CATHODE INTERFACE COATING LAYERS FOR SOLID STATE BATTERIES

Information

  • Patent Application
  • 20250096276
  • Publication Number
    20250096276
  • Date Filed
    September 26, 2024
    7 months ago
  • Date Published
    March 20, 2025
    a month ago
Abstract
The invention provides compounds that can be used as cathode interface coating layers in solid state batteries. The compounds disclosed herein provide enhanced dynamic stability.
Description
FIELD OF THE INVENTION

The invention is directed to the field of solid state rechargeable batteries.


BACKGROUND OF THE INVENTION

Thermodynamically stable interface voltage windows of solid electrolytes are often narrower than the operational voltage range necessary in a commercial battery. When batteries with solid electrolytes are utilized outside of their stable interface voltage windows, interfacial decomposition reactions occur that reduce the operational lifetime of the batteries. Previous attempts to solve this problem have focused on finding and incorporating coating materials for the solid electrolytes that are thermodynamically stable within the desired operational voltage range. Such searches have produced few materials containing all of the desired characteristics for a commercial battery.


Thus, there is a need for improved solid state batteries incorporating solid electrolytes.


SUMMARY OF THE INVENTION

The invention provides compounds that can be used as cathode interface coating layers in solid state batteries. The compounds disclosed herein provide enhanced dynamic stability.


In one aspect, the invention provides a compound selected from Table 1:










TABLE 1





Compound
Chemical formula
















1
Ba1Li1B1O3


2
Ba1Li1B9O15


3
Ba1Na1Li3B6O12


4
Ba2Li1O6


5
Ba2Li2Zr4F22


6
Ba2Na2Li6B12O24


7
Ba4Li1Bi3O12


8
Ba4Li1Nb3O12


9
Ba4Li1Ta3O12


10
Ba4Li4Al4F24


11
Ba4Li8P8O28


12
Ba5Li2W3O15


13
Ba6Li4B20H12O44


14
K1Li1B4O7


15
K1Li1C1O3


16
K1Li1Nd2Mo4O16


17
K1Li1S1O4


18
K1Li1Sm2Mo4O16


19
K1Li3Si12Sn2O30


20
K1Li3Zr2Si12O30


21
K1Na1Li2S2O8


22
K1Na2Li3Fe2Si12O30


23
K2Li1SC1F6


24
K2Li1V1O4


25
K2Li2Si4O10


26
K2Li6Ca14Ti4Si24O72F4


27
K2Li6Zr4Si24O60


28
K4Li1I1O6


29
K4Li2Al2F12


30
K4Li4Y4F20


31
K5Li2Nd1F10


32
K5Li2Pr1F10


33
K6Li2Mg8Si24O60


34
K8Li12B4P16O56


35
K8Li4B4P8O32


36
K8Li8B32O56


37
Li1Al1P1H1O5


38
Li1Al1Si4O10


39
Li1Al2H6Br1O6


40
Li1B1H4O4


41
Li1B5H2O9


42
Li1Bi1O3


43
Li1Ca1P1O4


44
Li1Ca9Mg1P7O28


45
Li1Cd1B1O3


46
Li1Cl1O4


47
Li1CO1H1S1O5


48
Li1Co1Ni1O4


49
Li1Co1O2


50
Li1Co2O4


51
Li1Eu6B3O14


52
Li1F1


53
Li1Fe1C2O6


54
Li1Fe1Si2O6


55
Li1Gd6B3O14


56
Li1H2Cl1O5


57
Li1H3O2


58
Li1H6Br1O7


59
Li1La2Fe1O6


60
Li1La2S2O8F3


61
Li1La2Sb1O6


62
Li1La3Mn1O7


63
Li1Mg1Al1F6


64
Li1Mg1Al1Mo3O12


65
Li1Mg4Al1Mo6O24


66
Li1Mn1H1S1O5


67
Li1N1O3


68
Li1Nd6B3O13F2


69
Li1Ni2O3


70
Li1Ni2O4


71
Li1O8


72
Li1PriS2O8


73
Li1Sc1Si2O6


74
Li1Si1B1O4


75
Li1Si2B1O6


76
Li1Ta1Si1O5


77
Li1Ta3O8


78
Li1Ti1P1O5


79
Li1Ti4Mn1P6O24


80
Li1Tm1Si1O4


81
Li1Y1Si1O4


82
Li1Y3Si2O8F2


83
Li1Yb1Al1F6


84
Li1Zr2P3O12


85
Li10B14Cl2O25


86
Li10Co1Ni9O20


87
Li10Fe3Ni7O20


88
Li10Mg12Fe1P12O48


89
Li10Sc9Fe1Si20O60


90
Li12Al4Si4O20


91
Li12B20H8O40


92
Li12Mn11Fe1P12O48


93
Li12P12O36


94
Li12Sc8P12O48


95
Li12Ta4O16


96
Li13Mg1Ni12O26


97
Li13Ni15O28


98
Li14Nb14O42


99
Li16Mn15Fe1P16O64


100
Li16Mn8P16O56


101
Li16P8O28


102
Li16Zr4F32


103
Li18Al6F36


104
Li19Ni23O42


105
Li2Al2P2H2O10


106
Li2Al2Si8O20


107
Li2Al4H12Br2O12


108
Li2Al4H12Cl2O12


109
Li2C1O3


110
Li2Ca18Mn2P14O56


111
Li2Ca2Al2F12


112
Li2Cd1Si1O4


113
Li2Cl2


114
Li2Co1Ni3O8


115
Li2Co1O2F1


116
Li2Co3Ni1O8


117
Li2Dy2P8O24


118
Li2Fe1Co3O8


119
Li2Fe1O2F1


120
Li2Fe3Bi1O8


121
Li2Fe3Sb1O8


122
Li2Gd2P8O24


123
Li2Ho2P8O24


124
Li2La1N5O15


125
Li2La2P8O24


126
Li2Mg1B12H16O28


127
Li2Mg1Ti9O20


128
Li2Mg2S3O12


129
Li2Mn1O3


130
Li2Mn1S2O8


131
Li2Mn12P14O48


132
Li2Mn4P6O20


133
Li2Nd1N5O15


134
Li2Nd2P8O24


135
Li2Ni1O3


136
Li2Pr1N5O15


137
Li2S1O4


138
Li2Sc1Fe1Si4O12


139
Li2Sc2P4O14


140
Li2Sc2Si4O12


141
Li2Se1O4


142
Li2Si1O3


143
Li2Sm2P8O24


144
Li2Sn1H10O8


145
Li2Tb2P8O24


146
Li2Ti1O3


147
Li2Ti4P6O24


148
Li2Y2F8


149
Li2Y2P8O24


150
Li2Y6Si4O16F4


151
Li2Yb2Al2F12


152
Li2Zn1Si1O4


153
Li2Zr1F6


154
Li3Al1Si1O5


155
Li3B3F12


156
Li3Gd1N6O18


157
Li3La2H6N9O30


158
Li3La3Mo2O12


159
Li3Mg3Al3F18


160
Li3Nb1O4


161
Li3Nd3W2O12


162
Li3P1O4


163
Li3Sb1O4


164
Li3Ta1O4


165
Li3Tb1N6O18


166
Li3V1O4


167
Li3Yb1N6O18


168
Li4Al20O32


169
Li4Al4P16O48


170
Li4B12O18F4


171
Li4Ca36Mg4P28O112


172
Li4Co1Ni3O8


173
Li4H8Br4O4


174
Li4Mg12P12O44


175
Li4Mg4P4O16


176
Li4Mn4P12O36


177
Li4Mn4P4O16


178
Li4Mo1O5


179
Li4P4H8O16


180
Li4SC1Fe3Si8O24


181
Li4Sc2P4H2O16


182
Li4Sc4Si4O16


183
Li4Se1O5


184
Li4Si2O6


185
Li4Si4O10


186
Li4Ta4Si4O20


187
Li4Ti2F12


188
Li4Ti2Si2O10


189
Li4Ti4P4O20


190
Li4Tm4Si4O16


191
Li4W1O5


192
Li4Y4Si4O16


193
Li4Zr8P12O48


194
Li5I1O6


195
Li5Sc2Fe3Si10O30


196
Li6Al6Si6O24


197
Li6B14O24


198
Li6Ca6P6O24


199
Li6P2O8


200
Li6Sc1Fe5Si12O36


201
Li6Si3F18


202
Li6Ta6O9F18


203
Li6Zr8F38


204
Li6Co5O12


205
Li7Ni5O12


206
Li8Al6Si6Cl2O24


207
Li8B12O16F12


208
Li8B16O28


209
Li8B8H32O32


210
Li8Ca4B32H28O70


211
Li8P10H2O30


212
Li8Sc1Fe7Si16O48


213
Li8Sc5Fe3Si16O48


214
Li8Si12O28


215
Li8Si16B8O48


216
Li8Ti8P12O48


217
Li9Er3Cl18


218
Li9Ni10O20


219
Na1Li1B4O7


220
Na1Li1C1O3


22-
Na1Li1Fe2Si4O12


222
Na1Li1S1O4


223
Na1Li1Si1B3H1O8


224
Na1Li1Tm2F8


225
Na1Li1Zr1Si6O15


226
Na1Li2P1O4


227
Na1Li3Fe4Si8O24


228
Na1Li7Fe8Si16O48


229
Na1Li9Fe10Si20O60


230
Na12Li12Al8F48


231
Na12Li12Sc8F48


232
Na16Li8Al8P16H16O72


233
Na2Li1Al1F6


234
Na2Li2Er4F16


235
NazLi2Ho4F16


236
Na2Li2Tm4F16


237
Na2Li2Y4F16


238
Na2Li4B2P4O16


239
Na3Li1Fe4Si8O24


240
Na3Li1Mg4Si12O30


241
Na3Li1W1O5


242
Na3Li2Fe4Si10O30


243
Na4Li4B16O28


244
Na4Li4Mg4P4O16F4


245
Na4Li4Si4B12H4O32


246
Na4Li4Zr4Si24O60


247
Na4Li8P4O16


248
Na5Li1Fe6Si12O36


249
Na5Li1P2O8


250
Na6Li2Mg8Si24O60


251
Na8Li4Y4Si24O60


25
Na9Li1Fe10Si20O60


253
Sr1Li1B9O15


254
Sr2Li2Al2F12


255
Sr8Li2B22H2O43


256
Sr8Li4B24O46









An aspect of the invention provides a solid state battery including an anode and a cathode including cathode particles and solid state electrolyte particles, a solid state electrolyte separating the anode and cathode, and an interface coating layer between the cathode particles and solid state electrolyte. The interface coating layer includes a compound of Table 1.


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 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.





BRIEF DESCRIPTION OF THE DRAWINGS


FIGS. 1(a)-1(f) show an illustration of dynamic voltage stability concept. FIG. 1(a) shows voltage stability window is opened by constriction with certain effective modulus (Keff), where the effective stress ϵKeff is composed of an actual local stress (σlocal) and a kinetic contribution (σeffkinetic) caused by kinetic stability. FIG. 1(b) shows decomposition nuclei of electrolyte will compress the reaction front and freeze the ionic diffusivity (D) of the decomposition. FIG. 1(c) shows decomposition nuclei of electrode-electrolyte interface will compress the reaction front and freeze the ionic diffusivity (D) of the decomposition. FIG. 1(d) shows that due to compressive strain at the reaction front, the diffusivity of atoms drops dramatically, and the decomposition is kinetically stopped. FIG. 1(e) shows low porosity contacts of electrode and electrolyte at the micrometer scale. FIG. 1(f) shows solid-solid interface contact with many nanosized or sub-nanosized point contacts alternated by atomic scale gaps, giving inhomogeneous local chemical potential of lithium μLi(x) with strong x dependence and a development of reaction strain that cannot be easily released.



FIGS. 2(a)-2(d). FIG. 2(a) shows electrolyte dynamic voltage stability window, reaction strain and decomposition energy in response to constrictions by direct minimization method using LGPS as an example. The overall voltage stability window opens, and the reaction strain and decomposition energy decrease with increasing Keff. FIG. 2(b) shows the less than 4 GPa effective pressure σeff induced by 0 to 5 V electrochemical decomposition under 0 to 20 GPa effective modulus Keff for LGPS. FIG. 2(c) shows the metrics derived from the voltage window opening phenomenon: kox and kre are the slope by which the upper and lower stability limits of Uox and Ure increase and decrease with increasing Keff. FIG. 2(d) shows the electrolyte distribution on the map of the window opening slope difference kox−kre (kox>0 and kre<0) versus intrinsic voltage stability window.



FIGS. 3(a)-3(b). FIG. 3(a) shows the negative correlation between the intrinsic window and the logarithmic Li ion conductivity[6-7, 27-39]. FIG. 3(b) shows the electrolyte distribution on the map of the opening slope at oxidative voltage limit ko versus intrinsic voltage stability window.



FIG. 4 shows constriction induced voltage stability of Li solid-state electrolytes calculated by direct minimization method. Voltage window expansion at representative Keff of sulfides (blue bars), oxides (green bars) and halides (purple bars). The red and blue lines in each bar denote the reduction and oxidation limit of the electrolyte. The numbers on the right of each bar, e.g., 7.3V@20 GPa denote the voltage window at (@) a given Keff. The intensity of each color shows the magnitude of decomposition reaction strain.



FIGS. 5(a)-5(f) show high throughput search of coating materials for LGPS, LPSCl electrolytes and 4V—Li0.5CoO2 (LCO), 4V—Li0.5Ni1/3Mn1/3Co1/3O2 (NMC111) and 4V—Li1/3Ni7/9Mn1/9Co1/9O2 (NMC811). FIG. 5(a) shows the high-throughput screening procedure. FIGS. 5(b)-5(e) show electrochemical decomposition energy of the screened coating at SSE or cathode interfaces, and SSE/cathode interfaces as well, calculated by unconstrained ensemble (FIG. 5(b)) and constrained ensemble at Keff=2 GPa (FIG. 5(c)), Keff=20 GPa (FIG. 5(d)), and Keff=23 GPa (FIG. 5(e)). FIG. 5(f) shows the critical effective modulus K* of each interface.



FIGS. 6(a)-6(b) show experimental examination of LiCoO2|LiNbO3 interface dynamic stability. FIG. 6(a) shows LiNbO3 coated LiCoO2 (LCO) shows a better cycling performance than bare LCO in solid state battery with mechanical constriction. FIG. 6(b) LiNbO3 coated LCO shows a worse cycling performance than bare LCO in liquid battery without mechanical constriction.



FIGS. 7(a)-7(e) show critical effective modulus (K*) needed to stabilize the cathode/electrolyte electrochemical interface reaction at 4 V with different computational approaches. FIG. 7(a) shows the cathode and electrolyte are in direct contact. FIG. 7(b) shows a chemical interphase is formed first between the cathode and electrolyte, with which the electrolyte is in contact at 4V. FIG. 7(c) shows LCO-LGPS cathode composite solid-state battery cycling first at room temperature and then at 55° C. FIG. 7(d) shows the same battery cycled in the reversed temperature sequence. FIG. 7(e) shows temperature varying test for 811-LPSCl and 811-LGPS cathode composite cycled in solid-state batteries.



FIG. 8(a)-8(d) show high throughput search of coating materials for Li7La3Zr2O12 (LLZO) electrolytes and 4V—Li0.5CoO2 (LCO), 4V—Li0.5N1/3Mn1/3Co1/3O2 (NMC111) cathodes. FIG. 8(a) shows the high-throughput screening procedure. Electrochemical decomposition energy of the screened coating/SSE or cathode interfaces, and SSE/cathode interfaces calculated by unconstrained ensemble (FIG. 8(b)) and constrained ensemble at Keff=7 GPa (FIG. 8(c)), and the critical effective modulus K* of each interface at 4 V (FIG. 8(d)).



FIG. 9(a)-9(d) show high throughput search of coating materials for halide electrolytes and 4V—Li0.5CoO2, 4V—Li0.5Ni1/3Mn1/3Co1/3O2 (NMC111) cathodes. FIG. 9(a) shows the high-throughput screening procedure. Electrochemical decomposition energy of the screened coating/SSE or cathode interfaces, and SSE/cathode interfaces calculated by unconstrained ensemble (FIG. 9(b)) and constrained ensemble at Keff=7 GPa (FIG. 9(c)). FIG. 9(d) shows the critical effective modulus K of each interface.



FIG. 10 shows voltage stability window in response to mechanical constriction for different electrolytes.



FIGS. 11(a)-11(c). FIG. 11(a) shows comparison of hull energies at 4 V versus Li of {Li5.5PS4.5Cl1.5—LiAlO2}interface with unconstructed Li5.5PS4.5Cl1.5 and constricted Li5.5PS4.5Cl1.5 at Keff=20 GPa (Li5.5PS4.5Cl1.5@20 GPa). The dashed line corresponds to the sum of intrinsic instability of Li5.5PS4.5Cl1.5 and LiAlO2 at 4V. FIG. 11(b) shows illustration of the change of hull after applying 35 GPa mechanical constriction at the interface of {Li5.5PS4.5Cl1.5@20 GPa-LiAlO2} at 4 V, and the comparison between Kcrit(x)Vxεx and KeffVxεx. FIG. 11(c) shows KeffVxεx of {Li5.5PS4.5Cl1.5@20 GPa-LiAlO2} interface at 4V at Keff=35 GPa, and the definition of K*.



FIG. 12 shows halide electrolyte/oxide cathode coating after including LixCly as possible decomposition products.



FIG. 13 shows constriction induced voltage stability of the decomposition reaction of solid-state electrolyte (SSE). ΔGEC-RXN is the Gibbs free energy of the electrochemical decomposition reaction. Ure (Keff), Uox(Keff) and Uw (Keff) are the reduction limit, oxidation limit and the voltage stability window of the electrolyte, respectively, which are all functions of the effective modulus Keff in the unit of GPa representing the local level of mechanical constriction. ε is the reaction strain of a specific decomposition. (a) Perturbation method with just one oxidative decomposition reaction (red dots) and one reductive decomposition reaction (blue dots) at each voltage. The upward arrows show that the electrochemical decomposition energy is increased by mechanical constriction and the magnitude is proportional to reaction strain; (b) Direct minimization method demonstrated by an example of Li10GeP2S12 (LGPS): all decomposition reactions are considered and the 4 voltage window determining reactions in the illustration are labeled with 4 different colors. The 4 thin solid lines show the electrochemical reaction Gibbs free energy change with respect to voltage without mechanical constriction, and the 4 solid thick lines show that of the reactions with effective modulus Keff of 10 GPa.





DETAILED DESCRIPTION OF THE INVENTION

The invention provides a solid state battery with an interface coating layer between cathode particles and solid electrolyte particles in the cathode that, under applied voltage, evolves from unstable to stable, providing a dynamic voltage stability for advanced battery performance. A constrained ensemble computational approach systematically evaluated and compared dynamic stability voltage windows in response to the mechanical constriction effect. High-throughput calculations screened coating materials for different interfaces between sulfide, halide, and oxide electrolytes and typical cathode materials with enhanced dynamic voltage stability. A demonstration with an assembled battery containing cathode particles with an interface coating layer to solid state electrolyte in the cathode layer shows the value of these computations to confirm the validity of predicted compounds described.


Solid state batteries are one of the most promising next-generate energy storage technologies, due to the potential to apply lithium metal anode for high energy density and much improved safety by preventing lithium dendrite penetration.[1-4] For battery applications, the Li ion conductivity, voltage stability window, and mechanical properties are three key electrolyte parameters. Mechanical properties of solid electrolytes are of particular interest in solid state batteries. Low modulus of sulfides enables better contacts between the particles in the electrolyte and cathode mixture by a simple cold-press calendaring procedure.[5-7] More importantly, these three parameters are often strongly coupled in a solid-state battery to greatly influence electrochemical behaviors.


In theory, the strictest definition of voltage stability window refers to the voltage range that the electrolyte can work without any electrochemical decompositions thermodynamically. Precise calculations of such intrinsic voltage windows of various types of solid electrolytes have been performed previously.[8-12] However, in practice those intrinsic voltage windows are often narrower than the operational voltage range needed by a full battery, thus various decomposition reactions can still happen. This is especially true for sulfide solid electrolytes, where the intrinsic voltage window is only around 1.7˜2.3 V. Even considering the delithiation capacity in sulfide electrolyte, the effect can only widen the electrolyte voltage window to 2.5˜3 V.[13-14]


In stark contrast, sulfide electrolyte-based solid state batteries can cycle well in experiment in a wide voltage range with Li metal anode and 4V cathodes, up to high current densities around 50 mA/cm2, and in a wide operational pressure range from several hundred MPa down to a few MPa[2, 4, 15-20]. These experimental facts suggest that certain stabilization mechanism must play a critical role here to widen the practical operational voltage window of solid-state batteries beyond the intrinsic voltage stability predicted by the standard convex hull computational approach.


It was found that for all-solid electrolyte batteries, although small decomposition could happen beyond the intrinsic voltage window, they often show self-limiting decomposition, meaning that the decomposition can stop quickly at a certain stage, giving the wide operational voltage stability in practice. This is in drastic difference to the case when the solid electrolyte is immersed in a liquid electrolyte, where the electrolyte decomposes deeply[5]. This is because in the former case any volume expansion decomposition reaction has to overcome the mechanical constriction imposed at the solid-solid interface by the all-solid environment, which is a critical factor lacks in the latter case with liquid being added.


The local effective mechanical constriction modulus, Keff, on the order of the bulk modulus of electrolytes has been proposed to strongly correlate with operational electrochemical stability through interactions with such positive reaction strains,[4-5, 15, 21-23] where the reaction strain has been observed experimentally together with advanced battery performance. Solid-solid interface under mechanical constriction was shown to be able to penalize decomposition reaction nuclei with an energy scale on the order of KeffεV, where E is the local reaction strain and V is a reference volume. That is, the effect can lead to a dynamic evolution from interface instability to stability, giving the so-called dynamic voltage stability for advanced performance of solid-state batteries with greatly widened operational voltage window of sulfide electrolytes in contact with 4 V cathode and 0 V Li metal anode.[5, 16, 24]


In this work, we first articulate our state-of-the-art perspective on the thermodynamic and kinetic constitution of the dynamic voltage stability. We broaden the meaning of Keff to include the kinetic stability, which allows the KeffεV energy penalty to effectively stabilize interface reactions when the local stress is smaller than the fracture limit. This is a critical development of our constrained ensemble description for interface reactions in solid-state batteries, since most solid electrolyte materials do not have a high fracture toughness[25], but many of them can exhibit operational interface voltage stability way beyond the predicted limit of their thermodynamic voltage stability. We then further investigate the dynamic voltage stability for all the main types of Li solid electrolytes, including chalcogenides, oxides, halides and borohydrides, as well as their interface stability with coating materials for classic oxide cathodes. Here we apply our constrained ensemble computations across these solid-state electrolytes (SSEs) to systematically evaluate and compare their dynamic stability voltage windows in response to the mechanical constriction effect. High-throughput calculations based on pseudo-binary approach are used to search for coating materials for different interfaces between electrolyte and cathode materials with enhanced dynamic stability.


A comparison with experiment is given based on a readily available coating procedure for LiNbO3 to demonstrate the unique prediction capability of our computational approach to design dynamic voltage stabilities by interface coatings. The detailed agreement between computation and experiment further highlights the potential value of the ˜150 new cathode interface coating materials predicted in this work. Our work thus will speed up the solid-state battery development by providing a promising list of candidate coating materials to the field with a potential to significantly stabilize the cathode interface reactions during the battery cycling.


Batteries

Batteries of the invention include an anode, a cathode including cathode particles and solid state electrolyte particles, a solid state electrolyte, and an interface coating layer between the cathode particles and the solid state electrolyte particles in the cathode layer. The interface coating layer can include any compound from Table 1.


Interface Coatings

The interface coating between the cathode particles and solid state electrolyte particles includes a compound of Table 1. Interface coating layers may also include additional materials, such as polymers from the coating procedure as described herein. Upon battery cycling, the interface coating layer will react with either cathode or solid state electrolyte, or both, so that chemical elements from both cathode and solid state electrolyte may be mixed into the interface coating layer through interface reactions or forming new phases. These interface reactions, however, will be self-limited to stop quickly, so that the thickness of interphase reaction layer is well limited. The as-formed interphase layer will provide both electrochemical voltage stability in the following cycles and sufficient Li ion conductivity due to the limited thickness.


The thickness of the interface coating layer surrounding the cathode particles or solid electrolyte particles can be 0.1 nm to 1 μm, e.g., about 1-100 nm (e.g., about 1-10 nm, 1-25 nm, 10-20 nm, 20-30 nm, 25-50 nm, 30-40 nm, 40-50 nm, 50-60 nm, 50-75 nm, 60-70 nm, 70-80 nm, 75-100 nm, 80-90 nm, or 90-100 nm, e.g., about 1 nm, 5 nm, 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 100-110 nm, 100-125 nm, 100-200 nm, 200-300 nm, 250-500 nm, 300-400 nm, 400-500 nm, 500-600 nm, 500-750 nm, 600-700 nm, 700-800 nm, 750-1000 nm, 800-900 nm, or 900-1000 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).


Anodes

Anodes of the invention may be any suitable anode known in the art, such as Li metal. For example, lithium metal foil, e.g., Li metal foil on a current collector, e.g., of stainless steel. The lithium metal can also mix or alloy with 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.


Anodes may be deposited on an appropriate substrate, e.g., a fluoropolymer or carbon. For example, liquefied polytetrafluoroethylene (PTFE) has been used as the binder when making solutions 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. 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.


Cathodes

Cathode materials can be chosen to have optimum properties for ion transport. For example, the cathode may preferably be LiNi0.8Mn0.1Co0.1O2 (NMC811) due to its high capacity, energy density, and also cost effectiveness due to the decreased composition of the expensive Co element. Other materials for use as electrodes in solid state electrolyte batteries are known in the art.


The cathodes may be a solid piece of the material, or alternatively, may be deposited on an appropriate substrate, e.g., a fluoropolymer or carbon. For example, liquefied polytetrafluoroethylene (PTFE) has been used as the binder when making solutions of cathode materials for deposition onto a substrate. Other binders are known in the art. The cathode material can be used without any additives. Alternatively, the electrode material may have additives to enhance its physical and/or ion 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 can include, e.g., 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+zNixMnyCo*Al(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, or LiCo0.5Mn1.5O4. The cathode can be coated with LiNbO3, LiTaO3Li2ZrO3, 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. 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 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 materials can be 1 nm-30 μm.


The loading of the cathode can be 0.1-100 mg/cm2. The thickness of the cathode can be 5 μm-2000 μm. The cathode may be mixed with solid state electrolyte materials to provide increased cathode capacity.


Other cathode materials such as selenium or sulfur that exhibit promising high capacity and energy density also show much better cycling performance in our multilayer design than the single layer design.


In certain embodiments, the cathode can be mixed with polymer and carbon black, solid electrolytes can be mixed with polymer. Examples of polymers may include polyethylene oxide, polyvinylidene fluoride, poly(vinylidene fluoride-co-hexafluoropropylene), poly(ethyl methacrylate), or poly(vinylidene fluoride-co-trifluoroethylene). The thickness of the solid electrolyte layer is 5-1000 μm. The thickness of the cathode can be 5-2000 μm.


Solid State Electrolytes

Suitable solid state electrolytes that may be used 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).


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 electrolytes, e.g., GeaPbSc, e.g., GeP2S12, tin solid electrolytes, e.g., SndPeSf, e.g., SnP2S12, iodine solid electrolytes, e.g., P2Sal 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. The shell can include a compound of Table 1. 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.


Mechanical Constriction

In some embodiments, the battery interface is under local mechanical constriction. Mechanical constriction at the interface between the solid state electrolyte and the cathode can limit the extent of chemical or electrochemical decomposition of solid state electrolyte materials by volumetric constraint. Local stress on the order of a few GPa up to the fracture limit of solid electrolyte, may be generated from mechanical constriction. Local compressive strain at reaction front can indue a diffusion limiting process to limit interface reaction, contributing a kinetic part to the local effective constriction modulus beyond the fracture limit. One condition to implement the mechanical constriction can be an external pressure applied to the battery cell 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. Mechanical constriction 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° C.-500° C. 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. The mechanical constriction may result from an applied pressure 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, 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. Greater mechanical constriction may be applied during battery fabrication. After providing the formation pressure, the porosity of the cathode, and/or multilayer may be 0%-50%. In some embodiments, the mechanical constriction is sufficient to raise the local effective modulus above Keff, thereby preventing decomposition, or such that a local stress field caused by decomposition of the solid state electrolyte raises Keff above Kcrit, thereby arresting decomposition.


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 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.


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 compounds of Table 1 to cathode particles, e.g., chemical synthesis, atomic layer deposition, chemical vapor decomposition, sputtering, pulsed laser decomposition, etc.


Model

Here, we first explain the physical meaning of the dynamic voltage stability using our state-of-the-art understanding and formula description, which forms the foundation for further high-throughput search and design of interface coating materials with enhanced such stability. The local effective modulus Keff and the effective stress σeff=εKeff describe the level of local mechanical constriction. It is important to note that the effective stress can often be larger than the actual local stress σlocal (FIG. 1a), because σefflocaleffkinetic, where the latter term σeffkinetic is an effective stress contributed by a kinetic diffusion-limiting process.


The plastic local strain field ε together with the actual local stress σlocal from the initial local decomposition provide the common strain energy Estrain∝σlocalεV for thermodynamic metastability for any interface voltage reaction. More precisely, Estrain=∫σlocal Vdε. However, the magnitude of the strain energy is limited by the plastic deformation and the fracture limit of electrolyte materials, beyond which there is no local mechanical constriction. Simultaneously, at the reaction front, the same local inhomogeneous strain field ε can significantly decrease the ionic interdiffusion in the electrolyte by orders of magnitude to kinetically prevent further decomposition propagation, giving an ionic passivation effect from local reaction strain induced diffusion limiting process. Interface reactions will thus feel the significant effect from an additional energy stabilization term from the kinetic stability, Ekinetic, for much wider interface voltage stability than what can be provided by thermodynamic metastability.


Since both energy terms of Estrain and Ekinetic share the same local reaction strain term e, we have Ekinetic=∫σeffkineticVdε, which defines the kinetic part of the effective stress σeffkinetic. The total stabilization energy that includes both thermodynamic metastability and kinetic stability for interface reactions is thus Etotal=Estrain+Ekinetic=∫(σlocaleffkinetic) Vdε, which defines the total effective stress σefflocaleffkinetic. Since σeff=εKeff, we thus also have Etotal=ϵKeffV in the simplest format as the effective mechanical constriction energy.


More specifically, as illustrated in FIGS. 1b-c, the volume expansion decomposition with positive reaction strain (ϵ>0) compresses the surrounding electrolyte region, giving a local negative (compressive) strain (ϵ<0) at the reaction front of the undecomposed electrolyte. It was previously estimated that a 5% such local compressive strain will dramatically decrease the local ionic diffusivity D by orders of magnitude[22], giving a zero local diffusivity (D→0) at the reaction front in practice to shut down further interface reaction, as any solid-state decomposition will need sufficient ionic interdiffusion to happen kinetically (FIGS. 1b,c,d).


This kinetic stability mainly requires a positive reaction strain at a local reaction interface under mechanical constriction (i.e., low porosity at micrometer scale as in FIG. 1e), which in principle can be satisfied by most electrolytes upon a proper solid state battery design. For sulfide or halide, for example, a cold press is often sufficient. However, even if it is well constricted with low porosity at micrometer scale, at (sub)-nanometer scale the solid-solid interface between electrolyte and electrode materials can still be inhomogeneous spatially with a strong x dependence. This accordingly gives an inhomogeneous local lithium chemical potential μLi(x) due to the dry interface contact with many nanosized or sub-nanosized point contacts that are alternated by atomic scale gaps (FIG. 1f). In contrast, when a lithium-ion concentration is homogeneously surrounding a particle immersed in the liquid electrolyte, the electrolyte and electrode form the classical surface contact rather than point contacts, giving a homogeneous local chemical potential of lithium.


Thus, in liquid electrolyte batteries, the reaction front can propagate deeply to consume the electrolyte[5], as the reaction strain field is flat with small curvature to be more easily released to the liquid environment, giving little effective stress to self-limit the decomposition. In contrast, in solid state batteries, reaction strain was found to build up plastically without a release. This is due to the inhomogeneous μLi(x), giving large local curvatures of the strain field (FIG. 1f), where the local positive and negative strain fields are coupled and locked at the reaction front to give the self-limiting decomposition by the effective stress σeff.


The effective stress σeff=ϵKeff thus could be larger than both the actual local stress σlocal and the fracture limit σfrac of the electrolyte materials without forming any actual fractures, as long as σefffraclocal is satisfied. In practice it will need the initial local decomposition to be suppressed quickly so that σlocal is maintained at a low level, which is a property of interface reaction that can be designed. In addition, it also needs the electrolyte material to exhibit sufficient plastic deformation capability.


Therefore, in solid state batteries there could be an important dynamic evolution of electrochemical process, where the local compressive strain at the reaction front induced by the tensile strain from initial decomposition will kinetically shut down the ionic diffusion locally by encapsulating the local decomposition by the ionically passivated reaction front layer, preventing further decomposition and crack formation. To design such interface reactions, technically, for any electrolyte material or its interface with electrodes, there is a critical effective modulus, Kcrit[26] or K*[15], beyond which the local reaction can be fully suppressed. This critical modulus can be calculated by making KeffϵV equal the decomposition hull energy Ehull, thus a smaller K* or Kcrit is preferred, as it suggests that the decomposition is easier to be suppressed by Keff.


Importantly, we also point out here that since for a given decomposition hull energy Ehull, a larger local reaction strain ϵ will give smaller K* from Ehull=K*ϵV, and simultaneously, larger e also indicates stronger ionic passivation at the reaction front, looking for interfaces with smaller critical modulus K* thus also forms one important aspect to design the kinetic stability induced by the ionic passivation effect.


The above description forms our state-of-the-art understanding of the so-called dynamic voltage stability or simply dynamic stability that was proposed previously in an experimental work,[4] where advanced battery performance was demonstrated by utilizing the effect. This interpretation of dynamic voltage stability also goes beyond our previous works[5, 15, 26] by clearly stating that first, significant portion of the kinetic stability energy Ekinetic is already included in the term of KeffϵV; second, the inhomogeneous local lithium chemical potential μLi(x) at the solid-solid interface is critical to the formation of the plastic reaction strain; and third, the quantitative condition of σefffraclocal needs to be satisfied to avoid fractures with sufficiently small local reaction stress, which however shares the same local reaction strain to simultaneously prevent further decomposition by sufficient effective stress. This interpretation forms an indispensable foundation for our computational approach to design dynamic stability presented in the following sections regarding intrinsic voltage stability window and interface coating materials that is of importance to the performance of solid state batteries.


EXAMPLES
A. Electrolyte Dynamic Voltage Stability Window in Response to Constrictions

The dynamic voltage stability window of solid electrolytes is calculated by the minimization method (see Methods). We systematically calculated the voltage window and reaction strain in response to mechanical constriction for three mainstream types of electrolytes, including sulfides, halides and oxides (FIG. 10 for raw data). FIGS. 2(a)-2(c) use Li10GeP2S12 (LGPS) as an example to illustrate the phenomenon. FIG. 2(a) shows the voltage stability window and the reaction strain at different voltages from 0 to 5 V and at different Keff of 0, 10 and 20 GPa. With increasing Keff, the voltage window can be opened, if the reaction strain is positive at the voltage beyond the voltage window. Table 2 shows more detail of decomposition energy, reaction strain, and decomposition product at 4V at different Keff.


Outside the stability window at a given voltage, the thermodynamic decomposition energy decreases with increasing Keff. With increasing Keff the reaction strain also decreases and approaches zero eventually, giving the limit of voltage window opened by this thermodynamic metastable process. However, since the thermodynamic driving force for decomposition also decreases with increasing Keff, it makes other nonequilibrium decomposition processes with larger reaction strains become more competitive and thus more likely to happen. Those nonequilibrium reactions thus may override the thermodynamic metastable evolution pathway, which is an effect that could give an even wider operational voltage window in a properly designed practical battery than what can be predicted by the minimization method here.



FIG. 2(b) shows the effective stress induced by electrochemical decomposition under different effective modulus Keff calculated by multiplying the modulus with the reaction strain in the minimization method. We emphasize that the effective modulus and effective stress, although with the unit of GPa, are different from the actual local stress. The effective stress is less than 3 GPa at 0˜20 GPa Keff due to the less than 30% reaction strain at low Keff and the fact that with increasing Keff the reaction strain decreases. Since σefflocaleffkinetic and the compliant yet brittle nature of sulfide[25], it can be estimated that the magnitude of σlocal is comparable to σeffkinetic, and thus thermodynamic metastability and kinetic stability contribute comparably to the dynamic voltage stability of intrinsic voltage window.



FIG. 2© analyzes the change of the oxidation limit Uox and reduction limit Ure of LGPS with changing Keff. Uw0 is the intrinsic voltage window at zero constriction. Uox stops increasing at Keff=18 GPa, while U, stops increasing at Keff=10 GPa. We define kox and kre as the two average slopes of Uox(Keff) and Ure(Keff), where kox>0 and kre<0. The slope difference kox−kre reflects the net voltage window opening rate with respect to the application of mechanical constriction Keff, which can be considered as a metric to measure the susceptibility of the voltage window opening effect for different materials in response to mechanical constriction.


As shown in FIG. 2(d), sulfides and oxides show similar levels of kox−kre, while halides show higher kox−kre due to the high absolute value of both kox and kre (Table 5, FIG. 10). This suggests that halide electrolyte can show stronger voltage effect in response to mechanical constriction compared with sulfide electrolyte. For oxide electrolyte, at the reduction side kre is almost zero, which suggests that oxide solid electrolyte may benefit less from the dynamic voltage stability against lithium dendrite penetration that was found in sulfide and halide. However, oxides show kox values between sulfides and halides, suggesting the constriction effect may still play a role at the cathode side for oxide electrolyte if the solid-solid interface between electrolyte and cathode particles can be well constricted, i.e., forming a good interface contact.


For Uw0, the values for sulfides are the lowest, while oxides and halides with stronger chemical bonding due to higher electronegativity of O2−, Cl and Br show much higher Uw0. Therefore, in the (kox−kre) vs. Uw0 plot (FIG. 2(d)), sulfides, oxides, and halides occupy the bottom left region, middle-bottom right region, and top right region, respectively.



FIG. 3(a) shows an interesting negative correlation between intrinsic voltage window Uw0 and the logarithmic ionic conductivity. Sulfide occupies the bottom right corner, while oxides and halides occupy along the linear fitting line toward the top left region. A general picture for this relationship is that the fast lithium ion conduction in sulfide electrolyte is strongly contributed by certain soft phonon modes and their anharmonic couplingsl[40], which meanwhile also imply relatively weak bonding that reduces the intrinsic stability of the electrolyte, thus giving the narrower intrinsic voltage window for sulfides.[41]


Since kre is zero only for oxide, for a fair comparison with halide and sulfide, we plot kox vs. Uw0 in FIG. 3(b). The two correlations here (FIGS. 3(a)-(b)) suggest that electrolyte materials with high voltage opening susceptibility to mechanical constriction often tend to show low ionic conductivity together with hard phonon mode and chemical bonding. However, the fact that sulfide electrolytes can already show sufficient dynamic voltage stability suggests that when looking for new materials a kox or kre value at the level of sulfide around 0.1 V/GPa is sufficient and higher such susceptibility value will likely come at an expense of reduced ionic conductivity.



FIG. 4 shows the voltage stability and reaction strain at different Keff three types of solid electrolytes. Previously an inclusion or nucleation decay model was used to describe the decomposition inside a constricted LGPS,[22] which can be applied to the decomposition everywhere inside a theoretically dense pellet of polycrystalline SSE. According to the inclusion model, Keff≈0.5 Kv where Kc is the bulk modulus of the SSE, which gives Keff about 15-20 GPa for sulfides, Li3ClO and Li3BrO, and above 50 GPa for other oxides. Intermediate constriction values of Keff=10 GPa or 20 GPa are also considered for comparison. One obvious trend for all the electrolytes in FIG. 4 is that at each voltage, the reaction strain becomes smaller beyond the voltage window with increasing Keff, which is due to the larger energy penalty for larger-strain reactions in the reaction space at higher constriction level. This also reveals that the smaller-strain reactions are the thermodynamically most preferred.


A.1 Sulfides

The results of 7 representative sulfides are shown by the blue bars. Most of their oxidative limits can be opened from ˜2.5 V to larger than 3V. LGPS and Li5.5PS4.5Cl1.5 (LPSCl) can be opened to larger than 4V. The effect of mechanical constriction on glass sulfides, glass-ceramic sulfides, thio-LISICON, including Li3PS4, Li7P3S11, LGPS, LSPS have been retrospectively reviewed[23], suggesting that constriction induced voltage stability should have been a key concept in sulfides since the first glassy-ceramic sulfides.


Noted that other than LGPS and Li5.5PS4.5Cl1.5, the oxidative limits do not or barely further increase with the increase of Keff from 10 GPa to 20 GPa. This is due to the existence of decomposition with negative reaction strains (defined to be 0 in calculation, as discussed in Methods) shown by the light-blue color above the oxidative limit, causing no thermodynamic stability in response to constriction. In these cases, dynamic voltage stability can be further adjusted by using the strategies of coating or more generally the interface composition modification, as we will discuss in part B. Briefly, the requirement of Keff can be lowered for a given oxidative limit, as long as higher reaction strain can be designed to such an interface so that the decomposition can be more easily suppressed (i.e., reducing the critical effective modulus K*[15,26]).


A.2 Oxides

The result of six representative oxides is shown by the green bars in FIG. 4, including anti-perovskite type Li3OCl and Li3OBr, LIPON type Li2PNO2, garnet type Li7La3Zr2O12 (LLZO), perovskite type Li0.5La0.5TiO3 (LLTO), and NASICON type Li1.3Al0.33Th1.67(PO4)3 (LATP). Oxidative limits can be raised close to 5V or even higher than 7V, except for LLTO which decomposes to Li, LiO8, TiO2, Li3TiO3, La2Ti4O9 and La2Ti2O7 with negative reaction strain at 4.3 V at 10 GPa, limiting its oxidative limit at 4.3V. Note that at 0 K DFT computations, oxygen molecule crystal (13.5 Å3/atom) appears in the decomposition products of LLZO (11.6 Å3/atom), LLTO (12 Å3/atom) and LATP (12.3 Å3/atom), but the atomic volume of the oxygen is not too far from the electrolytes, so the reaction strain in our calculation here is not provided by the possible gas phase at room temperature (RT). For high modulus oxides such as LIPON, LLZO and LATP, to examine the effect of mechano-electrochemistry, it is important to get a dense electrolyte pellet with lowest possible porosity. Techniques such as pulsed laser deposition (PLD) or coating deformable materials under cold press at interface are thus needed for these oxides[42]. In addition, whether these electrolytes can exhibit sufficient plastic deformation upon local decomposition is yet to be investigated, which may be another factor to limit the expansion of voltage window by Keff.


Noted that Li3OCl and Li3OBr are with low enough modulus to be cold pressed into a dense pellet and have a 4.8 V oxidative limit at Keff≈0.5 Kv. Together with high Li conductivity on the order of 10−3-10−2 mS/cm[39, 43-44], they are also very promising high voltage electrolytes. In computation, the decomposition products are Li, LiCl, LiClO4 beyond oxidative limit at Keff from 0 GPa to 20 GPa. Experimentally, trace amount Ba doped Li3ClO has shown high RT Li conductivity of 25 mS/cm, and its oxidative limit is measured to be higher than 8 V even at 130° C.[43]. The much wider 8 V stability than the 4.8 V stability in our computation could be due to the high kinetic barrier in forming the high valence Cl7+ in the decomposition product of LiClO4. Other potential decomposition products in Li—Cl—O system could be non-solid ClxOy that become energetically competitive at RT than the OK products, which result in larger reaction strain and thus a dynamic voltage window beyond 4.8 V. Therefore the 8 V stability of Li3ClO could be due to such kinetic stability beyond the constriction induced thermodynamic metastability at RT.


A.3 Halides

Six halide electrolytes of Li3MX6 (M=Y, In, Er, Sc, X=Cl, Br) are considered. Their oxidative decomposition products are always Li, MX3 and X2 and the increase of reaction strain in a few tens of volts above the oxidative limit is due to the increasing portion of partial decomposition of Li3MX6 in the multi-phase equilibrium region of Li-M-X grand potential phase diagram. If there is any Cl2 gas release in such a battery, the contribution from the volume of Cl2 to reaction strain will disappear, causing negative reaction strain of ˜−15%, thus probably no broadening of voltage window above 4.3 V. As the data in Materials Project are calculated at 0 K, Cl2 is crystalized molecules cluster. Removing Cl2 from potential decomposition products in computation will give infinite oxidation limit since other compounds in the Li-M-X systems cannot compose a balanced reaction equation due to the lack of Cl-rich phases. Note that Cl-rich NaxCly phases, i.e. NaCl3 and NaCl7 can form under GPa order of pressure[45], Cl-rich LixCly counterparts may also exist and can form under GPa level mechanical constriction. As there is no report on Cl2 gas release experimentally, it is possible that halide electrolytes are either well constricted in batteries so that it is stable, or CI-rich LixCly phases are formed during decomposition. In such a case, the predicted voltage window is shown at the bottom of FIG. 4 with LixCly phases labeled in the corresponding voltage range where the related decomposition happens. Although the voltage window shrinks a little when unconstrained, it can still open to 6.6 V at 20 GPa level of local mechanical constriction. Similar scenarios may happen for Li-M-Br electrolytes as Br2 is in the liquid state at room temperature.


B Interface Dynamic Voltage Stability in Response to Constrictions

The interface electrochemical stability is calculated by pseudo-phase approach[12] within the perturbation method framework (see Methods and FIG. 11). The constriction induced dynamic voltage stability model is compatible with high-throughput computational platform to search for promising interface coating materials that can provide enhanced interface dynamic stability.


B.2 High-Throughput Search Under Constrained Ensemble for Li Sulfide Electrolyte Coating Materials


FIG. 5(a) shows the high-throughput screening procedure for searching potential coating materials for interfaces between cathode and sulfide electrolyte materials. We first screened out the materials with radiative elements and removed duplicates to reduce computational cost. The second screening criterion selected stable phase entries with hull energy <5 meV/atom. The third one considers the initial interface chemical stability of coating/pristine cathode and coating/electrolyte. Coatings whose interfacial decomposition energies are less than 50 meV/atom can pass the third screening step. There are 2089 materials that pass the third screening.


Lastly, we examine the electrochemical stability of the interfaces by unconstrained and constrained ensemble pseudo-binary interface simulations: If the interface electrochemical decomposition energy at 4 V is <50 meV/atom at Keff=20 GPa, the material will become a coating candidate to help stabilize cathode interface reaction. We choose 20 GPa because it is a value roughly half of the bulk modulus of sulfide or halide electrolyte materials, which is around the maximum mechanical constriction that can be provided at the solid-solid interface based on the inclusion model[22]. Our goal is thus to predict cathode coating materials that can bring the critical effective modulus K* below 20 GPa, where a lower K* below 10 GPa or 5 GPa is in general more preferred, as they make the interface reaction easier to be suppressed by local mechanical constriction Keff.


There are 91 Li containing materials that passed all the screening steps. We selected 49 of them within ICSD id to present in FIGS. 5(a)-5(e). FIGS. 5(b) to 5(e) show the interface decomposition energies of 49 candidates plus LGPS, LPSCl and a commonly used coating LiNbO3 for comparison, which is calculated by unconstrained ensemble (0 GPa in FIG. 5(b)), slightly constrained ensemble (2 GPa in FIG. 5(c)), and 20 GPa and 23 GPa constrained ensemble (FIGS. 5(d)-5€).


Without coating, the direct interface between cathode and electrolyte cannot be electrochemically stabilized even at 23 GPa due to small response to constriction as indicated by the large K* value in FIG. 5(f). Furthermore, all these coatings are highly electrochemically reactive with LGPS and LPSCl when unconstrained due to the electrochemical intrinsic instability of sulfide electrolytes and the interface reaction between coating and electrolyte. However, these coating interfaces are largely stabilized (<50 meV/atom) at 20 GPa or 23 GPa.


For the LiNbO3 and cathode interfaces, the decomposition products are just Li, O2 and Nb2O5, so the interface is in principle stable. However, LiNbO3 itself is thermodynamically unstable at 4V at 0 GPa. Nevertheless, we find that the 4V decomposition can be stabilized by a modest 2 GPa constriction. Note that such a small constriction might also be provided by Nb diffusion[46-47] induced surface tension at the cathode particle level in a liquid electrolyte battery, so that although unconstrained at the cell device level, Li—Nb—O coating can still improve the cycling performance of NCM811. Comparing LiNbO3 with other predicted coatings in FIG. 5(d), LiNbO3 shows the largest K* with LGPS, indicating that these predicted coatings could also be promising. For example, Li—Ta—O based coating (right most in the list) can show better rate performance than Li—Nb—O based coating.[48] The predicted Li—B—O based coating has also been proven to improve LiCoO2 performance, and can have better first cycle capacity than Li—Nb—O.[49-50] But since experimentally LiNbO3 coating can be easily implemented by a simple two-steps method of solution evaporation and calcination[46], coating a predicted material and achieving better cycling performance than that of LiNbO3-coated one may require some nontrivial innovations in the synthesis procedure.


Here we use LiNbO3|LiCoO2 (LCO) interface as a model system to experimentally demonstrate the importance of dynamic voltage stability in predicting coating materials for solid state batteries. For solid state battery with LGPS as cathode electrolyte (FIG. 6(a)), bare LCO shows much worse cycling stability than LiNbO3 coated LCO at room temperature, consistent with our prediction that the LCO and LGPS interface is unstable at any Keff values while LiNbO3 can help stabilize the interface when a nonzero Keff is applied.


Since it is difficult to remove mechanical constriction in a solid-state battery to make Keff=0, we tested liquid electrolyte batteries without mechanical constriction and thus Keff=0 (FIG. 6(b)). In contrast, LiNbO3 coated LCO now shows worse cycling stability than bare LCO, consistent with our prediction that LiNbO3 and LCO interface is not stable when Keff is zero. Note that the LCO case discussed here is different from LiNbO3 coated NMC811 discussed earlier, where the coating does improve the cycling in liquid electrolyte batteries.[46] This may suggest a lack of Nb diffusion induced surface tension in the coated LCO in comparison with coated NMC, as in the NMC case the surface tension can serve as a nonzero Keff in the liquid electrolyte battery to help stabilize the interface between NMC and LiNbO3.


Although coating is a general strategy to improve the interface stability, we found that LCO and Li(Ni0.8Mn0.1Co0.1)O2 (NMC811) can sometimes cycle with sulfide electrolytes even without cathode coating[4, 15-16]. For such an interface, the initial chemical interphase formed by the direct contact between the cathode and electrolyte during powder mixing in mortar and cathode film formation in battery assembly before the application of voltage for electrochemical reaction should be considered.[26]FIGS. 7(a)-7(b) show another computational approach by first considering such a preformed chemical interphase between the corresponding cathode and electrolyte from pseudo-phase calculation without applying a voltage (See Methods). We then calculate K* at the interface between the interphase and cathode at 4V (FIG. 7(b)), which greatly reduces K* by orders of magnitude than the interface between the solid electrolyte and cathode (FIG. 7(a)). This suggests that these new interphases, once preformed, can make the interface reactions much more easily stabilized at 4V.


We further tested uncoated LCO and NMC811 cathode with sulfide cathode electrolytes in solid-state batteries. For LCO-LGPS cathode composite, it can barely cycle directly at room temperature with less than 50 mAh/g capacity and a fast capacity decay, but surprisingly, we found that it can cycle at 55° C. (FIG. 7(c)). More importantly, after more than 100 stable cycles at 55° C., it then can be cycled at room temperature (FIG. 7(d)). We then test the NMC811-sulfide cathode composite with varying temperatures (FIGS. 7(e)-7(f)), which shows that NMC811-sulfide can already be cycled directly at room temperature, and high temperature does not improve its subsequent room temperature performance. These results suggest that LCO-sulfide chemical interphase, which serves to stop further decomposition by dynamic voltage stability and improve interface contacts, requires a higher temperature to form than that of NMC811-sulfide.


B.2 High-Throughput Search Under Constrained Ensemble for Li Oxide Electrolyte (LLZO) Coating Materials

A classic garnet type LLZO is used as an example of oxide electrolyte to explore the interface reaction by constrained ensemble (FIGS. 8(a)-8(d)). Note that we added an elemental screening to remove the expensive (>50 USD/lb) and toxic elements to narrow down the final list. The challenge for the garnet electrolyte-cathode interface lies in the good contact and low interfacial resistance within low thermal processing window.[51] Binding electrolyte and cathode together with a electrochemically stable coating material is a useful strategy.[52-54] When unconstrained, since LLZO itself is not stable at 4V, the interfaces with coating materials are mostly unstable with high interfacial reaction energies as indicated by the black grids. For the 4 non-black grids, it simply indicates that there is no interfacial reaction between LLZO and the particular coating, with the energy showing the 4V instability of the coating material itself. For the coating materials that have the same decomposition energies interfacing LCO and NMC (and LLZO if non-black), in most cases the decomposition is from the intrinsic 4V instability of the coating materials due to a lack of the interfacial mutual reaction. We use Keff=7 GPa in the screening here since LLZO itself is stabilized at 7 GPa at 4V. To achieve sufficient Keff, a dense contact is required. Softer coatings, such as Li2CO3 that is also included in the FIGS. 7(a)-7(f) prediction with lower bulk modulus of 63 GPa and shear modulus of 32 GPa (documented in Materials Project), may be a good candidate for minimizing the complexity of oxide processing (such as requirement for high temperature sintering) and working for high-voltage stability. Note that Li2CO3 itself is ionically insulating, which is one reason why the spontaneous forming of Li2CO3 conformal coating on LLZO in air needs certain engineering[55], and boron doping that enables Li conduction can make it a good coating material[53]. Another predicted Li3PO4 coating has also been experimentally examined between NMC811 and LLZTO to show high capacity and stable cycling.[54]


B.3 High-Throughput Search Under Constrained Ensemble for Li Halide Electrolyte Coating Materials

Similar screening procedure is used here for the interface between cathode and halide electrolyte. Most of the predicted coating materials for halide electrolytes are still oxides. When unconstrained (Keff=0, FIG. 9(b)), Li3YBr6 and Li3InBr6 show unstable interfaces in most cases (dark color in FIG. 9(b)), because Li3YBr6 and Li3InBr6 are not stable at 4V, and they also have relatively large K* as shown in FIG. 9(d). To stabilize the interphase, a Keff=7 GPa is applied in the last step of the high-throughput screening, since all 6 halide electrolytes themselves are stabilized at 7 GPa. We notice that non-solid Br2 appears in most decomposition products of bromide/coating interfaces, and ClO2 appears in 60% of the chloride/coating decomposition products, which won't really contribute to the solid reaction strain at RT that leads to the prediction above. Like the Li3YCl6 intrinsic stability case (FIG. 4), we add LixCly to possible decomposition products. The list is then shortened from 60 candidates to 46 (FIGS. 12(a)-12(c)), and 42% of the chloride/coating decomposition products includes LixCly (all LiCl3), while ClO2 appearance drops a little to 50%. Note that LiCl3 and ClO2 can coexist in a decomposition. ClO2 may be reacted to form other new solid compounds such as LixClyOz to contribute to the reaction strain. Similarly, other non-solid phases at RT (e.g., Br2) might also end up as LixBry and LixBryOz.


In this work, we systematically reinvestigated the voltage window response of mechanical constriction of different solid-state electrolytes. The oxidative limit of sulfide electrolytes can be opened to ˜4V, where kinetic stability can play an important role below 4V for the voltage stabilization. Oxide electrolytes can be opened to more than 6V if dense pellet can be achieved, where the additional role of plastic deformation in comparison with sulfides can be better evaluated in experiment. Halide materials have the highest window opening slope upon mechanical constriction, and LixCly phases may form during decomposition instead of the gas phase Cl2.


By applying constrained ensemble to high-throughput search, we predicted several lists of coatings for Li cathode/electrolyte interfaces for sulfide, oxide, halide electrolytes. For interfaces between sulfide electrolytes and oxide cathodes, coatings with lower critical mechanical modulus K* than LiNbO3 are predicted. LiNbO3—LiCoO2 interface shows better cyclability in solid state battery than in liquid battery in our experiment, giving experimental evidence of dynamic interface stability related to coating at the solid-solid interface. The fact that some batteries can cycle without coating can be explained by the more stable interfaces with chemically formed interphase during materials mixing. For oxide materials, potential coating materials that can act as electrochemically stable binder between cathode and garnet electrolyte are in the prediction list, including the existing B-doped Li2CO3 and Li3PO4. For halide materials, we discussed the possibility of forming LixCly at the interface with cathodes. Our work will shed light on the future design of electrolyte and electrode interface reaction by explicitly considering the effect of dynamic voltage stability. An application of the new design strategy in future experiments will further advance the performance of solid-state batteries.


Methods
1. Constrained Ensemble Computational Approach

The computational modeling for constriction induced voltage stability is illustrated in FIGS. 13(a)-(b) for perturbation (13(a)) and minimization (13(b)) methods, respectively. We first consider a solid-state electrolyte (SSE) with stability window Uw (Keff=0) between reduction limit Ure (Keff=0) and oxidation limit Uox (Keff=0) when being unconstrained mechanically (Keff=0). Above Uox(Keff=0), oxidation decomposition will happen, where Li ion in solid-state electrolyte decomposes to Li metal. Below Ure (Keff=0), reductive decomposition will happen, where external Li metal source from anode is consumed. In perturbation method, at each voltage point we only consider one oxidative (reductive) reaction with the largest decomposition energy.[23] The reaction equation, reaction strain ϵ, and reaction free energy ΔGEC-RXN can be written as









SSE






d
i



Dec
i



+
nLi





(
1
)












ϵ
=






d
i



V

Dec
i




+

nV
Li

-

V
SSE



V
SSE






(
2
)













Δ


G

BC
-
RXN



=


G
Dec

+

n

(


G
Li

-
eU

)

-

G
SSE

+


K
eff



V
SSE


ϵ






(
3
)







In eqn. (1), Deci denotes the ith decomposition product and di is its stoichiometry. In eqn. (2), the reaction strain is defined as the fraction of the difference between the final volume and the initial volume. Note that the reactant volume of Li metal in the reduction reaction at anode is not counted in the calculation of reaction strain, but Li metal product volume in the oxidative reaction at cathode is counted. Below the reduction limit, Li metal reactant is absorbed into the SSE to form the interface reaction decomposition, which contributes to the local volume expansion of the decomposition and the formation of the plastic strain field surrounding the decomposition reaction front that is of importance to the dynamic voltage stability of interest here. Since Li metal reactant initially is not inside the region of SSE, the volume of lithium metal reactant is thus not counted in the calculation of reaction strain that is inside SSE. Outside the region of the reaction front, Li+ ion and electron can still leave the anode region from the ion and electron reservoir to complete the reduction reaction as also required by the eU term in eq (3), which, however, does not influence the local positive reaction strain of the interface reaction, as all decomposition products are encapsulated by the ionically passivated reaction front layer. Similarly, beyond oxidation limit, although electron should go through outside circuit from cathode to anode side and then combine with a Li+ that is migrated from the Li reservoir at cathode to the anode, these electron and Li ion left the cathode are not from the reaction product of Li metal but from the reservoir outside the decomposition region encapsulated by the reaction front. Li+ ions as reaction product are trapped in the cathode decomposition region encapsulated by the ionically passivated reaction front layer, which then could combine with a neighboring electron to form Li metal. Li metal product in oxidative reaction thus contributes to the positive reaction strain.


In eqn. (3), GDec=ΣdiGDeci, where GDeci is the phase energy calculated by DFT obtained from the Materials Project. U is the voltage and the term KeffVSSEε denotes the mechanical constriction effect where Keff is the effective bulk modulus,[23] VSSE is the volume of solid electrolyte and e is the reaction strain, so at a given Keff, the positive increase of reaction energy is proportional to reaction strain. FIG. 13(a) depicts the relationship described by eqn. (3). The rimless blue or red dots show the reductive or oxidative decomposition energy at each voltage point at Keff=0, while the rimmed dots show the constrained decomposition energy. The upward arrow represents the magnitude of energy increase calculated from KeffVSSEε.


At Keff>0, if ΔGC-RXN(U) is moved from negative to positive values due to the positive KeffVSSEε, then the decomposition will not happen anymore, and the voltage U will be included into the expanded voltage window. Thus, the new voltage ranges from Ure (Keff>0) to Uox(Keff>0) defined by the two new reactions in FIG. 13(a) is the voltage window Uw (Keff>0) under certain mechanical constriction. In general, the voltage stability window Uw can be defined as:











U
w

(

K
eff

)

=



U
ox

(

K
eff

)

-


U
re

(

K
eff

)






(
4
)







The perturbation method only considers reactions with the largest decomposition energy, so that it is computationally effective. However, there are often more than one decomposition reactions competing in the reaction space with various reaction strains, which means other decomposition reactions with smaller positive reaction strains or even negative reaction strains that are neglected in the perturbation method could happen at voltages between Ure (0) and Ure (Keff>0), and between Uox (0) and Uox (Keff >0).


A more robust approach named direct minimization method is used to consider all reactions in the reaction space.[23]FIG. 13(b) shows an example of implementing minimization method to calculate the voltage window of LGPS. One pair of oxidative and reductive decompositions decide the voltage window at a given Keff. Electrochemical reaction energy of two pairs of decompositions corresponding to Keff=0 GPa and Keff=10 GPa are plotted in FIG. 13(b) as a straight line in the ΔGEC-RXN-U space defined by eqn. (3), whose reaction equations can be expressed in the form of eqn. (1) as following:











Li
10



GeP
2



S
12


=


10

Li

+

3

S

+


P
2



S
7


+

GeS
2






Reaction


1














Li
10



GeP
2



S
12


=


1.2
Li

+

0.2
S

+

0.2

P
2



S
7


+

0.2

Li
4



GeS
4


+

0.8

Li
10



GeP
2



S
12







Reaction


2














Li
10



GeP
2



S
12


=


12


Li
2


S

+
Ge
+

2

P

-

14

Li






Reaction


3














Li
10



GeP
2



S
12


=


6.86

Li
2


S

+

0.19

GeP
3


+

0.81
GeS

+

1.44

Li
2



PS
3


-

6.6
Li






Reaction


4







The x-interceptions of the reaction energy straight lines are the stability voltage limits, which can be expressed by equating eqn. (4) to 0:









U
=


(


G
Dec

+

nG
Li

-

G
SSE

+


K
eff



V
SSE


ε


)

/

(
ne
)






(
5
)







The slope is the negative stoichiometry of Li (−n) in the eqn. (3), and the positive increase of the decomposition energy by mechanical constriction is proportional to reaction strain ε, therefore the horizontal shifts are proportional to their ε/n. If the reaction strain is negative, void will form and the constriction effect will disappear locally, thus the KeffVSSEε term will become 0 instead of being negative. This means the voltage window will not change, or equivalently we can define ε=0 in this case.


Reactions 1 and 2 are oxidative decompositions, and reactions 3 and 4 are reductive decompositions. Reactions 1 and 3 decide the voltage window at Keff=0 GPa, and the reactions 2 and 4 decide the voltage window at Keff=10 GPa. Other reactions in the reaction space besides these four are not discussed here since it turns out that they do not determine the voltage window for LGPS here. But we should keep in mind that they do exist in the energy landscape, and solid-state electrolyte can decompose into other products if different voltage and Keff values are applied, or nonequilibrium decomposition pathways override such thermodynamic metastable decompositions.


For this specific case illustrated in FIG. 13(b), at Keff=0 GPa, started from any voltage inside the voltage window, when scanning the voltage towards 0 V, the x-interception Ure (0) will be met first, where all other reactions (e.g., reaction 4) in the reaction space except reaction 3 have positive reaction energy so that they are thermodynamically prohibited. Slightly below that voltage Ure (0), the energy of reaction 3 becomes negative so LGPS become unstable and will decompose to Li2S, Ge and P. Thus Ure (0) is the reductive limit of LGPS at Keff=0 GPa.


When increasing Keff to 10 GPa, the energy of all reactions will increase proportionally to their reaction strain (if positive) as described by eqn. (3) and indicated by the 4 arrows in FIG. 13(b). Reaction 3 with reaction strain as large as 25% increases a lot as indicated by the long blue arrow. When scanning voltage towards 0 V at Keff=10 GPa, the x-interception Ure (10) belonging to reaction 4 will be met first instead. Reaction 4 has slightly more positive ΔGEC-RXN than reaction 3 at Keff=0 GPa below Ure (0), but after applying mechanical constriction of Keff=10 GPa, its much smaller reaction strain of 6% causes a much smaller positive increase of energy. Note that the slope (−n) of the energy line of reaction 4 (−n4=6.6) is smaller than that of reaction 3 (−n3=14), and the horizontal shift of x-interception is proportional to e/n. The fact that the x-interception of reaction 4 is to the right of the x-interception of reaction 3 at Keff=10 GPa is mainly due to the much smaller reaction strain of reaction 4 than reaction 3. The competition between the two oxidization reactions 1 and 2 controlled by Keff follows a similar discussion.


With the illustration discussed above, we can more generally define Ure (Keff) and Uox (Keff). Each decomposition reaction has a n value, so we can scan n to scan all decompositions:











U
re

(

K
eff

)

=


max

n
<
0


[


(


G
Dec

+

nG
Li

-

G
SSE

+


K
eff



V
SSE


ε


)

/

(
ne
)


]





(
6
)














U
ox

(

K
eff

)

=


min

n
>
0


[


(


G
Dec

+

nG
Li

-

G
SSE

+


K
eff



V
SSE


ε


)

/

(
ne
)


]





(
7
)







A pseudo-phase[12] composed of x coating and (1−x) SSE is denoted as pp(x). DFT phase energy Gpp(x), composition x, and volume Vpp(x) of the pp(x) are interpolated from coating and SSE. Equation (3) can then be rewritten as










Δ



G

EC
-
RXN


(
x
)


=


G
Dec

+

n

(


G
Li

-
eU

)

-

G

pp

(
x
)


+


K
eff



V
SSE


ε






(
8
)







Let equation (8) equal to zero, it gives the critical Keff, i.e., Kcrit, that prohibits the electrochemical decomposition of the interface, and the maximum value of Kcrit(x) to prevent decomposition at all x composition is defined as K*:











K
crit

(
x
)

=

-



G
Dec

+

n

(


G
Li

-
U

)

-

G

pp

(
x
)





V

pp

(
x
)




ε
x








(
9
)













K
*

=

max



K
crit

(
x
)






(
10
)







More detailed illustration regarding pseudo-phase approach and critical modulus K* by a computational example can be found in FIGS. 11(a)-11(c).









TABLE 2







LGPS 4V stability


LGPS 4V stability (Reference Volume = VLGPS)











decomposition




Keff (GPa)
energy (eV/atom)
strain
Decomposition products













0
0.988
0.302
10 Li + 3 S + P2S7 + 1 GeS2


10
0.183
0.264
8.8 Li + 2.4 S1 + P2S7 +





0.7 Ge1S2 + 0.3 Li4Ge1S4


20
0.000
0.000
Li10Ge1P2S12









As shown in Table 2, without mechanical constriction, LGPS decomposition leads to 30.2% reaction strain with 0.988 eV/atom decomposition energy. When we assign KeffεVLGPS energy penalty to each reaction with different reaction strain ε, the sequence of the decomposition energy magnitude in the reaction space changes. Reactions with larger ε will have larger KeffεVLGPS penalty, thus increasing Keff will make reactions with smaller ε have larger decomposition energy in the reaction space, leading to a change of ground state reaction toward smaller ε with increasing Keff. At Keff=20 GPa, LGPS does not decompose, suggesting a critical Keff (i.e., Kcrit or K*) between 10 GPa and 20 GPa, beyond which there is no oxidative decomposition reaction for LGPS.


Technically, when Keff is small, perturbation method (see Methods) is approximately equal to minimization method. We know that in perturbation method, only the decomposition reaction with the highest reaction energy at 0 GPa is considered, so we take the derivative of equation (5) in Methods with respect to the Keff for both oxidation reaction and reduction reaction:












U


(

K
eff

)

ox

=




V
SSE



ε
ox




n
ox


e


=

k
ox






(
A
)















U


(

K
eff

)

re

=




V
SSE



ε
re




n
re


e


=

k
re






(
B
)







Equations. (A) and (B) show that the volume of the electrolyte, the reaction strain, and the number of charge (or Lithium) transferred together decide the kox and kre. For example, comparing the kox between Li3YCl6 and LGPS, Li3YCl6 shows 13% larger atomic volume, 28% larger reaction strain and 33% larger 1/nox that in the end gives 92% larger kox, which is very close to the 100% larger kox calculated by the minimization method (FIG. 2(d), Table 3).









TABLE 3







Summary of the ionic conductivity and computation results of the electrolytes.
















σionic
log




intrinsic



Electrolyte
(mS/cm)
σionic
Rw
kox
kre
kox − kre
window
reference


















Li10Ge(PS6)2
12
−1.92
0.19
0.09
−0.06
0.15
0.80

[27]



Li10Sn(PS6)2
4
−2.40
0.14
0.08
−0.02
0.10
0.70

[28]



Li7P3S11
17
−1.77
0.26
0.09
−0.07
0.16
0.60

[29]



Li10Si(PS6)2
23
−1.64
0.14
0.08
−0.05
0.13
0.90

[30]



Li20Si3P3S23Cl
25
−1.60
0.15
0.07
−0.05
0.12
0.80

[31]



Li3PS4
0.16
−3.80
0.18
0.08
−0.06
0.14
0.80

[13]



Li5.5PS4.5Cl1.5
12
−1.92
0.20
0.10
−0.07
0.16
0.80

[33]



Li3Ycl6
0.5
−3.30
0.09
0.18
−0.13
0.31
3.60


[6]



Li3Ybr6
1.7
−2.77
0.10
0.12
−0.15
0.27
2.60

[34]



Li3ErCl6
0.3
−3.52
0.10
0.20
−0.16
0.36
3.40


[7]



Li3InCl6
1.49
−2.83
0.14
0.17
−0.12
0.29
2.10

[33]



Li3ScCl6
3
−2.52
0.08
0.16
−0.13
0.29
3.50

[35]



Li1.3Al0.3Ti1.7(PO4)3
0.7
−3.15
0.10
0.14
−0.10
0.24
2.30

[36]



Li0.5La0.5TiO3
1.08
−3.24
0.03
0.08
0.00
0.08
2.50

[37]



Li7La3Zr2O12
0.5
−3.30
0.06
0.07
−0.10
0.17
3.00

[38]



Li3Ocl
0.85
−3.07
0.03
0.10
0.00
0.10
2.80

[39]










In calculating the stability of interface and the effect of mechanical constriction, the pseudo-phase method[12] is adopted to interpolate the phase energy, composition and volume of two phases. The solid black curve in FIG. 11(a) is an example of using the pseudo-phase method to calculate the interface hull of Li5.5PS4.5Cl1.5 and LiAlO2. The dashed line interpolates the hull of Li5.5PS4.5Cl1.5 and LiAlO2, showing the part of instability of the interface contributed by the intrinsic instability of the two ends. If the hull is below the dashed line, there is interfacial reaction between the two ends, which is the case of the (Li5.5PS4.5Cl1.5—LiAlO2) interface shown here. The Interface hull is defined as the most negative hull among all the composition x in the solid black curve. But due to large decomposition energy of sulfide electrolyte, the interface hull will be the hull of sulfide electrolyte itself in most cases, which does not reveal the meaningful information of the interface, therefore we apply certain Keff (20 gPa here) to stabilize the electrolyte by raising the Li5.5PS4.5Cl1.5 decomposition reaction energy to be positive and keeping the energy of Li5.5PS4.5Cl1.5 itself unchanged, so the difference between the hull curve of (Li5.5PS4.5Cl1.5—LiAlO2) and (Li5.5PS4.5Cl1.5@20gPa-LiAlO2) is the difference in hull at the end point of Li5.5PS4.5Cl1.5. From x=0 to x=0.1, the metastability of the Li5.5PS4Cl1.5 is perturbed by the interfacial reaction, thus the large decomposition energy. The interface hull then shifts from that of the Li5.5PS4.5Cl1.5 end point to that of x=0.1.


Treating pseudo phase at each composition x (pp(x)) as a solid-state electrolyte and using ΔGEC-RXN=GDec+n(GLi−eU)−GSSE+KeffVSSEε (eqn. 2 in Methods), we can evaluate the constriction induced voltage stability of the interface. Each pp(x) has its own GDec, n, Gpp(x), Vx and εx. FIG. 11(b) shows how 35 gPa mechanical constriction affects the hull of {Li5.5PS4.5Cl1.5@20 gPa-LiAlO2) interface. For example, at x=0.2, when being normalized to 1 closed atom per formula, the volume V( 1/7 Li5.5PS4.5Cl1.5)=128.78 Å3/closed atom, and the volume V(⅓ LiAlO2)=13.806 Å3/closed atom, thus at x=0.2, the pseudo phase volume V0.2=0.2*V(⅓ LiAlO2)+0.8*V( 1/7 Li5.5PS4.5Cl1.5)=0.2*13.806+0.8*128.78=105.79 Å3/closed atom. KeffV0.2ε0.2 well exceeds the hull and brings the decomposition reaction energy to ˜+1 eV as shown by the long red arrow, so that the decomposition is suppressed and the hull at x=0.2 becomes 0 by definition. At x=0.9, however, the KeffV0.2ε0.2 is not large enough to bring the decomposition energy to be positive, thus the interface can still decompose at Keff=35 gPa, but the decomposition energy is much smaller, suggesting a more stable {Li5.5PS4.5Cl1.5—LiAlO2) interface. We define Kcrit(x) to demonstrate the level of mechanical constriction just needed to suppress decomposition reaction of pp(x) as shown in FIG. 11(b) by the thick green arrow at x=0.9 and the black arrow at x=0.2, which is the Keff value to equate eqn. (8) in the main text to 0 and gives eqn. (9).


At composition x, the particular decomposition reaction is suppressed if and only if Keff >Kcritx. As Kcrit is a function of x, therefore, to suppress the reaction between two phases, the largest Kcrit(x) must be reached. We define the largest Kcrit(x) to be K′ (eqn. 10). FIG. 11(c)) shows the Kcrit of {Li5.5PS4.5Cl1.5—LiAlO2) interface at 4V and labels the K′. The KeffVxεx is also plotted in FIG. 11(c) and shows a minimum at x=0.9, coinciding the x for maximum Kcritx. From FIG. 11(a), the absolute value of hull at x=0.9 is actually the smallest among the hull from x=0.1 to x=0.9, but due to its smallest Vxεx (or smallest KeffVxεx), the Kcrit(0.9) becomes the largest Kcrit(x), suggesting that the smallest mechanical response is at x=0.9.


Battery

Li5.5PS4.5Cl1.5, was prepared by ball milling and solid state reactions. Stoichiometric amounts of Li2S (99.9% purity, Alfa Aesar), P2S5(99% purity, Sigma Aldrich), and LiCl (>99% purity, Alfa Aesar) were milled for 16 hours under argon protection. The precursor was transferred into a quartz tube and annealed at 550° C. for 1 hour with a temperature increasing rate of 5° C./min in an argon gas flow. LiNi0.83Mn0.06Co0.11O2 (NMC811) and LGPS (325 mesh) are purchased from MSE. LiCoO2 is purchased from Sigma Aldrich.


Solid state batteries were made with the configuration of Li/graphite-solid electrolyte layer(s)-cathode matrix. The Li metal foil of 0.63 cm diameter and 25 μm thickness (0.42 mg, 1.62 mAh, 5.2 mAh/cm2) was covered by a graphite thin film of 0.95 cm diameter to act as the anode. The graphite layer was made by mixing 95 wt % graphite (BTR, China) with 5 wt % PTFE, and the capacity ratio of lithium to graphite is 2.5:1. 30 mg LPSCl (120 μm thickness) and 100 mg central layer powder (400 μm thickness) were applied as the electrolyte. A 60 mg separating layer (240 μm) of the same electrolyte powder in the cathode matrix is added when the central layer is different from that in the cathode matrix. LiNbO3 (LNO) is coated on LiNi0.83Mn0.06Co0.11O2 (NMC811) or LiCoO2 (LCO) by 1.9 wt % following previous report[46]. 70 wt % bare 811, bare LCO, or LNO coated 811 or LiCoO2 was mixed with 30 wt % LPSCl or LGPS to serve as the cathode with an additional 3% PTFE to make a cathode film. The loading of the cathode is kept at 2 mg/cm2 for all the battery tests. The battery was initially pressed at 460 MPa and a stack pressure of 150 MPa was maintained by a pressurized cell. The batteries were cycled at 55° C. or room temperature on an Arbin battery testing station in an environmental chamber with the humidity controlled <10% inside Memmert hpp110, 1 C-rate=150 mA/g in this work. Liquid electrolyte batteries used glass fiber as separator and 1 M LiPF6 in EC/DMC (v:v=1:1) as electrolyte. Li metal is used as anode. The powder of cathode active material, carbon black, and PTFE are mixed with weight ratio of 85:10:5 and then roll into a thin film with diameter of 5/16″, and then assembled in a Swagelok cell.


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Other embodiments are in the claims.

Claims
  • 1. A compound from Table 1:
  • 2. A solid state battery comprising: a) an anode and a cathode comprising cathode particles and solid state electrolyte particles; andb) a solid state electrolyte separating the anode and cathode; andc) an interface coating layer between the cathode particles and the solid state electrolyte particles wherein the interface coating layer comprises a compound of claim 1.
  • 3. The battery of claim 2, wherein the anode comprises Li metal.
  • 4. The battery of claim 3, wherein the anode further comprises Li, Na, Mg, Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Rb, Sr, Y, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Bi, Cs, Te, or a combination thereof.
  • 5. The battery of claim 2, wherein the cathode comprises LiNi0.8Mn0.1Co0.1O2 (NMC811), LiNi0.93Mn0.33CO0.33O2 (NMC111), LiNi0.5Mn0.3Co0.2O2 (NMC532), LiNi0.8Mn0.2Co0.2O2 (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)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, or LiCo0.5Mn1.5O4.
  • 6. The battery of claim 5, wherein the cathode further comprises a polymer and/or carbon black.
  • 7. The battery of claim 2, wherein the battery is mechanically constrained.
  • 8. A method of storing energy comprising applying a voltage across the anode and cathode and charging the rechargeable battery of claim 2.
  • 9. A method of providing energy comprising connecting a load to the anode and cathode and discharging the rechargeable battery of claim 2.
Provisional Applications (1)
Number Date Country
63539467 Sep 2023 US