mV K −1 with 1 M KCl and 0.12 mV K −1 with 4 M KCl. The dependence of α on KCl concentration led to a trade-off between voltage gap (|αΔT|) and heat capacity. Since K + and Cl − were stored in the electrolyte, higher [KCl] indicated a smaller amount of KCl electrolyte was required and thus less energy was needed to heat the system. However, it also reduced the absolute value of α and the voltage gap between discharge and charge (|αΔT|).","To estimate the optimized concentration of KCl electrolyte, the efficiencies at different KCl concentrations were calculated and listed in Table 2. The thermogalvanic coefficients at different [KCl] were experimentally obtained as the value at 50% state of charge. The voltage gap was the average difference between discharge and charge voltage after taking overpotential into account. 12 mV was used for the overpotential based on data at 1 C and C/2 rates. The heat capacities of KCl electrolyte at all concentrations were assumed to be 4.0 J cm −3 K −1 . The heat capacities of NiHCF, Ag and the KCl electrolyte were taken into account. 3 M KCl was determined to be the optimal concentration, as it resulted in the highest efficiencies."," TABLE 2 Estimation of heat-to-electricity efficiency at different [KCl] thermogalvanic voltage Efficiency Efficiency [KCl] coefficient α αΔT gap W Q H C p ΔT with η HR = with η HR = (M) (mV K −1 ) (mV) (mV) (mWh g −1 ) (mWh g −1 ) (mWh g −1 ) 50% (%) 70% (%) 1 −1.04 41.6 29.6 1.07 12.3 72.3 2.20 3.14 2 −0.80 32 20 0.72 9.45 42.5 2.35 3.25 3 −0.75 30 18 0.65 8.86 32.5 2.58 3.48 4 −0.63 25.2 13.2 0.48 7.44 27.5 2.24 3.03 ","A thermal cycle of a NiHCF//Ag/AgCl full cell with 3 M KCl/0.2 M Ni(NO 3 ) 2 electrolyte was investigated. The temperature was well controlled, with fluctuations of less than 0.1° C. At the end of each discharge or charge, the cell was rested for three minutes to allow the temperature to change and the system to reach equilibrium. The dependence of electrode potentials on specific capacity at current rates of 1 C (40 mA g −1 ) and C/2 (20 mA g −1 ) was investigated. All electrode potentials were measured versus the Ag/AgCl reference electrode exposed to the same electrolyte in the pouch cell. The current rate and specific capacity were based on the mass of NiHCF. At both 1 C and C/2 rates, the battery was heated to 55° C. and charged to 640.0 mV. The battery was then cooled to 15° C., which increased the open circuit voltage (OCV) to 660.1 mV for 1 C and 661.6 mV for C/2. Next, the cell was discharged to 485 mV at 15° C. and then heated to 55° C. again. The electricity produced in one cycle (W) normalized to the mass of NiHCF could be written as: W=Q dis V dis −Q ch V ch =Q dis ( V dis − V ch /CE )  (22) where Q was the specific capacity normalized to the mass of NiHCF and V was the average full cell voltage. The subscripts dis and ch indicated discharge and charge, respectively. CE was the coulombic efficiency, which was defined as Q dis /Q ch . From equation (22), it could be seen that in addition to large specific discharge capacity and voltage gap between discharge and charge, high coulombic efficiency was also important to achieve high energy output and conversion efficiency. V dis − V ch and V dis − V ch /CE were defined as the apparent and effective voltage gap, respectively, as the latter one directly determined the energy difference between discharge and charge.","For 1 C rate, in discharge, the average voltages of NiHCF and Ag/AgCl were 566.27 mV and 4.37 mV, respectively, and the specific capacity was 35.4 mAh g −1 based on the mass of NiHCF. In charge, the average voltages of NiHCF and Ag/AgCl were 542.42 mV and −3.93 mV, respectively, and the specific capacity was 35.5 mAh g −1 . As a result, the apparent and effective voltage gaps were 15.8 and 14.2 mV, respectively. The total specific discharge and charge energies were 19.90 mWh g −1 and 19.40 mWh g −1 , respectively%3b thus, 0.50 mWh g −1 of heat energy was converted to electricity. The heat-to-electricity conversion efficiency (η) was calculated as:"," η = W Q H + Q HR = W T H ⁢ Δ ⁢ ⁢ S + Q HR = W discharge - W charge  α  ⁢ T H ⁢ Q c + ( 1 - η HR ) ⁢ C p ⁢ Δ ⁢ ⁢ T ( 23 ) where W was the difference between discharge and charge energy in a cycle. Q HR was the extra energy needed to heat the cell. Q c was the discharge capacity at T H , C p was the heat capacity of the cell. η HR was the heat recuperation efficiency, indicating how much energy rejected in the cooling process could be reused for the next heating process. Values of 50-70% were considered to be reasonable for η HR .","An example efficiency calculation for the 3 M KCl electrolyte cell with a T H =55° C.=328 K is shown. To simplify the calculations, all values were normalized to the mass of NiHCF. W was calculated based on the full cell voltage curves as W discharge −W charge . Its value was 0.50 mWh g −1 based on the mass of NiHCF. The value of Q H was calculated as follows: Q H =|α|T H Q c =0.74 mV K −1 ×328 K×35.5 mAh g −1 =8.62 mWh g −1 In calculating C p , the specific heat of NiHCF, Ag and 3 M KCl electrolyte were considered. The specific heat of NiHCF was 1.1 J g −1 based on differential scanning calorimetry (DSC) measurement. For 1 gram of NiHCF electrode, the amount of 3 M KCl electrolyte needed was 35.5 mAh/(96485 C mol −1 *3 mol L −1 )=0.442 mL. The specific heat of 3 M KCl was 3.1 J g −1 K −1 based on DSC measurement, and its density was 1.22 g mL −1 . The amount of Ag needed was 35.5 mAh/(96.485 C mol −1 /108 g mol −1 )=0.133 g. The specific heat of Ag was 0.24 J g −1 K −1 . Thus, the heat capacity based on the mass of NiHCF was 1.1+3.1*1.23*0.442+0.133*0.24=2.82 J g −1 K −1 . As ΔT=40 K, C p ΔT=112.8 J g −1 =31.3 mWh g −1 .","Consequently the heat-to-electricity conversion efficiency with η HR =50% was:"," η = 0.50 8.62 + 3.13 × ( 1 - 0.5 ) = 2.1 ⁢ % ","Heat-to-electricity efficiency values were also calculated for current rates of 1 C and C/2 and for heat recuperation efficiencies of 0%, 50%, and 70%. These values are shown in Table 3. For example, for a 3 M [KCl] cell at a 1 C (40 mA g −1 ) current rate, Q H =8.617 mWh g −1 with α of −0.74 mV K −1 . The total heat capacity of electrolytes and electrodes was 2.84 J g −1 K −1 , and C p ΔT=31.6 mWh g −1 for temperature cycling between 15 and 55° C. Based on these values, η reached 1.3%, 2.1% and 2.8% for η HR of 0%, 50% and 70%.","For a 3 M KCl cell at C/2 rate (20 mA g −1 ), the average discharge voltage increased to 565.7 mV, and the average charge voltage decreased to 545.8 mV, as lower current led to smaller overpotential. The specific capacity also increased to 36.0 mAh g −1 for discharge and 36.1 mAh g −1 for charge. Consequently, the discharge and charge energy were 20.35 mWh g −1 and 19.71 mWh g −1 , respectively. The energy converted to electricity reached 0.65 mWh g −1 , 29% higher than that at 1 C rate, and the corresponding η were 1.6%, 2.6% and 3.5% for η HR of 0%, 50% and 70%."," TABLE 3 Calculation of conversion efficiency at different current rate* Conversion efficiency Current V dis V ch Q dis CE W Q H C p ΔT at different η HR rate (mV) (mV) (mAh g −1 ) (%) (mWh g −1 ) (mWh g −1 ) (mWh g −1 ) 0% 50% 70% 1 C 561.9 546.4 35.4 99.72 0.50 8.62 31.6 1.3 2.1 2.8 C/2 565.7 545.8 36.0 99.72 0.65 8.76 32.1 1.6 2.6 3.5 *All symbols are the same as those in equations (22) and (23) ","For long term operation, cycle life of TREC is important. The specific capacity, coulombic efficiency, average charge/discharge voltage, and thermal-to-electricity efficiency were investigated against cycle number. The cell was cycled at 1 C rate for the first 35 cycles, then at C/2 for 50 cycles. The capacity fading rate was on average 0.10% and 0.18% per cycle at 1 C and C/2, respectively. The higher capacity fading at C/2 was likely due to a longer operation time at 55° C. The Coulombic efficiency was 99.2% at the beginning, but rapidly increased to about 99.5-99.7% after 5 cycles. The average charge/discharge voltage showed a steady increasing trend of about 0.1 mV per cycle. The apparent voltage gap between charge and discharge ( V dis − V ch ) was about 4 mV higher at C/2 compared to 1 C rate, as a result of lower overpotential. Moreover, the effective voltage gap ( V dis − V ch /CE) was lower than the apparent voltage gap ( V dis − V ch ) due to non-100% Coulombic efficiency. The difference was about 5 mV at the beginning and decreased to about 2 mV as the Coulombic efficiency gradually increased and stabilized around 99.7%. The absolute conversion efficiency (η) was a synergistic result of the three factors above based on equation (22). At 70% heat recuperation, η was 2.2% in the first cycle due to low Coulombic efficiency, and gradually increased to 2.9% after 30 cycles. The following cycles at C/2 showed η of 3.5% at the beginning, with η decreasing slowly to 2.9% after 50 cycles. This may have been because CE was steady in this part and the major fading factor was the decreasing capacity and apparent voltage gap. The fading rate was reduced, as evaporation was fully eliminated by employing pouch cell configuration.","A conversion of the efficiencies above to equivalent ZT values can help evaluate the performance of TREC cells against thermoelectric (TE) cells. For a temperature cycle between 15 and 55° C., at a heat recuperation efficiency of 70%, the efficiency achieved at 1 C was 2.8%, and the efficiency achieved at C/2 was 3.5%. A TE device would need to reach ZT of 1.4 and 2.1 to achieve the same efficiencies for the same high and low temperatures. At a heat recuperation efficiency of 50%, the efficiency achieved at 1 C was 2.1% and at C/2 was 2.6%. The corresponding effective ZT values were 0.94 and 1.3. State-of-the-art TE materials, however, have a ZT of 1-1.5 for temperatures below 100° C.","A possible concern of the NiHCF//AgCl/Ag system may be the cost of Ag. For Ag, the mass loading required 0.7 mg Ag cm −2 . Even if 5 mg cm −2 were needed in a commercial cell due to increased capacity per area, then 50 grams would be needed per square meter, which costs about $35 per square meter ($700 per kilogram). In contrast, the cost of a Nafion ion-selective membrane is about $200 per square meter. Even with the high mass loading of 5 mg per square centimeter, the cost would still be less than 20% of Nafion membranes. The cost could be further reduced by replacing Ag with inexpensive electrodes.","In summary, an ion-selective-membrane-free electrochemical system with nickel hexacyanoferrate (NiHCF, KNi II Fe III (CN) 6 ) cathode and Ag/AgCl anode was demonstrated to convert low-grade heat to electricity. As ions involved in each electrode did not interfere with the opposite electrode, expensive ion-selective membranes were not needed in this system. The system showed a heat-to-electricity conversion efficiency of 3.5% under 70% heat recuperation when it was cycled between 15 and 55° C. at a C/2 current rate. The system also showed adequate cycle life compared to previous results.","While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the functions and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, and/or methods, if such features, systems, articles, materials, and/or methods are not mutually inconsistent, is included within the scope of the present invention.","The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”","The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to “A and/or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A without B (optionally including elements other than B)%3b in another embodiment, to B without A (optionally including elements other than A)%3b in yet another embodiment, to both A and B (optionally including other elements)%3b etc.","As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.","As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B)%3b in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A)%3b in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements)%3b etc.","In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","Non-limiting embodiments of the present invention will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention. In the figures:","FIGS. 1A-1B are exemplary schematic illustrations of an electrochemical cell, according to certain embodiments%3b","FIG. 2 is, according to some embodiments, an exemplary plot of temperature as a function of entropy for an electrochemical cell undergoing a thermodynamic cycle%3b","FIG. 3A is an exemplary plot of voltage as a function of capacity for a thermally-regenerated electrochemical cell undergoing a thermodynamic cycle in which external electrical current is applied to complete the cycle, according to certain embodiments%3b","FIG. 3B is, according to some embodiments, an exemplary plot of voltage as a function of capacity for a thermally-regenerated electrochemical cell undergoing a thermodynamic cycle in which the cycle is completed without the application of external electrical current%3b","FIG. 4 is an exemplary schematic diagram illustrating heat transfer between two electrochemical cells, according to certain embodiments%3b","FIGS. 5A-5B are, according to some embodiments, exemplary schematic illustrations of electrochemical systems in which heat is transferred from hot electrochemical cells to cold electrochemical cells%3b","FIG. 6A is, according to certain embodiments, a schematic illustration of an electrochemical system in which heat is transferred between four electrochemical cells using a heat transfer fluid%3b","FIG. 6B is a schematic illustration of a pinch diagram, according to some embodiments, for a system in which heat is transferred between four electrochemical cells using a heat transfer fluid%3b","FIG. 7 is an exemplary schematic illustration of a system in which heat is transferred between two electrochemical cells, according to some embodiments%3b","FIG. 8A is an exemplary schematic diagram illustrating the thermodynamic cycling of an electrochemical cell, according to some embodiments%3b","FIG. 8B is, according to some embodiments, an exemplary plot of temperature as a function of entropy for an electrochemical cell undergoing a thermodynamic cycle%3b","FIG. 9 is an exemplary schematic plot of voltage as a function of charge for an electrochemical cell undergoing a thermally regenerative electrochemical cycle, according to some embodiments%3b","FIG. 10 is an exemplary schematic illustration of energy transfer at a heat exchanger during a cycle of an electrochemical cell, according to some embodiments%3b","FIG. 11 is, according to certain embodiments, an exemplary schematic view of an electrochemical cell%3b","FIGS. 12A-12C are, according to some embodiments, exemplary plots illustrating the behavior of an electrochemical cell using CuHCF and Cu/Cu 2+ electrodes undergoing a thermodynamic cycle%3b","FIGS. 13A-13B are exemplary plots of cycle efficiency of a thermally regenerative electrochemical system, according to some embodiments%3b","FIGS. 14A-14B are, according to some embodiments, exemplary plots illustrating the behavior of a CuHCF half cell under galvanostatic cycling at various temperatures%3b","FIGS. 15A-15B are, according to some embodiments, exemplary plots illustrating the cycling performance of an electrochemical cell using CuHCF and Cu/Cu 2+ electrodes%3b","FIGS. 16A-16B are exemplary plots illustrating behavior of an electrochemical cell undergoing long-term galvanostatic cycling, according to some embodiments%3b","FIG. 17A is, according to some embodiments, an exemplary schematic diagram of an electrically-assisted thermally regenerative electrochemical system undergoing a thermodynamic cycle%3b","FIG. 17B is, according to some embodiments, an exemplary schematic diagram of a purely thermally regenerated electrochemical system undergoing a thermodynamic cycle%3b","FIGS. 18A-18D are exemplary plots illustrating the discharging and regenerating characteristics of an Fe(CN) 6 3−/4− /Prussian Blue electrochemical cell, according to some embodiments%3b","FIGS. 19A-19D are, according to some embodiments, exemplary plots illustrating the cycling performance of an Fe(CN) 6 3−/4− /Prussian Blue electrochemical cell%3b","FIGS. 20A-20B are exemplary plots illustrating the heat-to-electricity conversion efficiency of an Fe(CN) 6 3−/4− /Prussian Blue electrochemical cell, according to some embodiments%3b","FIGS. 21A-21B are, according to some embodiments: (a) an exemplary schematic illustration of heat recuperation by direct contact%3b and (b) a commercial Li-ion battery with and without thermal paste%3b","FIG. 22 is exemplary plot of temperature as a function of time at the top surface of a hot cell (top), interface between a hot cell and a cold cell in direct contact (middle), and bottom surface of a cold cell in direct contact with the hot cell (bottom), according to some embodiments%3b","FIGS. 23A-23B are, according to some embodiments, exemplary schematic illustrations of: (a) step-wise cooling of a hot cell%3b and (b) step-wise heating of a cold cell%3b","FIGS. 24A-24B are exemplary photographs of a heat exchange system, according to some embodiments%3b","FIGS. 25A-25B are, according to some embodiments, exemplary plots of temperature as a function of time for: (a) a heating process%3b and (b) a cooling process%3b","FIGS. 26A-26B are, according to some embodiments: (a) an exemplary schematic illustration of a design for heat recuperation with heat exchangers%3b and (b) an exemplary pinch diagram of temperature as a function of heat duty for a heat recuperation cycle at a given time%3b","FIG. 27 is an exemplary plot of heat recuperation efficiency as a function of number of heat exchangers, according to some embodiments%3b and","FIG. 28 is, according to some embodiments, an exemplary schematic illustration of a pouch cell."]},"government_interest":"STATEMENT OF GOVERNMENT SUPPORT This invention was made with government support under Contract Nos. DE-SC0001299, DE-FG02-09ER46577, DE-EE0005806, and DE-AC02-76SF00515 awarded by the U.S. Department of Energy and under Contract No. FA9550-11-1-0174 awarded by the Air Force Office of Scientific Research. The government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,559,388","html":"https://www.labpartnering.org/patents/9,559,388","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,559,388"},"labs":[{"uuid":"169e248f-cebb-471b-8e1d-e65f77e43080","name":"Sandia National Laboratories","tto_url":"https://ip.sandia.gov/","contact_us_email":"contactus@sandia.gov ","avatar":"https://www.labpartnering.org/files/labs/19","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/169e248f-cebb-471b-8e1d-e65f77e43080"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Seok Woo Lee","location":"Palo Alto, CA, US"},{"name":"Yuan Yang","location":"Cambridge, MA, US"},{"name":"Hadi Ghasemi","location":"Boston, MA, US"},{"name":"Gang Chen","location":"Carlisle, MA, US"},{"name":"Yi Cui","location":"Stanford, CA, US"}],"assignees":[{"name":"Massachusetts Institute of Technology","seq":1,"location":{"city":"Cambridge","state":" MA","country":" US"}},{"name":"The Board of Trustees of the Leland Staford Junior University","seq":2,"location":{"city":"Stanford","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"An electrochemical cell, comprising:a first electrode comprising a first electrochemically active material having a first thermogalvanic coefficient and a second electrode comprising a second electrochemically active material having a second thermogalvanic coefficient, wherein:the electrochemical cell is configured to be discharged at a discharge voltage and at a discharge temperature at or below about 200° C. such that the first electrochemically active material is at least partially electrochemically consumed%3bthe electrochemical cell is configured to regenerate first electrochemically active material from a product of at least a portion of the first electrochemically active material consumed during discharge at a regeneration voltage that is at least about 5 mV lower than the discharge voltage and a regeneration temperature that is different than the discharge temperature and at or below about 200° C. such that at least a portion of the regeneration of the first electrochemically active material is driven by a change in temperature of the electrochemical cell, wherein the regeneration of the first electrochemically active material occurs via a process in which reverse reactions of electrochemical reactions that occur during discharge proceed%3b andat least one of the first electrochemically active material and the second electrochemically active material is in a solid phase in both a reduced state and an oxidized state,wherein the absolute value of the difference between the first thermogalvanic coefficient of the first electrochemically active material and the second thermogalvanic coefficient of the second electrochemically active material is at least about 0.5 millivolts/Kelvin."},{"idx":"00002","text":"The electrochemical cell of claim 1, wherein the at least one of the first electrochemically active material and the second electrochemically active material in the solid phase comprises particles."},{"idx":"00003","text":"The electrochemical cell of claim 1, wherein the at least one of the first electrochemically active material and the second electrochemically active material in the solid phase is suspended in a fluid, wherein the at least one of the first and second electrodes comprising the electrochemically active material in the solid phase is a flowable electrode."},{"idx":"00004","text":"The electrochemical cell of claim 1, wherein the at least one of the first electrochemically active material and the second electrochemically active material in the solid phase comprises an intercalation compound, wherein the intercalation compound comprises a metal oxide, a metal chalcogenide, a Prussian Blue analogue, and/or a graphitic compound."},{"idx":"00005","text":"The electrochemical cell of claim 1, wherein the at least one of the first electrochemically active material and the second electrochemically active material in the solid phase is capable of undergoing a conversion reaction and/or comprises an elemental metal."},{"idx":"00006","text":"The electrochemical cell of claim 1, wherein the electrochemical cell is configured to regenerate first electrochemically active material from a product of at least a portion of the first electrochemically active material consumed during discharge at a regeneration voltage that is from about 5 millivolts to about 10 volts lower than the discharge voltage."},{"idx":"00007","text":"The electrochemical cell of claim 1, wherein the electrochemical cell is located in an ambient environment having a temperature, and the electrochemical cell is discharged at a discharge temperature that is within about 5° C. of the temperature of the ambient environment and/or the electrochemical cell is regenerated at a regeneration temperature that is within about 5° C. of the temperature of the ambient environment."},{"idx":"00008","text":"The electrochemical cell of claim 1, wherein the temperatures of the first and second electrodes of the electrochemical cell are within about 5° C. of each other during regeneration and/or discharge."},{"idx":"00009","text":"The electrochemical cell of claim 1, wherein the specific heat capacity of at least one of the first electrode and the second electrode is less than about 5 J/g K."},{"idx":"00010","text":"The electrochemical cell of claim 1, wherein a charge capacity of at least one of the first electrode and the second electrode is greater than about 30 mAh/g."},{"idx":"00011","text":"The electrochemical cell of claim 1, wherein the regeneration temperature is at least about 5° C. different than the discharge temperature."},{"idx":"00012","text":"A system comprising a first electrochemical cell of claim 1 and further comprising a second electrochemical cell to which heat is transferred from the first electrochemical cell."},{"idx":"00013","text":"The system of claim 12, wherein the second electrochemical cell is configured to be regenerated while the first electrochemical cell is discharged."},{"idx":"00014","text":"A system comprising a first plurality of electrochemical cells, wherein each of the first plurality of electrochemical cells is an electrochemical cell of claim 1, and a second plurality of electrochemical cells, wherein heat is transferred from each of the first plurality of electrochemical cells to each of the second plurality of electrochemical cells."},{"idx":"00015","text":"An electrochemical cell, comprising:a first electrode comprising a first electrochemically active material having a first thermogalvanic coefficient, and a second electrode comprising a second electrochemically active material having a second thermogalvanic coefficient, wherein:the electrochemical cell is configured to be discharged at a discharge temperature such that the first electrochemically active material is at least partially electrochemically consumed, andthe electrochemical cell is configured to regenerate first electrochemically active material from a product of at least a portion of the first electrochemically active material consumed during discharge at a temperature different than the discharge temperature, such that at least a portion of the regeneration of the first electrochemically active material is not driven by the application of electrical current external to the electrochemical cell and is driven by a change in temperature of the electrochemical cell, wherein the regeneration of the first electrochemically active material occurs via a process in which reverse reactions of electrochemical reactions that occur during discharge proceed%3bwherein the electrochemical cell is configured such that the discharge and regeneration can occur without the application of an external electrical current,wherein the absolute value of the difference between the first thermogalvanic coefficient of the first electrochemically active material and the second thermogalvanic coefficient of the second electrochemically active material is at least about 0.5 millivolts/Kelvin, andwherein electricity is generated during each of the discharge and regeneration steps."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"4242","main-group":"10","action-date":"2017-01-31","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","M","4242","10","2017-01-31","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"24","main-group":"6","action-date":"2017-01-31","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"42","main-group":"10","action-date":"2017-01-31","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"58","main-group":"4","action-date":"2017-01-31","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"583","main-group":"4","action-date":"2017-01-31","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"66","main-group":"10","action-date":"2017-01-31","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"38","main-group":"4","action-date":"2017-01-31","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"48","main-group":"4","action-date":"2017-01-31","origination":"","symbol-position":"L"}],"document_number":"20150099150","document_published_on":"2015-04-09","document_kind":"","document_country":""},{"number":"9,750,124","artifact":"grant","title":"Piezoelectric particle accelerator","filed_on":"2016-03-28","issued_on":"2017-08-29","published_on":"2016-11-17","abstract":"A particle accelerator is provided that includes a piezoelectric accelerator element, where the piezoelectric accelerator element includes a hollow cylindrical shape, and an input transducer, where the input transducer is disposed to provide an input signal to the piezoelectric accelerator element, where the input signal induces a mechanical excitation of the piezoelectric accelerator element, where the mechanical excitation is capable of generating a piezoelectric electric field proximal to an axis of the cylindrical shape, where the piezoelectric accelerator is configured to accelerate a charged particle longitudinally along the axis of the cylindrical shape according to the piezoelectric electric field.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims priority from U.S. Provisional Patent Application 62/142,810 filed Apr. 3, 2015, which is incorporated herein by reference.","STATEMENT OF GOVERNMENT SPONSORED SUPPORT","This invention was made with Government support under contract HR0011515265 awarded by the Defense Advanced Research Projects Agency, and under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","FIELD OF THE INVENTION","The invention relates generally to particle accelerators. More specifically, the invention relates to a piezoelectric accelerator for charged particles.","BACKGROUND OF THE INVENTION","A neutron source typically relies on collisions between accelerated charged particles and a target to provide neutrons. X-ray sources also tend to have this configuration, where the relevant charged particles are electrons. In either case, the required particle accelerator can be the most large, complex and costly part of the neutron source (or X-ray source). Accordingly, it would be an advance in the art to provide a smaller and simpler particle accelerator.","SUMMARY OF THE INVENTION","To address the needs in the art, a particle accelerator is provided that includes a piezoelectric accelerator element, where the piezoelectric accelerator element includes a hollow cylindrical shape, and an input transducer, where the input transducer is disposed to provide an input signal to the piezoelectric accelerator element, where the input signal induces a mechanical excitation of the piezoelectric accelerator element, where the mechanical excitation is capable of generating a piezoelectric electric field proximal to an axis of the cylindrical shape, where the piezoelectric accelerator is configured to accelerate a charged particle longitudinally along the axis of the cylindrical shape according to the piezoelectric electric field.","According to one aspect of the invention, the piezoelectric accelerator element is a material that includes Lithium Niobate, Lithium Tantalate, Quartz, or Lead Zirconate Titanate.","In another aspect of the invention, the piezoelectric accelerator element includes a plurality of the hollow tubes, where the plurality of hollow tubes are configured in an arrangement that includes a monolithic, single hollow tube, a series connection of hollow tubes, a concentric arrangement of nested hollow tubes, or a concentric arrangement of solid rods.","According to one aspect of the invention, the input transducer includes a piezoelectric disk disposed on one end of the piezoelectric accelerator element, where the piezoelectric disk is disposed to impart a displacement onto the piezoelectric tube, where the displacement is capable of exciting a first extensional vibration mode of the piezoelectric accelerator element, where a stress in the material of the piezoelectric accelerator element induces an electric field that is disposed to electrostatically accelerate a charged particle. In one aspect, the displacement includes a CW sinusoidal displacement. In a further aspect, the CW sinusoidal displacement is in a range of 1-20 μm. In another aspect, the induced electric field has a field strength in a range of 0 to 4 MV/m. According to one aspect, the invention includes a target mounted at the end of the piezoelectric accelerator element, where the charged particle is electrostatically accelerated by the electric field until impacting the target mounted at the end of the piezoelectric accelerator element.","According to another aspect of the invention, the charged particle includes protons, deuterium ions, tritium ions, electrons, or charged particles that are heavier than the electrons.","In yet another aspect of the invention, the electric field lines are proximally parallel with the axis of the hollow tube, where an injected beam is accelerated down the hollow tube.","According to one aspect of the invention, the piezoelectric accelerating element is disposed to operate in a bipolar mode or a single polarity mode.","In another aspect of the invention, an end of the piezoelectric accelerator is mass loaded, where the mass loading is disposed to equalize the stress in the hallow tube to increase an effective gradient.","In a further aspect of the invention, a target or an ion source is at ground or high voltage.","DETAILED DESCRIPTION","The current invention provides a piezoelectric accelerator for charged particles. In one embodiment, a combination of an ion source and a deuterated target with the piezoelectric accelerator provides a compact neutron generator system. In a further embodiment, a combination of an electron source and a suitable X-ray target with the piezoelectric accelerator provides a compact X-ray source.","According to one embodiment of the invention, a piezoelectric accelerating structure is provided for use in a portable neutron generator system. This system includes a low voltage AC power source, a piezoelectric vibration source, and an electrostatic piezoelectric accelerator.","In a further embodiment, deuterium ions or electrons (for use in, say, X-ray production) can be accelerated. The final energy of the particles is equal to the potential difference over the length of the piezoelectric column. A gated particle source ensures neutron production only occurs when the potential is above a desired threshold. This approach could also be used to provide a portable, low-cost x-ray source.","The current invention provides cylindrical piezoelectric crystal geometry to accelerate particles. From this, the geometry has ideal alignment of the electric field from the source to the target, where no confining magnetic field is required, and all the injected particles are accelerated.","In a Rosen-type device construction, approximately half of the transformer is at or near ground potential. According to one embodiment of the current invention, through the use of crystal-crystal bonding, a more-compact configuration of a series of tubes, rather than the Rosen-type, is provided, where a separate vibration source is configured to induce the extensional vibration mode in the piezoelectric tube.","There are many applications for the piezoelectric accelerator neutron source embodiment. Thermal neutron radiography is a non-destructive inspection technique, which interrogates materials via interactions with elements such as hydrogen or boron. Further applications include imaging corrosion in aircraft structures, detecting explosive charges, and locating faulty connections in electronics. Fast neutron radiography can inspect light materials within a dense outer casing. Neutron activation analysis can be used to assay nuclear fuel assemblies or detect gold in bore-hole cores. Finally, there is a growing application of thermal neutrons for medical therapy and imaging. The accelerator can be used for active interrogation purposes, since the accelerator will produce up to 7 MeV neutrons that could then produce in-elastically scattered gamma lines from Carbon, Nitrogen, and Oxygen. These lines allow for determining if explosives are in the scanned package or cargo. Additionally, the use of neutrons allow the package or cargo to be scanned for fissile or fertile nuclear materials, and also allow neutron radiography of thick packages or cargos. In a highly portable format, there are multiple applications in the homeland security and counter-terrorism space. For example it could be used in a port for scanning cargo, or it could be used in the field by for military counter-terrorism operations.","In one exemplary embodiment, Lithium Niobate (LN, or LiNbO 3 ) is used as the piezoelectric material for its high mechanical strength, piezoelectric constant, dielectric strength, and mechanical quality factor.","Turning now to the figures, FIG. 1 shows one embodiment of the current invention, where the beam is axially injected down center of single or set of tubes. Here, the beam is accelerated as it passes axially down the center of the tubes, rather than from the high voltage source of a separate device. Here, a multi-function piezoelectric material provides the structural support, insulation, and high-voltage generation for the electrostatic accelerator. This unique geometry and two-element piezoelectric transformer yields a dramatic size, weight, and power improvement over what is known in the art.","In one aspect, the piezoelectric accelerator element includes a plurality of hollow tubes that are configured in an arrangement that can include a monolithic, single hollow tube, a series connection of hollow tubes, a concentric arrangement of nested hollow tubes, and a concentric arrangement of solid rods. In the last case, the geometrical effect of a hollow tube can be approximated by a number of rods evenly placed around the azimuths of a circle with the same diameter as the hollow tube, which is being approximated.","According to one embodiment, the electric field lines are primarily parallel with the axis of the cylinder to ensure the entire injected beam is accelerated down the tube, as shown in FIG. 2 . In the previous art, unless complex field shapers are used, much of the beam is not productively accelerated, reducing system efficiency. As shown in FIG. 2 , the electric field vectors are parallel to the axis of the tube. With the piezoelectric-generated fields present, to represent a pulsed current source, for example a 1 keV, 500 μA deuterium beam is injected into the tube. The beam remains confined due to the small space-charge forces and is accelerated to the end of the tube. Note that all of the beam is accelerated and is mono-energetic, which is a significant advancement over what is known in the art of piezoelectric-based particle acceleration.","Another advantage of the proposed geometry is the low resonant frequency. For a simplified case, constant average stress (T avg ), piezoelectric voltage constant (g 33 ), and frequency constant (N), the maximum induced voltage (V out ) is inversely proportional to the resonant frequency (ƒ),"," V out = T avg ⁢ g 33 ⁢ N 2 ⁢ f . ( 1 ) Also, the mechanical loss (P DM ) in the piezoelectric scales as ƒ 3 as shown in"," P DM = V out 2 ⁢ 4 ⁢ ⁢ π ⁢ ⁢ f 3 g 33 2 ⁢ L 2 ⁢ YQ m . ( 2 ) Equation (2) also illustrates that a high mechanical quality factor (Q m ) increases system efficiency. It is for this reason that LiNbO 3 (Q m ˜10,000) is initially considered instead of the more-common PZT (Q m ˜500). Additional LiNbO 3 advantages include a high dielectric breakdown strength (\u003e10 kV/mm) and a high Curie temperate (\u003e1000° C.). The low vibration frequency is achieved by using long, bonded piezoelectric elements.","There are several effects of driving the tube near the extensional resonance. First, the effective “transformer ratio” near resonance is higher than off-resonance. In other words, to achieve the same output voltage, a larger driving displacement is required when off-resonance. Near resonance, a smaller vibration driver may be used (say, +/−5 μm could be used rather than +/−15 μm). On the other hand, the elastic losses increase near resonance. Hence, an important the metric is output voltage per power dissipation (V/W), where a higher voltage can be obtained for the same amount of power dissipation.","A pressurized gas such as SF6 may be used in a grounded chamber. Vacuum could also be used, however, the piezoelectric and target need to be cooled. Utilization of gas insulation opens up the possibility of using gas jets for targeted cooling.","FIGS. 3A-3E show one embodiment configured to maximize the use of space within the chamber. Equipotential shields reduce the peak electric field on the corona rings. The reduced size incorporates weighed versus electrical loading to account for stray capacitance, where mechanical mounting uses low elastic loss bonds.","Mitigation of many of the issues associated with electrical loading, peak material stress, and power dissipation may be possible by altering the baseline geometry. Instead of a series stack of tubes, alternatively, the tubes can be nested, with the high voltage tube in the innermost diameter, shown in FIG. 4 . In this geometry, for a given total length, the required voltage to be produced by any one piezoelectric decreases. Therefore, the peak stress and power dissipation reduce. The peak field along the length of the cylinder decreases, reducing the probability of flashover. The outermost cylinder “shields” the high-potential inner cylinder from the grounded chamber wall.","Therefore, a much smaller distance from the piezoelectric accelerating column to the chamber wall may be possible. In effect, the piezoelectric cylinders can take the place of the equipotential shields shown in FIG. 4 .","The smallest possible volume would be obtained with a stack diameter equal to the stack length. To simplify fabrication, instead of a large diameter tube, outer tubes 1 and 2 could potentially be replaced by multiple rods located at a constant radius. Note, as shown, most of the beam acceleration occurs between the vibration source and the entrance into tube 3 .","In one exemplary embodiment, 4 MV/m and 1 MV is provided. For this example, a 0.25 m tube generates 1 MV. If five nested tubes each ˜0.25 m long are used, the voltage across each decreases from 1 MV to 200 kV, and the peak stress decreases from 120 MPa to about 24 MPa. The average tube surface field decreases from 4 MV/m to about 0.8 MV/m, and the highest potential at the outside of the stack is about 200 kV. The overall power dissipation also decreases (see eq. (2)).","The design of such a structure is not trivial. First, the tubes must vibrate in-phase to sum potentials. Second, the bonding of the structure is more involved than the baseline design (however, metal-crystal bonds are typically simpler than crystal-crystal bonds) and requires electrically conductive, low loss disks. Third, increased numbers of tubes may increase weight. However, the embodiment is much more compact than the baseline and the LiNbO 3 is able to operate at a much less stressed level.","In yet another aspect of the invention, the center of the tube is in a vacuum state and the piezoelectric forms the vacuum envelope. This enables the outside of the piezoelectric to have substantial cooling by either air or liquid dielectric. Conventional devices typically require the piezoelectric to be completely in vacuum, which limits the amount of cooling that could reach the piezoelectric or target. FIG. 5 shows an air-cooled particle accelerator with a vacuum inner region, according to one embodiment of the invention.","In a further embodiment, the system includes two or more tubes joined together, or a monolithic tube. Depending on the application, it may be desired to have a single, low voltage tube, or extend the device to enable high voltage operation. FIGS. 6A-6B show drawing of a single tube ( 6 A) and multiple serially connected tubes ( 6 B), according to embodiments of the current invention.","FIG. 7A shows a side view and FIG. 7A shows a top view of a nested series connection of rods. These rods approximate the geometry shown in FIG. 4 .","In another embodiment of the invention, a tilted electric field is achieved by changing the crystal rotation of the LN, where the beam does not travel in a straight line down the center of the tubes. Further, several different tubes can be joined end to end, each with successively different rotations. This enables the beam to spiral down the center of the device providing a “tilted field” electrostatic accelerator configuration to approximately double the achievable gradient. This is achieved because electrons that are field-emitted from the accelerator walls are swept away by the tilted field. If the field were parallel to the accelerator walls, the electrons would gain substantial energy and result in a breakdown. In a tilted-field arrangement, only a small amount of energy is gained prior to the electrons being benignly swept away. In the current invention, this feature comes passively. Conversely, in conventional accelerators, such as the cockroft-walton or pelatron, a lot of hardware and complexity is needed to achieve this configuration. FIGS. 8A-8B show serially connected tubes having aligned crystal orientation ( 8 A) and rotated crystal orientations ( 8 B). In one aspect, the crystal-rotated series configuration is capable of establishing a tilted electric field, where an injected beam does not travel in a straight line down the center axis of the hollow tubes, where the hollow tubes are joined end to end having successively different rotations, where the injected beam is induced to spiral along the center of the hollow tube to provide the tilted electric field. In another aspect, a center hollow tube of the concentric hollow tubes is in a vacuum state, where the center hollow tube forms the vacuum envelope, where the outer hollow tubes are capable of being cooled by air or a liquid dielectric.","As described above, a gated ion and/or electron source injects charged particles axially into the accelerator column, which is a stack of piezoelectric hollow cylinders (tubes). A separate piezoelectric vibrating disk imparts a CW sinusoidal displacement (˜1-5 μm) onto the piezoelectric tube. This displacement excites the first extensional vibration mode of the tube. The stress in the material in-turn induces a large electric field (4 MV in one exemplary embodiment). Charged particles are electrostatically accelerated by this electric field until impacting a target mounted at the end of the tube. Because the frequency is low, the accelerating force is electrostatic.","The sinusoidal displacement induces an electric field that oscillates from positive to negative 4 MV. Because the frequency is low, the accelerating force is electrostatic. Deuterium ions or electrons (for use in, say, X-ray production) can be accelerated. The final energy of the particles is equal to the potential difference over the length of the piezoelectric column. A gated particle source ensures neutron production only occurs when the potential is above a desired threshold, as shown in FIGS. 9A-9B .","FIGS. 9A-9B show the electrostatic acceleration invention, where ( 9 A) shows a gated ion or electron source injects particles into the acceleration column and the repetition rate is the resonant frequency of the piezoelectric accelerator%3b ( 9 B) shows the induced electric field in the piezoelectric tube accelerates deuterium ions in the center of the column, according to one embodiment of the invention.","In a further aspect of the invention, the electric field gradient achievable with a piezoelectric, that is (output voltage)/(effective device length), is proportional to the maximum strength of the piezoelectric times the effective piezoelectric constant. If at a given strength and piezoelectric constant, the invention operates in a bipolar mode, for example as a sinusoid oscillating between plus and minus 100 kV, then the device can also operate in a single polarity mode at twice the voltage, for example 0 to 200 kV. This takes advantage of the fact that a DC bias can be placed on the crystal because the electrical conductivity is extremely low in LN, for example. The DC bias can be applied by injecting excess positive or negative charge into the device for a period of time until the desired bias is achieved.","Piezoelectric transformers are traditionally very high output impedance devices%3b they operate with low output current. Scaling the Rosen-type transformer to higher current means changing the output frequency, and changing the gradient of the device. According to a further aspect of the current invention, changing the cross-sectional area of the tube results in a directly proportional change in the achievable output current. The gradient can remain high, where moving to a very high output current is achieved by increasing the diameter of the tube.","In a further embodiment of the invention, instead of a series stack of tubes, the tubes are nested, with the high voltage tube in the innermost diameter. In this geometry, for a given total length, the required voltage to be produced by any one of the piezoelectric devices decreases. Therefore, the peak stress and power dissipation are reduced. The peak field along the length of the cylinder decreases, reducing the probability of flashover. The outermost cylinder “shields” the high-potential inner cylinder from the grounded chamber wall. Therefore, a much smaller distance from the piezoelectric accelerating column to the chamber wall is made possible.","In a further embodiment of the invention, corona rings reduce the peak electric field in high voltage devices in order to reduce the volume needed to hold off high voltage. In one aspect of the invention, toroids are added in-between tubes to reduce the peak electric field at those junctions, as well as the peak electric field from the tube to the grounded chamber wall. In conventional piezoelectric geometries, these rings or structures may not be added as simply because they would spoil the primary mode of vibration. In the current invention, an extra mode of vibration is not introduced because corona rings are placed close to the center of the tube, and the mass of the corona ring is evenly distributed around the circumference of the device.","According to another aspect, the invention operates in a first length extensional mode, rather than second or higher, which is the highest possible gradient. With respect to Rosen-type and other transformers, they typically operate in modes higher than the first. If they are operated in the second mode, half of the device will be at or very near ground potential. This wastes about half of the device. In tube geometry of the current invention, only a small portion of the device is at ground. Thus, the achievable gradient over conventional approaches is approximately doubled.","In a further embodiment of the invention, the end of the device is mass loaded to even out the stress in the tube to increase the effective gradient.","According to another embodiment of the invention, the target or the ion source is at ground or the high voltage end of the tube.","Other new aspects provided by the invention include the ability to have separate driver rather than a monolithic construction. The crystal rotation can be optimized. High-Q bonding is enabled. A flexible pulse structure width is enabled. And the invention is self-neutralizing.","The present invention has now been described in accordance with several exemplary embodiments, which are intended to be illustrative in all aspects, rather than restrictive. Thus, the present invention is capable of many variations in detailed implementation, which may be derived from the description contained herein by a person of ordinary skill in the art. All such variations are considered to be within the scope and spirit of the present invention as defined by the following claims and their legal equivalents."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 shows a beam axially injected down center of a tube, where the beam is accelerated as it passes axially down the center of the tube, according to one embodiment of the invention.","FIG. 2 shows a multi-physics COMSOL simulation of a piezoelectric crystal tube accelerating a deuterium beam, where represented are both the equipotential surfaces as well as the kinetic energy of the injected beam, according to one embodiment of the invention.","FIGS. 3A-3E show Maxwell simulation of corona rings and electrostatic shields used to shape the electric fields in the chamber, where ( 3 A) shows a simulated structure, ( 3 B) shows the electric field magnitude with shield, ( 3 C) shows the electric potential lines with shield, ( 3 D) shows electric field magnitude without shield, ( 3 E) shows the equipotential lines without shield, and shown is a 2 MeV (0.5 m long) accelerator, according to one embodiment of the invention.","FIG. 4 shows a schematic drawing of alternative geometry using nested tubes having a vibrating source and bonding disks supporting the tubes, according to one embodiment of the invention.","FIG. 5 shows an air-cooled particle accelerator with a vacuum inner region, according to one embodiment of the invention.","FIGS. 6A-6B show drawing of a single tube ( 6 A) and multiple serially connected tubes ( 6 B), according to embodiments of the current invention.","FIGS. 7A-7B shows a side view ( 7 A) and top view ( 7 B) of a nested series connection of rods. These rods approximate the geometry shown in FIG. 4 .","FIGS. 8A-8B show serially connected tubes having aligned crystal orientation ( 8 A) and rotated crystal orientations ( 8 B), according to embodiments of the invention.","FIGS. 9A-9B show the electrostatic acceleration invention, where ( 9 A) shows a gated ion or electron source injects particles into the acceleration column and the repetition rate is the resonant frequency of the piezoelectric accelerator%3b ( 9 B) shows the induced electric field in the piezoelectric tube accelerates deuterium ions in the center of the column, according to one embodiment of the invention."]},"government_interest":"STATEMENT OF GOVERNMENT SPONSORED SUPPORT This invention was made with Government support under contract HR0011515265 awarded by the Defense Advanced Research Projects Agency, and under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in the invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/9,750,124","html":"https://www.labpartnering.org/patents/9,750,124","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=9,750,124"},"labs":[{"uuid":"e136cac4-b384-4e12-abc9-6768254c2d10","name":"Savannah River National Laboratory","tto_url":"http://srnl.doe.gov/tech_transfer/tech_transfer.htm","contact_us_email":"partnerships@srnl.doe.gov","avatar":"https://www.labpartnering.org/files/labs/20","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/e136cac4-b384-4e12-abc9-6768254c2d10"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Mark A. Kemp","location":"Belmont, CA, US"},{"name":"Erik N. Jongewaard","location":"Sunnyvale, CA, US"},{"name":"Andrew A. Haase","location":"Belmont, CA, US"},{"name":"Matthew Franzi","location":"Burlingame, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A particle accelerator comprising:a) a piezoelectric accelerator element, wherein said piezoelectric accelerator element comprises a hollow cylindrical shape%3b andb) an input piezoelectric transducer, wherein said input piezoelectric transducer is disposed concentric to a first end of said hollow cylindrical piezoelectric accelerator element and is configured to provide an input signal to said hollow cylindrical piezoelectric accelerator element first end, wherein said input signal at said hollow cylindrical piezoelectric accelerator element first end induces a mechanical excitation along said hollow cylindrical piezoelectric accelerator element, wherein said mechanical excitation is capable of generating a piezoelectric electric field proximal to an axis of said cylindrical shape, wherein said piezoelectric accelerator is configured to accelerate a charged particle that is input to said first end of said hollow cylindrical piezoelectric accelerator element longitudinally along said axis of said cylindrical shape according to said piezoelectric electric field."},{"idx":"00002","text":"The particle accelerator according to claim 1, wherein said piezoelectric accelerator element comprises a material selected from the group consisting of Lithium Niobate, Lithium Tantalate, Quartz, and Lead Zirconate Titanate."},{"idx":"00003","text":"The particle accelerator according to claim 1, wherein said piezoelectric accelerator element comprises a plurality of said hollow tubes, wherein said plurality of hollow tubes are configured in an arrangement selected from the group consisting of a monolithic, single hollow tube, a series connection of hollow tubes, a concentric arrangement of nested hollow tubes, and a concentric arrangement of solid rods."},{"idx":"00004","text":"The particle accelerator according to claim 3, wherein said crystal-rotated series configuration is capable of establishing a tilted electric field, wherein an injected beam does not travel in a straight line down said center axis of said hollow tubes, wherein said hollow tubes are joined end to end having successively different rotations, wherein said injected beam is induced to spiral along said center of said hollow tube to provide said tilted electric field."},{"idx":"00005","text":"The particle accelerator according to claim 3, wherein a center hollow tube of said concentric hollow tubes is in a vacuum state, wherein said center hollow tube forms the vacuum envelope, wherein outer said hollow tubes are capable of being cooled by air or a liquid dielectric."},{"idx":"00006","text":"The particle accelerator according to claim 1, wherein said input piezoelectric transducer comprises a piezoelectric transducer disk disposed on one end of said piezoelectric accelerator element, wherein said piezoelectric transducer disk is disposed to impart a displacement onto said piezoelectric tube, wherein said displacement is capable of exciting a first extensional vibration mode of said piezoelectric accelerator element, wherein a stress in the material of said piezoelectric accelerator element induces an electric field that is disposed to electrostatically accelerated a charged particle."},{"idx":"00007","text":"The particle accelerator according to claim 6, wherein said displacement comprises a CW sinusoidal displacement."},{"idx":"00008","text":"The particle accelerator according to claim 7, wherein said CW sinusoidal displacement is in a range of 1-20 μm."},{"idx":"00009","text":"The particle accelerator according to claim 6, wherein said induced electric field has a field strength in a range of 0 to 4 MV/m."},{"idx":"00010","text":"The particle accelerator according to claim 6 further comprises a target mounted at the end of said piezoelectric accelerator element, wherein said charged particle is electrostatically accelerated by said electric field until impacting said target mounted at the end of said piezoelectric accelerator element."},{"idx":"00011","text":"The particle accelerator according to claim 1, wherein said charged particle is selected from the group consisting of protons, deuterium ions, tritium ions, electrons, and charged particles that are heavier than said electrons."},{"idx":"00012","text":"The particle accelerator according to claim 1, wherein electric field lines are proximally parallel with said axis of said hollow tube, wherein an injected beam is accelerated down said hollow tube."},{"idx":"00013","text":"The particle accelerator according to claim 1, wherein said piezoelectric accelerating element is disposed to operate in a bipolar mode or a single polarity mode."},{"idx":"00014","text":"The particle accelerator according to claim 1, wherein an end of said piezoelectric accelerator is mass loaded, wherein said mass loading is disposed to equalize the stress in said hallow tube to increase an effective gradient."},{"idx":"00015","text":"The particle accelerator according to claim 1, wherein a target or an ion source is at ground or high voltage."}],"cpc":{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"00","main-group":"15","action-date":"2017-08-29","origination":"","symbol-position":"F","further":["05","","H","B","US","H","","H","00","15","2017-08-29","","F"]},"ipc":[{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"00","main-group":"15","action-date":"2017-08-29","origination":"","symbol-position":"F"}],"document_number":"20160338186","document_published_on":"2016-11-17","document_kind":"","document_country":""},{"number":"8,853,531","artifact":"grant","title":"Photon enhanced thermionic emission","filed_on":"2009-10-16","issued_on":"2014-10-07","published_on":"2010-06-10","abstract":"Photon Enhanced Thermionic Emission (PETE) is exploited to provide improved efficiency for radiant energy conversion. A hot (greater than 200.degree. C.) semiconductor cathode is illuminated such that it emits electrons. Because the cathode is hot, significantly more electrons are emitted than would be emitted from a room temperature (or colder) cathode under the same illumination conditions. As a result of this increased electron emission, the energy conversion efficiency can be significantly increased relative to a conventional photovoltaic device. In PETE, the cathode electrons can be (and typically are) thermalized with respect to the cathode. As a result, PETE does not rely on emission of non-thermalized electrons, and is significantly easier to implement than hot-carrier emission approaches.","description":{"text":["CROSS REFERENCE TO RELATED APPLICATIONS","This application claims the benefit of U.S. provisional patent application 61/196,268, filed on Oct. 16, 2008, entitled “Thermally Enhanced Photoemission for Energy Harvesting”, and hereby incorporated by reference in its entirety.","GOVERNMENT SPONSORSHIP","This invention was made with Government support under contract number DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","FIELD OF THE INVENTION","This invention relates to harvesting of radiant energy, such as solar energy.","BACKGROUND","Conversion of sunlight into electricity usually takes one of two forms: the “quantum” approach using the large energy of solar photons in photovoltaic (PV) cells, or the “thermal” approach using solar radiation as the heat source in a classical heat engine. Quantum processes boast high theoretical efficiencies as the effective photon “temperature” is T solar ˜5800° C., yet suffer in practice from a limited spectral energy collection window and thermalization losses. Thermal processes take advantage of energy throughout the entire spectrum, but efficiency is curbed by practical operating temperatures. Combinations of the two are predicted to have efficiencies \u003e60%, yet fail in practice because PV cells rapidly lose efficiency at elevated temperatures, while heat engines rapidly lose efficiency at low temperatures. As a result, these two approaches remain disjointed.","Hot-carrier solar energy converters provide a helpful example of the difficulties typically encountered in combining quantum and thermal conversion approaches. In hot-carrier solar energy converters, efficiency is improved by having photo-generated electrons be emitted from a cathode before thermalization of the generated electrons with respect to the cathode can occur. If this can be accomplished, efficiency can be significantly increased, because a significant source of loss (i.e., thermalization in the cathode) is thereby mitigated. However, typical thermalization time scales in condensed matter are on the order of picoseconds, so it is extremely difficult to provide high-efficiency emission of non-thermalized (i.e., hot) electrons.","Accordingly, it would be an advance in the art to provide combined thermal and quantum conversion that can more readily be realized in practice.","SUMMARY","In the present approach, a physical effect referred to as Photon Enhanced Thermionic Emission (PETE) is exploited to provide improved efficiency for energy conversion by harvesting both thermal and photon energy via an electron emission process. Briefly, a hot (greater than 200° C.) semiconductor cathode is illuminated such that it emits electrons to a collector anode. Because the cathode is hot, significantly more electrons are emitted than would be emitted from a room temperature (or colder) cathode under the same illumination conditions, or by thermionic emission without illumination. In PETE, the cathode electrons can be (and typically are) thermalized with respect to the cathode. As a result, PETE does not rely on emission of “hot” non-thermalized electrons, and is significantly easier to implement than hot-carrier emission approaches.","DETAILED DESCRIPTION","The present approach to solar power conversion is referred to as Photon Enhanced Thermionic Emission (PETE), because it uses photon excitation in conjunction with thermal processes to generate electricity. Calculations here show that the use of both heat and photon energy from the solar spectrum allows the PETE process to exceed the Shockley-Queisser limit on single-junction photovoltaics (W. Shockley and H. J. Queisser, J. App. Phys. 32, 510 (1961)), and simulated nanomaterials show even higher possible performance. Unlike PV cells, PETE operates at the temperatures compatible with solar thermal conversion systems (300-800° C.), enabling an efficient two-stage cycle with theoretical efficiencies \u003e50%, providing a novel approach to efficient large scale solar power conversion.","In a conventional PV cell, incident above-band gap photons excite electrons into the conduction band and leave holes in the valence band, which are then collected by electrodes. The major losses are due to ineffective use of the solar spectrum: photons with less energy than the band gap are not absorbed, which is known as absorption loss (η abs ), while electrons which absorb photons with energies greater than the band gap release their extra energy in the form of heat, which is known as thermalization loss (η thermalization ) In silicon solar cells, these two processes account for approximately 50% of the incident solar energy, which is the majority of the total energy loss. Unfortunately, photovoltaic cells cannot reclaim this thermal energy since waste heat harvesting requires elevated operating temperature, and heating a conventional photovoltaic cell is highly detrimental due to increased dark current, resulting in an approximately linear decrease in open circuit potential with temperature.","PETE offers a route to generating photocurrent which recycles this ‘waste heat’. PETE is based in part on thermionic emission, where a fraction of Boltzmann-distributed electrons have sufficient thermal energy to overcome the material%27s work function and emit into vacuum. This current is governed by the Richardson-Dushman equation: J=A*T 2 e −φ e /kT where A* is the material-specific Richardson constant, and φ e is the work function. Traditional thermionic conversion is plagued by low operating voltages, high required temperatures (\u003e1200° C.), and space-charge effects largely due to the high currents necessary for power conversion. However, when photons are absorbed in a semiconductor, electrons are excited into the conduction band and establish an electron ‘quasi-Fermi level’ E F,eff which is considerably higher than the ‘dark’ Fermi level, E F,i .","FIG. 1 shows relevant band structure parameters. A cathode 104 and anode 102 have respective work functions φ C and φ A with respect to the vacuum level E vac . Cathode 104 is a semiconductor having a valence band E V and conduction band E C separated by an energy gap E g . The electron affinity χ is the energy separation between the vacuum level and cathode conduction band. When cathode 104 is not illuminated, a conduction band electron distribution 114 is present, having a concentration dependent on cathode temperature and cathode device parameters. As is well known in the art, this concentration can be expressed in terms of the above-referenced dark Fermi level, E F,i .","When cathode 104 is illuminated, photons (one of which is shown as 106 ) can be absorbed to generate electron-hole pairs (here the hole of a pair is shown as 108 and the corresponding electron is shown as 110 ). Generated electrons (e.g., electron 110 ) are assumed to thermalize within the cathode conduction band, thereby giving rise to a conduction band electron distribution 112 that has greater concentration than the ‘dark’ distribution 114 . As is well known in the art, this concentration can be expressed in terms of the above-referenced electron quasi-Fermi level, E F,eff .","As seen in FIG. 1 , this boosts the entire electron energy distribution by E F,eff −E F =kT(n/n eq ), where n is the total conduction band electron density including photocarriers, and n eq is the equilibrium carrier concentration in the absence of illumination. A greater number of thermally-distributed electrons in the conduction band are then able to surmount the electron affinity barrier χ, with higher potential energies and lower temperatures than in thermionic emission. This PETE current can still be described by the Richardson-Dushman equation by redefining the work function relative to E F,eff . Each emitted electron carries both the energy of the photon that excited it into the conduction band and the thermal energy needed to overcome χ, thus harvesting both types of energy. One such emitted electron is shown as 116 on FIG. 1 . Emitted electrons are received by anode 102 .","FIG. 2 shows the effect of illumination on thermal electron emission from semiconductors. This example assumes χ=0.6 eV, E g =1.1 eV and 100× solar concentration. Total current is shown with a solid line, thermionic current is shown with a dashed line, and photocurrent is shown with a dash-dotted line. At low temperatures, thermalized carriers cannot overcome χ and recombine instead. Thermionic emission remains negligible in this example until ˜1000° C., when electrons can overcome the material work function. However, with 100× solar illumination substantial electron emission can occur at 350° C., fully 1000° C. lower than the equivalent thermionic current. The magnitude of this current depends directly upon the number of absorbed photons, as can be seen by rewriting the PETE current as:"," J PETE = en 4 ⁢ 〈 v 〉 ⁢ ⅇ - χ / kT where v is the average thermal velocity. Illumination is clearly seen to increase current through the conduction band concentration n, while thermal excitation determines the rate electrons can overcome χ. Significantly, this process does not require non-equilibrium ‘hot’ electrons, and assumes complete thermalization. On FIG. 2 , it is helpful to regard temperature range 202 as pertaining to a photoemission regime, where the thermal contribution is negligible, and temperature range 206 as pertaining to a thermionic regime, where the thermal dark current is non-negligible. The intermediate temperature regime 204 pertains to photon enhanced thermionic emission. For fixed cathode parameters, power output decreases as temperature increases, due to the increase of cathode Fermi level as temperature increases.","Illumination also increases the output voltage at a given temperature. The ‘flat band’ voltage generated by the PETE process with no field between cathode and anode is given by: V fb =φ C −φ A =( E g −E F +χ)φ A , where φ C is the cathode work function, and φ A is the anode work functions, which are both assumed to be 0.9 eV. Here the large per-quanta photon energy directly boosts the output voltage by E F,eff −E F which is often a sizeable fraction of the band gap (on the order of one volt), while χ represents a ‘thermal voltage’. The combination of the two provides a significant boost over the voltage of a thermionic process. However, as in photovoltaic cells, there is a tradeoff between higher voltages (large E g ), and lower photon absorption, requiring parameter optimization.","The theoretical power conversion efficiencies for a number of different material properties, solar concentrations, and operating temperatures are shown in FIGS. 3 a - c . The steady-state concentration electron n was solved self-consistently accounting for PETE, Auger, and radiative recombination processes, and the power efficiency was calculated as η=IV/P solar . Materials parameters were chosen to be as realistic as possible based on p-type (10 18 cm −3 ) Si, and calculations assume full thermalization of one carrier for each photon hv\u003eE g , with all sub-bandgap photons absorbed in the cathode as heat.","Maximum efficiencies occurred for E g =1.1−1.4 eV, topping 30% for 100× concentration and 42% for 3000× concentration. Impressively, PETE exceeds the Shockley-Queisser limit for a single junction cell for concentrations above 1000× even including realistic recombination losses, as exemplified by a direct comparison of PETE and ideal PV at 3000× (dashed line). This is due to PETE harvesting heat as described above. Higher efficiencies are possible at higher temperatures ( FIG. 3 b ) by enabling electrons to overcome a larger χ and thus generate higher output voltages. Efficiencies above 30% are possible even at 550° C., which would match the input temperature for many commercial steam systems.","Since PETE current is determined by thermionic emission, the current-voltage characteristics are significantly different from those of photovoltaic cells ( FIG. 3 c ). The maximal power point occurs at an output voltage slightly less than V fb , which increases with E g or χ, as shown here. For V\u003eV fb the current decreases exponentially, which reflects the distribution of emitted electron energies. This rapid decay leads to very large fill-factors (FF), often exceeding 90%.","Further insight into the results of FIGS. 3 a - c are provided by FIGS. 4 a - b . On FIG. 4 a , the solid line shows the χ at which device efficiency is maximized, and the dashed line shows the maximum χ at which unity emission efficiency is obtained (neglecting blackbody losses and reverse currents). A noteworthy feature of these results is that the χ at which device efficiency is maximized can be significantly above the maximum χ for unity emission efficiency (i.e., left half of FIG. 4 a ). The reason for this is that the output voltage at unity yield can be very low. In such cases, it is beneficial to reduce yield (i.e., current) in exchange for higher output voltage. FIG. 4 b shows the yield for the optimized devices of FIG. 3 a . It is apparent that optimization of low bandgap devices leads to reduced yield, while the yield for bandgaps above 1.2 eV is about 95%.","Nanostructuring can dramatically increase PETE%27s performance by decoupling photon absorption and electron emission lengths. Forests of nanowires or nanotubes have achieved near unity absorption over a wide spectral range through a combination of low effective index and scattering processes, effectively eliminating the requirement of thick films for maximal light absorption. Thin nanowires can thus be used to ensure each photoexcited electron is within the electron escape length of the material surface. Enhanced emission efficiency also results from an increased surface collision rate and lifetime. Nanowire simulations show the surface collision rate increases as 1/D, where D is nanowire diameter, as the electron is always within one diameter from a wall. ( FIG. 5 a ) The nanowire geometry is further beneficial as the electron may escape from all directions perpendicular to the axis, increasing surface collision rate by a factor of four over thin films. This effect may also be advantageous for traditional photoemission cathodes. On FIG. 5 a , the solid line relates to thin films, while the dashed line relates to nanowires. Nanowire surface collision rates are seen to significantly exceed thin film collision rates.","Increasing carrier lifetime also enhances conversion efficiency by increasing the number of surface collisions and therefore chances for electron emission. FIG. 5 b shows the required carrier lifetime for 95% emission efficiency from a 40 nm diameter nanowire as a function of electron affinity and temperature. These lifetimes are feasible with suitable surface passivation, as recent published photoluminescence experiments on silicon nanowires have demonstrated lifetimes of over 50 μs for 1-4 eV photo-illumination. For 50 nm diameter nanowires, this lifetime corresponds to ˜10 8 surface collisions (one every 500 fs) prior to recombination, such that even a low per-collision escape probability can yield extremely high quantum efficiencies. Due to the logarithmic dependence of performance on lifetime, even nanosecond lifetimes are sufficient to obtain high efficiencies.","An important advantage of PETE over PV cells is operation at high temperatures so that unused heat energy can be used to power solar thermal generators, such as steam turbines or Stirling engines. A diagram of the energy flow in a PETE/solar thermal tandem architecture is shown in FIG. 6 a. ","In this example, energy source 608 provides radiant energy 610 which is incident on cathode 602 . Electron current 614 emitted from cathode 602 is received at anode 604 . As a result, PETE device 620 including cathode 602 and anode 604 is capable of providing electrical power to an external load 606 . Also shown on FIG. 6 a are reverse electron current 615 and radiant blackbody emission 612 from anode and cathode. Loss due to these processes is included in the preceding calculated results. Preferably, the temperature of the cathode is passively determined by heat transfer to and from the cathode. In this situation, no separate heating and/or temperature control for the cathode is needed, and the combination of incident radiation and suitable heat engines and/or heat sinking can keep the cathode and anode at their intended operating temperatures.","Electrons and photons emitted from the PETE cathode deliver heat energy to the anode. A thermal engine 618 can remove this excess heat 616 from the anode and use it to generate additional electrical power. Tandem PETE/solar thermal efficiency for a concentration of 1000× suns is displayed in FIG. 6 b , assuming an anode temperature of 285° C. and a thermal-to-electricity efficiency of 31.5%, based on Rankine steam systems. The solid line on FIG. 6 b is for PETE alone, and the dashed line is for PETE+heat engine. Total conversion efficiencies exceeding 52% are possible, constituting more than a 65% improvement over a thermal cycle alone. This dramatic improvement is possible because the PETE process harvests a sizable fraction of its energy from quantized high-energy photons, effectively capitalizing on the 5800° C. to T cathode temperature differential which is normally discarded. Although this example shows a heat engine operating at the anode, it is possible to harvest heat from the cathode and/or anode with heat engines.","By utilizing both thermal and photon energy, PETE can potentially achieve device efficiencies which exceed the fundamental limits on single junction cells and rival those of complex multi-junction cells, the best of which are around 40% efficient. Even a PETE module with modest 20% efficiency in tandem with a 30% efficient thermal engine could achieve total system efficiencies of 44%, which would exceed the current records for either single or multi-junction cells. PETE devices are naturally synergistic with solar thermal convertors, and could be implemented as a modular attachment to existing infrastructure. Further efficiency improvements may be possible through new materials, nanostructures, and processes such as plasmonics that can increase light absorption, electron concentration, and emission probability.","Design principles that have been identified to date include the following. The operating temperature of the cathode is greater than 200° C. and is preferably between 300° C. and 1000° C. The cathode band gap, at the operating temperature, is preferably between 1 eV and 2 eV. Any semiconductor having a bandgap in this range can be employed as the cathode material. Suitable cathode materials include but are not limited to diamond, Si, SiC, and GaAs. The cathode electron affinity, at the operating temperature, is preferably between 0 eV and 1 eV. Solar concentration is preferably greater than 100 suns. A parallel plate arrangement of cathode and anode is a preferred device geometry. The anode work function is preferably less than 2.5 eV and is more preferably less than 2 eV, and still more preferably is as low as possible.","FIG. 7 a shows an example of a cathode structure having a surface coating. Here coating 704 is disposed on cathode 702 . Such coatings are helpful for setting the cathode electron affinity. Suitable materials for coating 704 include Ba, Sr, Cs, their respective oxides, and any alloy or mixture thereof. Diamond and diamond-like thin films can also be suitable cathode coatings. The cathode and any cathode surface coating that may be present are preferably designed and selected to withstand high temperature operation (i.e., temperature greater than 200° C.).","FIG. 7 b shows an example of a anode structure having a surface coating. In this example, a transparent conductive oxide, such as fluorinated indium-tin-oxide (FTO) 706 is covered with metallic or metal oxide surface films to lower the work function. For example, these films can be a thin film of tungsten 708 with an over layer of BaO 710 . Diamond and diamond-like thin films can also be suitable anode coatings. Phosphorous doped diamond has the lowest reported work function, and is accordingly a preferred anode coating. The anode and any anode surface coating that may be present are preferably designed and selected to withstand high temperature operation (i.e., temperature greater than 200° C.). Any other anode materials/structures capable of withstanding high temperature and providing a low work function can also be employed.","FIG. 8 shows an example of an optical concentrator arrangement. In this example, incident radiation is focused and/or concentrated by concentrator 806 to increase the incident intensity on cathode 802 . Electrons emitted from cathode 802 are received at anode 804 , and can provide electrical power as described above. Suitable optical concentrators are well known in the art.","FIGS. 9 a - c show examples of nano-structured cathodes. Nano-structuring of the cathode is helpful for reducing the photon absorption length in the cathode, compared to a corresponding unstructured thin film cathode of the same cathode material. Such reduction of the absorption length is helpful for improving device efficiency, because it reduces recombination loss. Any nano-structuring geometry that provides a reduced photon absorption length can be employed. Some specific examples are shown on FIGS. 9 a - c. ","In these examples, incident radiation is shown as 910 , a transparent mechanical substrate is shown as 902 , and a transparent and electrically conductive layer (e.g., indium tin oxide (ITO)) is shown as 908 . On FIG. 9 a , the cathode material is disposed as a forest of nano-wires or nano-tubes 904 . On FIG. 9 b , the cathode material is disposed as a textured nano-layer 906 having nano-scale lateral features (i.e., less than 500 nm feature size) determined by corresponding features of layer 908 . The features of layer 908 can be any shapes, such as cones or pyramids. On FIG. 9 c , the cathode material is disposed as nano-cones or nano-pyramids 912 of emitter material. In this example, the islands of emitter material have less than 500 nm feature size. Alternatively, any other nano-scale shape for the islands of emitter material can be employed.","FIG. 10 shows an example of a cathode including a surface plasmon concentrator. In this example, incident radiation 1004 passes through substrate 1002 and induces electron emission from cathode 1008 . A metallic plasmon concentrator 1006 is disposed such that enhanced fields associated with plasmon resonances and/or surface plasmon resonances of concentrator 1006 extend into cathode 1008 . Design principles of suitable metallic structures to act as plasmon concentrators are known in the art. In some embodiments, cathode emitter material islands are disposed in alignment with plasmon resonances. For example, cathode nano-cones or nano-pyramids as in FIG. 9 c can be disposed at locations in the device where plasmon-resonance enhanced fields are present."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","FIG. 1 shows a band diagram relating to operation of embodiments of the invention.","FIG. 2 show an example of electron emission from a cathode illuminated with 100× solar radiation as a function of cathode temperature.","FIG. 3 a shows an example of calculated PETE efficiency as a function of cathode band gap, where cathode electron affinity and temperature are optimized to maximize efficiency.","FIG. 3 b shows examples of calculated PETE efficiency as a function of cathode temperature for several values of electron affinity.","FIG. 3 c shows J-V curves corresponding to the examples of FIG. 3 b.","FIG. 4 a shows electron affinities that maximize the efficiencies of the example of FIG. 3 a . The maximum electron affinity that provide unity emission (ignoring blackbody losses and reverse currents) is also shown.","FIG. 4 b shows the quantum yield corresponding to the efficiency-maximizing affinities of FIG. 4 a.","FIG. 5 a shows calculated surface collision rates vs. thickness for thin film and nanowire geometries.","FIG. 5 b shows calculated electron lifetimes needed for 95% emission efficiency as a function of temperature for various electron affinities.","FIG. 6 a shows an exemplary embodiment of the invention, along with energy and electron flows.","FIG. 6 b shows calculated efficiencies for an exemplary PETE device and for this PETE device in combination with a heat engine for recovering heat from the PETE device anode.","FIGS. 7 a - b show examples of cathode and anode structures having surface coatings.","FIG. 8 shows an example of a concentrator arrangement.","FIGS. 9 a - c show examples of nano-structured cathodes.","FIG. 10 shows an example of a cathode including a surface plasmon concentrator."]},"government_interest":"GOVERNMENT SPONSORSHIP This invention was made with Government support under contract number DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/8,853,531","html":"https://www.labpartnering.org/patents/8,853,531","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=8,853,531"},"labs":[{"uuid":"821ee9f1-0f89-4a1e-b067-20a1e8ccf782","name":"Los Alamos National Laboratory","tto_url":"http://www.lanl.gov/feynmancenter","contact_us_email":"astern@lanl.gov","avatar":"https://www.labpartnering.org/files/labs/21","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/821ee9f1-0f89-4a1e-b067-20a1e8ccf782"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Jared Schwede","location":"Menlo Park, CA, US"},{"name":"Nicholas Melosh","location":"Menlo Park, CA, US"},{"name":"Zhixun Shen","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"Apparatus for radiant energy conversion, the apparatus comprising:a semiconductor photocathode having a positive electron affinity surface%3b andan anode separated from said photocathode%3bwherein absorption of incident radiation in said photocathode during operation of said apparatus gives rise to a distribution of electrons in a conduction band of said cathode%3bwherein some or all electrons in said distribution are thermalized with respect to a temperature of said photocathode, wherein said temperature of said photocathode is greater than 200° C. during operation of said apparatus%3bwherein some or all electrons in said distribution are emitted from said photocathode and received by said anode%3bwherein a potential difference is established between said photocathode and said anode by electrons received at said anode to provide output electrical power%3bwherein said photocathode comprises a surface coating to determine said positive electron affinity%3bwherein an electron affinity of said photocathode is between 0 eV and 1 eV, and wherein said photocathode can operate at an operating temperature greater than 200° C."},{"idx":"00002","text":"The apparatus of claim 1, wherein said photocathode is nano-structured such that a photon absorption length in said photocathode is less than a photon absorption length in a corresponding thin film cathode."},{"idx":"00003","text":"The apparatus of claim 2, wherein said nano-structured photocathode comprises a forest of nano-wires or nano-tubes."},{"idx":"00004","text":"The apparatus of claim 2, wherein said nano-structured photocathode comprises a nano-layer of said semiconductor disposed on an electrically conductive and nano-textured substrate."},{"idx":"00005","text":"The apparatus of claim 2, wherein said nano-structured photocathode comprises nano-islands of said semiconductor."},{"idx":"00006","text":"The apparatus of claim 1, wherein a conversion efficiency from said incident radiation to said output electrical power is greater than 10%."},{"idx":"00007","text":"The apparatus of claim 1, further comprising a heat engine to generate work from heat generated at said anode and/or cathode."},{"idx":"00008","text":"The apparatus of claim 1, wherein said incident radiation comprises sunlight."},{"idx":"00009","text":"The apparatus of claim 1, further comprising an optical concentrator to increase an intensity of said incident radiation at said photocathode."},{"idx":"00010","text":"The apparatus of claim 1, further comprising a plasmon resonance concentrator to increase an intensity of said incident radiation at said photocathode."},{"idx":"00011","text":"The apparatus of claim 1, wherein said temperature of said photocathode is passively determined."},{"idx":"00012","text":"The apparatus of claim 1, wherein a work function of said anode is less than 2.5 eV and wherein said anode can operate at an operating temperature greater than 200° C."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"06","main-group":"40","action-date":"2014-10-07","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","J","06","40","2014-10-07","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"L","subgroup":"00","main-group":"31","action-date":"2014-10-07","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"06","main-group":"40","action-date":"2014-10-07","origination":"","symbol-position":"L"},{"class":"02","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"S","subgroup":"00","main-group":"10","action-date":"2014-10-07","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"00","main-group":"45","action-date":"2014-10-07","origination":"","symbol-position":"L"}],"document_number":"20100139771","document_published_on":"2010-06-10","document_kind":"","document_country":""},{"number":"8,410,729","artifact":"grant","title":"Special purpose modes in photonic band gap fibers","filed_on":"2010-08-02","issued_on":"2013-04-02","published_on":"2011-12-08","abstract":"Photonic band gap fibers are described having one or more defects suitable for the acceleration of electrons or other charged particles. Methods and devices are described for exciting special purpose modes in the defects including laser coupling schemes as well as various fiber designs and components for facilitating excitation of desired modes. Results are also presented showing effects on modes due to modes in other defects within the fiber and due to the proximity of defects to the fiber edge. Techniques and devices are described for controlling electrons within the defect(s). Various applications for electrons or other energetic charged particles produced by such photonic band gap fibers are also described.","description":{"text":["CROSS REFERENCE TO RELATED APPLICATIONS","This is a utility patent application filed pursuant to 35 U.S.C. §111 (a), and claims priority pursuant to 35 U.S.C. §119 from provisional patent application 61/230,292 filed Jul. 31, 2009. The entire contents of the aforesaid provisional patent application is incorporated herein by reference for all purposes.","STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT","This invention was made with Government support under Contract No. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","BACKGROUND OF THE INVENTION","1. Field of the Invention","This invention relates to the general field of photonic band gap (PBG) fibers, more particularly to the excitation, propagation, control and use of various electromagnetic modes in PBG fibers and to structures of PBG fibers facilitating same. Most particularly, some embodiments relate to the acceleration and control of electrons moving axially along one or more PBG defects, leading to an improved source for electron beams having useful and improved characteristics, advantageous for a variety of applications.","2. Background and Related Art","The confinement and propagation of electromagnetic energy along fibers is a key technology in many important areas of the modern economy including communications, detection, sensing, probing (often remotely or within a patient for medical purposes), as well as many other areas of application. Perhaps the most common technique for confining electromagnetic waves within a fiber is total internal reflection, typically involving an optical fiber having a central axial strand of material surrounded by a cladding layer in which the central strand has a higher index of refraction (or “index”) than the index of the surrounding cladding layer. This arrangement of a high index axial strand surrounded by a low index cladding is constructed so as to cause electromagnetic waves propagating along the central strand and striking the strand-cladding interface at a glancing angle to undergo total internal reflection and thereby to remain propagating within the axial strand. The lower index of refraction in the cladding can be achieved by using a cladding material with inherently lower index than the material comprising the axial strand, or fabricating the cladding with numerous gaps, inclusions or other regions of low index such that the effective index of the total cladding structure is less than that of the axial strand.","However, the limitation that the cladding have a lower index of refraction than the axial strand in order to achieve confinement by total internal reflection is a serious limitation for many potential applications. For example, it would be advantageous to propagate a beam or cluster of electrons along a hollow central core (or “defect”) of a fiber-like structure concurrently with one or more confined electromagnetic modes such that the electrons gain energy from the electromagnetic mode(s). In such a structure, different modes can be used for bending, focusing and exerting other controls over the electrons. Unfortunately, the effective propagation of electrons requires a space free of material as electrons are scattered and/or captured by encounters with virtually any atom or molecule. No cladding material has a lower index of refraction than a vacuum, so a mode of confinement is required that allows electromagnetic mode confinement and propagation along a fiber having a defect region free of material.","Photonic band gap (PBG) fibers were developed in the 1990%27s to provide an alternative technique for confining electromagnetic waves within a defect region of an optical fiber. In essence, the defect region of an optical fiber (otherwise containing material with a relatively high index of refraction) can be hollow and air-filled, gas filled, evacuated, or partially evacuated, if it is surrounded by a structure having periodic variations in optical properties serving as the “cladding”. It is well known that when waves encounter a periodic structure, certain wavelengths will propagate through the structure while other wavelengths will not, analogous to the formation of electronic energy bands and band gaps that arise when electrons (having wave-like properties) interact with the periodic structure of a crystal lattice. That is, certain wavelengths (or ranges of wavelengths) will propagate through the periodic structure of the cladding and be lost to the propagation of the wave along the defect, while other wavelengths will lie in one of the (possibly several) wavelength “band gaps” and remain confined within the defect region of the fiber. Thus, electromagnetic waves having wavelengths in the range of a “photonic band gap (PBG)” will be confined to the defect region even though this core or defect region has an index of refraction lower than that of the surroundings. An extensive discussion and analysis of the propagation of electromagnetic modes through structures having periodic variations can be found in Photonic Crystals, 2 nd Ed. , J. D. Joannopoulos et al, (Princeton University Press, 2008), the contents of which is incorporated herein by reference for all purposes.","A typical PBG fiber is depicted in FIG. 1 , taken from FIG. 4 of X. E. Lee, “Photonic Band Gap Fiber Accelerator,” Physical Review Special Topics—Accelerators and Beams , Vol. 4, pp. 051301-1, -7 (2001), hereinafter “Lin”. The entire contents of Lin is incorporated herein by reference for all purposes.","FIG. 1 depicts as 10 a dielectric material that includes an array of elements, 11 , having different optical properties from the background 10 and are intended to create one or more band gaps, thereby preventing the propagation of electromagnetic modes having frequencies lying in the band gap(s). Elements 11 creating the band gap(s) are typically capillaries running axially through the fiber as depicted in cross-section in FIG. 1 and are referred to herein as “capillaries” or “band gap elements.” Material 10 is referred to herein as “background dielectric,” “dielectric material,” or simply “dielectric.”","However, since the central core is a distinct element of the fiber from those typically used as band gap elements 11 , (such as a larger hole or absence of one or more band gap elements from an otherwise uniform fiber), analogous to a “lattice defect” as used in solid state physics, central core 12 is also referred to in literature as a “defect,” “core defect,” “central defect” and the like. These terms are typically used interchangeably to describe the central region of a PBG fiber, that is “central core,” “central region,” “defect,” “core defect,” and “central defect” are used without distinction. Essentially all fibers discussed herein are PBG fibers lacking high index material in the central core and will be so understood unless clearly indicated otherwise. Thus, it is customary in the field of PBG fiber technology to refer to the central core 12 , having a different geometry from the surrounding capillaries 11 , as the “central defect” or “defect.”","In addition, many of the PBG fibers considered herein pursuant to some embodiments of the present invention have more than one propagation region (defect), with some or all of such defects displaced from the central axis of the PBG fiber. Thus, “core” and “central core” and the like may carry the (erroneous) implication that the central axial region of the PBG fiber is intended when that is not necessarily the case. For clarity and economy of language we refer to such region(s) of propagation as the “defect” or “defects” understanding that a defect may, but need not, be located along the central axis of the fiber.","It is important to appreciate that, in contrast with the special modes discussed herein, PBG fibers used in telecommunications generally make use of electromagnetic modes largely confined to a PBG central defect, 12 , for carrying information along the fiber. In contrast, the modes useful for different applications, such as electron acceleration, guidance and control as discussed herein, typically involve defect/surface modes in which the modes are not completely confined in the defect but in which important contributions to the performance of the PBG fiber arise from electric and magnetic fields (“fields”) lying outside the defect in the region of dielectric 10 and band gap elements 11 . To be precise, we express the electromagnetic modes propagating axially along the PBG fiber (whether or not along the central axis) as propagating “in the region of, in the vicinity of, in the neighborhood of the defect,” reserving “in the defect” for those modes actually lying substantially within defect 12 .","The creation, acceleration, control and use of electron beams by means of PBG fibers is one application for the technology described herein, and is expected to be an important practical example. In such cases, it is anticipated that laser light will be an advantageous source of the required electromagnetic energy. However, that is not an essential limitation and electromagnetic radiation outside the visible portion of the spectrum, and derived from sources other than lasers, are included within the scope of the present descriptions. For economy of language, “laser” or “light” is used herein to indicate general electromagnetic energy not necessarily limited to visible portions of the spectrum. Those with ordinary skills in the art will clearly realize when other wavelengths can be utilized for different purposes in appropriate circumstances.","The dielectric material 10 is depicted in FIG. 1 as a uniform background in which an array of other elements are embedded, typically band gap elements or capillaries, 11 . While this is a typical structure for PBG fibers currently in use, it is not a fundamental limitation. Regions of different material having different optical properties can also be employed in place of a substantially uniform background dielectric 10 , providing additional design parameters for making the properties of the PBG fiber precisely as desired. However, to be concrete in our descriptions, we describe the typical case in which 10 represents a substantially uniform dielectric material.","The periodic array of band gap elements or capillaries 11 is depicted as a hexagonal array in FIG. 1 , but that is not an essential limitation. A hexagonal pattern provides advantageous packing or close packing for the arrangement of capillaries 11 , and also is conveniently manufactured with present fiber fabrication technology. To be concrete, many of the descriptions herein depict or describe hexagonal patterns for capillaries 11 , but other arrangements, such as square, may also be used advantageously in some cases, and are included within the scope of the present descriptions.","Central defect 12 as depicted in FIG. 1 denotes the central, axial region of the PBG fiber within which, or within the vicinity of which, electromagnetic radiation with appropriate wavelength(s) typically propagates (at least for those cases lacking multiple defects). To be precise in our terminology, we use “strand” or “central strand,” “axial strand” and the like to indicate the central light-carrying region of a conventional optical fiber confining light by means of internal reflection at the strand-cladding interface with a higher index strand surrounded by a lower index cladding. In other words, “strand” or phrases including “strand” are used herein to denote a light-carrying fiber structure having material with relatively high index of refraction along its central axis. We distinguish the central region of PBG fibers as “central defect (core),” “central defect (core) region,” and the like to indicate the central axial region of a PBG fiber lacking high index material, typically evacuated or partially evacuated, but may optionally contain low index material such as air or other gases.","The mechanism confining electromagnetic radiation to the vicinity of the central core of a PBG fiber does not require material to be present in the core, so one may envision including within the core substances that interact with the confined radiation to produce advantageous results. For example, Lin proposes that a properly constructed PBG fiber having radiation propagating along the central core has the potential to provide an effective electron accelerator. Whereas conventional electron accelerators are capable of adding energy to the accelerated electrons at about 50 MeV/m (50×10 6 electron volts per meter), even estimating performance of superconducting accelerators, a PBG fiber accelerator (“PBG accelerator”) has the potential to impart energy at the rate of more than about 1 GeV (10 9 ev)/m. Thus, PBG accelerators may provide a very compact, perhaps portable, accelerator.","To be concrete in our descriptions, we presume that electrons are the particles to be accelerated in a PBG accelerator, understanding thereby that this is by way of illustration not limitation since any charged particle in the PBG%27s defect region will interact with the electromagnetic fields therein, potentially producing useful effects. In particular, positive charged electrons (positrons) can make use of PBG accelerators in a manner very much like electrons and with the same structure as an equivalent PBG electron accelerator. Positrons are already useful in medicine, for example, in positron emission tomography.","Clearly, it is important to be able to insert electromagnetic energy into the defect region of a PBG fiber in sufficient quantity and having the desired electromagnetic field structure. In other words, electromagnetic energy must be coupled into the fiber in such a way so as to excite the electromagnetic modes desired and do so as efficiently as is reasonably possible.","Thus, a need exists in the art for improved structures, devices, materials and procedures for exciting, propagating and controlling various electromagnetic modes with defect region(s) of a PBG fiber so as to produce desired effects therein, including acceleration and control of charged particles, for an improved source of electron beams having one or more advantages of high energy, compactness, low cost, among others.","BRIEF SUMMARY OF THE INVENTION","Accordingly and advantageously, some embodiments of the present invention provide PBG fibers containing more defect regions through which charged particles can be accelerated, guided, controlled, extracted and otherwise used for a variety of applications. Computer calculations of the performance of PBG accelerators indicate that, in comparison to conventional particle accelerators, much larger field gradients can be achieved, hence much larger particle energies can be achieved in a smaller region. Other embodiments include several axial defect regions in parallel along the PBG fiber, allowing increased intensity to be achieved by means of multiple accelerating beams in a single PBG fiber. These and other advantages are achieved in accordance with the present invention as described in detail below.","DETAILED DESCRIPTION","The present invention relates to PBG fibers and the excitation of special purpose modes of electromagnetic radiation in and near one or more defects. While propagation of electromagnetic radiation has been well studied in PBG fibers for telecommunications, exciting other optical modes for special purposes, such as charged particle acceleration, is much less understood. We describe herein PBG fibers and the excitation of such modes including techniques for the excitation, control and use of such modes, and several potential applications. PBG fibers containing several defects are also studied including possible deleterious coupling between the electromagnetic fields existing in neighboring defects. Possible effects on electromagnetic fields in defects due to the proximity of the edge of the PBG fiber are also studied. Unless stated otherwise, all results presented herein have been obtained by computer simulations.","We present numerical simulations of electromagnetic fields generated under a variety of conditions for a variety of PBG fibers having various configurations of defect(s), a variety of structures for coupling electromagnetic energy into the central core region, exciting thereby particular modes. The CUDOS code is available through the University of Sydney and was used for many of the simulations described herein. We focus attention on the particular examples of electromagnetic fields that are expected to be useful for the application of accelerating electrons along one or more defects of various PBG fibers. These simulations are by way of illustration and not limitation since modifications and other applications would be readily apparent to those having ordinary skills in the art. However, we direct our chief consideration to beams of electrons which are expected to be among the early applications of this technology.","To be concrete in our detailed description, we typically discuss the specific example of coupling laser energy into and through a PBG fiber defect (and possibly interacting with electrons or other charged particles therein) as illustration and not limitation. Those having ordinary skills in the art will readily appreciate that the techniques, structures and materials described herein can readily be modified in a straight-forward manner and applied to the utilization of other forms of electromagnetic radiation with PBG systems whose defect or defects (hereinafter “defect(s)”) contain charged particles other than electrons.","In principle, the electromagnetic fields confined within the region PBG fiber defect(s) will interact with any charged particle also present in the central core. However, it is envisioned that electron acceleration by a PBG accelerator is likely to provide one of the first practical applications for this technology. Energetic electrons produced by conventional accelerators can be used to produce intense bursts of synchrotron radiation, often in the form of X-rays, capable of being used to study the structures of materials and for numerous other purposes. Energetic electron beams can be caused to wiggle by passage through an “undulator”, typically an array of magnets causing the beam to deflect in alternating directions, for example, as depicted in FIG. 8 . The resulting radiation can be arranged in a cavity to produce a free electron laser ( FIG. 7 ) that can be used for numerous purposes such as to produce laser radiation or, for sufficiently energetic electrons, even an x-ray laser.","It is also envisioned that accelerator and lab on a chip depicted schematically in FIG. 9 can be combined with a microundulator unit (or “wiggler”) to provide radiation from the accelerator on a chip. One example of such a microundulator is depicted schematically in FIG. 10 in a current-dominated configuration.","Table 1 is a list of a few candidate PBG fibers, F 1 -F 7 , including those for which numerical simulations are presented. 2-Dimensional simulations were performed which are expected to give an adequate description of electric and magnetic fields based on presumed cylindrical symmetry. The fibers F 1 -F 7 of Table 1 have the basic geometry of the fiber depicted in FIG. 1 . In Table 1, n is the index of refraction of the dielectric material 10 given in the column labeled “Material” in Table 1. n eff is the effective (complex) index of refraction. λ is the free space wavelength of the electromagnetic mode appropriate for accelerating electrons in the defect (in μm, 1 μm=10 −6 meter). r is the radius of the capillaries or outer cylinders (band gap elements). R is the defect or central core radius, p is the pitch (that is, the center-to-center spacing of the outer cylinders, 11 ). N missing is the number of capillary rings, or cylinders, removed from the center of the fiber to construct the central defect, that is, one capillary ring (comprising one capillary) removed for N missing =1, and 7 capillaries removed (1 for first ring+6 for second ring) for N missing =2.","FIG. 2 is a cross sectional depiction of a computer aided design or CAD model for fiber F 2 with a central defect or central core cavity for electron beam passage and acceleration. The white background, 10 , in FIG. 2 is taken to be fused silica and the red areas 11 are free of material. Possible coupler sections at the entrance and exit are also depicted as 20 a , 20 b , which can be largely free of material as coupler gaps or slots, or filled with a suitable (typically dielectric) material. Unless otherwise stated, the numerical computations described herein did not include 20 a and 20 b. ","One salient characteristic of PBG fibers pursuant to some embodiments of the present invention is apparent in FIGS. 3 , 4 a and 4 b . FIG. 3 is a cross sectional depiction of the electric field in the z-direction E z (perpendicular to the figure) for the acceleration mode computed for fibers F 6 (scaled down by the wavelength ratio) and F 7 . The colors indicate the magnitude of E z , increasing from blue to green to yellow to orange to red. FIGS. 4 a and 4 b depict E z along two orthogonal planes. The colored vertical lines delineate boundaries between the silicon and holes such that the central defect lies in the region from the origin at x(y)=0 out to the first vertical line at about x(y)=1.4 μm. The near uniformity of the acceleration field in this central defect region is clearly evident in FIGS. 3 , 4 a and 4 b. ","We note in FIG. 3 that the maximum E z occurs in the silicon material at a number of “hot spots” 21 indicated by the red spots in FIG. 3 . Thus, the maximum electric field gradient that is achievable with this fiber is limited by the breakdown field at the location where breakdown first occurs. The achievable gradient based on the breakdown field in Si is about 0.6 GeV/m.","While FIGS. 3 , 4 a and 4 b show results for a TM 01 -like accelerating mode having a very high axial or longitudinal field into the plane of the page (and is approximately uniform within the central defect where the particle beam passes), other types of fields will be useful for focusing, guiding or otherwise directing the electron beam, typically in higher order fields. In particular, a sextuple field is advantageous for precise focusing of electron beams as needed for high resolution lithography, high resolution electron microscopy and other uses.","FIGS. 5 , 6 show results for a rotated, transverse, electric sextuple mode. FIG. 5 depicts E x for the sextuple mode in fiber F 6 using the same color coding as FIG. 3 . FIG. 6 depicts E x vs x along the line y=x ( 6 a ) and y=−x ( 6 b ) for the sextuple mode in fiber F 6 . Fits were done on the data within 80% of the radius of the central core or defect. The curve is well fit with E x =6.4Cx 2 .","The results provided herein demonstrate that PBG accelerators have the potential to be, an important extension and improvement of conventional RF accelerators and have the potential to increase significantly the frequency and accelerating gradients achievable, as discussed in more detail below.","The electromagnetic energy delivered to the PBG fibers may be arranged so as to be delivered into modes leading to acceleration of the electron beam (“accelerator modes”) as well as into optical modes that can be used for beam steering, focusing and a variety of control functions. In some embodiments, both accelerator modes and other modes can be excited in the PBG fiber by the same coupling mechanism. That is, the intensity and other characteristics of the laser radiation coupled into the PBG fiber control the accelerating gradient as well as the strength of at least one of the excited optical modes for a sufficiently broadband source. Thus, tuning the laser power used to excite these modes, and/or using lasers producing different wavelengths, can provide different patterns of excitation in various modes. Other embodiments use different laser frequencies to excite different modes, for example, modes lying in distinct band gaps of the PBG fiber leading to independent tunability of modes.","Lasers are expected to provide the drive power for PBG accelerators and play a role similar to that of klystrons in conventional accelerators. The PBG accelerators discussed herein are composed of dielectric materials that typically allow much higher breakdown fields than are ordinarily possible with conventional copper cavities. Thus, much higher accelerating gradients and control fields can be applied depending upon the materials used, e.g. fused silica is expected to give up to an order of magnitude improvement over silicon.","Excitation of various modes in PBG accelerators can be achieved by means of lasers matched to the coupling modes to be excited, e.g. TM-like for acceleration or TE-like for focusing. Coupling into and out of the PBG structure is achievable in some embodiments of the present invention by means of thin coupler slots, disks or sections, typically located at the entrance and exit. These sections can be integral to the accelerating structure or separated from it. These sections can be made by a variety of techniques, in a variety of configurations, allowing these sections to perform other or additional functions such as electro-optical functions or other insertions, for example, a free electron laser, among others, but also including conventional lasers.","The embodiments of electron accelerators with PBG fibers as described herein offer considerable flexibility in design and control. In addition to the design of the PBG fiber itself, various insertion or control disks can be employed. That is, specially designed insertion disks can be made part of the PBG fiber to affect the electron beam in desirable ways. One example is the delivery of energy to the beam from a direction transverse to the beam direction by means of coupling slots ( 20 a , 20 b ) or other waveguide or cavity-like elements surrounding the beam into which laser energy is directed. The location, position, geometry and material(s) of such cavities can be adjusted to deliver energy preferentially to one or more desired modes.","However, insertion disks can also be used to control the electron beam in many other ways such as focus, deflect, extract or otherwise exert beam control. Some examples are given in FIG. 11 in which control elements are fabricated directly into the central defect or central core of the PBG fiber which then can be assembled into a stack of arbitrary length. Similar control elements can be used for the laser beam or pulse, e.g. to produce it, to regenerate it, and/or to control its phase relative to the electron bunch.","It is important to consider in connection with insertion discs a question that arises when addressing the relative synchronization of joint laser and electron beams. For concreteness, we again consider the specific case of electrons in some detail with the idea that this is an illustration, not a limitation, and can be modified, extended and applied to many other cases.","Of particular relevance is a component referred to herein as a “disk phase shifter,” or an insert that has the basic PBG fiber structure that supports an accelerating mode but is perturbed in such a way as to increase or decrease the local effective index in the vicinity of the defect. This can be done in several ways e.g. by introducing additional capillaries close to the defect or by changing the material(s) in the vicinity of the defect—possibly by loading some of the capillaries with material, not necessarily the same material(s) in every capillary so loaded. We note that “loaded” as used here does not necessarily mean material(s) added to capillaries after the fiber is constructed (although that is included), but also includes fibers originally fabricated with different capillary properties in the vicinity of the defect. The greater the change in optical properties in the vicinity of the defect, the greater the effect that is expected.","Mathematically, let β represent the longitudinal propagation constant, possibly complex, for the unperturbed solution where the phase velocity is v p =ω/β=c/n eff . It then can be shown that the perturbed propagation constant β +βkηδn(x,y) where k is the free space wavenumber of the mode and η is the overlap efficiency between the power density of the unperturbed case (Poynting vector) and the index perturbation. If the mode%27s wavenumber in the fiber is k z then k z =k n eff and the group velocity is v g =dω/dk z =c/ ( n eff +ωdn eff /dω ). ","To maximize the mode%27s group velocity for a better match to that of relativistic particles, one wants to minimize both n eff and its derivative e.g. by reducing the fractional amount of glass in the lattice and also making the dispersion (proportional to the second derivative) zero.","This example distinguishes an important difference between the other modes such as relevant in the telecom field and those of interest here based on the constraints imposed by the particle beam. Thus, since the PBG group velocities in our examples are v g /c ˜0.6, this is matched to an electron kinetic energy of only 128 keV. While there are many important applications lying below this energy such as SEMs it is clear that we may have to phase slip the two beams relative to one another quite often. The virtue of this approach for a higher energy accelerator is that it allows a very efficient test or prototyping procedure to implement along an accelerator for a variety of uses beyond simply trying to optimize an accelerator into a fixed monolithic structure.","In addition to insertion disks having integrally-fabricated control elements in the central defect as depicted in FIG. 11 , control elements can be located outside the central core of the PBG fiber and, in fact, on the external surface of the fiber itself. Control elements residing outside the central core can be fabricated so as to be able to couple more easily to sources of voltage, current, laser light, etc. from outside the fiber assembly, thereby allowing some characteristics of the PBG fiber system to be controlled from locations external to the fiber assembly.","A single PBG fiber accelerator lattice (or matrix) producing parallel bunches of accelerated electrons can also be used to produce multiple serial bunches of electrons. Use of a high repetition rate laser has the capability of producing such multiple serial bunches of electrons likewise at a high repetition rate. Also, it is anticipated that multiple beams of bunched electrons might also be propagated in parallel through a multiple defect array within a single, suitably-configured PBG fiber. Alternatively, it is envisioned that multiple electron beams can also be produced in parallel by bundling multiple PBG fiber accelerators into a single, compact structure, typically having multiple correlated lasers directed thereon, thereby multiplying the beam power that is obtainable. That is, the energy of each beam is determined by the beam acceleration characteristics of each individual PBG fiber. The power obtained (volts x current) substantially increases as the beam current is increased through the use of multiple, parallel beams. Increasing beam power typically reduces the time required for procedures employing electron beams. In addition, some applications call for multiple electron beams for parallel processing (e.g. lithography), material processing or pellet compression, among other applications naturally obtainable with a multiple PBG structure.","FIG. 12 depicts an end view of a fiber bundle which is a prelude to the fabrication of parallel PBG fibers. It is envisioned that the separate PBG accelerators will have hexagonal geometries and be closely packed, substantially as indicated by the hexagonal areas delineated in FIG. 12 . The central cores or defects were not created in the bundle of FIG. 12 (nor depicted therein), chiefly because the fiber “pull” resulting in FIG. 12 was intended as a test for achievable dimensions rather than a full PBG fiber bundle fabrication.","It is envisioned that the full PBG fiber bundle structure, generalized from FIG. 12 , will allow for a degree of independent control over the characteristics of the individual beams emerging from the structure. For example, a parallel array of serial PBG structures as depicted schematically in FIG. 11 could allow for some independent control of the parallel beams by means of various control structures in some or all of the serial PBG components assembled into the PBG bundle of FIG. 12 . Some examples of possible control structures are depicted schematically in FIG. 11 .","In addition, waveguides and/or coupling channels could be placed transversely through the disc structures of FIG. 12 to provide another means of independent control to the electron beam, examples of which are depicted in FIGS. 24(A) and 24(B) . Extrapolation from coupling techniques used in telecommunications applications of PBG fibers generally provide poor guidance for coupling techniques appropriate for exciting the different modes of interest here. Metalized waveguide couplers can be replaced by dielectric equivalents (or variations) due to the shorter attenuation lengths for metals at these wavelengths. However, the scales are drastically reduced for the present cases so that, in some cases, using metals in disk couplers can still be considered since the length scales involved can be less than about 1 mm. Non-optimized examples of couplers exciting an array of defects are shown for a directional coupler ( FIG. 24A ) and pass-through coupler ( FIG. 24B )","It is interesting to notice that conventional waveguides e.g. WR 1 reach up to 1.1 THz and we have designed metallic disk couplers with length scales up to a mm that provide both directional and pass-through variants using HFSS for defect arrays such as shown below in FIG. 21 .","FIGS. 14 and 15 show that significant alterations or perturbations can be made to the basic periodic lattice structure (as depicted in FIGS. 1 , 3 ) leading to different modes but retaining the substantial uniformity of the field within the central core 31 , suggesting the excitation of new special purpose modes by means of symmetric, aperodicities.","FIG. 13 is a numerical simulation for a TM 01 -like mode computed near the speed of light line at λ sol =1 μm for a lattice vacancy pitch of p=1.3 μm, vacancy diameter 2 r=0.92 μm and a central core or defect diameter D=1.4 μm. The electric field intensity in the longitudinal direction (z-direction) is indicated by the colors, increasing from blue (smallest) to green through yellow, orange and red (largest). λ sol denotes the wavelength of the line ω=k in the band gap diagram. While not precisely the same as λ in Table 1, λ sol and λ are typically not too different.","We note in particular in FIG. 13 regions of high electric field intensity or “hot spots,” 30 a , 30 b . The six-fold symmetry leads to two rings of 6 hot spots (in red), 6 closer to the central core (one of which is denoted by 30 a in FIG. 13 ), and a second ring of 6 hot spots further removed from the central core, e.g. 30 b . The maximum electric field accelerating gradient that is achievable in the device is limited by the breakdown field at the locations of maximum field intensity, that is at the hot spots. Thus, even though the maximum electric field does not occur at the location of the central core containing the electron beam, 31 , that maximum field away from central core 31 in fact limits the delivery of energy into the beam. This is a general consideration for such PBG structures, especially accelerators, that the maximum field that can be tolerated before breakdown will likely not occur at the site of the beam to be accelerated but nevertheless determines the maximum accelerating gradients that can be achieved with that particular design.","Numerical simulations have been performed using HFSS electromagnetic simulation code in which a 6-fold pattern of slot couplers (waveguide-like structures) was introduced into the fiber of FIG. 13 such that each coupler extended from the outer circumference of the fiber in to either the outer hot spots ( 30 b ), or the inner hot spots ( 30 a ), at which points each coupler terminated. The laser energy delivered through such coupler(s) typically delivers energy to the TM 01 -like mode efficiently but it is expected that improved efficiency can be obtained by testing the transverse field hot spots in this way and by the imposition of the additional capillaries (examples of which are depicted in FIGS. 14 and 15 ) for the longitudinal field.","For purposes of the simulations reported herein (some results of which are depicted in FIGS. 16-18 ), a high index material was used to model the couplers. However, we believe the use of such a material in the simulations does not alter our conclusions presented below in any substantial way.","Since the maximum electric field achievable in the PBG accelerator is limited by the first portion of the device to experience a breakdown, one approach to improving performance is to identify the locations of the hot spots and modify only those portions of the device. Perhaps such modifications will modify the overall performance of the device in unacceptable ways, but numerical simulations performed herein indicate that this is not the case, although other modifications of the lattice may be necessary in order to adjust other characteristics, such as modifications to the effective index arising from the presence of the added waveguide, among other changes.","We depict in FIG. 14 the calculated electric fields for the structure of FIG. 13 , modified such that hot spots 30 a no longer occur at the locations of matter (which is subject to breakdown), but in newly introduced holes, 40 a . That is, the fiber of FIG. 13 is modified to introduce additional holes, 40 a , into its structure at those locations at which hot spots occurred in the unmodified PBG fiber. The numerical simulations indicate that the introduction of these holes eliminates those hot spots while introducing no substantially detrimental modifications to the other electrical characteristics of the device. The persistence of the outer ring of hot spots having 6-fold symmetry when the fiber of FIG. 13 is modified to become the fiber of FIG. 14 , 30 b 40 b , even when capillaries 40 a are introduced close to the central core or defect 31 , is evidence of no substantial changes in the overall field of FIG. 14 , especially in the defect.","We provide computational results elsewhere herein indicating that extending a coupler from the outer edge of the PBG fiber and terminating on a hot spot can be an effective way to suppress the hot spot at the coupler%27s inner terminus. Thus, one may consider combining these effects, for example, dealing with interior hot spots 30 a by the use of additional capillaries, 40 a , and dealing with the outer hot spots, 30 b , 40 b , by introducing couplers having one terminus at the locations of the outer hot spots. However, introducing a coupler to the depths of the hot spots is facilitated by having the hot spots of interest further away from the central core or defect and closer to the outer circumference of the fiber. In fact, this displacement of hot spots can be accomplished as demonstrated by the PBG fiber depicted in FIG. 15 .","Additional capillaries or holes, 50 a , can be introduced into the fiber having larger diameters than the general capillaries, 52 , while retaining the overall symmetry of the structure (6-fold symmetry for the example considered here FIGS. 13-15 ). The numerical simulation, the results of which are depicted in FIG. 15 , shows that hot spots 50 b can be made to occur further from the central core 31 , and thus more accessible to suppression by waveguide-like couplers or further addition of capillaries, presumably small as in FIG. 14 . We especially point out that the same effects just discussed for the longitudinal hot spots apply to the transverse field hot spots and that these provide the preferred terminations for the waveguides for the most efficient excitation of the accelerating mode. Other modes may well differ in this characteristic, but it is expected that the basic techniques discussed here can be applied in those cases as well.","We show in FIGS. 16 and 17 electric field calculations for a side-coupled dielectric waveguide with 6-fold symmetry in which the waveguide ends at a hot spot further from the central defect, that is, 30 b in FIG. 13 . FIG. 16 a is a schematic cross sectional depiction of the dielectric waveguide from the exterior of the PBG fiber (upper left of FIG. 16 a ) to the central core 31 . The computed electric fields are depicted in FIG. 16 b . The waveguide depicted in FIG. 16 would have reflections (that is, S 11 ) but the mismatch is not bad as evidenced by the uniform spreading toward the defect.","FIG. 17 depicts computed electric field strengths E z for an input coupler and output coupler separated by λ/2 and located in parallel as depicted in FIG. 17 . These dual input-output couplers also have 6-fold symmetry. We observe in FIG. 17 the absence of hot spots.","The results depicted in FIGS. 16 , 17 show that insertion of a dielectric waveguide, even as far as hot spot 30 b , has no serious effect on the fundamental defect mode generated in the central defect 31 . Evidence of this non-disruption can be found in the apparent absence of serious changes to the field pattern in the central defect from FIG. 13 (no waveguides) to FIGS. 16 b , 17 having 6-fold symmetric input waveguides or 6-fold symmetric input and output waveguides respectively.","Dielectric waveguide structures can be extended into the PBG fiber beyond the location of outer hot spots 30 b , and as far as inner hot spots 30 a . E z values calculated for the case of a single waveguide (that is, an extended version of FIG. 16 ) are depicted in FIG. 18 . It is observed that passing the waveguide through the outer hot spots to terminate at the inner hot spots automatically eliminates the outer hot spots as well. We also observe that even this intrusion much closer to the central core of the PBG fiber at location 31 , appears to cause no serious disruption to the field pattern in the central core.","In addition, we note that if this set of waveguides were the only source of energy into the fiber, the coupling of energy into the central defect appears to be better when the waveguides terminate at the inner, rather than the outer, hot spots, although no attempt was made to optimize this coupling by considering the effects of other variations of waveguide length or cross section into the PBG fiber or especially of using the transverse hot spots expected to be a better match.","As noted elsewhere herein, it is expected that increased electron beam intensity can be achieved by constructing a PBG fiber having several defects running axially along the PBG fiber but may also include directions around or across the width of the PBG fiber (perhaps in spiral or more complex patterns) all within a single, common boundary allowing, in principle, parallel production of several electron beams. For economy of language we refer to a PBG fiber having more than one defect running axially along the fiber as a “PBG fiber matrix,” “fiber matrix” or simply “matrix.” Accelerating several beams of electrons through one or more of these defects (but not necessarily all defects present) constitutes a “matrix accelerator”.","However, it is important to understand what effects, if any, might arise from a coupling of electromagnetic modes between defects and/or arise from the proximity of one or more defects to the edge of the PBG fiber in such a fiber matrix. Also, the electromagnetic modes in one defect may be affected by the presence of a nearby neighboring defect even though the neighboring defect contains no electromagnetic modes. Numerical calculations have been done to address these questions.","Calculations are reported for the mode appropriate for accelerating electrons through a defect, that is, a TM 01 -like mode. This is by way of illustration, not limitation, since this mode is easily identifiable and has many and varied embodiments. A person having ordinary skills in the field can readily introduce modifications to these specific examples within the scope of the present invention.","FIG. 19 depicts electric field intensities in the z-direction computed for a fiber matrix having five defects in which modes have been excited in one or two of the defects. FIG. 19B is comparable to FIG. 13 . One can see in FIG. 19 a hexagonal pattern of “hot spots” of relatively high electric field intensity in the z-direction, E. The device is expected to fail at that value of electric field in which the strength of the field first exceeds the breakdown field at that field%27s location. Since different field values occur at different locations in the fiber matrix (as depicted in FIG. 19 and elsewhere), and different locations may have different breakdown fields, a fiber structure placing the largest fields at those locations having the largest breakdown fields results in increasing the fields the device can tolerate before breakdown. Thus, in the operation of a matrix accelerator similar to FIG. 19 , it is expected that these hot spots will limit the accelerating gradients that are obtainable and can be placed in favorable locations with proper fiber design as discussed previously in reference to FIGS. 13-15 and 16 - 18 .","FIGS. 19A and 19C would be identical if the arrangement of capillaries extended to very large distances. However, a careful comparison of FIG. 19A with FIG. 19C indicates slight differences in electric field intensity. In particular, 19 C has somewhat higher field intensities in the direction of the central defect while FIG. 19A shows higher field intensities in the direction perpendicular to the line directed towards the central defect. It is expected that these slight differences are due to the proximity of the edge of the fiber matrix. That is, the surface geometry of capillaries affecting the modes of FIG. 19A is different from the surface geometry of capillaries affecting the modes of FIG. 19C , resulting in slightly different mode structures. Since the differences in mode structure are not very great, it is expected that the addition of an additional ring of capillaries between the outer defects of FIG. 19 and the edge of the fiber matrix will reduce the electric field differences due to edge effects to insignificance.","FIGS. 20 and 21 show additional examples of collective modes for differing defect arrays and provide information about the possible disruption of the basic accelerating mode in one defect due to similar modes propagating in one or more neighboring defects (not necessarily nearest neighbor defects). While many geometric arrangements of defects can be considered within a fiber matrix, it is expected that the major effect upon the basic mode structure will be due to the separation of the defects rather than on particular geometric effects (materials, capillaries, etc. being held constant). We see in FIGS. 20 and 21 , similar to FIG. 19 , that the proximity of the edge of the matrix tends to perturb the modes in the outer defects, perhaps by increasing losses and draining intensity. However, these disturbances are seen to be relatively small so we can expect no substantial deleterious effects if we maintain adequate separations between defects and from defects to the edge of the matrix. Based on these calculations, it is expected that an adequate approximation to unperturbed performance can be obtained with a defect period or pitch “P” about 6× the capillary pitch (or separation) or P about (7 to 8)λ or about 15 μm for λ=2 μm. In other words, a fiber matrix of 1 sq. mm is expected to be able to support an array of defects about 130×130=16,900 defects without substantial coupling between modes in the defects.","Before passing on to a discussion of coupling schemes, it is important to point out that the additional defects or capillaries that we have discussed have many other uses such as modifying the coupling symmetries that would typically apply which is discussed in more detail below but before that we discuss another important use related to those of quenching hot spots as in FIGS. 14 , 15 and those related to the disk phase shifters and the arrays of FIGS. 19-21 . By using additional capillaries placed strategically and filled with different material types and densities that may also include optically active materials that lase and that can be coupled to the accelerating defects or others cavity types one has the potential to effectively solve several problems simultaneously. Materials such as YAG have the kinds of characteristics that appear ideally suited to such purposes.","FIG. 22 is a more detailed field pattern (Re[E z ]) for the defect configuration of FIG. 21 showing |E z |. It is seen that the radiative field pattern is dominated by the constructive interference arising from the radiative losses from the defects when they are excited by the same longitudinal accelerating mode. FIG. 22 clearly shows the different radiation paths tracing back to the peripheries of the different defects. As opposed to the six fold symmetric pattern required to side-couple power into FIG. 3 , this appears to show that only a twofold, opposing laser array is required to excite these three defects. Thus, it indicates that bombarding the fiber matrix with inbound laser pulses directed towards the central%27axis of the fiber matrix, and having a far-field pattern deriving from the radiation pattern computed as in FIG. 22 , is expected to produce in the fiber matrix those modes that would cause the complimentary pattern of radiation. This provides one prescription for exciting the desired modes in the desired defect(s) of a fiber matrix by means of a properly tailored collection of laser pulses side-coupled to the fiber matrix bundle. While end coupling of radiation may be sufficient for exciting many modes of interest in such PBG fibers and fiber bundles, side coupling schemes deriving from a time-reversed consideration of radiation patterns such as FIG. 22 provides an alternative coupling scheme that can be simpler through a reduced number of laser beams.","FIG. 23A depicts the far field radiation pattern computed by propagating the accelerating mode down the fiber to encounter a cleaved end for the single defect shown in FIG. 13 . Thus, FIG. 23A provides the time reversed profile of laser intensity to be end-coupled back into the fiber in order to produce the accelerating mode. The intensity distributions from one of the hot spots (red) of FIG. 23A are depicted in FIG. 23B . The E and H fields are transversely polarized and orthogonal in this area with E polarization pointing towards the polar axis for all spots around the azimuth.","Further examples and computational details can be found in “Transmission and Radiation of an Accelerating Mode in a Photonic Bandgap Fiber,” by C.-K. Ng et al Submitted for publication Jul. 7, 2010 to Phys. Rev. ST: Accel and Beams, the entire contents of which is incorporated herein by reference for all purposes. A copy of this document is submitted herewith as part of an Information Disclosure Statement and is made a part hereof.","FIG. 25 provides macro and SEM photomicrographs at different magnifications of a thin sliced wafer from a PBG accelerating mode manufactured for the SLAC National Accelerator Laboratory by Incom, Inc. of Charlton, Mass. The wafer has an outer diameter of 36 mm and a thickness of 1 mm. Examples run down to 2 μm wavelength. The example shown in FIG. 25 supports an accelerating mode at 8.4 μm. The darkening in the upper left portion of FIGS. 25(B) and 25(C) is believed to be due to charge buildup.","Although various embodiments which incorporate the teachings of the present invention have been shown and described in detail herein, those skilled in the art can readily devise many other varied embodiments that still incorporate these teachings."," TABLE 1 Fiber Material n n eff λ(μm) r(μm) R(μm) p(μm) N missing F1 Silica 1.46 1.001 + i*2.110*10 −4 1.008 0.458 0.678 1.3098 1 F2 Silica 1.46 1.002 + i*3.224*10 −4 2.0 0.868 1.272 2.5445 1 F3 Silicon 3.45 1.029 + i*3.338*10 −3 2.0 0.603 0.844 1.507 2 F4 Silicon 3.45 1.005 + i*1.086*10 −5 1.5 0.377 1.207 0.942 2 F5 Silicon 3.45 1.005 + i*1.086*10 −5 2.0 0.503 1.609 1.257 2 F6 Silicon 3.45 1.006 + i*2.900*10 −5 1.5 0.359 1.077 0.897 2 F7 Silicon 3.45 1.006 + i*2.900*10 −5 2.0 0.478 1.435 1.196 2 "],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","Unless otherwise noted, the figures presented herein are schematic and not to scale, and the relative dimensions of components depicted in various figures are also schematic and not to scale. All data depicted is derived from computer simulations unless stated otherwise.","FIG. 1 : A cross sectional schematic depiction viewed along the axial direction of a typical PBG fiber following Lin.","FIG. 2 : A cross sectional depiction of a PBG fiber viewed along the axial direction of a CAD model of the fiber F2 with the addition of coupler sections 20 a and 20 b depicted schematically. This figure depicts a central defect cavity 12 for electron beam passage and acceleration. The background 10 is taken to be fused silica and 11 is free of material. For the simulations described herein, coupler sections 20 a , 20 b were omitted, unless stated otherwise.","FIG. 3 : A cross sectional depiction of the electric field in the z-direction E z (perpendicular to the figure) for the (λ/2) acceleration mode computed for fibers F 6 , F 7 . The colors indicate the magnitude of E z , increasing from blue to green to yellow to orange to red.","FIG. 4 : A graphical depiction of E z from FIG. 3 along two orthogonal coordinate planes, along x for y=0 ( 4 a ) and along y for x=0 ( 4 b ). In both cases the origin of coordinates is taken to be the center of the central core 12 . y=0 is in the horizontal direction in FIG. 3 while x=0 is in the vertical direction. The vertical lines indicate the locations of the boundaries between the silicon 10 and the holes 11 and the blue wavy line in 4 a and 4 b gives the E z field strength. The particular colors used in FIG. 4 have no significance.","FIG. 5 : A cross sectional depiction of the electric field in the x-direction E x for the sextuple mode computed for fibers F 6 , F 7 . The color coding is the same as FIG. 3 .","FIG. 6 : A graphical depiction of E x vs. x along the line y=x ( 6 a ) and y=−x ( 6 b ) for a sextuple mode in fibers F 6 , F 7 .","FIG. 7 : Schematic depiction of potential free electron laser employing an electron accelerator pursuant to some embodiments of the present invention.","FIG. 8 : Schematic depiction of electromagnetic radiation produced by an electron beam from an electron accelerator pursuant to some embodiments of the present invention.","FIG. 9 : Block diagram of potential radiation source employing PBG electron accelerator.","FIG. 10 : Schematic depiction of a portion of a microundulator in a current-dominated configuration.","FIG. 11 : A schematic depiction of a linear array of PBG fibers into a stack having various control and guiding elements.","FIG. 12 : Schematic cross sectional depiction of typical bundle of PBG fibers. The central core region of each PBG fiber in the bundle is not depicted.","FIG. 13 : A cross sectional depiction of computed E z values near the speed of light line for a PBG fiber F 1 having the geometry depicted. The color coding is the same as FIG. 3 .","FIG. 14 : A cross sectional depiction of computed E z values for the fiber of FIG. 13 with additional holes 40 a introduced at the location of hot spots 30 a (from FIG. 13 ). The color coding is the same as FIG. 3 .","FIG. 15 : A cross sectional depiction of computed E z values for the fiber of FIG. 14 with additional, large diameter capillaries 50 a . The color coding is the same as FIG. 3 .","FIG. 16 : 16 a is a schematic cross sectional depiction of a dielectric waveguide from the exterior of the PBG fiber (upper left of FIG. 16 a ) to the central core 31 . The computed electric fields E z for the fiber including this waveguide are depicted in 16 b.","FIG. 17 : This depicts computed electric field strengths E z for an input coupler and output coupler separated by λ/2 as depicted in FIG. 17 .","FIG. 18 : E z values calculated for the case of a single waveguide extended from the outer surface of the PBG fiber to the inner hot spots are depicted for the case of a single waveguide (that is, a lengthened version of the waveguide depicted in FIG. 16 ).","FIG. 19 : A cross sectional depiction of the electric field in the z-direction for various modes in a multi-defect PBG fiber matrix as modeled with CUDOS.","FIG. 20 : A cross sectional depiction of electric field intensity for new modes, complimentary to those in FIG. 19 , whose local distributions resemble those of FIG. 3 and FIG. 19 , also showing the effects of radiative losses due to proximity of the fiber matrix borders in this example.","FIG. 21 : A cross sectional depiction of electric field intensity for a linear three-defect array showing a mode in which all the defects are excited with the same accelerating mode shown in previous figures.","FIG. 22 : Cross sectional depiction of Re[Ez] that is dominated, in this example, by constructive interference between the radiative losses from the three defects excited by the same longitudinal accelerating mode. Notice the reduction in symmetry from the single defect cases considered earlier.","FIG. 23 : (A) Poynting flux on the forward hemisphere at R=80λ from the fiber termination at z=0. The z-axis is normal to the source plane and coincident with the symmetry axis of the fiber. In the far field, beyond about R=60λ, this distribution closely approximates a Gaussian distribution as shown by the profiles in (B).","FIG. 24 : E z values computed for a rectangular waveguide coupler: (A) a directional coupler using a slot septum (not optimized). (B) a pass-through coupler (not optimized) that is usable either for exciting a linear array or specific combinations of defects when dynamic elements are added that are equivalent to mirrors or septa as in 24 (A).","FIG. 25 : Photomicrographs at different magnifications of a thin sliced wafer for the PBG accelerating mode, manufactured for the SLAC National Accelerator Laboratory by Incom, Inc. of Charlton, Mass."]},"government_interest":"STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with Government support under Contract No. DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/8,410,729","html":"https://www.labpartnering.org/patents/8,410,729","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=8,410,729"},"labs":[{"uuid":"330f3f51-f678-4a42-a1c6-7495179af50f","name":"Thomas Jefferson National Accelerator Facility","tto_url":"https://www.jlab.org/techtransfer","contact_us_email":"contactus@jlab.org","avatar":"https://www.labpartnering.org/files/labs/22","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/330f3f51-f678-4a42-a1c6-7495179af50f"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"James Spencer","location":"Menlo Park, CA, US"},{"name":"Robert Noble","location":"San Jose, CA, US"},{"name":"Sara Campbell","location":"Exeter, NH, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A charged particle accelerator comprising: a photonic band gap fiber having one or more defects therein capable of transmitting charged particles axially therealong, a plurality of capillaries disposed around said one or more defects, one or wherein at least one of said one or more defects is capable of supporting an accelerating TM01-like mode, and one or more couplers for depositing energy into said accelerating TM01-like mode from lasers external to said photonic band gap fiber."},{"idx":"00002","text":"A charged particle accelerator as in claim 1 wherein said one or more couplers included at least one coupler chosen from the list consisting of:dielectric waveguide coupler, rectangular waveguide coupler, directional coupler, or slot coupler."},{"idx":"00003","text":"A charged particle accelerator as in claim 1 further comprising at least one disk phase shifter, wherein said disk phase shifter has the photonic band gap structure supporting said TM01-like mode and wherein said capillaries are modified so as to provide a changed index of refraction in at least one region surrounding said one or more defects."},{"idx":"00004","text":"A charged particle accelerator as in claim 1 further comprising one or more sextupole fields in said one or more defects wherein said one or more sextupole fields are capable of focusing and/or guiding the charged particles traversing axially said one or more defects."},{"idx":"00005","text":"A charged particle accelerator as in claim 1 wherein said one or more defects comprise at least two defects wherein the separation between each of said at least two defects is at least about 7 λ, thereby reducing coupling between modes in said defects."},{"idx":"00006","text":"A charged particle accelerator as in claim 1 wherein the distance from each of said one or more defects to the edge of said photonic band gap fiber is at least about 7 λ thereby reducing effects of said edge of said photonic band gap fiber on modes in said one or more defects."},{"idx":"00007","text":"A photonic band gap fiber comprising one or more defects and a plurality of capillaries disposed around said one or more defects, wherein said photonic band gap fiber is capable of supporting one or more electromagnetic modes propagating along at least one of said one or more defects including a preferred mode, wherein said plurality of capillaries are disposed around said one or more defects in such manner so peak values for the transverse and longitudinal fields of said preferred mode occur at one or more locations resistant to breakdown, thereby increasing the power said photonic band gap fiber is capable of carrying."}],"cpc":[],"ipc":[{"class":"05","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"H","subgroup":"00","main-group":"7","action-date":"2013-04-02","origination":"","symbol-position":"F"}],"document_number":"20110298397","document_published_on":"2011-12-08","document_kind":"","document_country":""},{"number":"8,190,537","artifact":"grant","title":"Feature selection for large scale models","filed_on":"2008-10-31","issued_on":"2012-05-29","published_on":"","abstract":"Disclosed are a method and system for receiving a plurality of potential features to be added to a model having existing features. For each of the potential features, an approximate model is learned by holding values of the existing features in the model constant. The approximate model includes the model having existing features and at least the potential feature. A performance metric is computed for evaluating performance of the approximate model. The performance metric is used to rank the potential feature based on a predetermined criterion.","description":{"text":["BACKGROUND","This disclosure relates to machine learning.","In recent years, machine-learning approaches for data analysis have been widely explored for recognizing patterns which, in turn, allow extraction of significant information contained within large datasets. Learning algorithms include models that may be trained to generalize using data with known outcomes. Trained learning machine algorithms may then be applied to predict the outcome in cases of unknown outcome, i.e., to classify the data according to learned patterns.","In data mining problems, features (i.e., quantities that describe the data in a model), are typically selected from a pool of features. The choice of which features to use in the model can have a significant effect on the accuracy of the learned model. Peculiar problems arise when the number of features is large, e.g., thousands of genes in a microarray. For example, data-overfitting may occur if the number of training records, e.g., number of patients, is smaller compared to the number of genes. In some situations, the large number of features can also make the learning model expensive and labor intensive.","SUMMARY","In one aspect, a method includes receiving a plurality of potential features from a set of data records corresponding to a model having existing features. For each of the potential features, an approximate model is learned by holding values of the existing features in the model constant, the approximate model including the model having existing features and at least the potential feature. A performance metric is computed for evaluating a performance of the approximate model, and the performance metric is used to rank the potential feature based on a predetermined criterion.","The following are examples within the scope of this aspect.","Learning the approximate model includes deriving an estimated coefficient for the potential feature by computing a maximum likelihood measure as a function of values of predicted probabilities and observed outcomes corresponding to the model. The method includes deriving in parallel estimated coefficients for a predetermined set of the potential features. The method includes, for each non-binary categorical feature, transforming the feature into a feature class having a plurality of independent binary features. The method includes selecting only records containing the potential feature, from the set of data records. The approximate model is computed using a one dimensional heuristic single feature optimization over the potential feature to estimate an optimum coefficient corresponding to the potential feature.","The performance metric is selected from a group consisting of an area under curve metric, a log-likelihood measure, and a measure of prediction error. The method includes forming a histogram over values of predicted probabilities associated with the plurality of potential features corresponding to the predetermined set of data records, and learning the approximate model based on the histogram. Each bin in the histogram tracks a first number of data records in a predetermined range of values of predicted probabilities. Each bin in the histogram tracks a second number of data records having positive outcomes from the first number of data records, the positive outcomes determined by values of predicted probabilities being substantially equal to one.","In another aspect, a method of evaluating potential features to be added to a model having existing features includes, for each data record of a plurality of data records associated with the model, computing a value of predicted probability for the model based on the existing features, and storing the value of the predicted probability along with an observed outcome of the model for each potential feature in an intermediate data set. The method includes, for each potential feature, based on the values of the predicted probability and the observed outcome in the intermediate data set, computing an estimated coefficient for the potential feature by optimizing a maximum likelihood measure over the potential feature, and deriving an approximate model using the estimated coefficient, the approximate model including the model having existing features and at least the potential feature. The potential features are scored based on performance metrics of the approximate models.","The following are examples within the scope of this aspect.","The method includes, for each potential feature, computing a difference between a log-likelihood measure of the approximate model and a log-likelihood measure of the model. Computing the value of the predicted probability for the model based on the existing features is carried out in parallel over the plurality of data records. Computing the estimated coefficient for the potential feature is carried out in parallel over the potential features. The method includes, for each potential feature, computing a new predicted probability of the approximate model. The method includes aggregating the differences between the log-likelihood measure of the approximate model and the log-likelihood measure of the model, of all the potential features in a feature class.","In another aspect, a method includes providing a model having existing features that have been trained and produce a first accuracy when the model is used to predict an outcome, and evaluating a plurality of approximate models, each including one or more potential features, each approximate model including the model and the one or more potential features, where the existing features are held constant and the one or more potential features are trained, where evaluating includes determining a second accuracy one for each of the approximate models.","In another aspect, the method includes scoring the one or more potential features based on performance metrics of the approximate models. The method includes providing a machine learning model, the model having a plurality of existing features and features being trained including setting values for one or more coefficients associated with each of the existing features, identifying a plurality of potential features, fixing the model including maintaining values for the coefficients associated with the existing features, adding one or more first potential features to the model including training the first potential features to create a first new model, and determining a first performance metric associated with the first new model, adding one or more second potential features to the model including training the second potential features to create a second new model, and determining a second performance metric associated with the second new model%3b and comparing the first performance metric with the second performance metric, and ranking the first and second potential features based on the comparing.","Other aspects include other combinations of the features recited above and other features, expressed as methods, apparatus, systems, computer-readable media, program products, and in other ways. Other features and advantages will be apparent from the description and from the claims.","DESCRIPTION","FIG. 1 is a block diagram of an example computer system 100 configured to implement a machine learning module 120 . The machine learning module 120 includes software for executing methods in accordance with example aspects of a logistic regression model 130 (also simply referred to as a logistic model 130 ) described in detail below.","An underlying data set, i.e., data records 125 , on which the logistic model 130 is run, may include a large number of instances. Each instance, in turn, may have values for many attributes. However, not all the attributes are relevant to defining characteristics of an instance. Accordingly, the attributes need to be screened (i.e., evaluated and ranked) to identify relevant attributes. Along these lines, in some examples, a feature selection component 135 is provided for selecting the most desirable attributes, i.e., “features,” from a pool of attributes, or potential features that are to be added to the logistic model 130 .","In general, the logistic model 130 is described by a vector of coefficients or “parameters” (i.e., weights assigned to each feature in the model 130 ). A value of a predicted probability (e.g., a probability whether an event occurs) of an event is computed based on the vector of coefficients. To evaluate the performance of the logistic model 130 , the value of the predicted probability is compared with an observed, or “actual” outcome, e.g., either 1 or 0, depending on whether an event occurs (e.g., an actual value for an instance).","An aspect of the feature selection component 135 is that the features to be included in the logistic model 130 can be determined, or “trained,” without having to re-learn the entire logistic model 130 for each potential feature. Accordingly, potential or “candidate” features for the logistic model 130 are evaluated and ranked based on their estimated effect on the performance of a newly learned approximate model.","For each new feature being evaluated, the approximate model is derived based on a process that is similar to a single iteration of back-fitting (i.e., relearning the model by holding the existing features constant), and a value of a coefficient corresponding to the new feature is evaluated. In this manner, the approximate model provides a fast and accurate estimate of each new feature%27s coefficient in the logistic model 130 . The approximate model is analyzed to determine performance metrics for the model. In some examples, performance metrics such as loglikelihood measures are used to determine the approximate model%27s performance. Other performance metrics, including mean-squared-error, area-under-curve metrics, and absolute error, can also be used. Finally, in some examples, the new features are ranked based on the performance metrics.","One aspect of the feature selection component 135 is that the evaluation and ranking of the potential features can be performed in parallel over both data records and potential features, allowing for evaluation of many (e.g., billions) of potential features. For example, as described in further detail below, the logistic model 130 can be run in the context of a map-reduce framework described in the paper, “Mapreduce: Simplified data processing on larger clusters,” by Dean, J., and Ghemawat, S, presented at the Sixth Symposium on Operating System Design and Implementation, in San Francisco, Calif. in 2004. Accordingly, values of predicted probabilities and observed outcomes corresponding to the potential features can be determined in parallel for data records associated with the logistic model 130 . Subsequently, approximate models to score the potential features are derived in parallel for the potential features based on the values of predicted probabilities and observed outcomes.","As shown in FIG. 1 , in some examples, the logistic model 130 can be adapted to run on data associated with Internet images 140 . Accordingly, the computer system 100 is connected over, e.g., wired or wireless network 150 , to the Internet 160 . Typically, the Internet 160 is presented to users 170 of the computer system 100 in the form of web browser pages 180 having Internet images 140 . Users 170 may wish to enhance their browsing experience by filtering out Internet images 140 that are advertisements from the web browser pages 120 . Accordingly, the logistic model 130 can be used to identify whether an Internet image 140 is an Internet advertisement based on a set of predetermined features.","In some examples, the logistic model 130 can be adapted to determine whether, for example, an incoming e-mail message is spam based on predetermined features of the incoming message.","In some examples, the logistic model 130 can be adapted to receive, for example, data points associated with specimen mushrooms, and determine whether a specimen is poisonous based on predetermined features of the specimen.","In some examples, the logistic model 130 can be adapted to receive, for example, data points associated with articles on a range of topics. The logistic model 130 can determine categories of topics (e.g., economics) for the articles, based on stemmed tokens (e.g., “deficit,” “budget”) from the articles.","It is understood that various implementations of the logistic model 130 can be adapted to other situations.","As shown in FIG. 2 , in some examples, the data points may be contained in data records 205 that are stored in databases 200 . The databases 200 can be local to the computer system 100 , or remotely accessed over, e.g., wired or wireless network 250 by the computer system 100 .","As described above, each data record 205 includes values for features corresponding to an instance in an underlying data set. For example, in the specimen mushrooms example, each data record 205 may include information about a specific instance of a specimen mushroom, such as, values for “odor,” “gill color,” “ring type,” or “stalk-surface-above-rim.”","In some examples, the data records 205 include training data records 207 . The logistic model 130 is run on the training data records 207 before being run on the rest of the data records 205 . The training data records 207 may include additional information about actual outcomes corresponding to the instances in the data records 205 . In some examples, the training data records 207 may further include potential features to be added to the logistic model 130 .","For example, a training data record 207 may include an actual outcome field, y i , which can be either 1 or 0, indicating whether a specific instance of a specimen mushroom is poisonous. In this manner, a predicted probability of the logistic model 130 can be compared with the actual outcome to measure performance of the logistic model 130 .","In some examples, the data records 205 also include evaluation data records 208 . The evaluation data records 208 can also include potential features to be added to the logistic model 130 . In some examples, the evaluation data records 208 also include additional information about actual outcomes corresponding to the instances in the data records 205 . As described below, in some examples, the feature selection component 135 evaluates and ranks the potential features in the evaluation data records 208 .","Returning now to the example of Internet images 140 , as shown in FIG. 3 , features 300 a - h , collectively 300 (mathematically represented as a vector, {right arrow over (x)}), are drawn from a pool of potential features that are attributes of the underlying Internet image 140 . Features 300 may include attributes of an Internet image 140 , such as image height 300 a , image width 300 b , image caption, image text style 300 c , image type 300 d , image color 300 e , and image universal resource locator (URL) 300 f. ","In some implementations, in the logistic model 130 , values of features 300 are assumed to be binary. Non-binary features may be transformed into binary values using techniques known to those skilled in the art. For example, non-binary categorical features may be transformed using an “exploding” technique, i.e., for each value of the non-binary categorical feature a new Boolean feature is created that is true if and only if the original feature had that value. For example, if the non-binary categorical feature was “car_color” then the Boolean features derived using this technique are “car_color_red,” “car_color_blue,” etc. Accordingly, using this technique a “feature class” having, e.g., k disjoint binary features is created in which each binary feature corresponds to a discrete value of the non-binary categorical feature. In some examples, the same technique may be applied to continuous features.","As described above, the logistic model 130 is described by a vector of coefficients, {right arrow over (β)}, or weights assigned to each feature 300 in the logistic model 130 . The value of a predicted probability, p, of an event, e.g., probability whether the Internet image 140 is an Internet advertisement, is computed based on the logistic model 130 . To evaluate the performance of the logistic model 130 , the value of the predicted probability, p, is compared with the observed outcome y, which can have a value of 1 or 0, depending on whether the Internet image 140 is actually an Internet advertisement. The logistic model 130 represents log odds of the event as a linear model given in equation (1) below."," log ⁡ ( p 1 - p ) = β -\u003e · x -\u003e ( 1 ) ","Expression (1) above is equivalent to the representation of p, shown below as equation (2)."," p = P ⁡ ( y = 1 ) = f ⁡ ( x -\u003e , β -\u003e ) = ⅇ x -\u003e · β -\u003e 1 + ⅇ x -\u003e · β -\u003e ( 2 ) ","The vector of coefficients, {right arrow over (β)}, is typically learned by optimizing the data%27s unpenalized loglikehood function as shown by expressions (3) and (4) below."," L ⁡ ( X , β -\u003e ) = ∑ i = 1 N ⁢ ( y i ⁢ ln ⁢ ⁢ f ⁡ ( x -\u003e i , β -\u003e ) + ( 1 - y i ) ⁢ ln ⁡ ( 1 - f ⁡ ( x -\u003e i , β -\u003e ) ) ) ( 3 ) β -\u003e opt = arg ⁢ ⁢ max β -\u003e ⁢ ∑ i = 1 N ⁢ ( y i ⁢ ln ⁢ ⁢ ( x -\u003e i , β -\u003e ) + ( 1 - y i ) ⁢ ln ⁡ ( 1 - f ⁡ ( x -\u003e i , β -\u003e ) ) ) ( 4 ) ","Referring now to FIG. 4 , the feature selection component 135 evaluates a new feature 405 , x′ d , from a pool of potential features 410 (x′ 1 , x′ 2 , . . . ). In some examples, the pool of potential features 410 are contained in training and evaluation data records 205 in databases 200 .","The logistic model 130 , f d , (having an associated predicted probability, p) is described by existing features (x 1 , x 2 , . . . ). The feature selection component 135 uses an optimization process for determining whether the new feature 405 x′ d , should be added to the logistic model 130 . For example, the feature selection component 135 uses a single feature optimization (SFO) process. As described in detail below, in the SFO process, each potential feature 410 is evaluated and ranked based on its estimated effect on performance of a newly learned approximate model 420 .","The approximate model 420 is derived for each new feature 405 , x′ d , being evaluated by re-learning the logistic model 130 over the new feature 405 , while holding the existing features 430 constant. A value of an estimated coefficient, β′ d , corresponding to the new feature 405 , x′ d , is determined based on the approximate model 420 . For example, the estimated coefficient β′ d can be determined by maximizing the loglikelihood of the data corresponding to the new feature 405 as shown by expression (5)."," arg ⁢ ⁢ max β d ′ ⁢ ∑ i = 1 N ⁢ ( y i ⁢ ln ⁢ ⁢ f d ⁡ ( x -\u003e i , β -\u003e ) + ( 1 - y i ) ⁢ ln ⁡ ( 1 - f d ⁡ ( x -\u003e i , β -\u003e ) ) ) ( 5 ) ","As shown in FIG. 4 , f d ({right arrow over (x)} i ,{right arrow over (β)}) denotes the newly learned approximate model 420 over the existing features 430 and the new feature 405 . The approximate model 420 is given by expression (6) below."," f d ⁡ ( x -\u003e i , β -\u003e ) = ⅇ β -\u003e · x -\u003e i + x id ′ ⁢ β d ′ 1 + ⅇ β -\u003e · x -\u003e i + x id ′ ⁢ β d ′ ( 6 ) ","In this manner, an approximate model 420 is derived for each potential feature 405 in the pool of potential features 410 . The approximate model 420 provides a fast and accurate estimate of the potential feature%27s 405 coefficient in the logistic model 130 . As described below, the approximate model 420 is analyzed to determine performance metrics for the approximate model 420 . In some implementations, the potential features 410 are ranked based on the performance metrics.","In some examples, Newton%27s method is used for maximizing the loglikelihood function in equation (5) to achieve an optimum value of the estimated coefficient, β′ d . Accordingly, as shown in expression (7), a first derivative of the loglikelihood function is set to zero."," ∂ L ∂ β d ′ = 0 ( 7 ) ","Starting at ∂β′ d =0, the value of β′ d is iteratively updated using expression (8) below until convergence is achieved."," β d ′ = β d ′ - ∂ L ∂ β d ′ ∂ 2 ⁢ L ∂ β d ′2 ( 8 ) ","Applying the above functions in expressions (7) and (8) to the function in expression (5), expressions (9) and (10) are achieved."," ∂ L ∂ β d ′ = ∑ i = 1 N ⁢ x id ′ ⁡ ( y i - f d ⁡ ( x -\u003e i , β -\u003e ) ) ( 9 ) ∂ 2 ⁢ L ∂ β d ′2 = - ∑ i = 1 N ⁢ x id ′2 ⁢ f d ⁡ ( x -\u003e i , β -\u003e ) ⁢ ( 1 - f d ⁡ ( x -\u003e i , β -\u003e ) ) ( 10 ) ","The above technique for optimizing the estimated coefficient, β′ d , corresponding to a new feature 405 , can be used with other objective functions for optimizing the estimated coefficient, β′ d , known to those skilled in the art. For example, applying the above technique to an L2-regularization objective function having an additional penalty term, λβ′ d 2 , the loglikelihood function changes form to that as shown in expression (11)."," ∑ i = 1 N ⁢ ( y i ⁢ ln ⁢ ⁢ f d ⁡ ( x -\u003e i , β -\u003e ) + ( 1 - y i ) ⁢ ln ⁡ ( 1 - f d ⁡ ( x -\u003e i , β -\u003e ) ) ) - λβ d ′2 ( 11 ) ","Accordingly, the derivative expressions are given by expressions (12) and (13)."," ∂ L ∂ β d ′ = ∑ i = 1 N ⁢ x id ′ ⁡ ( y i - f d ⁡ ( x -\u003e i , β -\u003e ) ) - 2 ⁢ λβ d ′ ( 12 ) ∂ 2 ⁢ L ∂ β d ′2 = - ∑ i = 1 N ⁢ x id ′2 ⁢ f d ⁡ ( x -\u003e i , β -\u003e ) ⁢ ( 1 - f d ⁡ ( x -\u003e i , β -\u003e ) ) - 2 ⁢ λ ( 13 ) ","In some implementations, a different metric of the logistic model 130 can be optimized. For example, a squared error measure of the logistic model 130 can be optimized.","In some examples, as described above, the feature selection component 135 uses the single feature optimization process. The single feature optimization process can be described as a “cascaded” model, where a current model%27s activation, “a,” which is a dot product of the vector of coefficients and a vector of features of the current model as indicated in expression (14) below, is fed into a later stage logistic model 130 as a feature."," a i = β -\u003e · x -\u003e i = log ⁡ ( f ⁡ ( x -\u003e i , β -\u003e ) 1 - f ⁡ ( x -\u003e i , β -\u003e ) ) ( 14 ) f d ⁡ ( x -\u003e i , β -\u003e ) = ⅇ a i + x id ′ ⁢ β d ′ 1 + ⅇ a i + x id ′ ⁢ β d ′ ( 15 ) ","Along these lines, the single feature optimization process can be characterized as learning a single feature to “correct” an earlier logistic model 130 .","FIG. 5 illustrates an example single feature optimization (SFO) process 500 for evaluating potential features 410 to be added to a logistic model 130 . The feature selection component 135 considers a new feature 405 to be added to the logistic model 130 . (Step 510 ) For example, in connection with Internet images 140 , the new feature 300 may be the image URL 300 f (see FIG. 3 ). As described above, the feature selection component 135 computes an estimated coefficient, β′ d , corresponding to the new feature 405 . (Step 520 ) In some examples, the coefficient is computed by optimizing, i.e., maximizing a loglikelihood measure of the data using the new feature.","In some examples, feature types other than binary can occur in the data records 205 . In fact, many real-world problems typically contain categorical or continuous attributes that are potential features 410 to be added to the logistic model 130 . Accordingly, the feature selection component 135 computes an estimated coefficient vector, {right arrow over (β′)}, for feature types other than binary. (Step 530 )","As described above, these features can be transformed into a series of disjoint binary features belonging to a single logical grouping called a feature class. In some implementations, such a transformation is particularly well suited for the single feature optimization process 500 . Since all of the other coefficients corresponding to the existing features 430 are held fixed, each feature of the feature class can be optimized independently, and later combined to form the complete approximate model 420 . Further, each of these optimizations only needs to run over those data records 205 containing the relevant feature.","For an categorical attribute having an arity A (i.e., A discrete values) that has been exploded into {right arrow over (x)}′={{right arrow over (x′)} 1 , . . . , {right arrow over (x′)} A }, a vector of estimated coefficients corresponding to the feature class, {right arrow over (β′)}={{right arrow over (β′)} 1 , . . . , {right arrow over (x′)} A }, is computed by maximizing, for example, the loglikelihood function shown in expression (16) independently for each 0\u003cd\u003cA."," ∑ i : x id ′ = 1 ⁢ ( y i ⁢ ln ⁢ ⁢ f d ⁡ ( x -\u003e i , β -\u003e ) + ( 1 - y i ) ⁢ ln ⁡ ( 1 - f d ⁡ ( x -\u003e i , β -\u003e ) ) ) ( 16 ) ","In this manner, the problem of evaluating large arity categorical attributes is divided into a series of smaller independent optimizations.","The feature selection component 135 generates an approximate model 420 based on the newly learned estimated coefficient, β′ d . (Step 540 ) The feature selection component 135 then evaluates a performance metric for the approximate model 420 . The performance metric can include, for example, a loglikelihood measure, an area-under-curve metric, or a prediction error measure. (Step 550 ) The potential features 410 are scored and ranked based on the performance metric. (Step 560 ) For example, potential features 410 can be scored based on loglikelihood as shown by expression (17), where X represents a training set or test set of data records 205 . score(β′ d )= L ( X,{right arrow over (β)} + )  (17) ","In some examples, as the number of data records 205 in the training set increases, the single feature optimization process 500 can involve non-trivial computations. For example, during each step of the Newton%27s method described above, all data records 205 that contain the new feature 405 being evaluated must be considered. This process can be simplified further by using an approximate optimization based on histograms.","The approximate optimization based on histograms can result in significant savings for problems with a large number of data records 205 . In some implementations, further savings can be achieved by using sparse representation and efficient binning schemes. In some example implementations, a sparse representation is used such that only the histogram bins that contain a non-zero count (along with a bin number) are stored so that bins with zero counts do not have to be stored. In some example implementations, an efficient binning scheme can be used that sets the bin widths such that each bin includes approximately the same count as another bin.","Accordingly, instead of performing the optimization directly over the data records 205 , a histogram over the predicted probabilities is formed, and used as a basis for deriving the approximate model 420 . For example, two histograms with an equal number of bins, B, for each attribute are stored in, for example, the memory unit 115 . Each bin tracks a number of data records 205 falling into a predetermined range of predicted probabilities, N b , and also, a number of data records 205 that have positive outcomes, N +b .","In some implementations, an original activation value, a=β′·{right arrow over (x)}, that produces a midpoint probability of a bin p b , is also stored along with the histogram bins. In some examples, this activation is derived as shown in expression (18) below."," a b = log ⁡ ( p b 1 - p b ) ( 18 ) ","From the activation, a b , a modified predicted probability that accounts for the new feature 405 can be computed as shown in expression (19)."," p b ′ = ⅇ a b + β d ′ 1 + ⅇ a b + β d ′ ( 19 ) ","In this manner, optimization of the estimated coefficient, β′ d , need only be performed over the bins in the histogram, using modified derivative computations as shown in expressions (20) and (21) below."," ∂ L ∂ β d ′ = ∑ b = 1 B ⁢ N b + - p b ′ · N b ( 20 ) ∂ L ∂ β d ′2 = - ∑ b = 1 B ⁢ N b · p b ′ · ( 1 - p b ′ ) ( 21 ) ","In some examples, the single feature optimization process 500 can be implemented in the context of a mapreduce framework. Referring to FIG. 6 , an example mapreduce framework scheme 600 includes two distinct phases, i.e., a mapping phase 610 , and a reducing phase 620 . In the mapreduce scheme 600 computations are carried out in parallel over training data records 630 , and intermediate data records 640 (i.e., data records produced by the mapping phase 610 and grouped by potential features), respectively.","In the example mapreduce scheme 600 , the training data records 630 (blocks 1 - 3 ) are shown as data blocks, each having at least one training data record, e.g., training record 632 in block 1 . The intermediate data records 640 (x′ id1 and x′ id2 ) correspond to two potential features 405 . It is understood that the mapreduce scheme 600 can be extended to evaluate many (e.g., billion) training data records 630 and potential features 410 .","In the mapping phase 610 , separate processors, referred to as map workers 635 , operate on the training data records 630 , ({right arrow over (x)} i ,y i , {right arrow over (x′)} i ), to produce intermediate data records 640 , (x′ id ,y i ,{circumflex over (p)} i ) for each new feature 405 , x′ d , in a training data record 630 .","In the reduce phase 620 , separate processors, referred to as reduce workers 645 , operate on each of the intermediate data records 640 , computing estimated coefficients, β′ d , corresponding to each new feature 405 .","A parallel single feature optimization process 700 is shown is FIG. 7 . The feature selection component 135 selects a training data record (i.e., data record, i) from a set of available data records. (Step 710 ) The feature selection component 135 computes a set of current features, x id , and evaluation features, x′ id , in the data record, i. (Step 715 ) Based on the set of current and evaluation features, the feature selection component 135 fixes a logistic model 130 by determining coefficients β i for the current and evaluation features.","Using the values of the coefficients β i corresponding to the current features and evaluation features, the feature selection component 135 calculates a predicted probability p i that is associated with the logistic model 130 . (Step 720 ) The feature selection component 135 then looks up the actual outcome y i for the logistic model 130 from the training data record i. (Step 725 )","For each new feature x′ d in the training data record i, the feature selection component 135 appends a predicted probability and actual outcome pair (p i , y i ) to a list for the new feature d. (Step 730 ) The feature selection component 135 uses the list of predicted probability and actual outcome pairs (p i , y i ) to determine an approximate model b′ d for the new feature x′ d . (Steps 735 - 740 )","For each evaluation data record j, the feature selection component 135 computes a set of current features x jd and evaluation features x′ jd in the evaluation record j. (Steps 745 - 750 ) For each new feature d in the evaluation record, the feature selection component 135 computes a new predicted probability p′ i based on the approximate model b′ d . (Step 755 )","The feature selection component 135 computes a performance score for the old logistic model 130 based on the predicted probability p i and performance scores for the approximate models b′ d based on the predicted probabilities p′ i . (Step 760 ) The feature selection component 135 ranks the new features based on a comparison of the performance scores of the approximate models with the performance score of the old logistic model 130 . (Step 765 )","The computer system 100 of FIG. 1 that is configured to implement a machine learning module 120 can include a processing unit and memory. The memory can include databases, disk drives, tape drives, etc., or a combination thereof. A random access memory can be implemented as a work area to store data used during execution of the logistic regression module 120 in the processing unit. A read only memory can be implemented to function as a program memory for storing instructions associated with the logistic regression module 120 executed in the CPU 110 . Input/output devices can include any of a keyboard, a mouse, a liquid crystal display (LCD), a cathode ray tube (CRT) display, or a printer.","Various implementations of the machine learning module 120 can be realized in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and/or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and/or interpretable on a programmable system including but not limited to at least one programmable processor, which may be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.","These computer programs (also known as programs, software, software applications or code) include machine instructions for a programmable processor, and can be implemented in a high-level procedural and/or object-oriented programming language, and/or in assembly/machine language. As used herein, the terms “machine-readable medium” “computer-readable medium” refers to any computer program product, apparatus and/or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and/or data to a programmable processor, including but not limited to a machine-readable medium that receives machine instructions as a machine-readable signal. The term “machine-readable signal” refers to any signal used to provide machine instructions and/or data to a programmable processor.","To provide for interaction with a user, the machine learning module 120 can be implemented on a computer having a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well%3b for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback)%3b and input from the user can be received in any form, including but not limited to acoustic, speech, or tactile input.","The machine learning module 120 can be implemented in a computing system 100 that includes a back end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front end component (e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the machine learning module 120 ), or any combination of such back end, middleware, or front end components.","The components of the system 100 can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (“LAN”), a wide area network (“WAN”), and the Internet.","The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.","Other embodiments are within the scope of the following claims."],"drawings":["DRAWINGS","FIG. 1 is a block diagram of an example computer system implementing a machine learning module.","FIG. 2 is a block diagram of an example computer system connected to databases.","FIG. 3 is an example Internet image.","FIG. 4 is an example block diagram showing feature selection.","FIG. 5 is an flowchart illustrating an example single feature optimization process.","FIG. 6 is a block diagram of an example mapreduce scheme for the single feature optimization process.","FIG. 7 is a flowchart illustrating parallelized single feature optimization process."]},"government_interest":"","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/8,190,537","html":"https://www.labpartnering.org/patents/8,190,537","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=8,190,537"},"labs":[{"uuid":"a048c1f6-922e-4f3a-a1cd-461044b36ee9","name":"SLAC National Accelerator Laboratory","tto_url":"https://partnerships.slac.stanford.edu/","contact_us_email":"susans@slac.stanford.edu","avatar":"https://www.labpartnering.org/files/labs/23","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/a048c1f6-922e-4f3a-a1cd-461044b36ee9"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Sameer Singh","location":"Amherst, MA, US"},{"name":"Eldon S. Larsen","location":"McMurray, PA, US"},{"name":"Jeremy Kubica","location":"Wexford, PA, US"},{"name":"Andrew W. Moore","location":"Pittsburgh, PA, US"}],"assignees":[{"name":"Google Inc.","seq":1,"location":{"city":"Mountain View","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A method performed by a computer, comprising:receiving a selection of a potential feature from a plurality of potential features for inclusion in a model, the model comprising existing features%3bgenerating an approximate model comprising the model and the potential feature, wherein values of the existing features in the model are held constant in the approximate model%3bcomputing a performance metric of the approximate model%3b ranking, based on the performance metric, the potential feature relative to other potential features in the plurality of potential features for inclusion in the model%3b anddetermining, based on ranking, whether the potential feature is included in the model."},{"idx":"00002","text":"The method of claim 1, wherein generating the approximate model comprises:computing a likelihood measure as a function of values of predicted probabilities and observed outcomes corresponding to the model%3b andderiving, based on computing, estimated coefficient for the potential feature."},{"idx":"00003","text":"The method of claim 1, further comprising deriving estimated coefficients for a predetermined set of the plurality of potential features."},{"idx":"00004","text":"The method of claim 1, further comprising:determining that the potential feature comprises a non-binary categorical feature%3b andtransforming the potential feature into a feature class having a plurality of independent binary features."},{"idx":"00005","text":"The method of claim 4, further comprising selecting records comprising the potential feature, from a set of data records for the model."},{"idx":"00006","text":"The method of claim 1, wherein generating comprises:generating the approximate model based on use of a one dimensional heuristic single feature optimization over the potential feature to estimate an optimum coefficient corresponding to the potential feature."},{"idx":"00007","text":"The method of claim 1, wherein the performance metric is selected from a group comprising one or more of an area under curve metric, a log-likelihood measure, and a measure of prediction error."},{"idx":"00008","text":"The method of claim 1, further comprising:generating a histogram based on values of predicted probabilities associated with the plurality of potential features%3b andwherein generating the approximate model comprises:generating the approximate model based on the histogram."},{"idx":"00009","text":"A system comprising:one or more processors%3b andone or more machine-readable media configured to store instructions that are executable by the one or more processors to perform operations comprising:receiving a selection of a potential feature from a plurality of potential features for inclusion in a model, the model comprising existing features%3bgenerating an approximate model comprising the model and the potential feature, wherein values of the existing features in the model are held constant in the approximate model%3bcomputing a performance metric of the approximate model%3branking, based on the performance metric, the potential feature relative to other potential features in the plurality of potential features for inclusion in the model%3b anddetermining, based on ranking, whether the potential feature is included in the model."},{"idx":"00010","text":"The system of claim 9, wherein generating the approximate model comprises:computing a likelihood measure as a function of values of predicted probabilities and observed outcomes corresponding to the model%3b andderiving, based on computing, estimated coefficient for the potential feature."},{"idx":"00011","text":"The system of claim 9, wherein the operations further comprise:deriving estimated coefficients for a predetermined set of the plurality of potential features."},{"idx":"00012","text":"The system of claim 9, wherein the operations further comprise:determining that the potential feature comprises a non-binary categorical feature%3b andtransforming the potential feature into a feature class having a plurality of independent binary features."},{"idx":"00013","text":"The system of claim 9, wherein the operations further comprise:selecting records comprising the potential feature, from a set of data records for the model."},{"idx":"00014","text":"The system of claim 9, wherein generating comprises:generating the approximate model based on use of a one dimensional heuristic single feature optimization over the potential feature to estimate an optimum coefficient corresponding to the potential feature."},{"idx":"00015","text":"The system of claim 9, wherein the performance metric is selected from a group comprising one or more of an area under curve metric, a log-likelihood measure, and a measure of prediction error."},{"idx":"00016","text":"One or more machine-readable media configured to store instructions that are executable by one or more processors to perform operations comprising:receiving a selection of a potential feature from a plurality of potential features for inclusion in a model, the model comprising existing features%3bgenerating an approximate model comprising the model and the potential feature, wherein values of the existing features in the model are held constant in the approximate model%3bcomputing a performance metric of the approximate model%3branking, based on the performance metric, the potential feature relative to other potential features in the plurality of potential features for inclusion in the model%3b anddetermining, based on ranking, whether the potential feature is included in the model."},{"idx":"00017","text":"The one or more machine-readable media of claim 16, wherein generating the approximate model comprises:computing a likelihood measure as a function of values of predicted probabilities and observed outcomes corresponding to the model%3b andderiving, based on computing, estimated coefficient for the potential feature."},{"idx":"00018","text":"The one or more machine-readable media of claim 16, wherein the operations further comprise:deriving estimated coefficients for a predetermined set of the plurality of potential features."},{"idx":"00019","text":"The one or more machine-readable media of claim 16, wherein the operations further comprise:determining that the potential feature comprises a non-binary categorical feature%3b andtransforming the potential feature into a feature class having a plurality of independent binary features."},{"idx":"00020","text":"The one or more machine-readable media of claim 16, wherein the operations further comprise:selecting records comprising the potential feature, from a set of data records for the model."}],"cpc":[],"ipc":[{"class":"06","value":"","source":"H","status":"B","country":"US","section":"G","version":"","subclass":"F","subgroup":"18","main-group":"15","action-date":"2012-05-29","origination":"","symbol-position":"F"}],"document_number":"","document_published_on":"","document_kind":"","document_country":""},{"number":"8,154,185","artifact":"grant","title":"Diamondoid monolayers as electron emitters","filed_on":"2007-02-12","issued_on":"2012-04-10","published_on":"2008-08-14","abstract":"Provided are electron emitters based upon diamondoid monolayers, preferably self-assembled higher diamondoid monolayers. High intensity electron emission has been demonstrated employing such diamondoid monolayers, particularly when the monolayers are comprised of higher diamondoids. The application of such diamondoid monolayers can alter the band structure of substrates, as well as emit monochromatic electrons, and the high intensity electron emissions can also greatly improve the efficiency of field-effect electron emitters as applied to industrial and commercial applications.","description":{"text":["STATEMENT OF GOVERNMENTAL SUPPORT","The invention described and claimed herein was made in part utilizing funds supplied by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The Government has certain rights in this invention.","Federally-Sponsored Research or Development","This invention was made with Government support under contracts DE-AC03-76SF00098, DE-AC02-76SF00515 awarded by the Department of Energy, 0304981 awarded by the National Science Foundation, and N00014-04-1-0048 awarded by the Office of Naval Research. The Government has certain rights in this invention.","FIELD OF THE INVENTION","Monolayers of diamondoids, particularly higher diamondoids, have been found to provide surprising electron emission. Use of such materials can be realized in improved field emission devices.","DESCRIPTION OF THE RELATED ART","Carbon-containing materials offer a variety of potential uses in microelectronics. As an element, carbon displays a variety of different structures, some crystalline, some amorphous, and some having regions of both, but each form having a distinct and potentially useful set of properties.","A review of carbon%27s structure-property relationships has been presented by S. Prawer in a chapter titled “The Wonderful World of Carbon,” in Physics of Novel Materials (World Scientific, Singapore, 1999), pp. 205-234. Prawer suggests the two most important parameters that may be used to predict the properties of a carbon-containing material are, first, the ratio of sp 2 to sp 3 bonding in a material, and second, microstructure, including the crystallite size of the material, i.e. the size of its individual grains.","Elemental carbon has the electronic structure 1s 2 2s 2 2p 2 , where the outer shell 2s and 2p electrons have the ability to hybridize according to two different schemes. The so-called sp 3 hybridization comprises four identical a bonds arranged in a tetrahedral manner. The so-called sp 2 -hybridization comprises three trigonal (as well as planar) σ bonds with an unhybridized p electron occupying a π orbital in a bond oriented perpendicular to the plane of the σ bonds. At the “extremes” of bonding structure are diamond and graphite. In diamond, all the carbon atoms are tetrahedrally bonded with sp 3 -hybridization. Graphite comprises planar “sheets” of purely sp 2 -hybridized atoms, where the sheets interact weakly through perpendicularly oriented π bonds. Carbon exists in other morphologies as well, including amorphous and mixed diamond/graphite forms often called “diamond-like carbon,” and amorphous carbon (α-C), as well as the highly symmetrical spherical and rod-shaped structures called “fullerenes” and “nanotubes,” respectively.","Diamond is an exceptional material because it scores highest in a number of different categories of properties. Not only is it the hardest material known, but it has the highest thermal conductivity of any material at room temperature. It displays superb optical transparency from the infrared through the ultraviolet, has the highest refractive index of any transparent material, and is an excellent electrical insulator because of its very wide bandgap. It also displays high electrical breakdown strength, and very high electron and hole mobilities. However, diamond as a microelectronics platform has the drawback of being expensive, difficult to dope (in particular for n-type donors) and large areas pieces are not available.","Attempts to synthesize diamond films using chemical vapor deposition (CVD) techniques date back to about the early 1980%27s. An outcome of these efforts was the appearance of new forms of carbon, largely amorphous, in nature, yet containing a high degree of sp 3 -hybridized bonds, and thus displaying many of the characteristics of diamond. To describe such films the term “diamond-like carbon” (DLC) was coined, although this term has no precise definition in the literature. In “The Wonderful World of Carbon,” Prawer teaches that since most diamond-like materials display a mixture of bonding types, the proportion of carbon atoms which are four-fold coordinated (or sp 3 -hybridized) is a measure of the “diamond-like” content of the material. Unhybridized p electrons associated with sp 2 -hybridization form π bonds in these materials, where the π bonded electrons are predominantly delocalized. This gives rise to the enhanced electrical conductivity of materials with sp 2 bonding, such as graphite. In contrast, sp 3 -hybridization results in the extremely hard, electrically insulating and transparent characteristics of diamond. The hydrogen content of a diamond-like material will be directly related to the type of bonding it has. In diamond-like materials the bandgap gets larger as the hydrogen content increases, and hardness often decreases, reflecting the change in the amount of sp 2 vs sp 3 bonding.","Nonetheless, it is generally accepted that the term “diamond-like carbon” may be used to describe two different classes of amorphous carbon films, one denoted as “a:C—H,” because hydrogen acts to terminate dangling bonds on the surface of the film, and a second hydrogen-free version given the name “ta-C” because a majority of the carbon atoms are tetrahedrally coordinated with sp 3 -hybridization. The remaining carbons of ta-C are surface atoms that are substantially sp 2 -hybridized. In a:C—H, dangling bonds can relax to the sp 2 (graphitic) configuration. The role hydrogen plays in a:C—H is to prevent unterminated carbon atoms from relaxing to the graphite structure. The greater the sp content the more “diamond-like” the material is in its properties such as thermal conductivity and electrical resistance.","In his review article, Prawer states that tetrahedral amorphous carbon (ta-C) is a random network showing short-range ordering that is limited to one or two nearest neighbors, and no long-range ordering. There may be present random carbon networks that may comprise 3, 4, 5, and 6-membered carbon rings. Typically, the maximum sp 3 content of a ta-C film is about 80 to 90 percent. Those carbon atoms that are sp 2 bonded tend to group into small clusters that prevent the formation of dangling bonds. The properties of ta-C depend primarily on the fraction of atoms having the sp 3 , or diamond-like configuration. Unlike CVD diamond, there is no hydrogen in ta-C to passivate the surface and to prevent graphite-like structures from forming. The fact that graphite regions do not appear to form is attributed to the existence of isolated sp 2 bonding pairs and to compressive stresses that build up within the bulk of the material.","The microstructure of a diamond and/or diamond-like material further determines its properties, to some degree because the microstructure influences the type of bonding content. As discussed in “Microstructure and grain boundaries of ultrananocrystalline diamond films” by D. M. Gruen, in Properties, Growth and Applications of Diamond, edited by M. H. Nazare and A. J. Neves (Inspec, London, 2001), pp. 307-312, recently efforts have been made to synthesize diamond having crystallite sizes in the “nano” range rather than the “micro” range, with the result that grain boundary chemistries may differ dramatically from those observed in the bulk. Nanocrystalline diamond films have grain sizes in the three to five nanometer range, and it has been reported that nearly 10 percent of the carbon atoms in a nanocrystalline diamond film reside in grain boundaries.","In Gruen%27s chapter, the nanocrystalline diamond grain boundary is reported to be a high-energy, high angle twist grain boundary, where the carbon atoms are largely π-bonded. There may also be sp 2 bonded dimers, and chain segments with sp 3 -hybridized dangling bonds. Nanocrystalline diamond is apparently electrically conductive, and it appears that the grain boundaries are responsible for the electrical conductivity. The author states that a nanocrystalline material is essentially a new type of diamond film whose properties are largely determined by the bonding of the carbons within grain boundaries.","Another allotrope of carbon known as the fullerenes (and their counterparts carbon nanotubes) has been discussed by M. S. Dresslehaus et al. in a chapter entitled “Nanotechnology and Carbon Materials,” in Nanotechnology (Springer-Verlag, New York, 1999), pp. 285-329. Though discovered relatively recently, these materials already have a potential role in microelectronics applications. Fullerenes have an even number of carbon atoms arranged in the form of a closed hollow cage, wherein carbon-carbon bonds on the surface of the cage define a polyhedral structure. The fullerene in the greatest abundance is the C 60 molecule, although C 70 and C 80 fullerenes are also possible. Each carbon atom in the C 60 fullerene is trigonally bonded with sp 2 -hybridization to three other carbon atoms.","C 60 fullerene is described by Dresslehaus as a “rolled up” graphine sheet forming a closed shell (where the term “graphine” means a single layer of crystalline graphite). Twenty of the 32 faces on the regular truncated icosahedron are hexagons, with the remaining 12 being pentagons. Every carbon atom in the C 60 fullerene sits on an equivalent lattice site, although the three bonds emanating from each atom are not equivalent. The four valence electrons of each carbon atom are involved in covalent bonding, so that two of the three bonds on the pentagon perimeter are electron-poor single bonds, and one bond between two hexagons is an electron-rich double bond. A fullerene such as C 60 is further stabilized by the Kekulé structure of alternating single and double bonds around the hexagonal face.","Dresslehaus et al. further teach that, electronically, the C 60 fullerene molecule has 60 π electrons, one π electronic state for each carbon atom. Since the highest occupied molecular orbital is fully occupied and the lowest un-occupied molecular orbital is completely empty, the C 60 fullerene is considered to be a semiconductor with very high resistivity. Fullerene molecules exhibit weak van der Waals cohesive interactive forces toward one another when aggregated as a solid.","The following table summarizes a few of the properties of diamond, DLC (both ta-C and a:C—H), graphite, and fullerenes:"," Property Diamond ta-C A:C—H Graphite C 60 Fullerene C—C bond length (nm)    0.154 ≈0.152 0.141 Pentagon: 0.146 Density (g/cm 3 )    3.51 \u003e3 0.9-2.2 2.27    1.72 Hardness (Gpa)  100 \u003e40 \u003c60 Soft Van der Waals Thermal conductivity 2000 100-700 10    0.4 (W/mK) Bandgap (eV)    5.45 ≈3 0.8-4.0 Metallic    1.7 Electrical resistivity (Ωcm)  \u003e10 16   10 2 -10 12 10 −3 -1 \u003e10 8 Refractive Index    2.4 2-3 1.8-2.4 — — The data in the table is compiled from p. 290 of the Dresslehaus et al. reference cited above, p. 221 of the Prawer reference cited above, p. 891 a chapter by A. Erdemir et al. in “Tribology of Diamond, Diamond-Like Carbon, and Related Films,” in Modern Tribology Handbook, Vol. Two, B. Bhushan, Ed. (CRC Press, Boca Raton, 2001), and p. 28 of “Deposition of Diamond-Like Superhard Materials,” by W. Kulisch, (SpringerVerlag, New York, 1999).","A form of carbon not discussed extensively in the literature are “diamondoids.” Diamonoids are molecular-sized fragments of the diamond crystal structure, and may consist of one or more fused unit cells. These compounds have a “diamondoid” topology in that their carbon atom arrangements are superimposable on a fragment of an FCC (face centered cubic) diamond lattice. Diamondoids can also be considered bridged-ring cycloalkanes, and comprise adamantane, diamantane, triamantane, and the tetramers, pentamers, hexamers, heptamers, octamers, nonamers, decamers, etc., of adamantane (tricyclo[3.3.1.1 3 ,7]decane), adamantane having the stoichiometric formula C 10 H 16 , in which various adamantane units are face-fused to form larger structures. These adamantane units are essentially subunits of diamondoids. Unlike diamond, the diamondoid surfaces are entirely sp 3 -hybridized, with hydrogen-terminated surfaces.","Diamondoids are highly unusual forms of carbon because while they are hydrocarbons, with molecular sizes ranging in general from about 0.2 to 20 nm (averaged in various directions), they also retain some of the extraordinary properties of diamond. As hydrocarbons they can self-assemble into a van der Waals solid, possibly in a repeating array with each diamondoid assembling in a specific orientation. The solid results from cohesive dispersive forces between adjacent C—H x groups, and is known as a molecular solid. Alternatively, these diamondoids can be arranged or derivatized to arrange into molecular monolayers. These thin films are one molecule thick and intimately associated with their substrate, and can cover a large surface area. Thin films, with thicknesses between monolayers and bulk molecular solids are also possible.","Electron emitters are critical components of many current and future electronic devices. Recently, intensive efforts have been put toward inventing thin and low power consuming flat-panel displays. Field emission displays (FEDs), also called surface-conduction electron-emission displays (SEDs), are among the most promising techniques emerging from these efforts. Along these lines most of the major display manufacturers have launched their own FED projects in an attempt to top the huge market of flat-panel displays. According to market research company IDC, the television market alone will climb up to about $40 billion in the coming year.","A field-emission electron emitter is the heart of FED technology. Finding materials for emission sources is the most crucial issue. Original field-emission emitters are made from micro-tips of refractory metals like Molybdenum or Tungsten. By applying a strong electric field at the apex of the tip, electrons are emitted through a process known as field emission. Although micro-tip based field-emission emitters have been partially used for electron microscopes, they failed the display industry due to the high fabrication cost and short life time.","Carbon nanotubes are another candidate as a material for field-emission electron emitters. They feature high electron emission density and long life time, and aligned nanotube emitters have been fabricated. Prototype carbon nanotube based FED%27s were announced by Samsung in 2001, however, there is still no commercial product. The difficulties in making carbon nanotube based electronics rest with both the impurities and the unavoidable mixture of various types of tubes from the synthesis. So far, no low-cost route to substantial quantities of one type carbon nanotubes is available.","U.S. Pat. No. 7,160,529 describes the use of diamondoids in field emission devices. This discovery has great potential for improving field emission devices and their use in industrial and commercial applications. However, the previous work is unclear about the proper manner in which to make diamondoid field emitters and deals with molecular solid materials.","It should be noted that a field emission cathode comprising a diamond or unmodified molecular diamondoid electrode may suffer from poor electrical conductivity This is because of the wide bandgap of diamond. In a normal situation, few electrons are able to traverse the bandgap, in other words, move from electronic states in the valence band to electronic states in the conduction band. While electrons in the conduction band may be able to emit into the vacuum level for negative electron affinity (NEA) materials, such as hydrogen-terminated diamond surfaces, exciting electrons from the valence band into the conduction band to make them available for field emission may still be problematic. Thus, diamond is generally thought to be unable to sustain electron emission because of its insulating nature. To reiterate, although electrons may easily escape into the vacuum from the surface of a hydrogenated diamond film, due to the negative electron affinity of that surface, the problem is that there are no readily available mechanisms by which electrons may be excited from the bulk into electronic surface states.","SUMMARY OF THE INVENTION","The present invention provides improved electron emitters comprised of a monolayer of a diamondoid or functionalized diamondoid, most preferably a higher diamondoid, on a suitable substrate. The monolayer is generally a self-assembled monolayer (SAM). The resulting electron emitters demonstrate high-intensity electron emission. Such high-intensity emission can resolve longstanding problems of conventional field-effect electron emitters, and greatly improve their efficiency.","Among other factors, it has been discovered that by employing a monolayer of a diamondoid, particularly a higher diamondoid, preferably selected from the group consisting of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane, efficient, high intensity electron emission can be realized. Use of the monolayer, preferably using self assembled monolayer techniques as is known in the industry, is important to realizing the focused, high intensity electron emissions. The application of such higher diamondoid monolayers can also alter the band structures of normally un-useful substrates, as well as permit the emission of monochromatic electrons. The focused, high intensity electron emissions can greatly improve the efficiency of field-effect electron emitters as applied to industrial and commercial applications, particularly flat-panel displays and X-ray detectors. This application also describes a method to use functionalized monolayers of diamondoids for field emission, rather than bulk molecular solids.","DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS","According to embodiments of the present invention, diamondoids are provided, e.g., isolated from an appropriate feedstock, and then fabricated into a material that is specific for a particular microelectronics application. In the following discussion diamondoids will first be defined, followed by a description of how they may be recovered from petroleum feedstocks. After recovery diamondoids may be processed into polymers, sintered ceramics, and other forms of diamondoid-containing materials, depending on the application in which they are to be used.","Definition of Diamondoids","The term “diamondoids” refers to substituted and unsubstituted caged compounds of the adamantane series including adamantane, diamantane, triamantane, tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, undecamantane, and the like, including all isomers and stereoisomers thereof. The compounds have a “diamondoid” topology, which means their carbon atom arrangement is superimposable on a fragment of an FCC diamond lattice. Substituted diamondoids comprise from 1 to 10 and preferably 1 to 4 independently-selected alkyl substituents. Diamondoids include “lower diamondoids” and “higher diamondoids,” as these terms are defined herein, as well as mixtures of any combination of lower and higher diamondoids.","The term “lower diamondoids” refers to adamantane, diamantane and triamantane and any and/or all unsubstituted and substituted derivatives of adamantane, diamantane and triamantane. These lower diamondoid components show no isomers or chirality and are readily synthesized, distinguishing them from “higher diamondoids.”","The term “higher diamondoids” refers to any and/or all substituted and unsubstituted tetramantane components%3b to any and/or all substituted and unsubstituted pentamantane components%3b to any and/or all substituted and unsubstituted hexamantane components%3b to any and/or all substituted and unsubstituted heptamantane components%3b to any and/or all substituted and unsubstituted octamantane components%3b to any and/or all substituted and unsubstituted nonamantane components%3b to any and/or all substituted and unsubstituted decamantane components%3b to any and/or all substituted and unsubstituted undecamantane components%3b as well as mixtures of the above and isomers and stereoisomers of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane.","Adamantane chemistry has been reviewed by Fort, Jr: et al. in “Adamantane: Consequences of the Diamondoid Structure,” Chem. Rev. vol. 64, pp. 277 300 (1964). Adamantane is the smallest member of the diamondoid series and may be thought of as a single cage crystalline subunit. Diamantane contains two subunits, triamantane three, tetramantane four, and so on. While there is only one isomeric form of adamantane, diamantane, and triamantane, there are four different isomers of tetramantane (two of which represent an enantiomeric pair), i.e., four different possible ways of arranging the four adamantane subunits. The number of possible isomers increases non-linearly with each higher member of the diamondoid series, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, etc.","Adamantane, which is commercially available, has been studied extensively. The studies have been directed toward a number of areas, such as thermodynamic stability, functionalization, and the properties of adamantane-containing materials. For instance, the following patents discuss materials comprising adamantane subunits: U.S. Pat. No. 3,457,318 teaches the preparation of polymers from alkenyl adamantanes%3b U.S. Pat. No. 3,832,332 teaches a polyamide polymer forms from alkyladamantane diamine%3b U.S. Pat. No. 5,017,734 discusses the formation of thermally stable resins from adamantane derivatives%3b and U.S. Pat. No. 6,235,851 reports the synthesis and polymerization of a variety of adamantane derivatives.","In contrast, the higher diamondoids, have received comparatively little attention in the scientific literature. McKervay et al. have reported the synthesis of anti-tetramantane in low yields using a laborious, multistep process in “Synthetic Approaches to Large Diamondoid Hydrocarbons,” Tetrahedron, vol. 36, pp. 971 992 (1980). To the inventor%27s knowledge, this is the only higher diamondoid that has been synthesized to date. Lin et al. have suggested the existence of, but did not isolate, tetramantane, pentamantane, and hexamantane in deep petroleum reservoirs in light of mass spectroscopic studies, reported in “Natural Occurrence of Tetramantane (C 22 H 28 ), Pentamantane (C 26 H 32 ) and Hexamantane (C 30 H 36 ) in a Deep Petroleum Reservoir,” Fuel, vol. 74(10), pp. 1512 1521 (1995). The possible presence of tetramantane and pentamantane in pot material after a distillation of a diamondoid-containing feedstock has been discussed by Chen et al. in U.S. Pat. No. 5,414,189.","The four tetramantane structures are iso-tetramantane [1(2)3], anti-tetramantane [121] and two enantiomers of skew-tetramantane [123], with the bracketed nomenclature for these diamondoids in accordance with a convention established by Balaban et al. in “Systematic Classification and Nomenclature of Diamond Hydrocarbons-I,” Tetrahedron vol. 34, pp. 3599 3606 (1978). All four tetramantanes have the formula C 22 H 28 (molecular weight 292). There are ten possible pentamantanes, nine having the molecular formula C 26 H 32 (molecular weight 344) and among these nine, there are three pairs of enantiomers represented generally by [12(1)3], [1234], [1213] with the nine enantiomeric pentamantanes represented by [12(3)4], [1(2,3)4], [1212]. There also exists apentamantane [1231] represented by the molecular formula C 25 H 30 (molecular weight 330).","Hexamantanes exist in thirty-nine possible structures with twenty eight having the molecular formula C 30 H 36 (molecular weight 396) and of these, six are symmetrical%3b ten hexamantanes have the molecular formula C 29 H 34 (molecular weight 382) and the remaining hexamantane [12312] has the molecular formula C 26 H 30 (molecular weight 342).","Heptamantanes are postulated to exist in 160 possible structures with 85 having the molecular formula C 34 H 40 (molecular weight 448) and of these, seven are achiral, having no enantiomers. Of the remaining heptamantanes 67 have the molecular formula C 33 H 38 (molecular weight 434), six have the molecular formula C 32 H 36 (molecular weight 420) and the remaining two have the molecular formula C 30 H 34 (molecular weight 394).","Octamantanes possess eight of the adamantane subunits and exist with five different molecular weights. Among the octamantanes, 18 have the molecular formula C 34 H 38 (molecular weight 446). Octamantanes also have the molecular formula C 38 H 44 (molecular weight 500)%3b C 37 H 42 (molecular weight 486)%3b C 36 H 40 (molecular weight 472), and C 33 H 36 (molecular weight 432).","Nonamantanes exist within six families of different molecular weights having the following molecular formulas: C 42 H 48 (molecular weight 552), C 41 H 46 (molecular weight 538), C 40 H 44 (molecular weight 524, C 38 H 42 (molecular weight 498), C 37 H 40 (molecular weight 484) and C 34 H 36 (molecular weight 444).","Decamantane exists within families of seven different molecular weights. Among the decamantanes, there is a single decamantane having the molecular formula C 35 H 36 (molecular weight 456) which is structurally compact in relation to the other decamantanes. The other decamantane families have the molecular formulas: C 41 H 52 (molecular weight 604)%3b C 45 H 50 (molecular weight 590)%3b C 44 H 48 (molecular weight 576)%3b C 42 H 46 (molecular weight 550)%3b C 41 H 44 (molecular weight 536)%3b and C 38 H 40 (molecular weight 496).","Undecamantane exists within families of eight different molecular weights. Among the undecamantanes there are two undecamantanes having the molecular formula C 39 H 40 (molecular weight 508) which are structurally compact in relation to the other undecamantanes. The other undecamantane families have the molecular formulas C 41 H 42 (molecular weight 534)%3b C 42 H 44 (molecular weight 548)%3b C 45 H 18 (molecular weight 588)%3b C 46 H 50 (molecular weight 602)%3b C 48 H 52 (molecular weight 628)%3b C 49 H 54 (molecular weight 642)%3b and C 50 H 56 (molecular weight 656).","Isolation of Diamondoids from Petroleum Feedstocks","Feedstocks that contain recoverable amounts of higher diamondoids include, for example, natural gas condensates and refinery streams resulting from cracking, distillation, coking processes, and the like. Particularly preferred feedstocks originate from the Norphlet Formation in the Gulf of Mexico and the LeDuc Formation in Canada.","These feedstocks contain large proportions of lower diamondoids (often as much as about two thirds) and lower but significant amounts of higher diamondoids (often as much as about 0.3 to 0.5 percent by weight). The processing of such feedstocks to remove non-diamondoids and to separate higher and lower diamondoids (if desired) can be carried out using, by way of example only, size separation techniques such as membranes, molecular sieves, etc., evaporation and thermal separators either under normal or reduced pressures, extractors, electrostatic separators, crystallization, chromatography, well head separators, and the like.","A preferred separation method typically includes distillation of the feedstock. This can remove low-boiling, non-diamondoid components. It can also remove or separate out lower and higher diamondoid components having a boiling point less than that of the higher diamondoid(s) selected for isolation. In either instance, the lower cuts will be enriched in lower diamondoids and low boiling point non-diamondoid materials. Distillation can be operated to provide several cuts in the temperature range of interest to provide the initial isolation of the identified higher diamondoid. The cuts, which are enriched in higher diamondoids or the diamondoid of interest, are retained and may require further purification. Other methods for the removal of contaminants and further purification of an enriched diamondoid fraction can additionally include the following nonlimiting examples: size separation techniques, evaporation either under normal or reduced pressure, sublimation, crystallization, chromatography, well head separators, flash distillation, fixed and fluid bed reactors, reduced pressure, and the like.","The removal of non-diamondoids may also include a pyrolysis step either prior or subsequent to distillation. Pyrolysis is an effective method to remove hydrocarbonaceous, non-diamondoid components from the feedstock. It is effected by heating the feedstock under vacuum conditions, or in an inert atmosphere, to a temperature of at least about 390° C., and most preferably to a temperature in the range of about 410 to 450° C. Pyrolysis is continued for a sufficient length of time, and at a sufficiently high temperature, to thermally degrade at least about 10 percent by weight of the non-diamondoid components that were in the feed material prior to pyrolysis. More preferably at least about 50 percent by weight, and even more preferably at least 90 percent by weight of the non-diamondoids are thermally degraded.","While pyrolysis is preferred in one embodiment, it is not always necessary to facilitate the recovery, isolation or purification of diamondoids. Other separation methods may allow for the concentration of diamondoids to be sufficiently high given certain feedstocks such that direct purification methods such as chromatography including preparative gas chromatography and high performance liquid chromatography, crystallization, fractional sublimation may be used to isolate diamondoids.","Even after distillation or pyrolysis/distillation, further purification of the material may be desired to provide selected diamondoids for use in the compositions employed in this invention. Such purification techniques include chromatography, crystallization, thermal diffusion techniques, zone refining, progressive recrystallization, size separation, and the like. For instance, in one process, the recovered feedstock is subjected to the following additional procedures: 1) gravity column chromatography using silver nitrate impregnated silica gel%3b 2) two-column preparative capillary gas chromatography to isolate diamondoids%3b 3) crystallization to provide crystals of the highly concentrated diamondoids.","An alternative process is to use single or multiple column liquid chromatography, including high performance liquid chromatography, to isolate the diamondoids of interest. As above, multiple columns with different selectivities may be used. Further processing using these methods allow for more refined separations which can lead to a substantially pure component.","In a preferred embodiment of the present invention, a diamondoid or diamondoid containing material is utilized as a cold cathode filament in a field emission device suitable for use, among other places, in flat panel displays. The unique properties of a diamondoid make this possible. These properties include the negative electron affinity of a hydrogenated diamond surface, in conjunction with the small size of a typical higher diamondoid molecule. The latter presents striking electronic features in the sense that the diamond material in the center of the diamondoid comprises high purity diamond single crystal, with the existence of significantly different electronic states at the surface of the diamondoid.","In a chapter entitled “Novel Cold Cathode Materials,” in Vacuum Micro-electronics (Wiley, New York, 2001), pp. 247-287, written by W. Zhu et al., the requirements for a microtip field emitter array are given, as well as the properties an improved field emission cathode are expected to deliver. Perhaps the most difficult problem presented by a conventional field emission cathode is the high voltage that must be applied to the device in order to extract electrons from the filament. Zhu et al. report a typical control voltage for microtip field emitter array of about 50-100 volts because of the high work function of the material typically comprising a field emission cathode. Voltage requirements for diamondoid field emitters will be much smaller due to the fact that diamonds in general, and in particular a hydrogenated diamond surface, offer a unique solution to this problem because of the fact that a diamond surface displays an electron affinity that is negative. Diamondoids are single molecules, which our results show has negative electron affinity.","The electron affinity of the material is a function of electronic states at the surface of the material. When a diamond surface is passivated with hydrogen, that is to say, each of the carbon atoms on the surface are sp 3 -hybridized, i.e., bonded to hydrogen atoms, the electron affinity of that hydrogenated diamond surface can become negative. The remarkable consequence of a surface having a negative electron affinity is that the energy barrier to an electron attempting to escape the material is energetically favorable and in a “downhill” direction.","In more specific terms, the electron affinity χ of a material is negative, where χ is defined to be the energy required to excite an electron from an electronic state at the minimum of the conduction band to the energy level of a vacuum. For most semiconductors, the minimum of the conduction band is below that of the vacuum level, so that the electron affinity of that material is positive. Electrons in the conduction band of such a material are bound to the semiconductor, and energy must be supplied to the semiconductor to excite and electron from the surface of that material, known as the work function.","Diamondoid SAMs also exhibit NEA behavior, and thus will readily emit electrons excited into the conduction band into vacuum. The voltage required for this process may be reduced due to diamondoid characteristics, functionalization, or size.","According to one embodiment of the present invention, a field emission cathode comprises a diamondoid, a derivatized diamondoid, a polymerized diamondoid, and all or any of the other diamondoid containing materials discussed in previous sections of this description. Many different geometries can be used, but two exemplary field emission cathodes comprising a diamondoid are shown in FIGS. 1 and 2 .","Referring to FIG. 1 , A three terminal field emission device is depicted generally. The device comprises a substrate 1 made of gold, another metal or semiconductive material such as silicon. On the substrate 1 is a diamondoid monolayer 2 , comprised of a diamondoid 3 . Preferably, the diamondoid is derivatized in order to better adhere to the substrate by means of a linker 4 . The diamondoid derivative can be a thiol, silane, alkene, halogen, isocyanate, carbonyl, ether, siloxy or any suitably group with can create a stable connection to the underlying substrate. Any suitable attachment method generally known to the skilled artisan can be used.","The anode 5 of the device can be within a conductive layer positioned behind a phosphorescent coating, or simply an electrode 5 positioned adjacent to the cathode. As shown in FIG. 2 , the anode 10 is adjacent the cathode 11 . The cathode comprises the substrate 12 comprised of the diamondoid monolayer 13 . The diamondoid 14 of the layer is preferably functionalized with a linking group 15 to better attach to the substrate 12 .","In FIG. 1 , the device depicted is operated in a “gated” fashion, wherein the bias exists between the “gate” electrode 6 and the cathode 7 , which initiates electron emission, and the electrons are collected by a positive bias on the anode 5 . A typical operating voltage (that is, the potential difference between the cathode and the anode or gate electrode) is between 5-200 volts. This is what allows the cathode to be operated in a so-called “cold” configuration. A typical electronic affinity for a diamondoid surface is contemplated to be less than about 3 eV, and in other embodiments it may be negative. An electron affinity that is less than about 3 eV is considered to be a “low positive value.”","Although undoped diamond materials are generally considered electrically insulating, the diamondoid monolayer 2 may be small enough to allow electrons to tunnel (in a quantum mechanical sense) onto the diamondoid 3 . This tunneling process may enable considerable current to pass through even an insulating molecule, which is a unique feature of diamondoid monolayers as opposed to thick films or bulk materials. It will be appreciated by those skilled in the art that it is not essential for the diamondoid monolayer to have an apex or tip, since the surface of the diamondoid is hydrogenated and sp 3 -hybridized. In an alternative embodiment, the surface of the cathode may comprise a diamondoid-containing material that is at least partially derivatized such that the surface comprises both sp 2 and sp 3 -hybridization.","An advantage of the present invention is that much greater resolution of the device may be realized relative to a conventional field emission device because of the small size of a typical diamondoid, derivatized diamondoid, self-assembled diamondoid structure, or diamondoid aggregate. The discovery of the surprisingly improved high intensity and efficient electron emission realized when using a diamondoid monolayer greatly advances this advantage.","We have shown that many different diamondoids can be chemically attached to a substrate (e.g. tetramantane thiol deposited on gold) to form SAMs. In addition, we have shown that SAMs made from tetramantane thiol on gold or silver shows unusual and unexpected field emission properties. They show strong NEA (even stronger than hydrogen terminated diamond itself) and most of the electrons are emitted at a relatively narrow wave length. These results will lead to improvements in flat panel display technology.","NEA based emitters have several advantages over micro-tip or nanotube field-emission emitters. First of all, NEA-based emitters should exhibit emission at very low “turn-on voltage”, or the voltage necessary to achieve an appreciable amount of current. For display panels, low turn-on voltage means a reduction of black luminance, which is directly related to contrast ratio. Secondly, both thermionic and field-emission emitters exhibit fluctuations from the statistics of electron distributions, the so-called occupied states in the materials. On the contrary, the energy distribution of the emitted electron from a NEA material is extremely narrow, and the noise is mainly from the resistance. Therefore, NEA emitters feature high emission density and low noise.","NEA materials have long been sought due to their unique advantages. Some wide band semiconductors, for example, cesiated GaN, and H-terminated diamond surfaces have been studied for their NEA properties. Two critical issues blocked the way to commercialized products. One is the difficulty of supplying electrons to the emission surface, because the materials are wide band semiconductors. The other is the non-uniform emission normally observed on diamond surfaces, isolation from contaminants such as oxygen and water.","In the present invention, diamondoid based monolayer films are applied onto suitable substrates such as metal substrates and semiconductive substrates, e.g., gold, silver or silicon, and show strong evidence of NEA property. Since the electrons can be supplied by tunneling through a single molecule, and low voltages may be used, two of the critical problems for NEA emitters as mentioned above are resolved.","The commercialization of NEA diamondoid monolayer films is very straightforward. Langmuir-Blodgett (LB) and self-assembled monolayers (SAM) processing are mature techniques for sample preparation, and can be easily applied with the diamondoids to ensure a monolayer on a surface that is reasonably stable. In fact, measurements on SAM films were taken after the films were exposed to the air, and NEA still persisted. In addition, field emission may be enhanced by depositing Cs onto the surface. This is also a common technique in industry for reducing the work function of electron sources. In brief, electron emitters based on the NEA diamondoid monolayer films could simply replace conventional field emission devices and provide better properties. This replacement could conquer the several difficulties for commercializing field emission displays as discussed above.","In particular, a spectacularly sharp, strong and unique electron emission peak on self assembled monolayers (SAMs) of tetramantane-thiol was observed. The intensity of this superior peak contains up to 68% of the total number of emitted electrons, much higher than that of hydrogen terminated diamond. Spectral and energetic considerations suggest that the SAM of this diamondoid shows negative electron affinity. This finding directly demonstrates that monolayer films of diamondoids exceed bulk diamond and even thicker diamondoid films on some novel characteristics. The unique electron emission property provides opportunities for technological breakthroughs on electron emitters.","In addition, it is quite easy to make very large arrays of diamondoid SAMs. As such, the unusual electron emission properties of large-area self-assembled diamondoid monolayers (SAMs) are realized. Moreover, the diamondoid SAMs appear to act as molecular monochrometers which synchronize the energy of emitted electrons. Given the recent discoveries leading to the availability of many different diamondoids and the low cost for large scale manufacturing of diamondoid SAMs, field emission findings reveal special properties of diamondoids that circumvent problems encountered in bulk diamond, creating new windows of opportunity for possible breakthrough technologies in flat panel display, microwave amplifiers, electron microscopy and electron beam lithography, vacuum microelectronic devices, solid state lighting, and X-ray detectors.","EXAMPLES","The following three preparational/analytical methods were employed in the various examples provided thereafter, which are provided as illustrative, and are not meant to be limitative.","[Method 1] SAMs of [121] 6-tetramantane-thiol in centimeter size were prepared in solution at room temperature through a routine procedure (5-8). A layer of 3 nm Ti followed by 100 nm Au was deposited by e-beam evaporation at a base pressure of approximately 1×10 −6 torr onto either Cu or Ag substrates. The SAMs were grown by immersing the metal surfaces in solution for one to two days. Upon removal from solution, the films were washed in toluene and ethanol under N 2 environment, then immediately loaded into vacuum chamber.","[Method 2] NEXAFS spectra were recorded at beamlines 8.2 and 10.1 of the Stanford Synchrotron Radiation Laboratory (SSRL, SPEARIII) at the Stanford Linear Accelerator (SLAC). NEXAFS spectra were recorded using total electron yield, obtained by measuring the total current leaving the experimental sample as the X-ray energy was scanned across the absorption edge. The NEXAFS signals were normalized to the incident photon flux, as recorded by the TEY signal of a freshly gold coated grid in the beam. Note that the possible existence of multi-domains and/or imperfect dipole moments will lead to an overestimated angle by NEXAFS. However, it is clear that diamondoid molecules are roughly perpendicular to the sample surfaces with Sulphur at the bottom.","[Method 3] PES data were collected by using SCIENTA R4000 electron spectrometer at HERS endstation, BL10.0.1, Advanced Light Source (ALS). Firstly, the SAMs were very gently degassed, sometimes by annealing to about 300K, before exposed to synchrotron beam. The linear polarization of the incident beam is 20 degree off the sample surface. All the data were taken with pass energy as low as 2 eV, and samples were biased from 0 to −9 volts to exceed the spectrometer work function as well as to check the reliability of the low kinetic energy data. We observed obvious change in the spectra after a certain period of beam exposure. All the PES data shown here were collected at 30K with less than 20 minutes of the X-ray exposure%3b no sign of radiation damage on PES spectra was detected under this condition.","Large-area SAMs of a functionalized diamondoid, [121] 6-tetramantane-thiol, were grown on Ag or Au substrates through a routine procedure (Method 1). Near edge X-ray absorption fine structure (NEXAFS) measurements were carried out to investigate the detailed molecular geometry (Method 2). We then performed photoelectron spectroscopy (PES) experiments at BL10.0.1, Advanced Light Source, Lawrence Berkeley National Laboratory. Different samples on different substrates with different bias voltages (0-9V) were measured to check the reproducibility (Method 3).","Polarization-dependent NEXAFS on C 1s were used to characterize molecular orientation of the SAMs. The polarization selection rules are simple for transitions from C 1s core level to C 2p orbitals, i.e., the absorption intensity of an orbital depends directly on how the beam polarization is aligned with the orbital. The spectrum with 90° angle exhibits the strongest intensity for the (C—H)σ*peak, meaning the (C—H) orbitals lie more or less parallel to the sample surface. Additionally, the affinity of the thiol for the metal substrate bonds the sulphur at the bottom of the SAMs, bridging the diamondoids and the metal substrates, as can be easily verified by standard X-ray photoelectron spectroscopy (XPS). By comparing the experimental intensity ratio with the theoretical simulation, we get the best agreement if the 6-tetramantane-thiol molecules are tilted for about 30° from the normal to the surface (Method 2).","FIGS. 3 and 4 present the PES spectrum collected on [121] 6-tetramantane-thiol SAMs grown on Ag ( FIG. 3 a ) and Au ( FIG. 4 a ) substrates. An outstanding emission peak appears for both surfaces at about 1 eV kinetic energy, the onset of the spectra at low kinetic energy. The intensity of the peak is so strong that it greatly exceeds all the valence band features. For SAMs grown on Ag and Au, the sharp peak represents about 68% and 17% of the total electron yield respectively. This peak intensity is several times stronger than its analog peak for a hydrogen terminated diamond surface. Even with a logarithmic plot (insets), one can still see a sharp feature instead of the typical broad secondary electron background at this energy range.","In order to make sure that this unusual electron emission is from the top diamondoid monolayers, we tried two different ways to cover or remove the top monolayer in-situ. FIG. 3 b is the PES result on a SAM with C 60 introduced onto the surface. It is seen that the sharp emission feature vanished after covering the surface with C 60 . Interestingly, the valence band of the C 60 covered surface is neither from tetramantanethiol nor from C 60 . This may be due to some reaction between the tetramantanethiol and C 60 molecules, which is not covered in this report. Also, we tried to remove the top diamondoid layer by annealing a SAM in-situ at 825° K. As shown in FIG. 3 c , the low kinetic energy peak completely disappears after the annealing.","To further test the function of the thiol group attached to the diamondoid molecule, we measured underivitized [121] tetramantane films prepared in-situ. FIG. 4 b shows the PES spectrum collected on these tetramantane films without thiol groups. The film generates only a weak peak at low kinetic energy. Note that the intensity of all the valance band features in FIG. 3 and FIG. 4 is at the same scale, much lower than that of the unusual low energy features seen in FIG. 3 a and FIG. 4 a . This directly shows that the thiol group plays an important role in boosting the electron emission.","FIG. 5 shows the unusual electron emission feature detected by using different photon energies. The sharp feature remains at the same energy, ruling out any possibility of core level excitations. The stability of the peak position in FIG. 5 strongly suggests that the unusual emission feature is not from electrons directly excited by photons, but from electrons accumulated at an intrinsic energy level of the molecules themselves.","PES has been widely employed for studying NEA materials, and a sharp feature at low kinetic energy threshold is cited as evidence of NEA. Diamondoids share the same structure as H-diamond which exhibits NEA and a recent theoretical modeling approach suggested that NEA could exist in diamondoids. The outstanding peak shown in this report provides direct evidence that certain functionalized diamondoids are NEA materials, although we were not able to check the criteria based on band gap value.","Diamondoid SAMs appear to have many advantages over other electron emitters. For one, they can be easily and uniformly grown over large areas Furthermore, since wide band-gap semiconductors are bad electron conductors, without a good compensation for the electron loss on the emission surfaces, the space-charge seriously limits the emission ability. On a diamondoid SAM surface, electron conduction from the electron reservoir (metal substrate) to the emission surface is through a single molecule, which successfully avoids the low conductivity problem and greatly enhances the election emission. The sulphur atoms between diamondoid molecules and substrates may also play a role in bridging the electrons transferred from the substrate to the diamondoids. This may explain why the emission peak is much stronger for tetramantanethiol SAMs than for tetramantane films, suggesting the importance of electron conductance for employing NEA materials for applications. Furthermore, functionalized diamondoid SAMs have the advantage over all bulk NEA materials of sharper energy distribution.","In summary, the discovery of a spectacular electron emission property of functionalized diamondoids that appears to be much superior to other bulk NEA semiconductors has been discovered. The physics responsible for this novel emission property is not understood at this stage. Naively, one may consider that photoexcited electrons lose energy by creating phonons in the molecules. However, this would likely lead to the destruction of the molecules. The more likely scenario is that the excited electrons from the metal substrates create particle-hole pairs. With the holes quickly filled by electrons from substrate, a number of electrons slightly above the bottom of the conduction band are transferred to the diamondoids which further lower their energy to reach to the bottom of the conduction band through phonon emission at the interface or on the molecule. These electrons then are emitted, contributing to the sharp peak. Other properties of diamondoid molecules which are not well understood may also contribute to the unique peak. An important aspect is the use of a monolayer, i.e., single molecule layer, of a diamondoid, and most preferably a higher diamondoid.","New technologies and applications are now possible. The unusual field emission properties described here, the recent findings leading to the availability of higher diamondoids such as the tetramantane used in this study, the newly-shown ability to specifically functionalize higher diamondoids, along with the low-cost for large area SAM manufacturing make the diamondoids desirable materials. Possible devices and applications include: flat panel displays, microwave amplifiers, electron microscopy and electron beam lithography, vacuum microelectronic devices, solid state lighting, and X-ray detectors.","Many modifications of the exemplary embodiments of the invention disclosed above will readily occur to those skilled in the art. Accordingly, the invention is to be construed as including all structure and methods that fall within the scope of the appended claims."],"drawings":["BRIEF DESCRIPTION OF THE DRAWING FIGURES","FIG. 1 depicts a typical three terminal field emission device.","FIG. 2 depicts a typical two terminal field emission device.","In FIG. 3 ( a ) Photoelectron spectra of [121] 6-tetramantanethiol SAMs grown on Ag substrates, collected with 55 eV photon energy. The uniquely strong peak at 1 eV contains 68% of the total photoelectrons. Dotted line is a 50 times blowup of valence band features which was suppressed by the strong peak. Inset shows the same spectra in double logarithm plot, a peak could still be seen with no exponential tail towards high kinetic energy. ( b ) Photoelectron spectrum collected on a C 60 covered 6-tetramantanethiol SAM. C 60 was sublimated in-situ towards the sample surfaces by heating up a well outgassed C 60 evaporator. The coverage is less than one monolayer, as approximately calibrated by a quartz thickness monitor. The pristine SAM exhibits the unusual electron emission peak which disappears after C 60 coverage. ( c ) Photoelectron spectrum collected on an annealed 6-tetramantanethiol SAM. Again, the peak observed for pristine SAM vanishes after the in-situ annealing to 825K. The difference between FIG. 3 c and a typical Ag PES spectrum could be due to some sulphur atoms still bonded to the surface after annealing. (b) and (c) conclude that the unusual electron emission peak in (a) is generated by the tetramantanethiol molecules.","FIG. 4 . ( a ) Photoelectron spectra of [121] 6-tetramantanethiol SAMs grown on Au substrates. The sharp peak at 1 eV contains about 17% of the total photoelectrons. Inset is a double logarithm plot, exhibiting the spike-like peak with no exponential tail. ( b ) Photoelectron spectra of [121] tetramantane films (without thiol) prepared in-situ by evaporating the tetramantane powder at 323-353K onto cleaned Au substrates. Inset is the blowup of the shaded area with only a weak peak, in sharp contrast with the data of tetramantanethiol.","FIG. 5 . Photoelectron spectra of [121] 6-tetramantanethiol SAMs on Ag collected with 25 eV, 40 eV, and 55 eV photon energy. The unusual electron emission peak at 1 eV persists. A quantitative analysis of the peak intensity upon photon energy turns out to be complicated, but it is evidently higher for 55 eV data compared with 40 eV and 25 eV data."]},"government_interest":"STATEMENT OF GOVERNMENTAL SUPPORT The invention described and claimed herein was made in part utilizing funds supplied by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The Government has certain rights in this invention. Federally-Sponsored Research or Development This invention was made with Government support under contracts DE-AC03-76SF00098, DE-AC02-76SF00515 awarded by the Department of Energy, 0304981 awarded by the National Science Foundation, and N00014-04-1-0048 awarded by the Office of Naval Research. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/8,154,185","html":"https://www.labpartnering.org/patents/8,154,185","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=8,154,185"},"labs":[{"uuid":"7bc62db1-89fa-4a4d-a321-13f6c4cdf431","name":"Kansas City National Security Campus","tto_url":"https://www.kcnsc.doe.gov/Partnering/Pages/partnering-agreements.aspx","contact_us_email":"Customer_Inquiry@kcp.com","avatar":"https://www.labpartnering.org/files/labs/24","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/7bc62db1-89fa-4a4d-a321-13f6c4cdf431"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Wanli Yang","location":"El Cerrito, CA, US"},{"name":"Jason D. Fabbri","location":"San Francisco, CA, US"},{"name":"Nicholas A. Melosh","location":"Menlo Park, CA, US"},{"name":"Zahid Hussain","location":"Orinda, CA, US"},{"name":"Zhi-Xun Shen","location":"Stanford, CA, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Stanford","state":" CA","country":" US"}},{"name":"The Regents of the University of California","seq":2,"location":{"city":"Oakland","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"An electron emitter which comprises a diamondoid monolayer, wherein the emission process of the electron emitter is selected from photoemission or thermal emission."},{"idx":"00002","text":"The electron emitter of claim 1, wherein the diamondoid monolayer comprises a higher diamondoid."},{"idx":"00003","text":"The electron emitter of claim 1, wherein the diamondoid monolayer comprises a diamondoid which is a higher diamondoid selected from the group consisting of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane."},{"idx":"00004","text":"The electron emitter of claim 3, wherein the higher diamondoid comprises an underivatized higher diamondoid."},{"idx":"00005","text":"The electron emitter of claim 3, wherein the higher diamondoid comprises a derivatized higher diamondoid."},{"idx":"00006","text":"The electron emitter of claim 5, wherein the diamondoid derivative is a thiol, silane, alkene, halogen, isocyanate, carbonyl, ether or siloxy."},{"idx":"00007","text":"The electron emitter of claim 6, wherein the diamondoid derivative is a silane."},{"idx":"00008","text":"The electron emitter of claim 6, wherein the diamondoid derivative is a thiol."},{"idx":"00009","text":"The electron emitter of claim 1, wherein the electron affinity of a surface of the diamondoid monolayer is negative."},{"idx":"00010","text":"The electron emitter of claim 1, wherein the electron affinity of a surface of the diamondoid monolayer is low positive."},{"idx":"00011","text":"The electron emitter of claim 1, wherein the diamondoid monolayer is on a conductive or semiconductor substrate."},{"idx":"00012","text":"The electron emitter of claim 11, wherein the substrate is comprised of gold, silver, silicon, platinum, palladium, aluminum or copper."},{"idx":"00013","text":"The electron emitter of claim 11, wherein the substrate is a silicon substrate."},{"idx":"00014","text":"An electron display device comprising the electron emitter of claim 1."},{"idx":"00015","text":"The electron display device of claim 14, wherein the device is a flat panel display, a microwave amplifier, an electron microscope, an electron beam lithograph, a vacuum microelectronic device, solid state lighting, or an x-ray detector."},{"idx":"00016","text":"The electron display device of claim 15, wherein the diamondoid monolayer is comprised of a diamondoid which is a higher diamondoid selected from the group consisting of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane."},{"idx":"00017","text":"The electron display device of claim 16, wherein the higher diamondoid comprises a derivatized higher diamondoid."},{"idx":"00018","text":"The electron display device of claim 16, wherein the diamondoid monolayer is a self-assembled monolayer."},{"idx":"00019","text":"The electron display device of claim 14, which comprises:a) a cathode comprising a conductive substrate and a diamondoid monolayer,b) an anode positioned opposite the cathode,c) a power supply for supplying a potential difference between the anode and cathode."},{"idx":"00020","text":"The electron display device of claim 19, wherein the electron affinity of the surface of the diamondoid monolayer is negative."},{"idx":"00021","text":"The electron display device of claim 19, wherein the diamondoid monolayer comprises a higher diamondoid which is selected from the group consisting of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane."},{"idx":"00022","text":"A flat panel display device comprising the electron emitter of claim 1."},{"idx":"00023","text":"A X-ray detector comprising the electron emitter of claim 1."},{"idx":"00024","text":"A method of altering the band structure of a substrate, which comprises:a) selecting a suitable substrate for electron emission, wherein the emission process is selected from photoemission or thermal emission%3b andb) applying a monolayer of diamondoid thereon."},{"idx":"00025","text":"The method of claim 24, wherein the diamondoid monolayer is assembled using a higher diamondoid selected from the group consisting of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane."},{"idx":"00026","text":"The method of claim 25, wherein the higher diamondoid is derivatized higher diamondoid."},{"idx":"00027","text":"The method of claim 24, wherein the surface of the diamondoid monolayer has an electron affinity that is negative."},{"idx":"00028","text":"A method of emitting monochromatic electrons, comprising applying to an electron emitter comprised of a diamondoid monolayer on a substrate a narrowly defined energy potential to effect the emission of monochromatic electrons by photoemission or thermal emission."},{"idx":"00029","text":"The method of claim 28, wherein the diamondoid of the diamondoid monolayer is a higher diamondoid selected from the group consisting of tetramantane, pentamantane, hexamantane, heptamantane, octamantane, nonamantane, decamantane, and undecamantane."},{"idx":"00030","text":"The method of claim 29, wherein the higher diamondoid is a derivatized higher diamondoid."}],"cpc":[],"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"13","main-group":"1","action-date":"2012-04-10","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"14","main-group":"1","action-date":"2012-04-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"04","main-group":"9","action-date":"2012-04-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"00","main-group":"9","action-date":"2012-04-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"J","subgroup":"30","main-group":"1","action-date":"2012-04-10","origination":"","symbol-position":"L"}],"document_number":"20080191598","document_published_on":"2008-08-14","document_kind":"","document_country":""},{"number":"8,951,673","artifact":"grant","title":"High rate, long cycle life battery electrode materials with an open framework structure","filed_on":"2012-05-29","issued_on":"2015-02-10","published_on":"2012-12-27","abstract":"A battery includes a cathode, an anode, and an aqueous electrolyte disposed between the cathode and the anode and including a cation A. At least one of the cathode and the anode includes an electrode material having an open framework crystal structure into which the cation A is reversibly inserted during operation of the battery. The battery has a reference specific capacity when cycled at a reference rate, and at least 75% of the reference specific capacity is retained when the battery is cycled at 10 times the reference rate.","description":{"text":["CROSS-REFERENCE TO RELATED APPLICATIONS","This application claims the benefit of U.S. Provisional Application Ser. No. 61/499,877, filed on Jun. 22, 2011, and the benefit of U.S. Provisional Application Ser. No. 61/529,766, filed on Aug. 31, 2011, the disclosures of which are incorporated herein by reference in their entireties.","STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT","This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","FIELD OF THE INVENTION","The invention generally relates to batteries and, more particularly, electrode materials for aqueous electrolyte batteries.","BACKGROUND","To a large extent, recent research and development on battery technology has involved work on various versions of lithium-ion systems, and has been focused on small- to medium-scale applications, such as portable electronics and vehicle propulsion. Much less attention has been given to energy storage problems related to the large scale electrical power grid, despite costly transient outages, a rapidly growing need for frequency regulation, and the necessity for load balancing in concert with the integration of intermittent energy sources such as solar and wind. Instead of emphasizing large values of energy density and specific energy, these grid-scale energy storage applications demand high durability (e.g., long cycle life), high short term power output (e.g., high rate), and low cost.","Current solutions to address short term, high power requirements include traditional lead-acid batteries and certain advanced battery technologies. However, lead-acid batteries have insufficient cycle life and typically cannot withstand deep discharge. Common metal hydride/nickel batteries, which have excellent cycle life, are considered to be too expensive for use on a large scale, as are the sodium/sulfur and lithium-ion systems. In addition, these battery technologies typically show significant voltage hysteresis, and thus have reduced round-trip energy efficiencies when operated at high rates.","It is against this background that a need arose to develop the battery electrode materials and related methods and systems described herein.","SUMMARY","Embodiments of the invention relate to a class of open framework battery electrode materials that exhibit extreme durability and high rate capability. In some embodiments, the battery electrode materials are zeolithic mixed-conducting ionic compounds with relatively stiff framework structures into which hydrated cations from an electrolyte can be rapidly and reversibly inserted. Various members of this class of materials can be inexpensively synthesized using a spontaneous precipitation approach with low cost precursors, and the synthesis can be readily scaled up for grid-scale energy storage applications as well as other applications.","In one embodiment described as follows, the insertion of either sodium or potassium ions into a nickel hexacyanoferrate electrode results in very little lattice strain, and such an electrode can reversibly operate over thousands of deep discharge cycles at high current densities. At low to moderate charge and discharge rates, round-trip energy efficiencies are very high, such as over about 99.7%, and more than about 66% of a low rate discharge capacity is still available at a very high 42 C rate.","In another embodiment described as follows, a copper hexacyanoferrate electrode can be operated at very high rates in a safe and inexpensive aqueous electrolyte with excellent capacity retention over a very large number of cycles. After 40,000 deep discharge cycles at a 17 C rate (3.5 seconds per cycle), about 83% of an original capacity is still available. Even at a more extreme cycling rate of 83 C, about two thirds of its maximum discharge capacity is retained. At more modest current densities, round-trip energy efficiencies of about 99% (or more) can be achieved. Copper hexacyanoferrate can be synthesized using a highly scalable room temperature bulk precipitation approach. Its extreme durability, high rate capability, safe operation, and inexpensive production make this material a desirable battery electrode material for grid-scale energy storage.","In another embodiment described as follows, a battery includes: (1) a cathode%3b (2) an anode%3b and (3) an aqueous electrolyte disposed between the cathode and the anode and including a cation A. At least one of the cathode and the anode includes an electrode material having an open framework crystal structure into which the cation A is reversibly inserted during operation of the battery. The battery has a reference specific capacity when cycled at a reference rate, and at least 75% of the reference specific capacity is retained when the battery is cycled at 10 times the reference rate.","In a further embodiment described as follows, a battery includes: (1) a cathode including a cathode material%3b (2) an anode including an anode material%3b and (3) an aqueous electrolyte disposed between the cathode and the anode and including a cation A and a different cation A′. During operation of the battery, the cation A is reversibly inserted into the cathode material, and the cation A′ is reversibly inserted into the anode material.","Other aspects and embodiments of the invention are also contemplated, including aspects and embodiments related to methods of manufacturing and operating the batteries described herein. The foregoing summary and the following detailed description are not meant to restrict the invention to any particular embodiment but are merely meant to describe some embodiments of the invention.","DETAILED DESCRIPTION","Definitions","The following definitions apply to some of the aspects described with respect to some embodiments of the invention. These definitions may likewise be expanded upon herein.","As used herein, the singular terms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to an object can include multiple objects unless the context clearly dictates otherwise.","As used herein, the term “set” refers to a collection of one or more objects. Thus, for example, a set of objects can include a single object or multiple objects. Objects of a set also can be referred to as members of the set. Objects of a set can be the same or different. In some instances, objects of a set can share one or more common properties.","As used herein, the term “adjacent” refers to being near or adjoining. Adjacent objects can be spaced apart from one another or can be in actual or direct contact with one another. In some instances, adjacent objects can be coupled to one another or can be formed integrally with one another.","As used herein, the terms “couple,” “coupled,” and “coupling” refer to an operational connection or linking. Coupled objects can be directly connected to one another or can be indirectly connected to one another, such as via an intermediary set of objects.","As used herein, the terms “substantially” and “substantial” refer to a considerable degree or extent. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation, such as accounting for typical tolerance levels or variability of the embodiments described herein.","As used herein, the terms “optional” and “optionally” mean that the subsequently described event or circumstance may or may not occur and that the description includes instances where the event or circumstance occurs and instances in which it does not.","As used herein, the term “size” refers to a characteristic dimension of an object. Thus, for example, a size of an object that is spherical can refer to a diameter of the object. In the case of an object that is non-spherical, a size of the non-spherical object can refer to a diameter of a corresponding spherical object, where the corresponding spherical object exhibits or has a particular set of derivable or measurable properties that are substantially the same as those of the non-spherical object. Thus, for example, a size of a non-spherical object can refer to a diameter of a corresponding spherical object that exhibits light scattering or other properties that are substantially the same as those of the non-spherical object. Alternatively, or in conjunction, a size of a non-spherical object can refer to an average of various orthogonal dimensions of the object. Thus, for example, a size of an object that is a spheroidal can refer to an average of a major axis and a minor axis of the object. When referring to a set of objects as having a particular size, it is contemplated that the objects can have a distribution of sizes around the particular size. Thus, as used herein, a size of a set of objects can refer to a typical size of a distribution of sizes, such as an average size, a median size, or a peak size.","Electrode Materials","Embodiments of the invention relate to battery electrode materials in which dimensional changes in a host crystal structure during charging and discharging are small, thereby affording long cycle life and other desirable properties. Such dimensional changes can otherwise result in mechanical deformation and energy loss, as evidenced by hysteresis in battery charge/discharge curves.","Some embodiments relate to a class of electrode materials having stiff open framework structures into which hydrated cations can be reversibly and rapidly intercalated from aqueous (e.g., water-based) electrolytes or other types of electrolytes. In particular, open framework structures with the Prussian Blue-type hexacyanometallate crystal structure afford advantages including greater durability and faster kinetics when compared to other intercalation and displacement electrode materials. A general formula for this class of materials is given by: A x P y [R(CN) 6-w L w ] z .(H 2 O) n   (I) where A corresponds to a cation that can be reversibly inserted into the crystal structure, such as selected from monovalent cations, divalent cations, and higher-valent cations%3b P corresponds to a metal and, in particular, a metal cation, such as selected from monovalent metal cations, divalent metal cations, and higher-valent metal cations%3b R corresponds to a metal and, in particular, a metal cation, such as selected from monovalent metal cations, divalent metal cations, and higher-valent metal cations%3b CN corresponds to a cyanide group and, in particular, a cyanide anion having a valence of 1 and an oxidation state of −1, namely CN −1 %3b L corresponds to a group that is optionally included to partially or fully replace CN −1 , such as selected from monovalent anions, divalent anions, and higher-valent anions%3b H 2 O corresponds to zeolitic water that can be present in the crystal structure%3b x, y, and z are related to achieve electrical neutrality according to valencies of A, P, R, CN, and L%3b x≧0, such as x\u003e0, 0\u003cx≦2, or 0.5≦x≦1.5%3b y≧0, such as y\u003e0, 0.5≦y≦1.5, or 0.7≦y≦1.3%3b z≧0, such as z\u003e0, 0.5≦z≦1.5, or 0.5≦z≦1.1%3b 0≦w≦6, such as 0\u003cw≦6%3b and n≧0, such as n\u003e0. ","A material given by formula (I) can include A, P, R, CN, L, and H 2 O, such that molar ratios of A, P, [R(CN) 6-w L w ], and H 2 O can be represented as A:P:[R(CN) 6-w L w ]:H 2 O=x:y:z:n, molar ratios of P and [R(CN) 6-w L w ] can be represented as P:[R(CN) 6-w L w ]=y:z, molar ratios of P and R can be represented as P:R=y:z, molar ratios of P and CN can be represented as P:CN=y:(6−w)·z, and molar ratios of P and L can be represented as P:L=y:w·z. In the case w=0, molar ratios of A, P, and [R(CN) 6 ] can be represented as A:P:[R(CN) 6 ]=x:y:z, molar ratios of P and [R(CN) 6 ] can be represented as P:[R(CN) 6 ]=y:z, molar ratios of P and R can be represented as P:R=y:z, and molar ratios of P and CN can be represented as P:CN=y:6z.","In some embodiments, a crystal structure of a material given by formula (I) is analogous to that of the ABX 3 perovskites, with P m+ and R n+ cations in an ordered arrangement upon “B” sites. The occupancy of the tetrahedrally-coordinated “A” sites in the large cages in this crystallographically porous framework can vary from x=0 to x=2, with corresponding changes in the valence of one or both of the P and R species. As a result, such a material becomes a mixed ionic-electronic conductor. The insertion of a species of appropriate size into the “A” sites can be performed electrochemically with rapid kinetics. Specifically and in view of this crystallographically porous framework, a number of different hydrated cations can readily move into and out of the “A” sites. The species that is reversibly inserted from an electrolyte also can be exchanged, thereby allowing the implementation of electrodes in hybrid-ion aqueous electrolyte batteries. In some embodiments, the electrode potential range is at least partly determined by the identities of the A, P, and R species, and therefore can be adjusted or modified by changing their identities. For example, a reaction potential can decrease with increasing Stokes ionic diameter of the A species, and can increase with an effective ionic diameter of the A species.","FIG. 1 illustrates the unit cell of a Prussian Blue crystal structure according to an embodiment of the invention. In this structure, hexacyanometallate groups (R(CN) 6 ) form a cubic framework with six-fold nitrogen-coordinated transition metal cations (P). Relatively large interstitial sites within this open framework can host cations (A), resulting in the formula of the form APR(CN) 6 . The relative quantities of A, P, and R(CN) 6 can vary from unity with defects in the framework. The channels between the interstitial “A” sites and hydrated A cations such as potassium are similar in size, allowing their rapid transport throughout the lattice. Furthermore, electrochemical cycling over a full composition range results in minimal lattice strain. Consequently, electrode materials with this type of crystal structure show stable cycling for tens of thousands of cycles, with extremely high rate capability.","Referring to formula (I), examples of suitable A cations include: (1) H + (2) alkali metal cations (e.g., Li + , Na + , K + , Rb + and Cs + )%3b (3) polyatomic, monovalent cations (e.g., NH 4 + )%3b (4) alkaline earth metal cations (e.g., Be 2+ , Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ )%3b and (5) polyatomic, divalent cations. In some embodiments, selection of a suitable A cation can be based on a size of the A cation relative to a size of interstitial sites and channels between the sites within the Prussian Blue crystal structure, which can be represented as a void having a diameter of about 3.5 Å. Because the A cation is typically hydrated in an aqueous electrolyte, it would be expected that a Stokes ionic diameter is the relevant measure of the size of the hydrated A cation, and thus a Stokes ionic diameter of about 3.5 Å is expected to represent an upper size limit for the A cation. Surprisingly, certain materials given by formula (I) also can accommodate A cations having a Stokes ionic diameter greater than 3.5 Å, albeit having an effective ionic diameter (e.g., a crystallographic diameter or other measure of size in the substantial absence of hydration) within, or no greater than, about 3.5 Å. Examples of A cations having a Stokes ionic diameter greater than 3.5 Å include Li + , Na + , Mg 2+ , Ca 2+ , and Ba 2+ . The flexibility in accommodating such A cations affords a number of advantages, such as in terms of the selection of a desired electrode potential range and improved kinetics, as well as facilitating the implementation of hybrid-ion aqueous electrolyte batteries and affording cost advantages. Selection of a suitable hydrated A cation also can be based on a size of the A cation relative to a size of channels between interstitial sites.","Still referring to formula (I), examples of suitable P and R metal cations include: (1) cations of transition metals, such as top row (or row 4) transition metals (e.g., Ti, Va, Cr, Mn, Fe, Co, Ni, Cu, and Zn), row 5 transition metals (e.g., Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, and Cd), and other transition metals%3b (2) post-transition metals (e.g., Al, Ga, In, Sn, Tl, Pb, and Bi)%3b (3) metalloids (e.g., B, Si, Ge, As, Sb, Te, and Po)%3b and (4) lanthanides (e.g., La and Ce). In some embodiments, selection of a suitable P metal cation can be based on the metal cation having the capability to take on different oxidation states. Top row (or row 4) transition metals are examples of metals that can take on a variety of oxidation states. In some embodiments, selection of a suitable R metal cation can be based on the metal cation having the capability to take on different oxidation states, chemical stability of the hexacyanometallate group R(CN) 6 , or a combination of these considerations. Fe, Mn, Cr, and Co are examples of metals that form stable hexacyanometallate groups. Examples of suitable L anions include monovalent anions, such as polyatomic, monovalent anions (e.g., NO − and CO − ). In some embodiments, selection of a suitable L anion can be based on chemical stability of its bonding with the R metal cation within the group [R(CN) 6-w L w ].","Additional examples of suitable cations for A, P, and R can be categorized in terms of their valency and include: (1) monovalent cations (e.g., Ag + , Cu + , Li + , Na + , K + , Hg + , Tl + , NH 4 + )%3b (2) divalent cations (e.g., Mg 2+ , Ca 2+ , Sn 2+ , Sr 2+ , Ba 2+ , Zn 2+ , Cd 2+ , Fe 2+ , Mn 2+ , Cu 2+ , Ni 2+ , Co 2+ , Pb 2+ , Cr 2+ , Hg 2+ , Os 2+ , Pd 2+ , Rh 2+ , Ru 2+ , Ti 2+ , Th 2+ , and V 2+ )%3b (3) trivalent cations (e.g., Al 3+ , Bi 3+ , Ce 3+ , Co 3+ , Cr 3+ , Cu 3+ , Fe 3+ , In 3+ , Ir 3+ , La 3+ , Mn 3+ , Mo 3+ , Nb 3+ , Ni 3+ , Os 3+ , Rh 3+ , Ru 3+ , Sb 3+ , Ta 3+ , Ti 3+ , V 3+ , and Y 3+ )%3b and (4) tetravalent cations (e.g., Ce 4+ , Co 4+ , Cr 4+ , Fe 4+ , Ge 4+ , Mn 4+ , Nb 4+ , Ni 4+ , Pb 4+ , Ru 4+ , Si 4+ , Sn 4+ , Ta 4+ , Te 4+ , Ti 4+ , V 4+ , W 4+ , and Zr 4+ ).","Specific examples of materials given by formula (I) include: A is selected from K + , Li + , Na + , NH 4 + , and Ba 2+ , R is Fe, and P is selected from Fe, Cr, Mn, Co, Ni, Cu, Zn, Sn, and combinations thereof, such as Fe, Ni, Cu, and combination thereof%3b A is selected from K + , Li + , Na + , NH 4 + , and Ba 2+ , R is Co, and P is selected from Fe, Mn, Co, Ni, Cu, Zn, and combinations thereof%3b A is selected from K + , Li + , Na + , NH 4 + , and Ba 2+ , R is Mn, and P is selected from Fe, Mn, Co, Cu, Zn, and combinations thereof%3b and A is selected from K + , Li + , Na + , NH 4 + , and Ba 2+ , R is Cr, and P is selected from Fe, Cr, Mn, Co, Ni, and combinations thereof. ","In formula (I), a mixture of different species can be included for any one or more of A, P, R, and L, such that formula (I) can be further generalized by: (1) representing A as A x-a′ A′ a′ or A x-a′-a″ . . . A′ a′ A″ a″ . . . %3b (2) representing P as P y-p′ P′ p′ or P y-p′-p″ . . . P′ p′ P″ p″ . . . %3b (3) representing R as R 1-r′ R′ r′ or R 1-r′-r″ . . . R′ r′ R″ r″ . . . %3b and (4) representing L as or L w-l′ L′ l′ or L w-l′-l″ . . . L′ l′ L″ l″ . . . . In the generalized version of formula (I), the different species for A can correspond to the same chemical element with different oxidation states, different chemical elements, or a combination thereof. Likewise, the different species for each of P, R, and L can correspond to the same chemical element with different oxidation states, different chemical elements, or a combination thereof.","Various materials given by formula (I) exhibit a number of desirable properties when implemented as electrode materials within batteries, including high efficiency, long cycle life, high rate capability, and high chemical stability.","For example, in terms of round-trip energy efficiency at a rate of 10 C (or another reference rate higher or lower than 10 C, such as 0.83 C, 8.3 C, 17 C, 42 C, or 83 C), batteries incorporating these electrode materials can have an energy efficiency (e.g., an initial or maximum energy efficiency or an average energy efficiency over a particular number of cycles, such as cycles 1 through 100 or cycles 1 through 1,000) that is at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, or at least about 98%, and up to about 99%, up to about 99.5%, up to about 99.9%, or more.","As another example, batteries incorporating these electrode materials can exhibit excellent retention of specific capacity over several charging and discharging cycles, such that, after 1,000 cycles to full discharge at a rate of 10 C (or another reference rate higher or lower than 10 C, such as 0.83 C, 8.3 C, 17 C, 42 C, or 83 C), at least about 75%, at least about 80%, at least about 85%, at least about 90%, at least about 95%, or at least about 98%, and up to about 99%, up to about 99.5%, up to about 99.9%, or more of an initial or maximum specific capacity is retained, and, after 10,000 cycles to full discharge at a rate of 10 C (or another reference rate higher or lower than 10 C, such as 0.83 C, 8.3 C, 17 C, 42 C, or 83 C), at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, or at least about 93%, and up to about 99%, up to about 99.5%, up to about 99.9%, or more of an initial or maximum specific capacity is retained. Likewise, batteries incorporating these electrode materials can exhibit excellent retention of round-trip energy efficiency over several charging and discharging cycles, such that, after 1,000 cycles or even after 10,000 cycles to full discharge at a rate of 10 C (or another reference rate higher or lower than 10 C, such as 0.83 C, 8.3 C, 17 C, 42 C, or 83 C), at least about 80%, at least about 85%, at least about 90%, at least about 95%, or at least about 98%, and up to about 99%, up to about 99.5%, up to about 99.9%, or more of an initial or maximum energy efficiency is retained.","As another example, batteries incorporating these electrode materials can exhibit excellent retention of specific capacity when cycled at high rates, such that, when cycled at a rate of 10 C (or another rate that is ten times a reference rate), at least about 75%, at least about 80%, at least about 85%, at least about 90%, or at least about 95%, and up to about 99%, up to about 99.5%, up to about 99.9%, or more of a maximum specific capacity or a low rate, reference specific capacity (e.g., at the reference rate of 1 C, 0.83 C, C/5, or C/10) is retained, and, when cycled at a rate of 100 C (or another rate that is hundred times the reference rate), at least about 50%, at least about 55%, at least about 60%, at least about 65%, or at least about 70%, and up to about 90%, up to about 95%, up to about 99%, or more of a maximum specific capacity or a low rate, reference specific capacity (e.g., at the reference rate of 1 C, 0.83 C, C/5, or C/10) is retained. Likewise, batteries incorporating these electrode materials can exhibit excellent retention of round-trip energy efficiency when cycled at high rates, such that, when cycled at a rate of 10 C (or another rate that is ten times a reference rate), at least about 75%, at least about 80%, at least about 85%, at least about 90%, or at least about 95%, and up to about 99%, up to about 99.5%, up to about 99.9%, or more of a maximum energy efficiency or a low rate, reference energy efficiency (e.g., at the reference rate of 1 C, 0.83 C, C/5, or C/10) is retained, and, when cycled at a rate of 100 C (or another rate that is hundred times the reference rate), at least about 50%, at least about 55%, at least about 60%, at least about 65%, or at least about 70%, and up to about 90%, up to about 95%, up to about 99%, or more of a maximum energy efficiency or a low rate, reference energy efficiency (e.g., at the reference rate of 1 C, 0.83 C, C/5, or C/10) is retained.","As a further example, various electrode materials given by formula (I) can exhibit high chemical stability over a wide pH range encompassing acidic conditions (e.g., pH%27s in the range of about 0 to about 6, about 1 to about 6, about 0 to about 5, about 2 to about 5, about 0 to about 3, or about 0 to about 2), neutral conditions (e.g., a pH of about 7), and basic conditions (e.g., pH%27s greater than about 7). In some embodiments, acidic conditions (e.g., an electrolyte having a pH that is no greater than or less than about 3, such as in the range of about 0 to about 3, about 0 to about 2.9, about 0 to about 2.7, about 0 to about 2.5, about 0 to about 2.3, about 0 to about 2, about 0.1 to about 1.9, about 0.3 to about 1.7, about 0.5 to about 1.5, about 0.7 to about 1.3, or about 0.9 to about 1.1) can be desirable to mitigate against solubility of certain electrode materials given by formula (I) at higher pH%27s. Such acidic conditions can correspond to optimized conditions for electrode materials that are in a bulk, powdered form.","Further mitigation against solubility of certain electrode materials given by formula (I) can be attained by the inclusion of one or more co-solvents in an electrolyte. In some embodiments, an electrolyte can include water as a primary solvent, and can further include one or more co-solvents having a reduced polarity relative to water. One measure of polarity of a solvent is given by its dielectric constant ∈, with the dielectric constant of water given by ∈ H20 of about 80 at 20° C. Suitable co-solvents include those having a dielectric constant ∈ co-solvent \u003c∈ H20 at a particular operational temperature, such as glycerine (or glycerol), with ∈ glycerine of about 47 at 20° C., ethylene glycol, with ∈ EG of about 37 at 20° C., and other organic solvents having dielectric constants less than about 80 at 20° C., such as no greater than about 78, no greater than about 75, no greater than about 70, no greater than about 65, or no greater than about 60, and down to about 30, down to about 25, down to about 20, down to about 15, or less. Other desirable properties of a co-solvent include having sufficient miscibility with water, having chemical stability in a desired operating potential range, and maintaining a sufficient level of solubility of an electrolyte salt. A single co-solvent can be included, or a combination of different co-solvents can be included. Each co-solvent can be included in an electrolyte in an amount of at least about 0.1% vol./vol. (or wt./wt.), such as at least about 0.5% vol./vol. (or wt./wt.), at least about 1% vol./vol. (or wt./wt.), at least about 2% vol./vol. (or wt./wt.), at least about 3% vol./vol. (or wt./wt.), at least about 4% vol./vol. (or wt./wt.), at least about 5% vol./vol. (or wt./wt.), or at least about 10% vol./vol. (or wt./wt.), and up to about 15% vol./vol. (or wt./wt.), up to about 20% vol./vol. (or wt./wt.), up to about 25% vol./vol. (or wt./wt.), up to about 30% vol./vol. (or wt./wt.), or more.","Various materials given by formula (I) can be synthesized using a spontaneous, bulk precipitation approach with low cost precursors, and the synthesis can be readily scaled up for applications such as grid-scale energy storage. For example, synthesis can be carried out by combining chemical precursors or other sources of A, P, R, CN, and L in an aqueous solution or another type of medium, with the precursors reacting spontaneously to form a powder product. In some embodiments, the chemical precursors can include a source of P (e.g., a salt of P) and a source of A and R(CN) 6 (e.g., a salt of A and R(CN) 6 such as A 3 R(CN) 6 ). Synthesis can be carried out by co-precipitation, with substantially simultaneous dropwise addition of the precursors to a common liquid medium to maintain a substantially constant ratio of the precursors (e.g., a molar ratio of about 2:1 for the source of P and the source of A and R(CN) 6 , or another molar ratio m:1 with m≧1, such as m\u003e1 or m≧1.5) and to provide a consistent composition of a precipitate. Heating can be carried out, such as to a temperature above room temperature and below about 100° C. (e.g., in the range of about 40° C. to about 99° C., about 50° C. to about 90° C., or about 60° C. to about 80° C.), to yield better crystallinity in the final product, and an acid or a base also can be added to the reaction mixture to inhibit side reactions. A particular A used during synthesis can be exchanged by a different A′ for implementation within a battery, thereby affording advantages such as the selection of a desired electrode potential range.","The resulting powder product can include particles having a grain size (e.g., an average or median grain size) no greater than about 10 μm, no greater than about 5 μm, no greater than about 1 μm, no greater than about 900 nm, no greater than about 800 nm, no greater than about 700 nm, no greater than about 600 nm, no greater than about 500 nm, no greater than about 400 nm, no greater than about 300 nm, no greater than about 200 nm, or no greater than about 100 nm, and down to about 20 nm, down to about 10 nm, down to about 5 nm, or less. Without wishing to be bound by a particular theory, small grain sizes can contribute towards improved kinetics and other desirable properties, such as by affording higher surface to volume ratios.","For implementation within a battery, the resulting powder product (e.g., about 80% by total weight) can be incorporated as an active material by mixing with a conductive carbon material (e.g., about 10% by total weight) and a binder (e.g., about 10% by total weight) to form a slurry, and this slurry can be deposited adjacent to a substrate, dried to form a coating, a film, or other layer adjacent to the substrate, and then assembled as an electrode into the battery. Examples of suitable conductive carbon materials include carbon black, acetylene black, graphite, vapor grown fiber carbon, and carbon nanotubes, and examples of suitable binders include polyvinylidene fluoride and other types of polymeric binders. A thickness of the coating (including the powder product as the active material) can be at least about 500 nm, at least about 1 μm, at least about 10 μm, at least about 20 μm, at least about 30 μm, at least about 40 μm, or at least about 50 μm, and up to about 150 μm, up to about 200 μm, up to about 300 μm, up to about 500 μm, or more. A mass loading of the active material within the resulting electrode can be at least about 500 μg/cm 2 , at least about 700 μg/cm 2 , at least about 1 mg/cm 2 , at least about 2 mg/cm 2 , at least about 3 mg/cm 2 , at least about 4 mg/cm 2 , or at least about 5 mg/cm 2 , and up to about 10 mg/cm 2 , up to about 15 mg/cm 2 , up to about 20 mg/cm 2 , up to about 30 mg/cm 2 , up to about 50 mg/cm 2 , up to about 100 mg/cm 2 , or more.","Uses of Electrode Materials","The electrode materials described herein can be used for a variety of batteries and other electrochemical energy storage devices. For example, the electrode materials can be substituted in place of, or used in conjunction with, conventional electrode materials for aqueous electrolyte batteries or other types of batteries.","FIG. 2 illustrates a battery 100 implemented in accordance with an embodiment of the invention. The battery 100 includes a cathode 102 , an anode 104 , and a separator 106 that is disposed between the cathode 102 and the anode 104 . The battery 100 also includes an aqueous electrolyte 108 , which is disposed between the cathode 102 and the anode 104 . The use of the aqueous electrolyte 108 affords a number of advantages relative to organic solvent electrolytes, including higher safety, lower cost, capability for operation at higher power, and higher conductivity.","The operation of the battery 100 is based upon reversible intercalation of cations from the aqueous electrolyte 108 into at least one of the cathode 102 and the anode 104 . Other implementations of the battery 100 are contemplated, such as those based on conversion or displacement chemistry. In the illustrated embodiment, at least one of the cathode 102 and the anode 104 is formed using an electrode material given by formula (I). For example, the cathode 102 can be formed using one type of electrode material given by formula (I) (e.g., represented as A x P y [R(CN) 6-w L w ] z .(H 2 O) n ), and the anode 104 can be formed using another type of electrode material given by formula (I) (e.g., represented as A′ x′ P′ y′ [R′(CN) 6-w′ L′ w′ ] z′ .(H 2 O) n ). The ability of the electrode materials given by formula (I) to reversibly intercalate a variety of cations allows the battery 100 to be implemented as a hybrid-ion aqueous electrolyte battery, in which one electrode (e.g., the cathode 102 ) reacts with one type of cation, and another electrode (e.g., the anode 104 ) reacts with a different type of cation. One example is where the aqueous electrolyte 108 is a dual-ion electrolyte including Na + and K + , the cathode 102 reacts with Na + , and the anode 104 reacts with K + . In addition to Na + /K + , other examples include combinations such as H + /Li + , Na + /Li + , K + /Li + , H + /Na + , H + /K + , as well as combinations including NH 4 + . The aqueous electrolyte 108 also can be implemented as a single-ion electrolyte, where the cathode 102 and the anode 104 react with the same type of cation. In other embodiments, the cathode 102 can be formed using an electrode material given by formula (I), and the anode 104 can be formed using another type of electrode material, such as one including a carbon-based material (e.g., activated carbon) or a mixture of a carbon-based material and a conductive polymer (e.g., polypyrrole).","EXAMPLES","The following examples describe specific aspects of some embodiments of the invention to illustrate and provide a description for those of ordinary skill in the art. The examples should not be construed as limiting the invention, as the examples merely provide specific methodology useful in understanding and practicing some embodiments of the invention.","Example 1","Copper Hexacyanoferrate","This example describes copper hexacyanoferrate (“CuHCF”), whose electrochemical reaction can be represented as KCuFe III (CN) 6 +xK + +xe − =K 1+x Cu[Fe II (CN) 6 ] x [Fe III (CN) 6 ] 1-x . The theoretical specific capacity for anhydrous KCuFe(CN) 6 is about 85 mAh/g for some embodiments. In practice and for some embodiments, capacities of about 60 mAh/g and lower are generally observed, as the framework structure contains zeolitic water. Inductively coupled plasma mass spectrometry of CuHCF synthesized by a bulk precipitation reaction found a K:Cu:Fe ratio of about 0.71:1:0.72. Following previous conventions for the hydration of the crystal structure, the formula for the material on the basis of copper is K 0.71 Cu[Fe(CN) 6 ] 0.72 .3.7 H 2 O. The theoretical specific capacity for the material with this formula is about 62 mAh/g, which agrees with the observed specific capacity. As the exact water content varies with temperature and humidity, a capacity of 60 mAh/g was used for the definition of C rates when describing current densities in this example.","CuHCF has the Prussian Blue crystal structure, in which octahedrally-coordinated transition metals such as Cu and Fe are linked by CN ligands, forming a face-centered cubic structure (see FIG. 3 ). Fe is six-fold carbon-coordinated, while Cu (e.g., Cu 2+ ) is six-fold nitrogen coordinated. Each of the eight subcells of the unit cell contains a large “A” site that can be occupied by zeolitic water or hydrated ions such as K + . Hydrated ions can readily pass between one “A” site and the next through channels in the \u003c100\u003e directions. This three-dimensional network of “A” sites and channels allows for rapid transport of K + through the material with little disturbance of the crystal structure. Full occupancy of the “A” sites, as shown in FIG. 3 , occurs when the material is fully reduced. Zeolitic water is omitted for clarity.","Bulk CuHCF powder was synthesized by simultaneous dropwise addition of 120 mL of 0.1 M Cu(NO 3 ) 2 (Alfa Aesar) and 120 mL of 0.05 M K 3 Fe(CN) 6 (Sigma Aldrich) to 60 mL H 2 O during constant stirring. A brown precipitate formed almost immediately. After sonicating for 20 minutes, the suspension was allowed to sit for six hours. The precipitate was then filtered, washed with water, and dried in vacuum at room temperature. Co-precipitation of CuHCF in the presence of excess Cu 2+ proceeds slowly, allowing for ordered growth of highly crystalline, polydisperse nanoparticles of 20-50 nm (see FIG. 9 ). These CuHCF nanoparticles readily precipitate into larger agglomerations, which can be easily filtered and processed for use in battery electrodes. The powder product was used for X-ray diffraction (“XRD”) and Transmission electron microscope (“TEM”) measurements. To prepare electrodes, a mixture of 80% wt./wt. CuHCF, 9% wt./wt. amorphous carbon (Timcal Super P Li), 9% wt./wt. polyvinylidene fluoride (Kynar HSV 900), and 2% wt./wt. graphite (Timcal KS6) was ground together by hand until a homogeneous black powder formed. A slurry containing this mixture and 1-methyl-2-pyrrolidinone was spread on carbon cloth (Fuel Cell Earth) current collectors with mass loading of at least 10 mg CuHCF/cm 2 . The electrodes were dried in air at 100° C.","Electrochemical measurements were performed in flooded three-electrode cells containing an electrolyte of aqueous 1 M KNO 3 /0.01M HNO 3 with a pH of about 2, a working electrode containing CuHCF, a Ag/AgCl reference electrode, and a counter electrode containing a large mass of partially reduced CuHCF or Prussian Blue. The counter electrode acted as a reversible sink for potassium ions, and is analogous to the use of lithium foil counter electrodes during the study of electrode materials for lithium-ion batteries. Its large mass (about fifty times that of the working electrode) ensured that the capacity of the cell was primarily limited by the mass of the working electrode. To prepare counter electrodes containing Prussian Blue, Fe(NO 3 ) 3 and K 4 Fe(CN) 6 were substituted for the above precursors, and the chemical synthesis was performed at 80° C. A preconditioning potential of 0.4 V vs. standard hydrogen electrode (“S.H.E.”) was applied to partially reduce the Prussian Blue before its insertion into the full cell as a counter electrode.","The mid-composition reaction potential of CuHCF during potassium intercalation was found to be about 0.946 V with respect to S.H.E. (see FIG. 4 a ). The potential profile indicates a solid solution intercalation reaction. During cycling at a rate of 0.83 C, a capacity of about 59.14 mAh/g was observed, and about 67% of this capacity, about 40.1 mAh/g, was retained during cycling at a rate 100 times greater, namely 83 C (see FIG. 4 b ). This capacity retention at high current densities compares favorably with that of two common lithium-ion battery electrode materials, LiFePO 4 and Li 4 Ti 5 O 12 . While the specific capacity of CuHCF in this example is less than that of those common lithium-ion cathode materials, that parameter is less important for stationary applications, such as in conjunction with grid-scale storage. Parameters of greater importance for stationary applications are high rate performance, cycle life, and cost.","In addition to its excellent capacity retention at high current densities, CuHCF has a much greater cycle life than other previously demonstrated battery electrodes. During galvanostatic cycling between 0.8 and 1.2 V vs. S.H.E. at a current density of 17 C (see FIG. 4 c ), about 94.6% of the initial discharge capacity of about 52.2 mAh/g was retained after 10,000 cycles, and about 83% was retained after 40,000 cycles. The coulombic efficiency was above about 99.7% for the duration of that cycling. Additional electrolyte was added to the cell after about 25,000 cycles to counteract evaporation during open cell tests. In comparison, commercial lithium-ion batteries rarely last more than several hundred deep cycles, lead-acid batteries may endure up to about a thousand cycles of shallow (50%) discharging, and the best vanadium flow batteries reach about 5,000 cycles at 70% discharge.","Experiments were undertaken to investigate the physical process that controls the kinetic behavior of CuHCF during high rate cycling. Impedance spectroscopy measurements using the same flooded cell geometry as that during galvanostatic cycling showed a charge transfer resistance of about 1 Ω/cm 2 , with a double layer capacitance of about 2.5 mF/cm 2 (see FIG. 10 ). The hysteresis observed between the potential during charging and discharging at the half-charged state increased linearly with the current density, indicating that the electrolyte resistance probably dominates the cell impedance. At a cycling rate of C/6, the charge/discharge voltage difference at the half-charged state was about 4.4 mV. It increased to about 47 mV at a 8.3 C rate, and to about 405 mV at a 83 C rate (see FIG. 4 d ). Thus, the kinetic behavior is impacted by the resistance of the electrolyte, rather than by the transfer of charge carriers in and out of the electrode material. Adoption of a pressed cell geometry that reduces electrolyte resistance can improve the kinetic behavior. The magnitudes of this voltage hysteresis compare favorably with those of the best lithium-ion electrodes. Recent results showed 700 mV hysteresis during 60 C cycling of lithium iron phosphate, and 350 mV hysteresis during 13 C cycling of the lithium titanium oxide Li 4 Ti 5 O 12 .","The unusually small voltage hysteresis of CuHCF means that it can be cycled with high round-trip energy efficiency. To illustrate this point, one can consider a hypothetical full cell containing a CuHCF electrode and a fixed-potential counter electrode at a potential of one volt below the mid-charge reaction potential of CuHCF. Using the observed coulombic efficiency of about 99.7% and C/6 voltage hysteresis of about 4.4 mV for CuHCF, this hypothetical cell has an energy efficiency of over about 99% during cycling at a C/6 rate (see FIG. 4 e ). In spite of the increase in voltage hysteresis at higher current densities, the round-trip energy efficiency for this hypothetical cell is still about 95% at an 8.3 C rate (see FIG. 4 e ). These values of energy efficiency of full cells containing CuHCF would far surpass the efficiencies observed for some conventional battery systems.","The physical properties of CuHCF were characterized using TEM and powder XRD. The polydisperse 20-50 nm particle sizes were found during the TEM imaging (see FIG. 5 a ). The small particle size allows rapid access of the entire structure to inserted ions, which contributes to the high capacity retention and energy efficiency during cycling at high current densities. The crystal structure of CuHCF was determined to be face-centered cubic with a lattice parameter of about 10.1 Å. The lattice parameter was found to increase with the charge state of the material, as illustrated by a diffraction peak shift to smaller diffraction angles during charging (see FIG. 5 b ). While the position of each diffraction peak shifted with charge state, no new peaks appeared during charging. This confirms that the electrochemical cycling of CuHCF is a single-phase reaction. The about 0.9% increase in lattice parameter (see FIG. 5 c ) from the fully reduced to fully oxidized state is explained by the increase in the radius of the [Fe 2+ (CN) 6 ] −4 group during its oxidation to [Fe 3+ (CN) 6 ] −3 . The ultra-long cycle life of CuHCF is due, at least in part, to a stable crystal structure that undergoes a small, isotropic lattice strain during cycling. Ex-situ XRD measurements were carried out as follows. Electrodes containing CuHCF were first fully discharged by fixing their potentials at 0.4 V vs. S.H.E. until the discharge current decayed to zero. Electrodes were then charged galvanostatically at a 1 C rate until the desired charge state was reached. The electrodes were removed from the cell, and their diffraction spectra measured. The lattice parameter of each sample was determined using a Treor fitting algorithm in the X%27Pert Highscore Plus software package.","Unlike the metal oxides and phosphates found in current lithium-ion battery electrodes, open frameworks with the Prussian Blue crystal structure can be synthesized in bulk at room temperature by spontaneous precipitation from aqueous solutions containing transition metal salts and hexacyanometallate precursors. During the work reported in this example, several grams of CuHCF were formed during each synthesis, and the synthesis is highly scalable.","Extremely long cycle life, high rate capability and round-trip energy efficiency, and inexpensive bulk synthesis make Prussian Blue analogues such as CuHCF very attractive for use in batteries for grid-scale energy storage. In addition, materials with this structure can be operated in inexpensive, safe, and highly conductive aqueous electrolytes. Thus, batteries relying on Prussian Blue-type materials enjoy a number of advantages when compared to current lithium-ion cells, without suffering from the safety concerns related to flammable organic electrolytes.","Example 2","Nickel Hexacyanoferrate","This example describes nickel hexacyanoferrate (“NiHCF”), whose electrochemical reaction can be represented as ANiFe III (CN) 6 +A + +e − =A 2 NiFe II (CN) 6 , where A + is a cation such as sodium or potassium. The following describes the unusual behavior of a high capacity battery electrode containing bulk NiHCF powder prepared by a chemical precipitation method.","NiHCF has the Prussian Blue crystal structure, in which transition metal cations such as Fe and Ni are bound by bridging CN ligands, forming a face-centered cubic structure (see FIG. 6 ). In the case of NiHCF, Fe is six-fold carbon coordinated, while Ni (e.g., Ni 2+ ) is six-fold nitrogen coordinated. The resulting framework has large channels oriented in the \u003c100\u003e directions, through which hydrated cations such as K + and Na + can diffuse. These cations occupy the interstitial “A” sites at the center of each of the eight subcells of the unit cell. Full occupancy of the “A” sites is achieved upon full reduction of the material to A 2 NiFe II (CN) 6 . Zeolitic water also occupies the structure, but is omitted here for clarity.","NiHCF powder was synthesized following a similar procedure used to synthesize CuHCF described in Example 1. Instead of a copper precursor, reagent grade Ni(NO 3 ) 2 (Sigma Aldrich) was used. NiHCF was synthesized by a co-precipitation method that ensured consistent reaction conditions. Slow, simultaneous dropwise addition of aqueous precursors to a common liquid medium maintains a substantially constant ratio of reactants, ensuring a consistent composition of a precipitate. The reaction was performed at 70° C. because NiHCF synthesized at room temperature had poor crystallinity for some embodiments. Electrodes containing NiHCF were made using a similar procedure as previously described. The mass loading of electrodes was between about 7 and about 12 mg/cm 2 .","Electrochemical cycling of electrodes containing NiHCF powder was performed in aqueous 1 M NaNO 3 or 1 M KNO 3 (Sigma Aldrich). Dilute HNO 3 was added to the electrolytes to attain a pH of about 2. Three-electrode flooded cells containing a Ag/AgCl reference electrode and a counter electrode containing a large, partially discharged mass of NiHCF were used. This counter electrode acted as a reversible ion sink, similar to the large masses of lithium foil used during half-cell tests of lithium-ion electrodes. The as-synthesized NiHCF is initially fully oxidized, with a high open circuit voltage. However, to avoid potassium contamination during experiments in the sodium electrolyte, mobile cations were removed from the counter electrodes by fixing their potentials at 1.0 V for 30 minutes in the desired electrolyte. After washing with water, partial discharging was carried out in fresh electrolyte by fixing the potential at the half-discharge potential of NiHCF (e.g., about 0.59 V for sodium insertion). NiHCF was found to react with sodium at about 0.59 V vs. S.H.E., while its reaction with potassium occurs at about 0.69 V (see FIGS. 7 a \u0026 b ). This indicates a trend to higher reaction potentials for the insertion of heavier alkali ions. For some embodiments, the theoretical capacity of NiHCF can be difficult to determine with precision because the zeolitic water content varies with temperature and humidity. The theoretical capacities of these materials can also vary by ten percent or more, depending on the concentration of defects in the framework structure. For this example, a current density of 60 mA/g is defined as 1 C.","The open framework structure of NiHCF permits rapid kinetics during the cycling of both sodium and potassium. During either sodium or potassium cycling, a specific capacity of about 59 mAh/g was observed at a C/6 rate (see FIG. 7 c ). Virtually all of this capacity is accessible in a small 0.3 V range around the half-charge reaction potential. During sodium cycling, about 86.5% of this maximum capacity is retained at a rate of 8.3 C, and about 67% is still retained at a 41.7 C rate. NiHCF behaves similarly during potassium cycling: about 85.5% of its maximum capacity is retained at 8.3 C, and about 66% is retained at 41.7 C. The capacity retention of NiHCF at high current densities is comparable to the best reported rate performance of conventional lithium-ion battery electrode materials. For example and over a one-volt cycling window between 3.0 and 4.0 V vs. Li + /Li, it has been reported that LiFePO 4 , a common lithium-ion cathode material, retains about 70% of its theoretical capacity at a 20 C rate.","NiHCF has low voltage hysteresis between charge and discharge during either sodium or potassium cycling (see FIGS. 7 a \u0026 b ). The voltage hysteresis at a half-charged state during sodium cycling is about 12.7 mV at 0.83 C (about 0.4 mA/cm 2 ). At the same current density in potassium electrolyte, the half-charge voltage hysteresis of NiHCF is about 8 mV. This voltage hysteresis increased linearly with current density, and during 41.7 C cycling (about 18 mA/cm 2 ), it was found to be about 178 mV during sodium cycling, and about 106 mV during potassium cycling. The ohmic behavior of the voltage hysteresis resulted from the flooded cell geometry%3b most of the impedance in the cell was electrolyte resistance. The difference between the voltage hystereses during cycling of sodium and potassium arose from variations in cell geometry. The use of a thinner pressed cell geometry can result in even lower voltage hysteresis.","The low voltage hysteresis of NiHCF allows higher energy efficiency than that of conventional battery electrodes. Round-trip energy efficiency also depends on coulombic efficiency, and the coulombic efficiency of NiHCF was found to be between about 99.7% and about 99.9% during cycling for some embodiments. Thus, the low voltage hysteresis of NiHCF has a predominant effect on its energy efficiency.","In a hypothetical cell of nominal voltage of 1.0 V that contains NiHCF and a perfectly reversible counter electrode, the round-trip energy efficiency is about 98-99% at a 0.83 C rate. At higher current densities, an energy efficiency of about 90% is attainable during potassium cycling at 41.7 C, and an efficiency of about 83% is attainable during sodium cycling at the same rate. The energy efficiency of full cells using NiHCF electrodes can be even higher using a pressed cell geometry, but the reported results already surpass conventional batteries: a typical efficiency for lead-acid and vanadium flow batteries is 75-80%, while, at very low current densities, lithium-ion batteries can achieve efficiencies above 90%.","NiHCF showed high stability during electrochemical cycling of sodium to full (100%) depth of discharge, with essentially zero capacity loss after 5,000 cycles at a 8.3 C rate (see FIG. 7 d ). In addition, NiHCF showed essentially no capacity loss during the cycling of potassium for 1,000 cycles, after which capacity was lost at a rate of about 1.75%/1,000 cycles. In contrast, lead-acid cells can last about 1,200 cycles upon shallow (50%) discharging, and current vanadium flow cells can last up to 5,000 cycles at 70% discharge. The stability of NiHCF during sodium cycling is even greater than that of CuHCF, which showed slow capacity fading, at a rate of about 0.5%/1,000 cycles at 100% discharge in a potassium electrolyte. However, in the previous study of CuHCF, electrodes were dried at a higher temperature (100° C. instead of 80° C.), which may have damaged the CuHCF framework structure to some extent.","The NiHCF material is composed of polydisperse nanoparticles of about 20-50 nm in diameter (see FIG. 8 d ). These form porous structures with a high surface area, allowing for rapid reaction with insertion ions. Physical characterization using scanning electron microscopy (“SEM”) and XRD revealed that the nanostructured morphology has a high degree of crystallinity. The as-synthesized NiHCF powder was found to have a XRD spectrum corresponding to a phase-pure face-centered cubic structure with a lattice parameter of about 10.2 Å (see FIG. 8 e ). The rigid open framework of the Prussian Blue structure provides structural and chemical stability, allowing for repeated cycling of NiHCF with sodium and potassium with essentially no loss in capacity. Ex-situ XRD measurements were carried out by cycling NiHCF electrodes ten times at 250 mA/g, ending at full discharge. The electrodes were then charged to the desired fractional charge state at the same current density. The duration of the final charging current was determined from the specific capacity of each electrode observed during the initial ten cycles. XRD was then performed on the electrodes, and the positions of diffraction peaks were determined using Gaussian fits. Ex-situ XRD spectra of NiHCF electrodes at different charge states revealed that the lattice parameter increases linearly with charge state, as illustrated by a shift in the position of the 400 diffraction peak to smaller angles (see FIGS. 8 a \u0026 b ). The isotropic lattice strain is about 1.1% during potassium cycling, and about 0.18% during sodium cycling, which correlates with the better cycle life during sodium ion cycling (see FIG. 8 c ). The small increase in lattice parameter during charging also is observed in CuHCF, and corresponds to an increase in the radius of the [Fe 2+ (CN) 6 ] −4 group during its oxidation to [Fe 3+ (CN) 6 ] −3 . The radius of the channel between the “A” sites in the Prussian Blue structure is comparable to the Stokes ionic radius of hydrated potassium, but smaller than the Stokes ionic radius of hydrated sodium. The possibility that potassium and sodium in the electrolyte might exchange with zeolitic water already present in the crystal structure may contribute to the mechanism for ion transport through the lattice. The reported lattice parameters (see FIG. 8 c ) are the means of the values calculated from the positions of six diffraction peaks for each sample. The error bars in this figure are one standard deviation from the mean calculated lattice parameter.","The NiHCF material can be synthesized in bulk using spontaneous chemical precipitation reactions from aqueous precursors at low temperatures. The synthesis is therefore both scalable and inexpensive. In addition, Prussian Blue analogues such as NiHCF operate in safe, inexpensive aqueous electrolytes, and possess superior rate capability, round-trip energy efficiency, and cycle life. Together, these properties make them desirable for a variety of energy storage systems, including the support of the large scale electric grid, especially against short-term transients.","Example 3","Copper Hexacyanoferrate and Nickel Hexacyanoferrate","This example describes additional measurements on CuHCF and NiHCF of some embodiments. To examine the effect of insertion species on the electrochemical properties of bulk CuHCF and NiHCF, these materials were cycled in aqueous electrolytes including lithium, sodium, potassium, or ammonium ions.","Syntheses of CuHCF and NiHCF nanopowder were performed using a co-precipitation method. Simultaneous, dropwise addition of about 40 mM copper or nickel nitrate, and about 20 mM potassium ferricyanide into deionized water allowed for controlled co-precipitation of solid CuHCF or NiHCF products. The synthesis of CuHCF was performed at room temperature, while the synthesis of NiHCF was performed at about 70° C. These solid products were filtered, washed with water, and dried in vacuum at room temperature. Up to about 3 g of product was produced during each synthesis, and these syntheses can be readily scaled to produce larger quantities of CuHCF and NiHCF. Slurries containing the as-synthesized hexacyanoferrates, amorphous carbon (Timcal SuperP Li), polyvinylidene difluoride (Kynar HSV 900), and graphite (Timcal KS6) in a ratio of 80:9:9:2 were prepared in 1-methyl-2-pyrrolidinone. These slurries were deposited on carbon cloth, and dried in vacuum at no more than about 80° C. The resulting CuHCF and NiHCF electrodes were about 100 μm thick, with a mass loading of about 5-10 mg/cm 2 .","Three-electrode flooded cells including a CuHCF or NiHCF working electrode, a Ag/AgCl reference electrode, and a large, partially charged CuHCF or NiHCF counter electrode were used to study the electrochemical behavior of CuHCF and NiHCF in various aqueous electrolytes. The electrolytes used were aqueous 1 M LiNO 3 , 1 M NaNO 3 , 1 M KNO 3 , and 0.5 M (NH 4 ) 2 SO 4 . The pH of all electrolytes was lowered to about 2 by the addition of nitric or sulfuric acid. The counter electrodes functioned as reversible ion sinks, analogous to the large mass of metallic lithium used for lithium ion half-cells. Both CuHCF and NiHCF initially include some potassium. To avoid contamination of the lithium, sodium, and ammonium electrolytes by potassium de-intercalated from the counter electrodes, the counter electrodes were pretreated. First, potassium was removed by fixing their potentials at 1.1 V vs. S.H.E. until the current decayed to zero. After washing with water, the counter electrodes were then partially discharged in fresh electrolyte by fixing their potentials at the half-charge potentials of CuHCF and NiHCF in each electrolyte. Each working and counter electrode pair was used in one type of electrolyte.","CuHCF and NiHCF were characterized by powder XRD and SEM. The materials were found to be phase pure, with the face-centered cubic Prussian Blue-type crystal structure. The lattice parameter of the as-synthesized CuHCF was about 10.16 Å, while the lattice parameter of the NiHCF powder was about 10.22 Å. TEM images revealed that both materials were composed of large, porous agglomerations of 20-50 nm nanoparticles. The small particle size and porous nature of the agglomerations are advantageous for battery electrodes, as the high surface-to-volume ratio of nanoparticles allows insertion ions to rapidly diffuse throughout the material.","To characterize the electrochemical behavior of CuHCF and NiHCF, galvanostatic cycling of these materials was performed in aqueous electrolytes containing Li + , Na + , K + , or NH 4 + . Though other electrochemical techniques such as cyclic voltammetry also can be used to examine the electrochemical properties of electrodes, galvanostatic cycling is attractive because it imitates the steady-state conditions under which batteries often operate. The cycling was performed at current densities between about ±10 and about ±2500 mA/g of active material.","Specific capacities of about 60 mAh/g were observed for NiHCF and CuHCF during slow cycling in electrolytes containing Li + , Na + , K + , and NH 4 + . For comparison, common lithium-ion battery cathodes such as LiCoO 2 and LiFePO 4 have specific capacities of between 130 mAh/g and 170 mAh/g. Though the specific capacities of NiHCF and CuHCF of some embodiments are lower, their inexpensive synthesis, high rate capability, and long cycle life suit them well for stationary applications, such as energy storage for the grid. For this example, 60 mAh/g is defined as 1 C. Thus, 50 mA/g is 0.83 C, and 2,500 mAh/g is 41.7 C.","The potential of NiHCF during insertion and extraction of both Na + and K + follows a smooth S-curve, indicative of a solid solution reaction. However, during the intercalation of Li + and NH 4 + into NiHCF, the behavior is more complex. The removal of Li + from NiHCF begins at about 0.4 V vs. S.H.E., and, although a single plateau is observed during charging at a 0.83 C rate, the charging curve shows a change in slope at a charge state of about one third at higher current densities (see FIG. 11 a ). Without wishing to be bound by a particular theory, the more complicated insertion behavior of Li + into NiHCF may suggest destabilization of its open framework structure in some embodiments, as dissolved Fe III (CN) 6 −3 was visually observed in the electrolyte after a few cycles. The reduction of dissolved Fe III (CN) 6 −3 to Fe II (CN) 6 −2 also resulted in a high discharge capacity during 0.83 C cycling of Li + with NiHCF. The reaction of NiHCF with NH 4 + also shows complex behavior, as a shoulder and second plateau is observed near 0.85 V (see FIG. 11 d ). The reaction potential of NiHCF was found to increase for the heavier alkali ions, and its highest reaction potential was observed during the cycling of NH 4 + (see FIG. 11 e ).","The electrochemical properties of CuHCF also vary with insertion ion. During its reaction with Li + (see FIG. 12 a ), a slight shoulder is observed near a charge state of one third, just as was observed during the cycling of NiHCF with Li + . However, the cycling of CuHCF with Na + , K + , and NH 4 + appears to be relatively straightforward, as a single reaction plateau is observed during each of these reactions (see FIGS. 12 b - d ). As was observed for NiHCF, the reaction potential of CuHCF increases for heavier alkali ions, with an even higher and flatter reaction potential for NH 4 + (see FIG. 12 e ).","The intercalation of Li + into both NiHCF and CuHCF occurs over a broader potential window than the insertions of the other ions, even at low current densities. NiHCF reacts with Li + over a window of about 0.5 V, and the reaction of CuHCF with Li + occurs over a range of about 0.7 V. The reactions of the other insertion ions with NiHCF and CuHCF occur more sharply. At a 0.83 C rate, the full capacity of NiHCF during the cycling of Na + and K + can be achieved in a span of about 0.3 V, while its reaction with NH 4 + occurs over a window of about 0.4 V. In CuHCF at the same rate, voltage ranges of about 0.4 V, about 0.3 V, and about 0.2 V are involved for the cycling of Na + , K + , and NH 4 + , respectively.","Both NiHCF and CuHCF have high rate capability, retaining most of their capacities even at high current densities. This can be attributed, at least in part, to the porous, nanoparticulate electrode morphology, and to the open framework crystal structure of these materials, each of which allows rapid ion transport through the electrodes. During the de-intercalation of both Na + and K + , NiHCF retains about 86% of its discharge capacity when cycled at 8.3 C, and about 66% of its discharge capacity at 2,500 mA/g, namely when cycled at a 41.7 C rate (see FIG. 13 a ). These results compare favorably with the capacity retention of lithium-ion battery electrodes such as LiFePO 4 , as well as the sodium-ion electrode Na 4 Mn 9 O 18 . The high similarities between both the shapes of the potential profiles and the capacity retentions at high rates suggest that the intercalation of Na + and K + into NiHCF proceeds by similar mechanisms. During the cycling of Li + and NH 4 + , NiHCF retains about 58% and about 39%, respectively, of the discharge capacities when cycled at a 41.7 C rate. The rate capability of CuHCF during K + cycling is even higher than that of NiHCF, with about 94.7% capacity retention at 8.3 C, and retaining about 84% of its capacity at 41.7 C (see FIG. 13 b ). Insertion of NH 4 + and Li + into CuHCF also occurs readily at high rates, as it retains about 75% and about 65% of its discharge capacity during these respective reactions, at 41.7 C. In contrast to NiHCF, CuHCF of some embodiments shows a less impressive rate capability during reaction with Na + , during which it retains about 34% of its capacity at 41.7 C.","NiHCF and CuHCF both show high rate capability during the insertion of K + and NH 4 + , but behave differently when cycling Na + and Li + . Lithium ions can be easily cycled in CuHCF at high rates, while cycling of Na + yields less impressive performance in some embodiments%3b the converse is observed for NiHCF. XRD indicates that these two materials had lattice parameters that differed by less than about 1%, and so the “A” sites and the channels between those sites should be closely similar in size for the two materials. Without wishing to be bound by a particular theory, it is possible that the difference in the ease of Na + and Li + insertion in CuHCF and NiHCF results from some other differences in their framework structures.","The use of aqueous electrolytes and scalable, low-temperature syntheses allow batteries based on NiHCF and CuHCF to be manufactured in an inexpensive fashion. Yet, for inexpensive operation, these materials also should be durable. Extended cycling of NiHCF and CuHCF at a 8.3 C rate (500 mA/g) was performed in Li + , Na + , K + , and NH 4 + electrolytes. NiHCF shows essentially zero capacity loss for 500 cycles during the cycling of Na + and K + (see FIG. 13 c ). After an initial capacity loss of about 10% during the first 100 cycles, NiHCF is stable during the cycling of NH 4 + , retaining about 88% of its initial capacity after 500 cycles. However, NiHCF of some embodiments shows greater capacity loss when Li + is cycled. Without wishing to be bound by a particular theory, this may be attributed to the dissolution of NiHCF during Li + cycling.","CuHCF also shows excellent durability during long cycling at the same rate. CuHCF retains about 99% of its initial capacity after 500 cycles of K + insertion (see FIG. 13 d ). The capacity retention of CuHCF during its reaction with other ionic species is lower for some embodiments. CuHCF retains about 91%, about 77%, and about 35% of its initial capacity after 500 cycles for NH 4 + , Na + , and Li + , respectively. The greater capacity loss of CuHCF during its cycling with Li + is similar to the behavior of NiHCF during Li + cycling.","In this example, the counter electrodes included large masses of the same hexacyanoferrate active materials as the working electrodes. In such fashion, the counter electrodes acted as reversible ion sinks with small changes in their potentials, and served to inhibit spurious side reactions such as electrolyte decomposition. However, the presence of large masses of CuHCF and NiHCF in the counter electrodes may mask the effects of trace solubility of these materials in aqueous electrolytes. While visual observation was made of dissolved Fe(CN) 6 −3 during the insertion of Li + into CuHCF and NiHCF, slower dissolution may also explain the smaller capacity losses observed during the cycling of NH 4 + for both materials, and during the cycling of Na + in CuHCF. Further optimizations can establish conditions under which CuHCF and NiHCF can be operated with long cycle life in full cells that do not include excess ferricyanide in counter electrodes.","It might have been expected that insertion species with Stokes ionic radii smaller than the radius of the channels between the “A” sites can be readily cycled, while larger sized species could not be readily cycled. Demonstration of Na + cycling in NiHCF indicates that this proposition is not generally true: the Stokes ionic radius of aqueous Na + is about 1.8 Å, while the radius of the channels connecting the “A” sites is about 1.6 Å. The reaction potential of both NiHCF and CuHCF decreases with an increase in the Stokes ionic radius of the insertion ion (see FIG. 13 e ). The higher the charge-to-radius ratio of an ion, the more strongly water molecules will typically coordinate to it, and so a larger Stokes ionic radius in aqueous solution typically correlates with a smaller effective ionic radius. Thus, for both NiHCF and CuHCF, higher potentials are observed during reactions with larger ions (see FIG. 13 f ) on the basis of the Shannon effective ionic radii (see Shannon, R. D., “Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides,” Acta Cryst ., A32, 751 (1976), the disclosure of which is incorporated herein by reference in its entirety).","Example 4","Electrochemical Performance of Full Cells","This example describes the use of Prussian Blue analogue electrodes in full cells. A device was assembled so as to include a CuHCF cathode, a non-Prussian Blue analogue anode, namely a mixed activated carbon (“AC”)/polypyrrole (“PPy”) anode, and an aqueous electrolyte including potassium ions at a pH of about 1. The potential profiles of the CuHCF cathode and the AC/PPy anode during cycling in the aqueous potassium ion electrolyte are illustrated in FIG. 14 . As can be appreciated, the potential profiles are substantially unchanged for several cycles. Without wishing to be bound by a particular theory, the combination of the electrolyte with a pH of about 1 and the use of the highly reversible, high capacity AC/PPy anode allows the CuHCF cathode to operate reversibly with essentially no chemical instability. Full cells of this type can be implemented with essentially zero capacity loss after 500 cycles.","Another device was assembled so as to include a copper iron hexacyanoferrate cathode (“CuFeHCF”) (i.e., a combination of elements (copper and iron) at the “P” sites of the crystal structure), a non-Prussian Blue analogue anode, namely an AC anode, and an aqueous electrolyte including sodium ions at a pH of about 1. As can be appreciated from FIG. 15 , there is essentially no capacity loss after 500 charge/discharge cycles of this device. The potential profile of this device during charge/discharge is similar to that of the device including the CuHCF cathode//AC/PPy anode in the potassium ion electrolyte.","Example 5","Cycling of Divalent Insertion Ions","To demonstrate the reversible cycling of a Prussian Blue analogue with a divalent insertion ion, cyclic voltammetry was performed on a CuHCF electrode in an aqueous electrolyte including Mg(NO 3 ) 2 at a pH of about 1. As illustrated in FIG. 16 , the electrode showed reversible electrochemical oxidation/reduction when its potential was swept over a wide range. The plot illustrates a representative charge/discharge cycle, and this behavior was observed to be reversible. It might have been expected that insertion species with Stokes ionic radii larger than the radius of the channels between the “A” sites cannot be readily cycled. Demonstration of Mg +2 cycling in CuHCF indicates that this proposition is not generally true: the Stokes ionic radius of aqueous Mg +2 is about 5 Å, while the radius of the channels connecting the “A” sites is about 1.6 Å.","Example 6","Copper Nickel Hexacyanoferrate","This example describes copper nickel hexacyanoferrate (“CuNiHCF”), which includes a combination of elements (copper and nickel) at the “P” sites of the Prussian Blue crystal structure (see FIG. 17 a ).","CuNiHCF was synthesized following a similar co-precipitation method as described in previous examples. Briefly, one aqueous precursor solution including Cu(NO 3 ) 2 and Ni(NO 3 ) 2 and another aqueous precursor solution of K 3 Fe(CN) 6 were combined in pure water by simultaneous dropwise addition. Solid products of the formula K x Cu 1-p′ Ni p′ [Fe(CN) 6 ] z (0≦p′≦1) rapidly precipitated. These products were filtered, washed with water, and dried in vacuum at room temperature. The relative amounts of Cu, Ni, and Fe in the products were measured using inductively coupled plasma mass spectrometry.","TEM characterization of CuNiHCF showed that these materials are composed of agglomerations of 20-50 nm nanoparticles ( FIG. 17 b ). XRD characterization revealed that these materials are phase-pure and highly crystalline ( FIG. 17 c ). The lattice parameter of CuNiHCF generally increases with nickel content (see FIG. 17 d ).","Electrochemical characterization of the CuNiHCF materials was performed using aqueous half-cells. Working and counter electrodes were prepared as described in previous examples. Electrolytes used were 1 M KNO 3 or 1 M NaNO 3 , with dilute HNO 3 added to achieve pH=2. Galvanostatic cycling was performed on CuNiHCF electrodes at 50 mA/g in potassium ion electrolyte (see FIG. 18 a ) and sodium ion electrolyte (see FIG. 18 b ). In both electrolytes, a reaction potential of the CuNiHCF materials was found to increase with copper content (see FIG. 18 c ). This result demonstrates that the reaction potential of Prussian Blue analogues can be controlled by changing relative amounts of species occupying the “P” sites. Materials of intermediate composition (including both Cu and Ni) showed a single reaction potential, so Cu and Ni are expected to be distributed randomly on the “P” sites, resulting in a substantially uniform, average electronic environment for electrochemically active hexacyanoferrate groups. The Cu/Ni occupancy of the “P” sites of the Prussian Blue crystal structure, therefore, can be described as a fully miscible solution of Cu and Ni. The electrochemical and XRD data is consistent with CuNiHCF as a single phase, regardless of its chemical composition within the tested range.","Long-term electrochemical cycling of CuHCF, NiHCF, and CuNiHCF (p′=0.42) was performed in both electrolytes. NiHCF and CuNiHCF showed essentially zero capacity loss after 2,000 cycles when cycled at 500 mA/g in 1 M NaNO 3 , while CuHCF loses about one quarter of its initial capacity when cycled under these conditions (see FIG. 18 d ). In 1 M KNO 3 , CuHCF and NiHCF showed essentially zero capacity loss after 2,000 cycles at 500 mA/g, while CuNiHCF showed a capacity loss of about 10% (see FIG. 18 e ). Without wishing to be bound by a particular theory, the mechanism for capacity loss may arise from slow dissolution of the Prussian Blue analogues.","Example 7","Electrochemical Performance of Full Cells","This example describes the use of Prussian Blue analogues in full, two-electrode cells including such materials in cathodes, and a different type of material in anodes. The choice of anodes is governed by conditions in which open framework structures operate: an acidic, water-based electrolyte (e.g., pH=1). One choice for anodes is a carbon-based material, namely AC. Full cell results using open framework structure cathodes and anodes including AC are described here. Experiments in full cells allowed the identification of cathode solubility issues hidden under other experimental conditions, and allowed the identification of ways to address the partial solubility of open framework structure materials. Solubility of battery electrodes can result in a loss of capacity, and can also result in electrochemical reactions that impede a battery from cycling properly.","The data presented in this example demonstrate the use of three Prussian Blue analogues for use as cathodes in full cells: CuHCF, NiHCF, and CuFeHCF. These are three examples of the Prussian Blue analogue class of materials, which includes other materials that also can be used as cathodes in full cell batteries. Furthermore, the data presented in this example demonstrate the operation of Prussian Blue analogue cathodes against two types of anodes: one including AC, and another including a mixture of AC and PPy, which is an electronically conductive polymer. The addition of electronically conductive polymers to AC provides improved properties in accordance with some embodiments. In brief, these conductive polymer additives can allow control of an operating potential of the AC, which can increase an overall voltage of full cells. In addition, these conductive polymer additives can be electrochemically active (as is the case for PPy), which can increase a specific capacity and an energy density of the AC/PPy electrode. Together, these results demonstrate the operation of a full cell including a Prussian Blue analogue electrode, another electrode based on a carbon-based material and an additive such as an electronically conductive polymer, and an electrolyte that is optimized to maintain the chemical and electrochemical stability and insolubility of both electrodes.","Experimental Procedures:","Both cathodes and anodes were prepared by drop-casting fine particle ink onto a carbon cloth (“CC”) current collector. The CC is particularly resistant to potentially corrosive conditions of water-based electrolytes and allows high mass loadings. The open framework structure ink was prepared by mixing 85% wt./wt. of active material, 8% wt./wt. of carbon black, and 7% wt./wt. of polyvinylidene fluoride. The AC ink was composed of 90% wt./wt. active material and 10% wt./wt. of polyvinylidene fluoride. N-methyl pyrrolidone was used as a solvent (about 0.8 g for every 0.2 g of powder). The loading of active material was in the order of 10-15 mg cm −2 for cathodes and 45-50 mg cm −2 for anodes.","Electrochemical performance of the devices was evaluated using a flooded cell, three electrode setup using Ag|AgCl| 3.5M as a reference electrode. In some tested configurations, the electrolyte was based on a 1M KH 2 PO 4 /H 3 PO 4 solution at pH=1. The choice of 1M KH 2 PO 4 /H 3 PO 4 as an electrolyte was governed by three main considerations: (1) it is electrochemically stable in the potential range tested%3b (2) it is inexpensive%3b and (3) it is a good buffer system, with a pH around 2, and a stable pH facilitates uniform performance over a long period of time. The solution was purged with nitrogen for 15 minutes before each experiment.","Results and Discussion:","FIG. 19 illustrates the galvanostatic cycling of an open framework structure/AC full cell battery. The potential profile of the negative electrode varies almost linearly with the state of charge, which is a typical behavior of an electrochemical double-layer capacitor (ultracapacitor) electrode. The open circuit potential of the AC varies between 0.4-0.8 V versus the reference electrode, depending on the presence of surface groups. The slope of the charge/discharge curve depends on the surface area of the AC exposed to the electrolyte (interface), and typically increases with AC loading. As a rule of thumb, a double layer capacitance in water-based electrolyte is about 25 μF cm −2 .","During initial trials with AC-based anodes, it was observed that the open framework structure cathodes show some solubility after long term cycling. This was evident by the observation that the electrolyte became colored, and a blue deposit appeared on the AC anode, due to local electrodeposition of Prussian Blue material.","To address the solubility issue, the pH-dependence of the solubility of both NiHCF and CuHCF was analyzed by placing 10 mg of each material in the electrolyte at different pH values and analyzing the solution by UV-vis spectroscopy. It was observed that the solubility increases with increasing pH of the solution in each case. After narrowing down a desirable pH range (to less than about 2) through the solubility analysis, the CuHCF material in a potassium-based electrolyte was used as a standard system for further optimization of the operating pH. As illustrated in FIG. 20 and FIG. 21 , the long term (20 cycles, more or less 3 days) stability of the material is improved by decreasing the pH from 2 to 1. A further decrease of the pH (tested to pH=0) can result in some material instability due to decomposition and subsequent HCN evolution, according to some embodiments.","The stability of open framework structure electrode materials was also analyzed in the presence of less polar co-solvents. The choice of the co-solvents was governed by three main considerations: (1) a co-solvent should be miscible with water%3b (2) a co-solvent should be stable in an operating potential range%3b and (3) the presence of a co-solvent should not interfere with the solubility of the 1M potassium salt. The inclusion of 5% and 10% glycerine and ethylene glycol (“EG”) was investigated. In order to test the electrochemical stability of the co-solvents, cyclic voltammetry measurements were made on a glassy carbon pin electrode in the potential stability range of water at pH=1. No measurable electrochemical activity was found in either of the 5% solutions, while the 10% solutions showed a small oxidative current at high potentials. FIG. 22 illustrates the charge/discharge profile for a CuHCF/AC full cell in the presence of 5% EG, and FIG. 23 illustrates the charge/discharge profile for a CuHCF/AC full cell in the presence of both 5% glycerine and 10% EG. FIG. 24 illustrates the charge/discharge profile for a CuHCF/AC full cell in the presence of 5% glycerine, and FIG. 25 illustrates the charge/discharge profile for a CuHCF/AC full cell in the presence of 10% glycerine. As can be appreciated, the devices exhibited excellent capacity retention in the presence of the co-solvents over the cycles tested. Without wishing to be bound by a particular theory, the presence of the co-solvents can decrease a solubility of Prussian Blue analogue electrodes in full cell devices.","Using operating conditions at pH=1, open framework structure materials were tested in full cells during long term cycling (500 cycles, 10 C, average of 80 h in electrolytes). Experiments were conducted in full cell setups with CuHCF, NiHCF, CuFeHCF in K + , Na + and NH 4 + -based electrolytes. The results demonstrate the long term cyclability of the open framework structure materials against a carbon-based anode material.","FIG. 26 illustrates long term cycling (450 cycles) of a NiHCF/AC full cell in 1 M Na + at pH=1. The device exhibited excellent capacity retention, with about 3% capacity loss over 500 cycles at 10 C. FIG. 27 illustrates long term cycling (350 cycles) of a NiHCF/AC full cell in 1 M K + at pH=1. The device exhibited excellent capacity retention, with essentially no capacity loss over 350 cycles at 10 C.","FIG. 28 illustrates long term cycling (500 cycles) of a CuHCF/AC full cell in 1 M K + at pH=1. The device exhibited excellent capacity retention, with essentially no capacity loss over 500 cycles at 10 C. FIG. 29 illustrates long term cycling (500 cycles) of a CuHCF//AC/PPy full cell in 1 M NH 4 + at pH=1. The device exhibited excellent capacity retention, with about 1.6% capacity loss over 500 cycles at 10 C.","FIG. 30 illustrates long term cycling (500 cycles) of a CuFe(50%)HCF//AC/PPy full cell in 1 M Na + at pH=1. The device exhibited excellent capacity retention, with essentially no capacity loss over 500 cycles at 10 C. FIG. 31 illustrates long term cycling (500 cycles) of a CuFe(50%)HCF//AC/PPy full cell in 1 M K + at pH=1. The device exhibited excellent capacity retention, with about 1.5% capacity loss over 500 cycles at 10 C.","While the invention has been described with reference to the specific embodiments thereof, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the true spirit and scope of the invention as defined by the appended claims. In addition, many modifications may be made to adapt a particular situation, material, composition of matter, method, or process to the objective, spirit and scope of the invention. All such modifications are intended to be within the scope of the claims appended hereto. In particular, while the methods disclosed herein have been described with reference to particular operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or re-ordered to form an equivalent method without departing from the teachings of the invention. Accordingly, unless specifically indicated herein, the order and grouping of the operations are not limitations of the invention."],"drawings":["BRIEF DESCRIPTION OF THE DRAWINGS","For a better understanding of the nature and objects of some embodiments of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.","FIG. 1 illustrates the unit cell of a Prussian Blue crystal structure according to an embodiment of the invention.","FIG. 2 illustrates a battery implemented in accordance with an embodiment of the invention.","FIG. 3 illustrates the unit cell of copper hexacyanoferrate, which has the Prussian Blue crystal structure according to an embodiment of the invention.","FIG. 4 illustrates the electrochemical characterization of copper hexacyanoferrate according to an embodiment of the invention. a: Galvanostatic cycling of copper hexacyanoferrate at various current densities between 0.6 and 1.4 V vs. S.H.E. showed a maximum specific capacity of about 59.14 mAh/g centered at about 0.946 V. b: The capacity retention of copper hexacyanoferrate at high current densities is greater than those of LiFePO 4 and Li 4 Ti 5 O 12 , two commonly studied lithium-ion electrodes. c: Long-term cycling of copper hexacyanoferrate at a 17 C rate between 0.8 and 1.2 V vs. S.H.E. shows about 83% capacity retention after 40,000 cycles, with about 99.7% coulombic efficiency. Additional electrolyte was added to the cell after 25,000 cycles to counteract evaporation (denoted by asterisk). d: The voltage hysteresis of copper hexacyanoferrate between the potentials during charging and discharging at a half-charge state is lower than that of Li 4 Ti 5 O 12 , and comparable to that of LiFePO 4 when normalized for current density. e: The low voltage hysteresis of copper hexacyanoferrate results in round-trip energy efficiency comparable to the best lithium-ion half cells.","FIG. 5 illustrates the physical characterization of copper hexacyanoferrate according to an embodiment of the invention. a: Transmission electron microscope image of copper hexacyanoferrate shows agglomerations of 20-50 nm grains. b: The increase in the lattice parameter of copper hexacyanoferrate during charging is illustrated by the shift of the 400 diffraction peak to smaller angles. c: The lattice parameter of copper hexacyanoferrate varies linearly between about 10.04 and about 10.14 Å during charging, with a total strain of about 0.9%.","FIG. 6 illustrates the unit cell of nickel hexacyanoferrate, which has the Prussian Blue crystal structure according to an embodiment of the invention.","FIG. 7 illustrates the electrochemical characterization of nickel hexacyanoferrate according to an embodiment of the invention. a, b: The potential profiles of nickel hexacyanoferrate during galvanostatic cycling of Na + and K + at various rates are shown. The potential profiles during both Na + and K + cycling show that the reversible reduction of fully charged nickel hexacyanoferrate proceeds by an insertion reaction, during which Na + and K + are miscible over a wide composition range in the stable open framework structure. Specific capacities of about 59 mAh/g were observed at a C/6 rate (see c, omitted from a and b for clarity), so about 60 mA/g was defined as a 1 C rate. c: The capacity of nickel hexacyanoferrate during galvanostatic cycling of Na + and K + at various rates is shown. About two thirds of the capacity observed at a C/6 rate is retained at 41.7 C. d: Nickel hexacyanoferrate shows essentially no capacity loss after 5,000 cycles of Na + insertion at a 8.3 C rate. During K + cycling, nickel hexacyanoferrate is stable for about 1,000 cycles, after which its capacity decays at a rate of about 1.75%/1,000 cycles.","FIG. 8 illustrates the physical characterization of nickel hexacyanoferrate according to an embodiment of the invention. a-c: Ex-situ X-ray diffraction on nickel hexacyanoferrate at various charge states showed isotropic lattice strain during charging. Changes in the diffraction pattern are illustrated by the shift of the 400 diffraction peak (a, b) to lower angles with increasing charge state. c: The lattice parameter increases linearly with charge state, with total strains of about 0.18% and about 1.1% during Na + and K + insertion, respectively. The lattice parameters at each charge state are the averages of those calculated from the positions of six diffraction peaks for each sample. The error bars are one standard deviation from each sample%27s mean calculated lattice parameter. d: Scanning electron microscope image reveals that the as-synthesized nickel hexacyanoferrate powder is composed of a porous network of 20-50 nm grains. e: Powder X-ray diffraction shows that synthesis of nickel hexacyanoferrate at 70° C. produces higher crystallinity than synthesis at room temperature, while co-precipitation synthesis of Prussian Blue results in poor crystallinity.","FIG. 9 illustrates the wide-angle powder X-ray diffraction spectra of co-precipitated copper hexacyanoferrate according to an embodiment of the invention and Prussian Blue (nominally KFe 3+ Fe 2+ (CN) 6 ). Due to the extreme insolubility of Prussian Blue, it precipitates too rapidly to form crystalline nanoparticles. However, copper hexacyanoferrate precipitates more slowly, allowing for the formation of a highly crystalline product. The spectrum of copper hexacyanoferrate is fully indexed to a FCC (Space Group Fm-3m) structure, with substantially no impurities.","FIG. 10 illustrates the electrochemical impedance spectrum of copper hexacyanoferrate that was measured using the same cell that was used to determine the high-rate performance of copper hexacyanoferrate according to an embodiment of the invention. The electrolyte resistance is about 18Ω, typical for flooded aqueous cells. The charge transfer resistance of this electrode was about 0.7Ω, corresponding to about 1 Ω/cm 2 , and the double layer capacitance was about 1.8 mF, corresponding to about 2.5 mF/cm 2 .","FIG. 11 illustrates the electrochemical performance of nickel hexacyanoferrate according to an embodiment of the invention. a-d: These plots show potential profiles of nickel hexacyanoferrate during galvanostatic cycling of Li + , Na + , K + , and NH 4 + , respectively, at several current densities. e: This plot shows potential profiles of nickel hexacyanoferrate during galvanostatic cycling of Li + , Na + , K + , and NH 4 + at 50 mA/g (0.83 C).","FIG. 12 illustrates the electrochemical performance of copper hexacyanoferrate according to an embodiment of the invention. a-d: These plots show potential profiles of copper hexacyanoferrate during galvanostatic cycling of Li + , Na + , K + , and NH 4 + , respectively, at several current densities. e: This plot shows potential profiles of copper hexacyanoferrate during galvanostatic cycling of Li + , Na + , K + , and NH 4 + at 50 mA/g (0.83 C).","FIG. 13 illustrates rate capability, cycle life, and effect of insertion ion size on nickel hexacyanoferrate and copper hexacyanoferrate according to an embodiment of the invention. a, b: These plots show capacity retention of nickel hexacyanoferrate and copper hexacyanoferrate with increasing current densities. c, d: These plots show cycle life of nickel hexacyanoferrate and copper hexacyanoferrate during cycling of Li + , Na + , K + , and NH 4 + . e: This plot shows that reaction potentials of nickel hexacyanoferrate and copper hexacyanoferrate decrease with increasing Stokes radius of the insertion ion. f: This plot shows that reaction potentials of nickel hexacyanoferrate and copper hexacyanoferrate increase with the effective ionic radius of the insertion ion.","FIG. 14 illustrates potential profiles of a copper hexacyanoferrate cathode and an activated carbon/polypyrrole anode during cycling at a 5 C rate in a pH=1 aqueous potassium ion electrolyte, according to an embodiment of the invention.","FIG. 15 illustrates capacity retention of a device including a copper iron hexacyanoferrate cathode, an activated carbon anode, and an aqueous electrolyte including sodium ions at a 5 C rate and pH=1, according to an embodiment of the invention.","FIG. 16 illustrates results of cyclic voltammetry performed on a copper hexacyanoferrate electrode in an aqueous electrolyte containing Mg(NO 3 ) 2 at pH=1, according to an embodiment of the invention.","FIG. 17 illustrates the physical characterization of copper nickel hexacyanoferrate, according to an embodiment of the invention. a: The unit cell of copper nickel hexacyanoferrate includes a framework of hexacyanoferrate groups linked by nitrogen coordinated “P” site transition metal ions of Cu and Ni. The large interstitial “A” sites can include either hydrated ions or zeolitic water. b: Transmission electron microscope image reveals that copper nickel hexacyanoferrate is composed of agglomerations of 20-50 nm particles. c: X-ray diffraction of copper nickel hexacyanoferrate powders reveals that the materials are highly crystalline, have a face-centered cubic Prussian Blue structure, and contain no impurity phases. d: The lattice parameter of copper nickel hexacyanoferrate decreases with decreasing Ni content.","FIG. 18 illustrates the electrochemical characterization of copper nickel hexacyanoferrate, according to an embodiment of the invention. a: These plots show potential profiles of copper nickel hexacyanoferrate during galvanostatic cycling in 1 M NaNO 3 . b: These plots show potential profiles of copper nickel hexacyanoferrate during galvanostatic cycling in 1 M KNO 3 . c: The reaction potential of copper nickel hexacyanoferrate increases with Cu content, in both sodium and potassium electrolytes. d: Nickel hexacyanoferrate and Cu 0.58 Ni 0.42 HCF show essentially no capacity loss after 2,000 cycles in 1 M NaNO 3 , while copper hexacyanoferrate loses about 25% of its initial capacity. e: Copper hexacyanoferrate and nickel hexacyanoferrate show essentially no capacity loss after 2,000 cycles in 1 M KNO 3 , while Cu 0.58 Ni 0.42 HCF shows a capacity loss of about 10%.","FIG. 19 illustrates the charge-discharge profile of a full cell at 2 C rate, 0.5 mA cm −2 , according to an embodiment of the invention. The full cell included a nickel hexacyanoferrate cathode and an activated carbon anode.","FIG. 20 illustrates capacity retention of a CuHCF/AC full cell in 1M KH 2 PO 4 /H 3 PO 4 at a 2 C rate and pH=2, according to an embodiment of the invention.","FIG. 21 illustrates capacity retention of a CuHCF/AC full cell in 1M KH 2 PO 4 /H 3 PO 4 at a 2 C rate and pH=1, according to an embodiment of the invention.","FIG. 22 illustrates capacity retention of a CuHCF/AC full cell in the presence of 5% ethylene glycol as a co-solvent a 2 C rate, according to an embodiment of the invention.","FIG. 23 illustrates capacity retention of a CuHCF/AC full cell in the presence of 10% ethylene glycol as a co-solvent a 2 C rate, according to an embodiment of the invention.","FIG. 24 illustrates capacity retention of a CuHCF/AC full cell in the presence of 5% glycerine as a co-solvent a 2 C rate, according to an embodiment of the invention.","FIG. 25 illustrates capacity retention of a CuHCF/AC full cell in the presence of 10% glycerine as a co-solvent a 2 C rate, according to an embodiment of the invention.","FIG. 26 illustrates long term cycling (500 cycles) of a NiHCF/AC full cell in 1 M Na + at pH=1, according to an embodiment of the invention.","FIG. 27 illustrates long term cycling (350 cycles) of a NiHCF/AC full cell in 1 M K + at pH=1, according to an embodiment of the invention.","FIG. 28 illustrates long term cycling (500 cycles) of a CuHCF/AC full cell in 1 M K + at pH=1, according to an embodiment of the invention.","FIG. 29 illustrates long term cycling (500 cycles) of a CuHCF//AC/PPy full cell in 1 M NH 4 + at pH=1, according to an embodiment of the invention.","FIG. 30 illustrates long term cycling (500 cycles) of a CuFe(50%)HCF//AC/PPy full cell in 1 M Na + at pH=1, according to an embodiment of the invention.","FIG. 31 illustrates long term cycling (500 cycles) of a CuFe(50%)HCF//AC/PPy full cell in 1 M K + at pH=1, according to an embodiment of the invention."]},"government_interest":"STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with Government support under contract DE-AC02-76SF00515 awarded by the Department of Energy. The Government has certain rights in this invention.","links":{"self":"https://developer.nrel.gov/api/lps/v/patents/8,951,673","html":"https://www.labpartnering.org/patents/8,951,673","source":"http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1\u0026Sect2=HITOFF\u0026d=PALL\u0026p=1\u0026u=/netahtml/PTO/srchnum.htm\u0026r=0\u0026f=S\u0026l=50\u0026TERM1=8,951,673"},"labs":[{"uuid":"f4c67d7f-e82b-4044-ba2f-2bd7d210924f","name":"Y-12 National Security Complex","tto_url":"https://www.y12.doe.gov/mission/partnerships/technologies","contact_us_email":"OTCP@cns.doe.gov","avatar":"https://www.labpartnering.org/files/labs/25","links":{"self":"https://developer.nrel.gov/api/lps/v/labs/f4c67d7f-e82b-4044-ba2f-2bd7d210924f"},"alias":null,"description":null,"contact_email":null,"contact_name":null,"location":null,"operator":null}],"inventors":[{"name":"Colin Wessells","location":"Eugene, OR, US"},{"name":"Robert Huggins","location":"Stanford, CA, US"},{"name":"Yi Cui","location":"Stanford, CA, US"},{"name":"Mauro Pasta","location":"Ubiale Clanezzo, IT, US"}],"assignees":[{"name":"The Board of Trustees of the Leland Stanford Junior University","seq":1,"location":{"city":"Palo Alto","state":" CA","country":" US"}}],"claims":[{"idx":"00001","text":"A battery comprising:a cathode%3ban anode%3b andan aqueous electrolyte disposed between the cathode and the anode and including a cation A different from Li+,wherein at least one of the cathode and the anode includes an electrode material having a Prussian Blue crystal structure into which the cation A is reversibly inserted during operation of the battery, andwherein the aqueous electrolyte has a pH that is less than 3."},{"idx":"00002","text":"The battery of claim 1, wherein the battery has a reference specific capacity when cycled at a reference rate of 1 C, and at least 75% of the reference specific capacity is retained when the battery is cycled at 10 times the reference rate."},{"idx":"00003","text":"The battery of claim 2, wherein at least 60% of the reference specific capacity is retained when the battery is cycled at 100 times the reference rate."},{"idx":"00004","text":"The battery of claim 2, wherein the battery has a reference, round-trip energy efficiency when cycled at the reference rate, and at least 85% of the reference, round-trip energy efficiency is retained when the battery is cycled at 10 times the reference rate."},{"idx":"00005","text":"The battery of claim 1, wherein the cation A is at least one of Na+ and Ba2+."},{"idx":"00006","text":"The battery of claim 1, wherein the cation A is at least one of K+, Rb+, Cs+, and NH4+."},{"idx":"00007","text":"The battery of claim 1, wherein the cation A has a Stokes ionic diameter greater than 3.5 Å."},{"idx":"00008","text":"The battery of claim 1, wherein the electrode material is represented as:AxPy[R(CN)6-wLw]z whereinA is at least one alkali or alkaline earth metal cation,P is at least one metal cation,R is at least one metal cation,L is an anion,x, y, and z are related based on electrical neutrality,x\u003e0,y\u003e0,z\u003e0, and0≦w≦6."},{"idx":"00009","text":"The battery of claim 8, wherein P is a cation of copper."},{"idx":"00010","text":"The battery of claim 8, wherein P includes cations of at least two different row 4 transition metals, and at least one of the transition metals is copper."},{"idx":"00011","text":"The battery of claim 8, wherein R is selected from cations of Fe, Mn, Cr, and Co."},{"idx":"00012","text":"The battery of claim 1, wherein at least one of the cathode and the anode includes a coating including the electrode material, and a thickness of the coating is at least 500 nm."},{"idx":"00013","text":"The battery of claim 12, wherein the thickness of the coating is at least 1 μm."},{"idx":"00014","text":"The battery of claim 1, wherein a mass loading of the electrode material within at least one of the cathode and the anode is at least 500 μg/cm2."},{"idx":"00015","text":"The battery of claim 14, wherein the mass loading is at least 1 mg/cm2."},{"idx":"00016","text":"The battery of claim 1, wherein the electrode material includes particles having a grain size no greater than 1 μm."},{"idx":"00017","text":"The battery of claim 16, wherein the grain size is no greater than 200 nm."},{"idx":"00018","text":"The battery of claim 1, wherein the pH is less than 2."},{"idx":"00019","text":"The battery of claim 1, wherein the aqueous electrolyte includes water as a primary solvent and at least one co-solvent having a reduced polarity relative to water."},{"idx":"00020","text":"The battery of claim 1, wherein the cathode includes the electrode material as a cathode material, and the anode includes an anode material into which the cation A is reversibly inserted during operation of the battery."},{"idx":"00021","text":"The battery of claim 1, wherein the cathode includes the electrode material, and the anode includes an electrochemical double-layer capacitor material."},{"idx":"00022","text":"The battery of claim 21, wherein the electrochemical double-layer capacitor material is activated carbon."}],"cpc":{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"054","main-group":"10","action-date":"2015-02-10","origination":"","symbol-position":"F","further":["01","","H","B","US","H","","M","054","10","2015-02-10","","F"]},"ipc":[{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"58","main-group":"4","action-date":"2015-02-10","origination":"","symbol-position":"F"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"054","main-group":"10","action-date":"2015-02-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"02","main-group":"4","action-date":"2015-02-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"505","main-group":"4","action-date":"2015-02-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"0525","main-group":"10","action-date":"2015-02-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"0568","main-group":"10","action-date":"2015-02-10","origination":"","symbol-position":"L"},{"class":"01","value":"","source":"H","status":"B","country":"US","section":"H","version":"","subclass":"M","subgroup":"04","main-group":"6","action-date":"2015-02-10","origination":"","symbol-position":"L"}],"document_number":"20120328936","document_published_on":"2012-12-27","document_kind":"","document_country":""}]}}