Rapidly chargeable and dischargeable electrochemical cells

Abstract

The invention provides a solid-state electrochemical cell, e.g., battery, including an anode and a cathode including cathode particles and solid-state electrolyte particles, and a solid-state electrolyte separating the anode and cathode. The cathode further includes a mixture of electrolyte particles of various sizes, e.g., to reduce tortuosity, shorten the conductive pathway, and improve the interface contact with electrode particles.

Description

[0001] PATENT ATTORNEY DOCKET NO.: 51198-053WO2 RAPIDLY CHARGEABLE AND DISCHARGEABLE ELECTROCHEMICAL CELLS STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH This invention was made with government support under DE-SC0012704 awarded by U.S. Department of Energy (DOE). The government has certain rights in this invention. FIELD OF THE INVENTION The invention is directed to the field of rechargeable solid-state lithium ion electrochemical cells, e.g., batteries. BACKGROUND OF THE INVENTION The speed at which a commercial solid-state battery charges and discharges has not been adequately explored. Although an electrode material’s ionic conductivity can be intentionally designed to boost the final product’s ionic transport, the design often does not result in a battery with a high power density, being limited by factors such as lithium dendrite growth and electrode tortuosity. The rate at which the ionic conductivity decreases with temperature is slower for a solid electrolyte than for a liquid electrolyte by orders of magnitude. However, the decrease of rate performance is much faster for a solid-state battery at the device level in comparison. Thus, rate-limiting kinetics continue to be an impediment to the commercialization of solid-state batteries. These observations suggest that the kinetics of charging and discharging in a non-pilot scale solid-state battery are not adequately explored. Thus, there is a need for improved rechargeable solid-state lithium ion batteries. SUMMARY OF THE INVENTION The invention provides a solid-state lithium electrochemical cell, e.g., battery, with a high cathode loading (> 15 mg / cm2) or areal capacity (0.1-15.0 mAh / cm2, e.g., at least 1 mAh / cm2) and a high C rate (> 2 C, e.g., > 4 C) at room temperature (e.g., 20-25 °C). In one aspect, the invention features a battery including an anode; a cathode including a mixture of cathode particles and solid-state electrolyte particles, the solid-state electrolyte particles including first particles having a first average diameter, and second particles having a second average diameter, the first average diameter at least about two times greater than the second average diameter; and a separator including a solid-state electrolyte disposed between the anode and cathode. In some embodiments, the separator is ion-permeable and configured to electrically isolate the anode from the cathode. In some embodiments, the separator includes a plurality of layers of one or more solid-state electrolytes. For example, the one or more solid-state electrolytes include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li5.5PS4.5Cl1.35I0.15. In another example, the plurality of layers includes a first layer disposed proximate to the anode, a second layer disposed proximate to the cathode, and a third layer interposed between the first layer and the second layer. In some embodiments, the first layer and the PATENT ATTORNEY DOCKET NO.: 51198-053WO2 second layer include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0, and the third layer includes at least one of Li5.5PS4.5Cl1.35I0.15. In some embodiments, the solid-state electrolyte particles include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0. In some embodiments, the first average diameter is in a range of between about 10 µm and about 200 µm. In some embodiments, the second average diameter is in a range of between about 2 nm and about 5 µm. In another aspect, the invention provides a battery including a first electrode including a mixture of active particles and solid-state electrolyte particles, the solid-state electrolyte particles including first particles having a first average diameter and second particles having a second average diameter, the second average diameter no more than about 50% of the first average diameter; a second electrode; and a separator including a solid-state electrolyte disposed between the first electrode and the second electrode. In some embodiments, the separator includes a plurality of layers of the solid-state electrolyte, the plurality of layers of the solid-state electrolyte including at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li5.5PS4.5Cl1.35I0.15. For example, the plurality of layers includes a first layer disposed proximate to the first electrode, a second layer disposed proximate to the second electrode, and a third layer interposed between the first layer and the second layer. In some embodiments, the first and second layers include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0, and the third layer includes Li5.5PS4.5Cl1.35I0.15. In some embodiments, the solid-state electrolyte particles include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0. In some embodiments, the first average diameter is in a range of about 10 µm to about 200 µm, and the second average diameter is in a range of about 2 nm to about 5 µm. In another aspect, the invention provides an electrochemical cell including an anode including an anode material and an anode current collector; a cathode including a cathode material and a cathode current collector, the cathode material including a mixture of cathode particles and solid-state electrolyte particles, the solid-state electrolyte particles including first solid-state electrolyte particles having a first average diameter, and second solid-state electrolyte particles having a second average diameter, the first average diameter at least about two times greater than the second average diameter; and a solid-state electrolyte separator disposed between the anode and the cathode. In some embodiments, the cathode material includes at least one of LiNi0.8Mn0.1Co0.1O2 (NMC811), LiNi0.33Mn0.33Co0.33O2 (NMC111), LiNi0.5Mn0.3Co0.2O2 (NMC532), LiNi0.6Mn0.2Co0.2O2 (NMC622), LiNi0.9Mn0.05Co0.05O2 (NMC955), LiNixMnyCo(1-x-y)O2, LiNixCoyAl(1-x-y)O2, LiMn2O4, LiMnO2, LiNiO2, Li1+zNixMnyCo(1-x-y-z)O2, Li1+zNixMnyCowAl(1-x-y-z-s)O2, Li1+zNixMnyCosW(1-x-y-z-s)O2, V2O5, selenium, sulfur, selenium-sulfur compound, LiCoO2 (LCO), LiFePO4, LiNi0.5Mn1.5O4, Li2CoPO4F, LiNiPO4, Li2Ni(PO4)F, LiMnF4, LiFeF4, LiCo0.5Mn1.5O4, Li10GeP2S12, Li6PS5Cl, or Li5.5PS4.5Cl1.5, where x, y, z, s, and w are each in a range of 0 ≤ x, y, z, s, w ≤1. In some embodiments, the solid-state electrolyte particles and the solid-state electrolyte separator include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li5.5PS4.5Cl1.35I0.15. In some embodiments, the anode material includes a first layer including lithium metal or PATENT ATTORNEY DOCKET NO.: 51198-053WO2 alloy, and a second layer including a mixture of electrolyte particles and metal or metalloid particles. In some embodiments, the anode material further includes a third layer disposed between the first layer and the second layer, the third layer including at least one of silicon, silicon dioxide, silicon nitride, silicon carbide, Li4Ti5O12, Li3V2O5, Au, Ag, Sn, SnO2, or carbon. In one aspect, the invention provides a solid-state battery including an anode and a cathode including cathode particles and solid-state electrolyte particles, and a solid-state electrolyte separating the anode and cathode. The cathode further includes a mixture of electrolyte particles of various sizes, e.g., to reduce tortuosity, shorten the conductive pathway, and improve the interface contact with electrode particles. In one aspect, the invention provides a battery including an anode and a cathode including a mixture of cathode particles, first particles of a solid-state electrolyte, and second particles of a solid-state electrolyte; and a separator and electrolyte separating the anode and cathode. The first particles have an average diameter at least two times larger than the second particles. In some embodiments, the anode includes a layer of lithium metal or alloy and a layer of a mixture of electrolyte particles and metal or metalloid particles, e.g., Si, Ag, or Mg, or an alloy thereof. In some embodiments, the layer of lithium metal or alloy and the layer of the mixture of electrolyte particles and metal or metalloid particles is separated by a layer comprising silicon, silicon dioxide, silicon nitride, silicon carbide, Li4Ti5O12, Li3V2O5, Au, Ag, Sn, SnO2, or carbon. In some embodiments, the mixture of electrolyte particles and metal or metalloid particles further includes particles of silicon, silicon dioxide, silicon nitride, silicon carbide, Li4Ti5O12, Li3V2O5, Au, Ag, Sn, SnO2, or carbon. In some embodiments, the electrolyte particles and metal or metalloid particles are of a size between 0.1 and 200 µm in diameter. In some embodiments, the ratio of electrolyte particles and metal or metalloid particles is from 1:99 to 99:1 (w / w). In some embodiments, the electrolyte particles in the anode include LPSCl. In some embodiments, the cathode particles include LiNi0.8Mn0.1Co0.1O2 (NMC811), LiNi0.33Mn0.33Co0.33O2 (NMC111), LiNi0.5Mn0.3Co0.2O2 (NMC532), LiNi0.6Mn0.2Co0.2O2 (NMC622), LiNi0.9Mn0.05Co0.05O2 (NMC955), LiNixMnyCo(1-x-y)O2 (0≤x,y≤1), LiNixCoyAl(1-x-y)O2 (0≤x,y≤1), LiMn2O4, LiMnO2, LiNiO2, Li1+zNixMnyCo(1-x-y-z)O2 (0≤x,y,z≤1), Li1+zNixMnyCowAl(1-x-y-z-s)O2 (0≤x,y,z,s≤1) , Li1+zNixMnyCosW(1-x-y-z-s)O2 (0≤x,y,z,w≤1), V2O5, selenium, sulfur, selenium-sulfur compound, LiCoO2 (LCO), LiFePO4, LiNi0.5Mn1.5O4, Li2CoPO4F, LiNiPO4, Li2Ni(PO4)F, LiMnF4, LiFeF4, LiCo0.5Mn1.5O4, Li10GeP2S12, Li6PS5Cl, Li5.5PS4.5Cl1.5, or a combination thereof. In some embodiments, the cathode particles are of a size between 0.1 and 100 µm. In some embodiments, the ratio of first particles to second particles is from 1:9999 to 9999:1 (w / w). In some embodiments, the average diameter of the first particles is between 10 and 200 µm. In some embodiments, the average diameter of the second particles is between 2 nm and 5 µm. In some embodiments, the first and / or second particles include LPSCl. In some embodiments, the cathode has an areal capacity of at least 1 mAh / cm2. In some embodiments, the battery is operated under external pressure. In some embodiments, the operational external pressure is 0.05-50 MPa. PATENT ATTORNEY DOCKET NO.: 51198-053WO2 In some embodiments, the electrolyte includes a multilayer of solid-state electrolytes. In certain embodiments, the multilayer of solid-state electrolytes is deposited, cast, or transferred onto the cathode, the anode, or a substrate in a layer-by-layer process. In some embodiments, the multilayer comprises n layers of solid-state electrolyte, wherein n = >2 (e.g., 2, 3, 4, 5, 6, 7, 8, 9, or 10 or more).In another aspect, the invention provides a method of storing energy including applying a voltage across the anode and cathode and stably cycling any rechargeable battery disclosed herein. In some embodiments, the charging has a C rate of greater than 2 at a temperature of 25 °C. In some embodiments, the charging has a C rate of greater than 4 at a temperature of 25 °C. In another aspect, the invention provides a method of providing energy including connecting a load to the anode and cathode and discharging any rechargeable battery disclosed herein. In another aspect, the invention provides a cathode material including a mixture of cathode particles, first particles of a solid-state electrolyte, and second particles of a solid-state electrolyte. The first particles have an average diameter at least two times larger than the second particles. In some embodiments, the cathode particles include (NMC532), LiNi0.6Mn0.2Co0.2O2 LiNixCoyAl(1-x-y)O2 (0≤x,y≤1), (1- x-y-z-s)O2 (0≤x,y,z,s≤1) , Li1+zNixMnyCosW(1-x-y-z-s)O2 (0≤x,y,z,w≤1), V2O5, selenium, sulfur, selenium-sulfur compound, LiCoO2 (LCO), LiFePO4, LiNi0.5Mn1.5O4, Li2CoPO4F, LiNiPO4, Li2Ni(PO4)F, LiMnF4, LiFeF4, LiCo0.5Mn1.5O4, Li10GeP2S12, Li6PS5Cl, Li5.5PS4.5Cl1.5, or a combination thereof. In some embodiments, the cathode particles are of a size between 0.1 and 100 µm. In some embodiments, the ratio of first particles to second particles is from 1:9999 to 9999:1 (w / w). In some embodiments, the average diameter of the first particles is between 10 and 200 µm. In some embodiments, the average diameter of the second particles is between 2 nm and 5 µm. In some embodiments, the first and / or second particles include LPSCl. BRIEF DESCRIPTION OF THE DRAWINGS Fig.1(a) shows the critical C-rates at different areal capacities of solid-state batteries at 22oC and 55oC described herein, in comparison with literature[6, 8-10, 12-16]. Fig.1(b) shows a battery configuration of a 2.7 mAh / cm2battery. Fig.1(c) shows the mechanism of fast Li ion transport kinetics from a catholyte network with mixed particle sizes (right panel) in comparison with large (left panel) and small (right panel) catholyte- only cases. Fig.1(d) shows the effect of sulfide anolyte mixed with Si to transport Li toward the current collector and to prevent Li dendrite penetration (right panel) in comparison with no electrolyte mixed in the Si-graphite (G) layer (left panel). Note that the figures show the effect at a fast C-rate, and, at medium or low C-rate, both anode designs also work. Fig.2(a) shows a rate performance comparison for solid-state batteries with different cell configuration at RT and a cathode loading of 18 mg / cm2. The label of Si-G represents anode layers made by a Si-Graphite composite layer above a Li metal layer (i.e., Si-G|Li), while Si-Cl represents anode structure of a layer of Si and argyrodite Li7-yPS6-yCly (LPSCly) composite above a graphite layer and a Li metal layer (i.e., Si-Cl|G|Li). PATENT ATTORNEY DOCKET NO.: 51198-053WO2 The mixed catholyte represents mixed small and large particle size of argyrodite Li5.5PS4.5Cl1.5 (LPSCl1.5) electrolyte in the cathode composite layer, while small or large catholyte represents cathode layer with only small or only large LPSCl1.5 electrolyte particles. Fig.2(b) shows corresponding charge-discharge voltage curves at different C-rates of the full cell configuration with mixed catholyte cathode vs Si-G anode (second from top trace in 2(a)). Fig.2(c) shows a comparison of charge-discharge voltage curves at 4 C-rate of the full cells with different cell configuration. Figs.2(d)-2(e) show SEM images of the pristine (large particle, Fig. 2(d)) and the ball milled (small particle, Fig.2(e)) LPSCl1.5 particles. The inset in Fig.2(e) is at a larger magnification. Fig.2(f) shows an FIB-SEM-EDS mapping of the cross-section of mixed catholyte cathode composite. The inset on the right enlarges the region in the dashed rectangle on the left. Fig.2(g) shows an impedance spectra analysis and comparison for different cell configurations. Fig.2(h) shows comparisons of capacities at various temperatures for different cell configurations. Fig.3(a) shows the cycling performance of full cells with the mixed catholyte paired with Si-Cl anode configuration at RT (temperature fluctuates in a range of 22oC to 30oC without environmental temperature control) with different areal capacity (2.5 ~ 4.6 mAh / cm2or 18 ~ 27 mg / cm2cathode loading), C-rate (3 C ~ 5 C-rate or 12 ~ 14 mA / cm2current density), and nominal NP ratio (1.6 ~ 1.9) at specific capacity around 150 mAh / gNMC. The central electrolyte separate layer used our iodine doped LPSCl1.5-I (See Methods). Fig.3(b) shows the cycling performance in a pouch cell at 10 MPa external pressure and 5 C charge and 5 C discharge with a separator thickness of 75 µm. The Coulombic efficiency is represented by the right y-axis and displayed as the top trace and the areal capacity is represented by the left y-axis and displayed as the bottom trace. Figs.3(b)-3(d) show corresponding voltage curves to Fig.3(a) as labeled in each panel. Figs. 3(e)-3(g) show corresponding specific capacity of NMC and Coulombic efficiency for the three batteries in 3(a) as labeled in each panel. Note that the lowest capacities in initial cycles, corresponding to the lowest temperature in the fluctuating range, were used to plot Fig.1(a). Fig.3(h) shows cycling performance in a pouch cell at 10 MPa external pressure and 5 C charge and 5 C discharge with a separator thickness of 75 µm. Figs.4(a)-4(f) show the electrochemical analysis and comparison of different anode configurations. Fig.4(a) shows the charging and Fig.4(b) shows the discharging voltage curves of solid-state batteries with Si-G|Li anode of the same total weight of Si and graphite but different Si weight percent. Fig.4(c) shows the corresponding dQ / dV curves. Fig.4(d) shows the tradeoff relationship between the critical C rate at short circuit and the turning point voltage at the end of discharge at 0.3 C for solid-state batteries with different anode configurations. The turning point is defined as the voltage at the capacity of full discharge capacity minus 15 mAh / g. Anode configurations include Si-G|Li and doped Si-G|Li (small dots) anodes at different NP ratios, and the Si-Cl|G|Li anodes with small or large Si and LPSCly particles. Fig.4(e) shows the b value obtained from CV cycling tests of cells with different anode_1|electrolyte|anode_2 configurations. Fig.4(f) shows a cycling performance comparison for different cathode (mixed catholyte vs. large catholyte only), anode (Si-G|Li vs. Si-Cl|G|Li), and central separator (LGPS vs. LPSCl-I) layer combinations with extreme C- PATENT ATTORNEY DOCKET NO.: 51198-053WO2 rates of 15 C charge (40.5 mA / cm2) and 10 C discharge. Fig.4(g) shows a comparison of CV curves of full cells with different anodes. Figs.5(a)-5(h) show impedance measurements and activation energies of different solid-state batteries. Figs.5(a), 5(c), 5(e), and 5(g) show circuit model fittings for different cathode and anode combinations of solid-state batteries at -5oC, 10oC, 25oC, and 55oC. Figs.5(b), 5(d), 5(f), and 5(g) show activation energies of R3 of different solid-state batteries, where R3 represents the interface resistance between active material and solid electrolyte. Figs.5(a) and 5(b) show mixed catholyte vs. Si-Cl. Figs.5(c) and (d) show mixed catholyte vs. Si-G. Figs.5(e) and 5(f) show large catholyte only vs. Si-Cl. Figs.5(g) and 5(h) show small catholyte only vs. Si-Cl. Figs.6(a)-6(g) show voltage profiles and cycling performances of batteries at different temperatures (55oC or RT), cathode loading (18 ~ 58 mg / cm2), and C-rates (0.3 C ~ 5 C), as identified in each panel. Fig.7 shows an example of critical C-rate and Vend measurement from a full cell with 18 mg / cm2cathode loading (2.7 mAh / cm2area capacity) and a battery configuration as labelled in the figure. The battery was first charged and discharged at 0.3 C to measure the Vend turning point defined at 15 mAh / g capacity to the full discharge. After cycling at 0.3 C, 0.5 C, and 1 C, the battery was then discharged to 2 V at 0.3 C. In subsequent cycles to evaluate the critical C-rate, the battery was charged at increasing C-rates started from 4 C and increased by 1 C per cycle, where the charge cutoff is always at 150 mAh / g charge capacity and discharged first quickly at 4 C to 2 V and then followed by 0.3 C to 2V in each cycle. Fig.8 shows a Si-G|Li anode discharge voltage profile in a solid-state battery with the configuration of Li|G|Li5.5PS4.5Cl1.5|LPSCl-I|Li5.5PS4.5Cl1.5|Si-G at the current density of 0.2 mA / cm2at room temperature. Figs.9(a)-9(d) shows a b value measurement from CV sweeping test of different anode configurations in the battery of anode_1| electrolyte |anode_2 in Figure 4(e). NP ratio is defined as if it is paired with 18 mg / cm2cathode to represent different thickness of the anode. Anode_1 is always the configuration of Si + 20wt%_Cl1.5|G|Li using large particles of Si and LPSCl1.5 (Large Si-Cl). Anode_2 in Fig.9(a) is Si-G|Li NP1.2. Anode_2 in Fig.9(b) is Si-G|Li NP3.6. Anode_2 in Fig.9(c) is large_Si-Cl|G|Li using large particles of Si and LPSCl1.5. Anode_2 in Fig.9(d) is small_Si-Cl|G|Li using small particles of Si and LPSCl1.0. Peak currents (y) at each CV scan rates (x) are used to fit y = axb. The average b value of top part (charge) and bottom part (discharge) of the CV scan is presented in Figure 3(e). Multi-electrolyte-layer configuration of LPSCl1.5|LPSCl-I|LPSCl1.5 is used as separator. Figs.10(a)-10(b) shows an FIB-SEM-EDS of cycled Li|Si-G anode after critical C-rate test of a solid-state battery with NP ratio of 2.4 and a battery configuration of mixed catholyte|LPSCl1.5|LPSCl-I|LPSCl1.5|Si- G|Li. The Li metal layer originally at the top surface of the SEM image here was largely stripped during cycling and merged into the Si-G layers. Fig.10(a) shows an FIB-SEM image. Fig.10(b) shows an EDS of the inset of Fig.10(a). PATENT ATTORNEY DOCKET NO.: 51198-053WO2 DETAILED DESCRIPTION OF THE INVENTION The invention provides a solid-state electrochemical cell, e.g., battery, with a high cathode loading and area capacity achieved with composite electrode materials. In the cathode, large electrolyte particles act as highways for Li ions to conduct through a thick cathode layer, and small electrolyte particles ensure interfacial contact between cathode particles and the electrolyte. In the anode, a layer of solid electrolyte particles with higher conductivity may be combined with metal or metalloid, e.g., Si, Mg. Ag, or an alloy thereof, particles to improve anode kinetics by increasing the critical C-rate and discharge voltage. The disclosure provides critical kinetic processes that limit rapid cycling at high cathode loadings and provide for high performance solid-state electrochemical cells, e.g., batteries. The layer of solid electrolyte mixed with metal or metalloid particles can be separated from a Li metal anode by a layer of graphite to prevent the initial interface reaction of electrolyte and Li metal. Solid-state batteries are considered to be the next generation battery technology with high energy density and safety for electric vehicles. Sulfide solid electrolyte, in comparison with other electrolyte types, is attractive due to its high ionic conductivity[1]. Power density and energy density usually exhibit a trade-off relationship. A cyclable battery can show high C-rate (> 4 ~ 40 C) at low cathode loading (~2 mg / cm2),[2-7]but, at commercial-relevant cathode loading (e.g., > 15 mg / cm2), the C-rate has to be significantly reduced (< 2.5 C)[6, 8-10]. Furthermore, although the drop of ionic conductivity for solid electrolyte with decreasing temperature is slower than liquid electrolyte by orders of magnitude, the device level capacity often still drops fast in solid- state batteries at lower temperatures. For example, at 1 C-rate, the areal capacity of a solid-state battery at room temperature can be less than 1 / 3 of that at 60oC.[8]A high areal capacity (> 1 mAh / cm2) with less than 15 min charge time (> 4 C-rate) has been challenging even at above 50oC (Fig.1(a)) in the field. To pair with the high-loading cathode, the anode may also be able to accommodate fast Li ion kinetics. At elevated temperatures, Si or Ag containing anodes can achieve a long cycle life at low C-rate.[8, 10, 11]When the temperature is lowered from 55oC to room temperature (RT, around 25oC); however, ionic conductivity drops, and Li dendrites grow more easily. Thus, high power density at high current density is difficult to demonstrate at RT. The disclosure provides unprecedentedly fast device kinetics for high loading and areal capacity Li-ion solid- state batteries and demonstrates both high power and high energy densities at RT and in a broad temperature range as well (Fig.1(a)). For cathode composite, we demonstrate for the first time that the electrolyte with designed ratio between large and small particles provides the best high rate performance (Figs.1(b)-1(c)). For anode composite, we added solid electrolyte and an optional separation layer, e.g., including graphite, to increase both the C-rate and the discharge voltage (Fig.1(d)). The disclosure provides PATENT ATTORNEY DOCKET NO.: 51198-053WO2 for fast device kinetics in solid-state batteries for high power densities, which will be important to the applications of high-performance electric vehicles and planes. Full cell kinetics at high cathode loading and area capacity has been achieved by designing electrode composites. In the cathode, the large electrolyte particle may act as a highway for Li ion conduction through the thick cathode layer, and the small electrolyte particle may act to ensure the interface contact between cathode particles and the electrolyte matrix. In the anode, adding solid electrolyte with much larger conductivity to the metal or metalloid, e.g., Si, layer significantly improves the overall anode kinetics, which increases the critical C-rate and discharge voltage. Electrochemical Cells Electrochemical cells, e.g., batteries, of the invention include two electrodes, e.g., an anode and a cathode, a separator, and a solid-state electrolyte. The anode and / or cathode may include active particles, i.e., anode or cathode particles. One electrode may include a mixture of active particles and first and second solid-state electrolyte particles. The first and second electrolyte particles are of different sizes. For example, the average diameter of the first and second electrolyte particles may differ by at least 2, e.g., at least 4, at least 10, at least 20, at least 50, or at least 100 or by at most 500, 100, 50, 20, or 10, e.g., wherein the second average diameter is no more than about 50% of the first average diameter or the first average diameter is at least about two times greater than the second average diameter. The first particles may have an average diameter of between 10 and 200 µm, e.g., between 50 and 150, 100 and 200, 10 and 100, 50 and 100, 10 and 50, or 15 and 25 µm. The second particles may have an average diameter of between 2 nm and 5 µm, e.g., between 1 and 5 µm or between 0.3 and 1 µm. Particle size may be determined by scanning electron microscopy. The first and second electrolyte particles may have a ratio from 1:9999 to 9999:1 (w / w), e.g., 2000:1 to 1:2000, 1:9999 to 3:7000, 1:1 to 4000:1, 1:4000 to 1:1, 7000:3 to 9999:1; 200:1 to 1:200 , 1:999 to 3:700, 1:1 to 400:1, 1:400 to 1:1, 700:3 to 999:1; 20:1 to 1:20 , 1:99 to 3:70, 1:1 to 40:1, 1:40 to 1:1, 70:3 to 99:1; 2:1 to 1:2 , 1:9 to 3:7, 1:1: to 4:1, 1:4 to 1:1:, or 7:3 to 9:1. The ratio of cathode particles to combined electrolyte particles may be 1:9 to 9:1 (w / w), e.g., 2:1 to 1:2 , 1:9 to 3:7, 1:1: to 4:1, 1:4 to 1:1:, or 7:3 to 9:1. Cathodes A cathode may include a mixture of cathode particles and first and second electrolyte particles. The first and second electrolyte particles are of different sizes. For example, the average diameter of the first and second electrolyte particles may differ by at least 2, e.g., at least 4, at least 10, at least 20, at least 50, or at least 100 or by at most 500, 100, 50, 20, or 10. The first particles may have an average diameter of between about 10 and about 200 µm, e.g., between 50 and 150, 100 and 200, 10 and 100, 50 and 100, 10 and 50, or 15 and 25 µm. The second particles may have an average diameter of between about 2 nm and about 5 µm, e.g., between 1 and 5 µm or between 0.3 and 1 µm. Particle size may be determined by scanning electron microscopy. The first and second electrolyte particles may have a ratio from 1:9999 to 9999:1 (w / w), e.g., PATENT ATTORNEY DOCKET NO.: 51198-053WO2 2000:1 to 1:2000, 1:9999 to 3:7000, 1:1 to 4000:1, 1:4000 to 1:1, 7000:3 to 9999:1; 200:1 to 1:200 , 1:999 to 3:700, 1:1 to 400:1, 1:400 to 1:1, 700:3 to 999:1; 20:1 to 1:20 , 1:99 to 3:70, 1:1 to 40:1, 1:40 to 1:1, 70:3 to 99:1; 2:1 to 1:2 , 1:9 to 3:7, 1:1: to 4:1, 1:4 to 1:1:, or 7:3 to 9:1. The ratio of cathode particles to combined electrolyte particles may be 1:9 to 9:1 (w / w), e.g., 2:1 to 1:2 , 1:9 to 3:7, 1:1: to 4:1, 1:4 to 1:1:, or 7:3 to 9:1. A cathode may also include a cathode current collector. The particles may be deposited on an appropriate substrate, e.g., a fluoropolymer or carbon. For example, polytetrafluoroethylene (PTFE) has been used as the binder when making dry cathode films. Other binders are known in the art. The cathode material can be used without any additives or binders. Alternatively, the electrode material may have additives to enhance its physical and / or ion and / or electron conducting properties. For example, the cathode materials may have an additive that modifies the surface area exposed to the solid electrolyte, such as carbon. Other additives are known in the art. In some embodiments, the cathode materials, e.g., particles, can include, e.g., LiNi0.8Mn0.1Co0.1O2 (NMC111), LiNi0.5Mn0.3Co0.2O2 (NMC532), LiNi0.6Mn0.2Co0.2O2 (NMC622), , LiNixMnyCo(1-x-y)O2 (0≤x,y≤1), LiNixCoyAl(1-x-y)O2 (0≤x,y≤1), LiMn2O4, LiMnO2, x-y-z)O2 (0≤x,y,z≤1), Li1+zNixMnyCowAl(1-x-y-z-s)O2 (0≤x,y,z,s≤1), Li1+zNixMnyCosW(1-x-y-z- s) selenium, sulfur, selenium-sulfur compound, LiCoO2 (LCO), LiFePO4, LiNiPO4, Li2Ni(PO4)F, LiMnF4, LiFeF4, or LiCo0.5Mn1.5O4. The cathode can be coated with LiNbO3, LiTaO3 Li2ZrO3, LiNbXTa1-XO3 (0≤x≤1), yLi2ZrO3-(1-y)LiNbXTa1-xO3 (0≤x, y≤1), Al2O3, TiO2, ZrO2, AlF3, MgF2, SiO2, ZnS, ZnO, Li4SiO4 Li3PO4. Li3InCl6, Li1+xAlxTi2-x(PO4)3(0<x<2), LiMn2O4, LiInO2-LiI, Li6PS5Cl, LiAlO2, a polymer, or carbon, or a combination thereof. In some embodiments, the cathode includes a polymer and / or carbon black, or the first and / or second solid electrolytes include a polymer. The cathode material may also include Li10GeP2S12, Li6PS5Cl, or Li5.5PS4.5Cl1.5. The cathode particle can be coated with another chemical compound to increase interface (electro)chemical stability and / or electron or ion conductivity. In one embodiment, the smaller solid-state electrolyte particles may include a core of a cathode material coated with the solid-state electrolyte, e.g., LPSCl. Such a structure can be used to increase the amount of cathode material relative to the solid-state electrolyte. The cathode can be mixed with polymer and / or carbon. Examples of polymers may include polyethylene oxide, polyvinylidene fluoride, poly(vinylidene fluoride-co-hexafluoropropylene), poly(ethyl methacrylate), or poly(vinylidene fluoride-co-trifluoroethylene). The particle size of cathode particles can be 1 nm – 30 µm. The loading of the cathode can be 0.1-100 mg / cm2, e.g., at least 5, 10, or 15 mg / cm2or 5-50, 10-50, 15-25, 15- 30, 15-50, 15-75, or 15-100 mg / cm2. The thickness of the cathode can be 5 µm- 2000 µm. In some embodiments, the cathode has an areal capacity of 0.1-15.0 mAh / cm2, e.g., 0.1-0.2 mAh / cm2, 0.2- 0.5 mAh / cm2, 0.5-1.0 mAh / cm2, 1.0-2.0 mAh / cm2, 1.0-5.0 mAh / cm2, 1.0-10.0 mAh / cm2, 2.0-5.0 mAh / cm2, 2.0-10.0 mAh / cm2, 5.0-10.0 mAh / cm2, 5.0-15.0 mAh / cm2, or 10.0-15.0 mAh / cm2. In some embodiments, the PATENT ATTORNEY DOCKET NO.: 51198-053WO2 cathode has an areal capacity of at least 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.0, or 15 mAh / cm2or at most 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.0, or 15.0 mAh / cm2. Anodes Anodes of the invention may include any suitable anode material known in the art, such as Li metal. An anode may include an anode current collector. For example, lithium metal foil, e.g., Li metal foil on a current collector, e.g., of stainless steel. The anode may have a layered structure of Li metal or alloy, with or without a separation layer, and a mixture of electrolyte particles and metal or metalloid particles. The separation layer may include silicon, silicon dioxide, silicon nitride, silicon carbide, Li4Ti5O12, Li3V2O5, Au, Ag, Sn, and SnO2 or carbon. Carbon can include amorphous carbon, carbon nanotube, graphene, carbon nanofiber, fullerenes (e.g., C60 fullerene), hard carbon, soft carbon, or graphite. The carbon particles and the metal or metalloid particles can also be mixed into one layer instead of two separate layers. The electrolyte particles and metal or metalloid particles may independently have a size between 0.1 and 200 µm, e.g., between 0.5 and 10 µm or between 10 and 50 µm. The electrolyte particles and metal or metalloid particles may have a ratio from 1:99 to 99:1(w / w), e.g., 20:1 to 1:20, 1:99 to 3:70, 1:1: to 40:1, 1:40 to 1:1:, 70:3 to 99:1; 2:1 to 1:2 , 1:9 to 3:7, or 7:3 to 9:1. Each layer may have a thickness of at most 100 µm. The metal or metalloid may be Na, Mg, Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, As, Rb, Sr, Y, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Bi, Cs, Te, or a combination thereof to form one single layer, e.g., Si, Ag, or Mg. This can also include alloys, such as Mg-Bi, Mg-Sn, Mg-Si, etc. Anodes may be deposited on an appropriate substrate, e.g., a fluoropolymer or carbon. For example, polytetrafluoroethylene (PTFE) has been used as the binder when making dry films of electrode materials for deposition onto a substrate. Other binders are known in the art. The anode materials described herein can be used without any additives or binders. Alternatively, the anode material may have additives to enhance its physical and / or ion conducting properties. For example, the anode materials may have an additive that modifies the surface area exposed to the solid electrolyte, such as carbon. Other additives are known in the art. Solid-state Electrolytes and Separators Suitable solid-state electrolytes that may be used as the electrolyte for the battery or in the cathode and / or anode in the invention include inorganic solid electrolytes, e.g., crystalline or glassy inorganic lattices with high ionic conductivity, in which ions (e.g., Li+ions) can diffuse through the lattice. SSEs may be, for example, oxides, halide, chalcogenides, borohydrides, phosphates, or sulfides of lithium (e.g., LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5 (LSPCl1.5), Li6PS5Cl1.0 (LPSCl1.0), Li5.5PS4.5Cl1.35I0.15). Separators may include multiple layers of solid-state electrolytes. Other solid-state electrolyte materials that may be suitable include sulfide solid electrolytes, e.g., SixPySz, e.g., SiP2S12, or β / γ-PS4. Other solid-state electrolytes include, but are not limited to, germanium solid PATENT ATTORNEY DOCKET NO.: 51198-053WO2 electrolytes, e.g., GeaPbSc, e.g., GeP2S12, tin solid electrolytes, e.g., SndPeSf, e.g., SnP2S12, iodine solid electrolytes, e.g., P2S8I crystals, glass electrolytes, e.g., alkali metal-sulfide-P2S5 electrolytes or alkali metal- sulfide-P2S5- alkali metal-halide electrolytes, or glass-ceramic electrolytes, e.g., alkali metal-PgSh-i electrolytes. Other solid-state electrolyte materials are known in the art. The solid-state electrolyte material may be in various forms, such as a powder, particle, clay, or solid sheet. An exemplary form is a powder. Solid electrolytes may be deposited or cast on an appropriate substrate, e.g., a polyester (PET) film, a cathode, an anode, or other layers of solid electrolytes. For example, nitrile rubber (NBR), acrylate rubber (ABR), polyisobutene (PIB) have been used as the binder when making solutions of electrolyte materials for deposition onto a substrate. Other binders are known in the art. Solid electrolytes may be mixed with solvents (e.g., p-xylene, isobutyl isobutyrate or a mixture thereof, e.g., anhydrous p-xylene and isobutyl isobutyrate (1:1 vol / vol)) and binders (e.g., a polymer, e.g., an arylate polymer, e.g., from 0.5% to 5 wt%) to prepare a slurry for layer formation. Multiple layers of electrolytes can be deposited or cast or transferred to a substrate layer-by-layer. The multilayer may contain ‘n’ layers of solid-state electrolytes (where n = e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.). Advantageously, the solid-state electrolyte may adopt a core-shell particle structure, e.g., core-shell LPSCl-X (where X is a halide) or LGPS (Li10GeP2S12) (see, WO 2019 / 104181, WO 2020 / 112843, and WO2022 / 094412). LGPS (Li10GeP2S12) may also adopt a core-shell particle structure. Solid-state electrolyte particles, e.g., core-shell particles, may have a cross sectional dimension, e.g., diameter, of between about 1 nm and about 30 µm, e.g., about 1-100 nm (e.g., about 10 nm, 20 nm, 30 nm, 40 nm, 50 nm, 60 nm, 70 nm, 80 nm, 90 nm, or 100 nm), e.g., about 100-1000 nm (e.g., about 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, or 1000 nm), e.g., about 1-10 µm (e.g., about 1 µm, 2 µm, 3 µm, 4 µm, 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, or 10 µm), or, e.g., about 10-30 µm (e.g., about 10 µm, 12 µm, 13 µm, 14 µm, 15 µm, 16 µm, 17 µm, 18 µm, 19 µm, 20 µm, 21 µm, 22 µm, 23 µm, 24 µm, 25 µm, 26 µm, 27 µm, 28 µm, 29 µm, or 30 µm). In core-shell particles, the shell may make up from about 0.1 % to about 99.9 % of the particle, e.g., about 1-10 %, about 10-20 %, about 20-30 %, about 25-50 %, about 40-60%, about 50-75%, about 60-80 %, about 75-90 %, or about 80-99 % of the particle, by, e.g., volume or mass. Stability may be determined experimentally. Solid-state electrolyte (SSE) multilayers may contain three or more layers and two or more solid-state electrolytes with different stabilities. The solid-state electrolytes may be arranged such that the less stable electrolyte is sandwiched between more stable electrolyte(s). Localized decomposition of the less stable electrolyte in SSE multilayers can block the formation or progression of cracks in the multilayer and arrest dendrite progress. The solid-state multilayer may include a first solid-state electrolyte (e.g., LPSCl) and a second solid-state electrolyte (e.g., LGPS, LSnPS, etc.). The multilayer may include at least one layer of a first solid-state electrolyte which is more stable with lithium metal than a second solid-state electrolyte. The second solid- state electrolyte may be separated from the anode by the first solid-state electrolyte. The multilayer may PATENT ATTORNEY DOCKET NO.: 51198-053WO2 contain ‘n’ layers of the second solid-state electrolyte and ‘n’ layers of the one or more first solid-state electrolytes (where n = e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.). The solid-state multilayer may alternatively be arranged in, e.g., a “sandwich” structure, e.g., with one layer of the second solid-state electrolyte between two layers of the one or more first solid-state electrolytes (e.g., LPSCl-LGPS or LPSCl-LGPS-LPSCl). Alternatively, the multilayer may contain ‘n’ layers of the second solid- state electrolyte and ‘n’ or ‘n+1’ layers of the one or more first solid-state electrolytes (where n = e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.). The second solid-state electrolyte may be less stable with lithium metal than one or more first solid-state electrolytes. Such an arrangement can allow the first solid-state electrolyte to protect the second solid-state electrolyte from, e.g., large-scale decomposition, while confined localized decomposition of the second solid- state electrolyte arrests the progression of metal dendrites. The multilayer may include multiple different first solid-state electrolytes; for example, at least two different first solid-state electrolytes, e.g., a solid-state electrolyte multilayer, may include two different solid-state electrolytes. The multilayer design is not limited to any specific materials, and many electrolytes can work in the central layer, as long as the second solid-state electrolyte can show such well-constrained decomposition with Li dendrite under mechanical constriction. Such solid-state electrolytes include, but are not limited to LGPS, LSPS, LSP(Sb)S, which show similarly stable cycling. In some embodiments, the separator is ion-permeable and configured to electrically isolate the anode from the cathode. A separator may include a plurality of layers of one or more solid-state electrolytes, such as LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li5.5PS4.5Cl1.35I0.15. The plurality of layers may include a first layer disposed proximate to one electrode, e.g., anode, a second layer disposed proximate to another electrode, e.g., cathode, and a third layer interposed between the first layer and the second layer. The first layer and second layer may include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0, and the third layer may include Li5.5PS4.5Cl1.35I0.15. Operation under External Pressure In some embodiments, the battery is operated under externally applied pressure. External pressure applied to the battery cell can include pressures of at least 0.1 MPa up to several hundred MPa. The level of external pressure for a battery is determined by the battery material, material processing, and battery assembly methods. External pressure may be provided by a formation pressure from cold and / or hot and / or warm isotropic and / or anisotropic press and / or rolling with the external pressure on the order of 0.1 MPa to 1000 MPa and temperature at 25 ℃-500 ℃. Examples of suitable assembly methods include, but are not limited to, warm isotropic pressing (WIP), cold isotropic pressing (CIP), and hydraulic cold pressing of the battery cell or pouch. Operation under applied pressure can include pressures of at least 0.05 MPa, e.g., at least 0.1 MPa, 0.5 MPa, 1 MPa, 5 MPa, 10 MPa, 15 MPa or 20 MPa, e.g., about 0.05 MPa to about 50 MPa, e.g., about 0.05 MPa to about 0.1 MPa, about 0.075 MPa to about 0.15 MPa, about 0.1 MPa to about 1 MPa, PATENT ATTORNEY DOCKET NO.: 51198-053WO2 about 0.1 MPa to about 10 MPa, about 1 MPa to about 30 MPa, about 20 MPa to about 40 MPa, about 30 MPa to about 50 MPa, about 40 MPa to about 60 MPa, about 50 MPa to about 70 MPa, about 60 MPa to about 80 MPa, about 70 MPa to about 90 MPa, or about 80 MPa to about 100 MPa, about 100 MPa to about 200 MPa, about 200 MPa to about 400 MPa, about 300 MPa to about 500 MPa, about 400 MPa to about 600 MPa, about 500 MPa to about 700 MPa, about 600 MPa to about 800 MPa, about 700 MPa to about 900 MPa, or about 800 MPa to about 1,000 MPa, e.g., about 70 MPa, about 75 MPa, about 80 MPa, about 85 MPa, about 90 MPa, about 95 MPa, about 100 MPa, about 150 MPa, about 200 MPa, about 250 MPa, about 300 MPa, about 350 MPa, about 400 MPa, about 450 MPa, about 500 MPa, about 550 MPa, about 600 MPa, about 650 MPa, about 700 MPa, about 750 MPa, about 800 MPa about 850 MPa, about 900 MPa, about 950 MPa, or about 1,000 MPa. When the battery is operating, the local stress can be maintained by applying an operational stack pressure on the order of between 0 MPa and 1000 MPa. Alternatively, the local stress may be maintained without applying an operational stack pressure. Methods Methods of storing and releasing electrical energy involve using electrical energy to charge a solid-state electrochemical cell, e.g., battery, by applying a voltage across the battery that causes Li to migrate as Li+ions from a cathode to an anode, where the Li deposited, thereby storing the electrical energy as chemical energy. In discharge, the Li metal is oxidized to Li+and migrates back to the cathode. To release (discharge) the stored chemical energy as electrical energy, a load is electrically connected between the anode and cathode in a circuit to allow the Li+ions to migrate from the anode via the solid-state electrolyte to the cathode. The method may include electrochemical cells, e.g., batteries, that charge at 25 °C with C-rates between C / 10 and 100 C, e.g., C / 10 to C / 5, C / 5 to C / 2, C / 2 to 1 C, 1 C to 2 C, 1 C to 5 C, 1 C to 10 C, 2 C to 5 C, 2 C to 10 C, 2 C to 20 C, 2 C to 50 C, 5 C to 10 C, 5 C to 20 C, 5 C to 50 C, 10 C to 20 C, 10 C to 50 C, 20 C to 50 C, 50 C to 100 C, at least C / 10, C / 5, C / 2, C, 2 C, 5 C, 10 C, 20 C, or 50 C, or at most C / 10, C / 5, C / 2, C, 2 C, 5 C, 10 C, 20 C, 50 C, or 100 C. Methods of the invention may involve repeating the above cycle multiple times, e.g., greater than 1000 times, e.g., 1000-20,000 times (e.g., 1,000-1,500 times, 1,250-1,750 times, 1,500-2,000 times, 1,500-2,500 times, 2,000-3,000 times, 2,500-5,000 times, 5,000-10,000 times, 5,000-15,000 times, 10,000-20,000 times, or 15,000-20,000 times). The method may include first allowing a portion of the interface coating layer to form a surface layer on the cathode, e.g., in an initial charge-discharge cycle. Alternatively, the cathode may already have an interface coating layer. All suitable techniques can be used to apply the cathode particles, e.g., chemical synthesis, atomic layer deposition, chemical vapor decomposition, sputtering, pulsed laser decomposition, etc. PATENT ATTORNEY DOCKET NO.: 51198-053WO2 Examples We first demonstrate that cell configuration design for cathode and anode layers can dramatically increase the rate performance of full cells at RT (Fig.2(a)). First, we used the two layers of silicon-graphite composite layer above the Li metal layer (Si-G|Li) as the anode to pair with different cathode layer configurations. The cathode composite with mixed particle sizes of argyrodite electrolyte Li5.5PS4.5Cl1.5 (LPSCl1.5) delivers much higher capacity from single crystal LiNi0.83Mn0.06Co0.11O2 (NMC) at high C-rates than the control cells with either large or small electrolyte particles in the cathode layer (Fig.2(a)). Fig.2(b) shows the corresponding voltage curves of the cell with optimized cathode at different C-rates, where cut-off voltages are adjusted at each C-rate for all batteries to compensate for polarization at large current. Fig.2(c) shows the comparison of voltage curves for different cell configurations at 4 C-rate. Figs.2(d)-2(e) show the SEM images of the as-synthesized pristine LPSCl1.5 with a particle size around 20 µm, and the ball milled LPSCl1.5 with a much-reduced particle size of mainly ~300 nm - 5 µm. Fig.2(f) shows the cross-section focused ion beam scanning electron microscopy energy dispersive spectroscopy (FIB-SEM-EDS) of the mixed catholyte cathode composite. The existence of small LPSCl particles makes NMC particles well surrounded by solid electrolytes, while the large particles of LPSCl provide fast Li ion conduction through them with the lowest possible local tortuosity. On the anode side, to improve Li conductivity in the anode layer, we mixed 20 wt% pristine Li7-yPS6-yCly (LPSCly, 0<y<2, e.g., y = 1, 1.5, etc.) with pure silicon to form the Si-LPSCly (Si-Cl) composite layer and moved the graphite to a thin separate layer between Li metal and Si-Cl layers to prevent the chemical reaction between Li and LPSCly (Si-Cl|G|Li), which further improved the high rate performance (Figs.2(a) and 2(c)). To further understand the cathode composite kinetics, we measured the impedance at 25oC (Fig.2(g)) and at various temperatures (Figs.5(a)-5(h)). In the circuit model to simulate the impedance spectra (Fig.2(g) top schematic), R1 (interception at x axis) is used to represent the resistance of the connected electrolyte network including separator layers, catholyte, and anolyte, and a constant phase element (CPE1) is used to represent the Li diffusion in NMC. Two depressed semicircles are fitted at around 500 Hz (R3-CPE3) and 10 kHz (R2-CPE2), respectively. The high-frequency 10 kHz semicircle is contributed by the Li ion transport through solid electrolyte within the electrode composite layers, while the low-frequency 500 Hz semicircle is contributed by the interface between electrode active material and solid electrolyte in the composite matrices[17-18]. The fitted results of R2 and R3 are presented in Table 1. Ta - R R3 (Ω) 480.9 592.3 756.5 177.7 PATENT ATTORNEY DOCKET NO.: 51198-053WO2 10oC Mixed catholyte vs. Mixed catholyte vs. Large catholyte Small catholyte R R 25oC Mixed catholyte vs. Mixed catholyte vs. Large catholyte Small catholyte R R 55oC Mixed catholyte vs. Mixed catholyte vs. Large catholyte Small catholyte R R A E E E When only using large LPSCl.5 particles or small LPSCl1.5 particles as the catholyte, we find that either the 10 kHz or the 500 Hz semicircle (but not both) becomes obviously small corresponding to much lower resistance (Figs.2(g) top two graphs). Small electrolyte-only configuration with the largest R2 also consistently shows an especially high R1 due to the electrolyte network connection to the separator. Based on the circuit model described above, this suggests that the large LPSCl1.5 particle is good at transporting Li ions across the catholyte layer network, giving smaller R2, while the small LPSCl1.5 particle is good at transporting Li ions across the interface between catholyte and NMC particles, giving smaller R3. Therefore, when mixing large and small LPSCl1.5 in the cathode, both 10 kHz and 500 Hz semicircles become small, giving the lowest overall cathode resistance (Fig.2(g) top right graph). The activation energies (Ea) of interfaces are calculated and presented in Figs.5(a)-5(h) and Table 1. Interestingly, despite the smallest resistance from impedance measurement, the cell configuration of mixed catholyte cathode paired with Si-Cl anode gives an Ea of 284 meV, which is 37 meV higher than the large catholyte-only configuration and 86 meV higher than the small This is because E a here corresponds to resistivity ^ rather than resistance R, ^ ^^ ). The much smaller interface resistance R3 but higher resistivity (^) for the mixed catholyte cell than the large catholyte-only cell thus suggests that although adding small LPSCl1.5 particles increases the resistivity at various interfaces, the overall interface contact area (A) is dramatically increased, thus giving a much lower resistance (^ = ^^ / ^) in the cathode layer, where ^ is the interface thickness. Comparing the mixed catholyte cell with the small catholyte-only cell, the interface R3 is comparable since both cells now contain the small LPSCl1.5 particles. However, the much smaller resistance R2 but higher interface resistivity here in the PATENT ATTORNEY DOCKET NO.: 51198-053WO2 mixed catholyte cell suggests that the existence of large catholyte particles with high bulk conductivity effectively transport Li ions across the thick catholyte network, which dramatically reduces R2. Furthermore, when comparing the anode configurations of Si-G|Li with Si-Cl|G|Li for the activation energy using the same mixed catholyte configuration, the latter is 42 meV larger than the former (Figs.5(a)-5(h)), suggesting that adding electrolyte to the anode layer may introduce extra interface reaction to increase the Ea and interface resistivity, but the benefit of the LPSCl1.0 region with much higher bulk ionic conductivity than Si, Li-Si alloy, and graphite effectively reduces the R3 in the latter to 39 Ω (Fig.2(g) bottom left graph) from the 51 Ω of the former case (Fig.2(g) bottom right graph). Fig.2(h) compares the specific capacities of different full cell configurations at 0.3 C-rate from RT to low temperatures. With the same mixed catholyte configuration, Si-Cl|G|Li anode shows better low temperature performance than the Si-G|Li anode, while with same Si-Cl|G|Li anode, the mixed catholyte configuration is much better than the other two configurations without mixing catholyte particle sizes. We then cycled the full cell with mixed catholyte cathode layer paired with Si-Cl|G|Li anode at RT (Fig.3(a)- 3(g)). Three batteries with different cathode loading from 18 to 27 mg / cm2can stably cycle with 2.5 to 4.6 mAh / cm2at charge rate ranging from 5 C to 3 C for more than 1300 to 3000 cycles (still running). At even higher loading, e.g., ~7 mAh / cm2and 10 mAh / cm2, the battery can still cycle at 1 C and 0.5 C (Fig.1(a) and Figs.6(a)-6(g)). Furthermore, a pouch cell is demonstrated to run 5000 cycles (Fig.3(h)). Such high power density at high areal capacity for solid-state batteries is for the first time demonstrated through the fast kinetics design at the battery device level (Fig.1(a)). Discussion We compare the charge-discharge voltage curve of the second cycle at a slow rate of 0.5 C for solid-state batteries made by mixed catholyte cathode paired with Si-G|Li anode of different Si weight percent (Figs. 4(a)-4(b)). Li metal anode liquid electrolyte battery is used as the reference for 0% Si. During charge, the initial voltage drops from 0% Si to 20% Si, and then the voltage profiles seem to converge from 35% Si up to 100% Si without obvious voltage drop (Fig.4(a)). Also note that the initial voltage at the turning point in the charge voltage profile (See Methods and Fig.7) is kept in a narrow voltage range of 0.1 V from 3.6 V to 3.5 V for batteries with 20% to 100% Si. This process is saturated due to the relatively flat voltage profile of Si-G anode when Li is charged toward it (Fig.8). While during discharge, the voltage profiles are much more separated by the Si composition change at anode in the Si-graphite composite layer, with higher average discharge voltage for lower Si percentage (Fig. 4(b)). Especially, the end-of-discharge voltage at the turning point distributes in a wide voltage range of 0.4 V from 3.3 V to 2.9 V for batteries with 20% to 100% Si. This charge-discharge asymmetry can also be observed in the dQ / dV analysis of these voltage profiles (Fig.4(c)), where the peaks in discharge show a shift in a much broader voltage range than the charge ones. PATENT ATTORNEY DOCKET NO.: 51198-053WO2 We further measure the critical C-rate before short circuit for solid-state batteries with thick cathode of 18 mg / cm2loading paired with different anode. These batteries show 150 mAh / g specific capacity (2.7 mAh / cm2areal capacity) in the charge regardless of the voltage cut-off. We increased the C-rate in every cycle from 0.3 C up to the C-rate with clear signal of short circuit (Fig.7). We defined the first C-rate in the series when short circuit happens as the critical C-rate. A negative correlation between critical C-rate and the end-of- discharge voltage turning point at 0.3 C-rate (Vend) is found for almost all the batteries we evaluated (Fig. 4(d)). These batteries include anode configurations of Si-G|Li at different nominal NP ratio, and doped Si- G|Li at a fixed NP ratio with small amount of additive (Ge, Sn, Ag etc., more details see Table 2) mixed to the Si powder by ball mill as well. Table 2. Data points in Figure 4(d) with Vend and critical C-rate being obtained following the procedure described in Fig.8. e Si + 20wt% Cl1.5|G (Large Si-Cl) NP1.9 3.27 8 For solid-state battery application, it is advantageous to break such a correlation, so that batteries can exhibit both high critical C-rate for high power density and higher discharge voltage for increased energy density, i.e., moving toward the right upper corner in Fig.4(d). The Si-Cl|G|Li anode configuration successfully breaks the correlation in such a way. When small particles of 1 µm Si and 3 µm LPSCl1.0 are mixed at 80:20 weight ratio (Small_Si-Cl) the battery shows a high critical C-rate above 10 C and a turning point voltage of 3.15 V, and when large particles of 20 µm Si and 20 µm LPSCl1.5 (Large_Si-Cl) are mixed, the battery shows higher turning point voltage at 3.27 V and critical C-rate at 8 C. PATENT ATTORNEY DOCKET NO.: 51198-053WO2 To understand more kinetics mechanism behind the phenomenon, we performed cyclic voltammetry (CV) measurement (Figs.9(a)-9(d)) of different anode_1| electrolyte |anode_2 cells at a set of sweeping rates to extract the b value that characterizes the overall kinetics

[0019] of the anode configuration, where the anode contains Si-G with different NP ratio, and Si-Cl with different particle size. In general, b-value ranges from 0.5, where the process is diffusion limited, to 1.0, where a surface limiting process dominates. Fig.4(e) shows that the b-value is much higher for Si-ClG|Li anodes, suggesting better overall kinetics, consistent with their higher critical C-rate. Since a softer sulfide electrolyte can also reduce the porosity of the Si layer and help transport Li+ to deposit into the bottom G-Li layer, there will be less Li deposition in the pore region where Li dendrite starts to grow at high C-rate, thus giving a higher critical C-rate. Moreover, Cl1.5 and Cl1.0 have ~4 orders of magnitude larger Li diffusivity than graphite and Li-Si alloy[20-22], so that they can extract Li from the anode more efficiently to reach a higher discharge voltage. Specifically, the Si-Cl|G|Li anode can be even thinner than the 20 µm Si-G|Li anode (Figs.10(a)-10(b)), as the graphite layer in the former is very thin. Thus, in the large_Si-Cl configuration, the 20 µm LPSCl1.5 particle in the Si layer can directly connect the neighboring layers of the G|Li and the electrolyte separator, to extract Li more efficiently than the small_Si-Cl configuration, giving a higher Vend. Our kinetic design of solid-state batteries at both cathode and anode layers also lead to an extreme C-rate of 15 C charge (40.5 mA / cm2) and 10 C discharge at 55oC that can be cycled for 1100 cycles (Fig.4(f)). Note that here the central electrolyte layer in the multi-separator-layer design[2]used iodine doped argyrodite of Li5.5PS4.5Cl1.35I0.15 (LPSCl-I) with optimized dynamic voltage stability for Li dendrite constriction[3]. Without such a design, an NMC-Cl1.5(7:3)|Cl1.5|LGPS|Cl1.5|Si-G|Li full cell shows a low initial specific capacity of 80 mAh / g that dropped to 80% after 600 cycles. With cathode optimization only, the capacity increased to 135 mAh / g but the cycle life decreased to 250 cycles. With additional Si-Cl|G|Li anode, both capacity and cycle life can be increased. Methods Materials Synthesis: Li5.5PS4.5Cl1.5 (LPSCl1.5) and Li5.5PS4.5Cl1.35I0.15 (LPSCl-I) were prepared by high energy ball milling and a subsequent annealing process. Stoichiometric amounts of Li2S (99.9% purity, Alfa Aesar), P2S5 (99% purity, Sigma Aldrich), LiCl (99% purity, Alfa Aesar) and LiI (99% purity, Sigma Aldrich) were milled for 16 h in a planetary mill PM200 (Retsch GmbH, Germany) under a protective Ar atmosphere followed by sintering at 550 °C in a quartz tube. Full cell assembly: A Li foil with a thickness of 25 µm was covered by a silicon-graphite composite film made by mixing silicon, graphite (BTR, China), and PTFE with a weight ratio of 47.6%:47.6%:4.8% (Si-G|Li), or by stacking graphite film and Si-Li7-yPS6-y Cly (LPSCly) composite film (Si-Cl|G|Li), where Si is mixed with 20 wt% of LPSCly in the Si-Cl layer. Nominal NP ratio was calculated based on the theoretical capacity of Si (practically 3000 mAh / g) and NMC83 (200mAh / g). All cathode loading is at 18 mg / cm2unless otherwise labelled in the plot. In Figs.2(a), 2(b), 2(c), 2(g), 2(h), and 4(f), cells are with a NP ratio of 2.4 for all the Si-G PATENT ATTORNEY DOCKET NO.: 51198-053WO2 cells and NP 1.9 for the Si-Cl cell. In Figs.4(a)-4(c), the Si to graphite weight ratio is changed in cells with a changing NP ratio as labelled in Fig.4(c) at a fixed cathode loading of 18 mg / cm2. In Fig.4(d), all the doped Si-G|Li anode cells are at NP 2.4, and all cells are at 18 mg / cm2NMC. The battery with Si-Cl|G|Li anode and 18 mg / cm2cathode loading in Figs.2(a), 2(c), and 3(a) are the same battery with our LPSCl1.5 mixed with Si in anode. All other Si-Cl|G|Li batteries are with LPSCl1.0 (Pascal, 3 µm) mixed in the Si-Cl layer in the anode. The cathode dry film was made by mixing 30 wt% solid electrolyte, 70 wt% single-crystal LiNi0.83Mn0.1Co0.07O2 (NMC83, 1–5 µm particle size, MSE Supplies) and an additional 3 wt% PTFE. For large-only catholyte configuration, all 30 wt% solid electrolyte is as synthesized LPSCl1.5. For small-only catholyte configuration, all 30 wt% solid electrolyte is ball-milled LPSCl1.5. The ball milling is conducted using MM500 nano (Retsch) with 8 Hz for 8 hr. For mixed catholyte, 20 wt% small LPSCl1.5 and 10 wt% large LPSCl1.5 are used. All batteries use multi-electrolyte-layer separator between cathode and anode layers, with 20 mg LPSCl1.5 and 100 mg LPSCl-I as LPSCl1.5|LPSCl-I|LPSCl1.5 separator configuration. The full battery, with a structure of anode|LPSCl1.5|LPSCl-I|LPSCl1.5|cathode, was pressed together in a homemade pressurized cell at 400 MPa and kept at 50 MPa during testing. All batteries were assembled in an argon atmosphere glovebox. For RT battery test, the temperature is not controlled to be constant and is fluctuating between 22oC and 30oC through the cycling test measured by thermometer. For non-RT tests, the batteries are tested inside a Memmert hpp110 or Espec environmental chamber. Battery cycling test was conducted using an Arbin instrument. Pouch cells were made layer by layer from slurry-casting electrode and a total thickness of 75 µm for electrolyte layers, with NP ratio of 1.5. Electrochemical Impedance Spectra (EIS): The EIS of full cells were measured in a Solartron 1455A, over the frequency range from 0.1 Hz to 1 MHz, with AC measuring voltage of 0.01 V, after testing the 0.3 C capacity between 2.5 V and 4.1 V at RT, 10oC, and -5oC, respectively. All Nyquist plots were fitted with R(RQ)(RQ)Q equivalent circuit by ZView. Cyclic voltammetry (CV): CV of anode_1| separator |anode_2 cells with Li metal layers on both sides were conducted at Solartron 1470E between -1.5 V to 1.5 V, with different sweep rates from 0.5 mV / s to 3 mV / s. 0.5 mV / s cycle is used as an activation cycle. Peak currents at each scan rate are plotted versus scan rate and fitted with y = axbto extract the exponent b value. Anode_1 is always the configuration of Si + 20wt%_Cl1.5|G|Li using large particles of Si and LPSCl1.5 (Large Si-Cl). Anode_2 is different for four different cell configurations of Si-G|Li at NP1.2, Si-G|Li at NP3.6, Large_Si-Cl|G|Li, and Small_Si-Cl|G|Li using small particles of Si and LPSCl1.5, respectively. The NP1.2 or NP 3.6 is calculated based on a hypothetical full cell as if the anode is paired with an 18 mg / cm2NMC cathode. Similarly, the two Si-Cl cells are at NP 1.9. For more details see Figs.9(a)-9(d). SEM: FEI Helios 660 was used for the cross-section focused ion beam scanning electron microscopy energy dispersive spectroscopy (FIB-SEM-EDS) imaging. The cycled pellet was transferred from an argon-filled glovebox using a sealed plastic bag. The sample is exposed to air within 1 minute during transfer. Ga+milling procedures were conducted to create a cleaned cross-section region at different currents. SEM-EDX imaging was conducted using the inner EDAX tools and detector of the instrument. PATENT ATTORNEY DOCKET NO.: 51198-053WO2 References [1] Y. Li, S. Song, H. Kim, K. Nomoto, H. Kim, X. Sun, S. Hori, K. Suzuki, N. Matsui, M. Hirayama, T. Mizoguchi, T. Saito, T. Kamiyama, R. Kanno, Science 2023, 381, 50. [2] L. Ye, X. Li, Nature 2021, 593, 218. [3] Y. Wang, L. Ye, X. Chen, X. Li, JACS Au 2022, 2, 886. [4] E. Gil-González, L. Ye, Y. Wang, Z. Shadike, Z. Xu, E. Hu, X. Li, Energy Storage Materials 2022, 45, 484. [5] E. A. Wu, C. Jo, D. H. Tan, M. Zhang, J.-M. Doux, Y.-T. Chen, G. 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Claims

PATENT ATTORNEY DOCKET NO.: 51198-053WO2 What is claimed is: CLAIMS 1. A battery, comprising: an anode; a cathode including a mixture of cathode particles and solid-state electrolyte particles, the solid-state electrolyte particles including first particles having a first average diameter, and second particles having a second average diameter, the first average diameter at least about two times greater than the second average diameter; and a separator including a solid-state electrolyte disposed between the anode and cathode.

2. The battery of claim 1, wherein the separator is ion-permeable and configured to electrically isolate the anode from the cathode.

3. The battery of claim 1, wherein the separator includes a plurality of layers of one or more solid-state electrolytes.

4. The battery of claim 3, wherein the one or more solid-state electrolytes include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li5.5PS4.5Cl1.35I0.

15.

5. The battery of claim 3, wherein the plurality of layers includes a first layer disposed proximate to the anode, a second layer disposed proximate to the cathode, and a third layer interposed between the first layer and the second layer.

6. The battery of claim 5, wherein: the first layer and the second layer include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0, and the third layer includes at least one of Li5.5PS4.5Cl1.35I0.

15.

7. The battery of claim 1, wherein the solid-state electrolyte particles include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0.PATENT ATTORNEY DOCKET NO.: 51198-053WO2 8. The battery of claim 1, wherein the first average diameter is in a range of between about 10 µm and about 200 µm.

9. The battery of claim 1, wherein the second average diameter is in a range of between about 2 nm and about 5 µm.

10. A battery, comprising: a first electrode including a mixture of active particles and solid-state electrolyte particles, the solid-state electrolyte particles including first particles having a first average diameter and second particles having a second average diameter, the second average diameter no more than about 50% of the first average diameter; a second electrode; and a separator including a solid-state electrolyte disposed between the first electrode and the second electrode.

11. The battery of claim 10, wherein the separator includes a plurality of layers of the solid-state electrolyte, the plurality of layers of the solid-state electrolyte including at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li5.5PS4.5Cl1.35I0.

15.

12. The battery of claim 11, wherein the plurality of layers includes a first layer disposed proximate to the first electrode, a second layer disposed proximate to the second electrode, and a third layer interposed between the first layer and the second layer.

13. The battery of claim 12, wherein: the first and second layers include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0, and the third layer includes Li5.5PS4.5Cl1.35I0.

15.

14. The battery of claim 10, wherein the solid-state electrolyte particles include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, or Li6PS5Cl1.0.PATENT ATTORNEY DOCKET NO.: 51198-053WO2 15. The battery of claim 14, wherein the first average diameter is in a range of about 10 µm to about 200 µm, and the second average diameter is in a range of about 2 nm to about 5 µm.

16. An electrochemical cell, comprising: an anode including an anode material and an anode current collector; a cathode including a cathode material and a cathode current collector, the cathode material including a mixture of cathode particles and solid-state electrolyte particles, the solid-state electrolyte particles including first solid-state electrolyte particles having a first average diameter, and second solid-state electrolyte particles having a second average diameter, the first average diameter at least about two times greater than the second average diameter; and a solid-state electrolyte separator disposed between the anode and cathode.

17. The electrochemical cell of claim 16, wherein the cathode material includes at least one of LiNi0.8Mn0.1Co0.1O2 (NMC811), LiNi0.33Mn0.33Co0.33O2 (NMC111), LiNi0.5Mn0.3Co0.2O2 (NMC532), LiNi0.6Mn0.2Co0.2O2 (NMC622), LiNi0.9Mn0.05Co0.05O2 (NMC955), LiNixMnyCo(1-x-y)O2, LiNixCoyAl(1-x-y)O2, LiMn2O4, LiMnO2, LiNiO2, Li1+zNixMnyCo(1-x-y-z)O2, Li1+zNixMnyCowAl(1-x-y-z-s)O2, Li1+zNixMnyCosW(1-x-y-z-s)O2, V2O5, selenium, sulfur, selenium-sulfur compound, LiCoO2 (LCO), LiFePO4, LiNi0.5Mn1.5O4, Li2CoPO4F, LiNiPO4, Li2Ni(PO4)F, LiMnF4, LiFeF4, LiCo0.5Mn1.5O4, Li10GeP2S12, Li6PS5Cl, or Li5.5PS4.5Cl1.5, where x, y, z, s and w are each in a range of 0 ≤ x, y, z, s, w ≤1. 18 The electrochemical cell of claim 16, wherein the solid-state electrolyte particles and the solid-state electrolyte separator include at least one of LGPS, LiSiPS, LiPS, Li5.5PS4.5Cl1.5, Li6PS5Cl1.0, or Li PS4.5Cl1.35I0.

15. 19 The electrochemical cell of claim 16, wherein the anode material includes a first layer including lithium metal or alloy, and a second layer including a mixture of electrolyte particles and metal or metalloid particles. 20 The electrochemical cell of claim 19, wherein the anode material further includes a third layer disposed between the first layer and the second layer, the third layer including at least one of silicon, silicon dioxide, silicon nitride, silicon carbide, Li4Ti5O12, Li3V2O5, Au, Ag, Sn, SnO2, or carbon.

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