Si-SUBSTITUTED LITHIUM THIOBORATE MATERIAL WITH HIGH LITHIUM ION CONDUCTIVITY FOR USE AS SOLID-STATE ELECTROLYTE AND ELECTRODE ADDITIVE

Abstract

Aspects disclosed herein include materials comprising: a lithium thioborate composition characterized by formula FX1: Li3−z[B+Q]1[S+G]3 (FX1); wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B; wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S; wherein z is a number greater than 0 and less than or equal to 0.40, optionally less than or equal to 0.05; and wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.

Description

BACKGROUND OF INVENTION

Solid state ion conducting materials have a number of useful applications, including as materials in a Li-ion all-solid-state battery (ASSB). To commercialize Li-ion ASSBs, a suitable Li-ion conducting solid-state electrolyte is required. A solid-state electrolyte should exhibit a wide electrochemical stability window and ionic conductivity near that of traditional liquid electrolytes. Three compounds with near-liquid-electrolyte conductivity (˜10⁻² S cm⁻¹) have been reported: Li₁₀GeP₂S₁₂ (LGPS), Li₆PS₅Br argyrodite, and a Li₇P₃S₁₁ glass ceramic. Unfortunately, all three discovered electrolytes exhibit electrochemical instability against the Li anode, limiting application in commercial products. Some materials are known or are predicted to have a wide electrochemical stability window, sufficient for resisting electron injection from the Li anode, but suffer from prohibitively low ionic conductivity in their pure or intrinsic form. Accordingly, there is a need for ion conducting solid state materials suitable as solid state electrolytes for battery technologies.

SUMMARY OF THE INVENTION

Aspects disclosed herein include materials comprising: a lithium thioborate composition characterized by formula FX1: Li_3−z[B+Q]₁[S+G]₃ (FX1); wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B; wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S; wherein z is 0 or a number greater than 0 and less than or equal to 0.40, optionally less than or equal to 0.05; and wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.

Aspects disclosed herein include solid state electrolytes comprising: a lithium solid state electrolyte comprising Li, one or more principal elements, and at least one dopant; wherein the dopant substitutes for a portion of the one of the one or more principal elements of the lithium solid state electrolyte and is aliovalent with the respective substituted principal elements; wherein the ionic conductivity of the lithium solid state electrolyte is greater than or equal to 1·10⁻⁵ S/cm at 25° C.

Aspects disclosed herein include doped lithium solid state electrolytes comprising: a doped inorganic composition having at least one dopant; wherein the doped composition has up to 20 at. % of one or more principal elements substituted with the at least one dopant relative to a reference composition of a reference lithium solid state electrolyte; wherein each dopant is one or more elements each aliovalent with the respective substituted principal element; wherein the presence of the one or more dopants provides for an ionic conductivity greater than or equal to 1·10⁻⁵ S/cm at 25° C.

Aspects disclosed herein include methods for increasing an ionic conductivity of a reference lithium solid state electrolyte, the method comprising: forming a doped lithium solid state electrolyte having a doped composition; wherein the reference lithium solid state electrolyte has a reference composition, and wherein the doped composition has up to 20 at. % of one or more principal elements substituted with at least one dopant relative to the reference composition; wherein each element of the at least one dopant is aliovalent with respect to the respective substituted principal element; and wherein the doped lithium solid state electrolyte has a greater ionic conductivity than the reference lithium solid state electrolyte by a factor of at least 10.

Without wishing to be bound by any particular theory, there may be discussion herein of beliefs or understandings of underlying principles relating to the devices and methods disclosed herein. It is recognized that regardless of the ultimate correctness of any mechanistic explanation or hypothesis, an embodiment of the invention can nonetheless be operative and useful.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: Schematic of the semi-supervised machine learning approach. Li-containing structures are aggregated from the ICSD and MP database. Each input structure is simplified and transformed to yield a unique descriptor representation. The descriptor representations are clustered with hierarchical agglomerative clustering. Each cluster is then labeled with experimental σ_{25° C.} data and the intracluster conductivity variance is calculated. Comparison of the composite intracluster conductivity variance (intracluster conductivity variance summed across all clusters) enables identification of descriptors that are well correlated with ionic conductivity.

FIG. 2: The composite intracluster conductivity variance (W_Q) for the first 50 clusters generated using each descriptor. Half-violin plots show the raw W_σ score for each cluster as symbols next to the violin distribution. Simplification-descriptor combinations are sorted in order of ascending mean. The control is a random assignment of clusters, with W_σ values averaged over 100 randomly assigned sets. The smooth overlap of atomic positions (SOAP) descriptor outperforms all other descriptors. Although not shown here, SOAP continues to outperform for all depths of clustering through 300.

FIG. 3: Agglomerative clustering dendrogram for the 2^nd-order SOAP descriptor. The hierarchical clustering representation is shown for the first 241 clusters. An arbitrary variance cutoff is placed such that 9 large clusters are produced to facilitate analysis. The violin plots show the σ_{25° C.} distribution for the labels within the 9 large clusters. Three outlier clusters are grouped into two additional clusters and are hereafter ignored. The density (per 241 clusters) of low E_a (<0.6 eV) and high conductivity (σ_{25° C.}>10⁻⁵ S cm⁻¹) labels is shown underneath the agglomerative dendrogram. The results illustrate that agglomerative clustering on the 2^nd-order SOAP descriptor results in favorable aggregation of most high-conductivity labels.

FIG. 4: W_σ vs. cluster number for three different SOAP-CAN models compared with the best-performing models for density-CAN, mXRD-A40, orbital field matrix, and structure heterogeneity-A40. The three SOAP-CAN models are those with the lowest W_σ mean for the clustering ranges: 2-100, 101-200, and 201-300. Almost all SOAP-CAN models outperformed the best non-SOAP models, irrespective of the specific combination of rcut, nmax, and Imax hyperparameters.

FIG. 5: The W_Ea for the first 50 clusters generated using each descriptor. Half-violin plots show the raw W_Ea score for each cluster as symbols next to the violin distribution. Simplification-descriptor combinations are sorted in order of ascending mean. The control is a random assignment of clusters, with W_Ea values averaged over 100 randomly assigned sets.

FIG. 6: The best performing 2^nd order descriptor: SOAP-CAN mixed with the sine Coulomb descriptor. The clustering performance is shown for the full label set of 219. Since the mXRD—A40 representation is also compatible with the full label set, it is shown for reference. The 2^nd order descriptor outperforms the 1^st order SOAP-CAN descriptor at most depths of clustering.

FIG. 7: The partial agglomerative dendrogram generated for the 2^nd-order SOAP-CAN descriptor-simplification. The area shown is the 2^nd mega cluster taken from FIG. 3 of the main text. At a clustering depth of 241, the 21 high-conductivity labels are sorted into 5 clusters which account for 2.2% of the input structures.

FIG. 8: The 2×2×2 supercell of Li₃VS₄ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 9: The primitive cell of Na₃Li₃Al₂F₁₂ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 10: The 2×2×2 supercell of Li₂Te used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 11: The 2×2×1 supercell of LiAlTe₂ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 12: The 2×2×1 supercell of LiInTe₂ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 13: The 2×2×2 supercell of Li₆MnS₄ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 14: The 2×2×1 supercell of LiGaTe₂ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 15: The 2×1×2 supercell of Li₃BS₃ used for the CI-NEB calculation of Li migration energy. Blue, green, and orange atoms represent the Li position from the CI-NEB output images.

FIG. 16: The 2×2×2 supercell of KLi₆TaO₆ used for the CI-NEB calculation of Li migration energy. Blue and orange atoms represent the Li position from the CI-NEB output images.

FIG. 17: The 2×1×2 supercell of Li₃CuS₂ used for the CI-NEB calculation of Li migration energy. Blue atoms represent the Li position from the CI-NEB output images.

FIG. 18: Nyquist data for a-Li_2.95B_0.95Si_0.05S₃ near room temperature. The partially resolved semi-circular features suggests the presence of at least two RC circuit elements.

FIG. 19: The 31 promising structures that are predicted to be stable and to exhibit Li-hopping activation energy below 600 meV.

FIG. 20A: Explored for use as both an anode³⁴⁰ and a cathode³⁴¹. NEB has been employed to predict an activation energy of 95 meV.³⁴² All Li occupies tetrahedral sites that are edge sharing with adjacent V tetrahedra.

FIG. 20B: The structure appears to be unexplored. Discussion of structural motifs by Geller et al.³⁴³ All Li atoms are in a tetrahedral bonding environment.

FIG. 20C: A screening approach using bond valence site energy calculations identified the oxide as a promising structure: Li₂Te₂O₅.³⁴⁴ All Li are in tetrahedral bonding environment.

FIG. 20D: All Li are in a tetrahedral environment with corner sharing. The structure hasn't been examined as an ionic conductor—ongoing research is focused on optoelectronic properties.³⁴⁵

FIG. 20E: All Li are in a tetrahedral environment with corner sharing. The structure hasn't been examined as an ionic conductor—ongoing research is focused on optoelectronic properties.³⁴⁶

FIG. 20F: All Li are in an edge-sharing tetrahedral bonding environment. Augustine et al. posit that the structure could be a viable cathode material. They performed ab-initio calculations to measure the enthalpy of formation and have concluded that the structure should be stable.³⁴⁷

FIG. 20G: All Li are in a tetrahedral environment with corner sharing. The structure hasn't been examined as an ionic conductor—ongoing research is focused on optoelectronic properties.³⁴⁸ Isaenko et al. report an experimental band gap of 2.41 eV.

FIG. 20H: All Li are in a tetrahedral bonding environment. Recent NEB work suggests an activation barrier of 250 meV.³⁴⁹

FIG. 20I: All Li are in a tetrahedral bonding environment with edge or corner sharing. Recent electrochemical characterization by Suzuki et al. found an ionic conductivity near 10⁻⁵ S cm⁻¹ with aliovalent substitution of Sn.³⁵⁰

FIG. 20J: All Li are in an edge-sharing tetrahedral bonding environment. Explored for use as a cathode by Kawasaki et al. in 2021.³⁵¹ They found an initial charge-discharge capacity of 380 mAh g⁻¹ with average voltage of 2.1 V vs. Li/Li⁺.

FIG. 20K: All Li are in an edge-sharing tetrahedral bonding environment. Never explored for battery purposes. Synthesis by Huang et al.³⁵²

FIG. 20L: All Li sits in four- and five-coordinate environments. Kahle et al. previously screened ˜1400 Li-containing compounds and identified Li₄Re₆S₁₁ as a potentially promising SSE using molecular dynamics simulation.³⁵³ Their simulations failed to resolve RT diffusion but found promising diffusivity at elevated temperatures.

FIG. 20M: All Li are in a tetrahedral bonding environment.

FIG. 20N: All Li are in an octahedral bonding environment. Muy et al. identify Li₃ErBr₆ as one of eighteen promising compounds using a phonon-band descriptor approach.³⁵⁴ They synthesize the Cl analogue and report an experimental conductivity of 0.05-0.3 mS cm⁻¹. The material also mentioned briefly in perspective by Li et al.³⁵⁵

FIG. 20O: All Li are in a tetrahedral bonding environment.

FIG. 20P: All Li are in a tetrahedral bonding environment. Sendek et al. identified Li₂HIO as promising using a combined ML and DFT approach.³⁵⁶ They predicted a RT diffusion barrier of 350 meV.

FIG. 20Q: All Li are in an edge-sharing tetrahedral bonding environment. Synthesis via Huang et al.³⁵²

FIG. 20R: Li ions are in a distorted octahedral and some 5-coordinate bonding environments.

FIG. 20S: All Li are in an octahedral bonding environment. Mentioned briefly in perspective by Li et al.³⁵⁵

FIG. 20T: All Li are in an octahedral bonding environment. Discussed briefly in perspective by Li et al.³⁵⁵ Predicted by Kahle et al. to be a fast ionic conductor using molecular dynamics simulations.³⁵³ They predict an activation energy of 350 meV.

FIG. 20U: All Li are in a tetrahedral bonding environments.

FIG. 20V: All Li are in a three coordinate bonding environment.

FIG. 20W: All Li are in a tetrahedral bonding environment. Optical properties and air-stability have been briefly discussed by Kim et al.³⁵⁷

FIG. 20X: All Li are in an edge-sharing tetrahedral bonding environment. Synthetic accounts appear to exist in some books.

FIG. 20Y: Li are all in an edge-sharing tetrahedral bonding environment. Wang et al. predicted that this might be a high-conductivity structure by using a “structure matching” algorithm.³⁵⁸

FIG. 20Z: All Li are in a 5-coordinate bonding environment. A hydrothermal synthetic method has been described by Li et al.³⁵⁹

FIG. 20AA: All Li are in 3-coordinate or 2-coordinate bonding environments. Identified by Snydacker et al. as a suitable coating for Li anode passivation via convex hull calculations.³⁶⁰

FIG. 20AB: All Li are in octahedral or tetrahedral bonding environments. The tetrahedra sit between the octahedral layers. Amorphous Li₄TiS₄ is thought to form upon discharge of TiS₄-based cathodes.³⁶¹

FIG. 20AC: All Li are in a tetrahedral bonding environment. Wang et al. predicted that LiGaS₂ might be a high-conductivity structure by using a “structure matching” algorithm.³⁵⁸ Separately, He et al. used ab initio calculation to predict the same.³⁶²

FIG. 20AD: All Li are in a corner-sharing tetrahedral bonding environments.

FIG. 20AE: Li are mostly in tetrahedral bonding environments, although some 5-coordinate environments exist. Kahle et al. identified Li₁₀B₁₄Cl₂O₂₅ as a potentially promising SSE material using a “pinball” model.³⁵³

FIG. 21: The 21 promising structures that are predicted to be within 15 meV of E_hull and to exhibit Li-hopping activation energy below 600 meV.

FIG. 22A: Li are in 8-coordinate sites surrounded by oxygens.

FIG. 22B: All Li are in tetrahedral bonding environments—corner sharing with Zn and P tetrahedra. Richard's et al. used NEB to predict that Li₁₀Zn₇P₈S₃₂ has a 252 meV activation energy for Li diffusion.³⁶³ They also predict a RT conductivity of 3.44 mS cm⁻¹.

FIG. 22C: All Li are in tetrahedral bonding environments—corner sharing with Zn and P tetrahedra. Richard's et al. used NEB to predict that Li₆Zn₃P₄S₁₆ has a 181 meV activation energy for Li diffusion.³⁶³ They also predict a RT conductivity of 27.7 mS cm⁻¹.

FIG. 22D: All Li are in tetrahedral bonding environments.

FIG. 22E: All Li are in tetrahedral bonding environments.

FIG. 22F: All Li are in tetrahedral bonding environment.

FIG. 22G: Octahedral Li layers with Li tetrahedra interspersed between.

FIG. 22H: All Li are in tetrahedral bonding environments.

FIG. 22I: All Li are in edge-sharing tetrahedral bonding environments. Previously examined as a cathode material by Chen et al.³⁶⁴

FIG. 22J: All Li are in tetrahedral bonding environments.

FIG. 22K: All Li are in tetrahedral bonding environments.

FIG. 22L: All Li are in tetrahedral bonding environments.

FIG. 22M: All Li are in tetrahedral bonding environments. Devlin et al. have previously published a synthetic method for Li₂MnSnS₄.³⁶⁵

FIG. 22N: All Li are in edge-sharing tetrahedral bonding environments.

FIG. 22O: All Li are in edge-sharing octahedral bonding environments. A synthetic method has been published by Steiner et al.³⁶⁶

FIG. 22P: All Li are in tetrahedral bonding environments.

FIG. 22Q: All Li are in corner-sharing tetrahedral bonding environments. Li₁₀Si₃P₃S₂₃Cl was theoretically studied by Rao et al.³⁶⁷ They used it is a model system for a neural-network molecular dynamics pipeline.

FIG. 22R: All Li are in tetrahedral or octahedral bonding environments.

FIG. 22S: All Li are in octahedral bonding environments. Muy et al. examined LiSnCl₃ using a phonon-band descriptor approach.³⁵⁴ Despite a promising band-center value, they suggest it has a low stability window. Körbel et al. identify it as a promising piezoelectric material.³⁶¹

FIG. 22T: All Li are in tetrahedral bonding environments.

FIG. 22U: All Li are in distorted tetrahedral bonding environments.

FIG. 23: The six promising structures that lack Materials Project data but are predicted to exhibit Li-hopping activation energy below 600 meV.

FIG. 24A: All Li are in tetrahedral bonding environments. Synthetic method by Prömper et al.³⁶⁹

FIG. 24B: All Li are in 5-coordinate bonding environments. Previously studied by Abdel-Khalek et al. in a glass ceramic.³⁷⁰ Discussed in some detail by Rousse et al.³⁷¹

FIG. 24C: All Li are in octahedral bonding environments.

FIG. 24D: All Li are in tetrahedral bonding environments. Synthetic method by Branford et al.³⁷²

FIG. 24E: All Li are in tetrahedral bonding environments. A melt flux synthesis has been developed by Li et al—they examined the material for second-harmonic generation response.³⁷³

FIG. 24F: Most Li are in tetrahedral bonding environments, with some partial substitution onto the octahedral Ti sites.

FIG. 25: Steady-state current of Au/a-Li_2.95B_0.95Si_0.05S₃/Au cell for different voltage polarizations. Measurements were done at 25° C. with applied voltages of 0.125 V, 0.25 V, 0.375 V, 0.5 V and 1.0 V.

FIGS. 26A-26G: Characterization of Li₃BS₃ with vacancy engineering. FIG. 26A: XRD patterns for Li₃BS₃, 2.5% Si substituted Li₃BS₃ (Li_2.975B_0.975Si_0.025S₃), 5% Si substituted Li₃BS₃ (Li_2.95B_0.95Si_0.05S₃), and amorphized 5% Si substituted Li₃BS₃ (a-Li_2.95B_0.95Si_0.05S₃). No impurities are observed in any pattern. FIG. 26B: Arrhenius fits for Li₃BS₃. FIG. 26C: Lattice parameter comparison for Li₃BS₃, Li_2.975B_0.975Si_0.025S₃, and Li_2.95B_0.95B_0.05S₃. FIG. 26D: Arrhenius fits for Li_2.95B_0.95Si_0.05S₃, and a-Li_2.95B_0.95Si_0.05S₃. FIG. 26E: Electrochemical impedance spectroscopy for the a-Li_2.95B_0.95Si_0.05S₃ at various temperatures. FIG. 26F: ⁷Li NMR and (FIG. 26G) ¹¹B NMR of the Li₃BS₃, Li_2.95B_0.95Si_0.05S₃, and a-Li_2.95B_0.95Si_0.05S₃. Results show that combined aliovalent substitution and amorphization can improve the ionic conductivity of Li₃BS₃ by over four orders of magnitude.

STATEMENTS REGARDING CHEMICAL COMPOUNDS AND NOMENCLATURE

In general, the terms and phrases used herein have their art-recognized meaning, which can be found by reference to standard texts, journal references and contexts known to those skilled in the art. The following definitions are provided to clarify their specific use in the context of the invention.

The term “dopant” is used herein broadly to refer to one or more elements intentionally provided in a material's composition to improve or enhance one or more properties or functionalities of the resulting doped material to compared to the undoped reference form of the material, which is typically intrinsic and stoichiometric. A doped composition is optionally referred to as an extrinsic composition, whereas the undoped composition is optionally referred to as the intrinsic or reference composition. As used herein, the term dopant is used broadly to include low concentration impurities or low concentration additive element(s), such that providing said dopant may be referred to as doping and/or alloying as these terms are known in the art. As used herein, a dopant is a substitute for another or principal element, where the dopant replaces or substitutes for a portion of the amount or concentration of the principal element relative to the amount or concentration the principal element in the undoped composition. For clarity and as a convenient handle, each element of a reference undoped composition may be referred to as a “principal element”. Generally, a principal element is an element identified (or which would be identified by one of skill in a relevant art) in a chemical formula of a composition and is exclusive of impurity elements present in the composition at less than 0.05 at. %, less than 0.05 mol. %, and/or less than 0.05 wt. % (optionally less than 0.04 at. %, less than 0.04 mol. %, and/or less than 0.04 wt. %; optionally less than 0.03 at. %, less than 0.03 mol. %, and/or less than 0.03 wt. %; optionally less than 0.02 at. %, less than 0.02 mol. %, and/or less than 0.02 wt. %; optionally less than 0.01 at. %, less than 0.01 mol. %, and/or less than 0.01 wt. %). Therefore, for example: Li, B, and S are principal elements of the composition Li₃BS₃; Li, V, and S are the principal elements of the composition Li₃VS₄; Na, Li, Al, and F are the principal elements of the composition Na₃Li₃Al₂F₁₂; Li and Te are the principal elements of the composition Li₂Te; Li, Al, and Te are the principal elements of the composition LiAlTe₂; Li, In, and Te are the principal elements of the composition LiInTe₂; Li, Mn, and S are the principal elements of the composition Li₆MnS₄; Li, Ga, and Te are the principal elements of the composition LiGaTe₂; K, Li, Ta, and O are the principal elements of the composition KLi₆TaO₆; Li, Cu, and S are the principal elements of the composition Li₃CuS₂; etc. Generally, materials disclosed herein comprise one or more dopants that are substitutes for one or more principal elements (optionally, non-Li principal elements) of a composition (i.e., a principal element other than Li of a composition, such as any of those listed in the prior sentence; e.g., a dopant may be a substitute for B or S in Li₃BS₃, where the B and S are principal elements (optionally, non-Li principal elements) of the composition Li₃BS₃). As used herein, a dopant is optionally one element being substitute for a principal element of a composition (e.g., Si being a dopant for B in Li₃BS₃). As used herein, a dopant is optionally two elements being substitutes for a principal element of a composition (e.g., Si and Ge together being a dopant for B in Li₃BS₃). As used herein, a dopant is optionally three or more elements being substitutes for a principal element of a composition. Herein, the terms “doped” and “substituted” are generally used interchangeably when referring to a material or composition having one or more dopants, as disclosed herein, substituting one or more principal elements, such as one or more principal elements (optionally, non-Li principal elements). A doped composition may have one dopant or more than one dopants. For example, a doped composition may have a first dopant (or, first type of dopant) being a dopant or substitute for a first principal element (optionally, a non-Li principal element) of a composition (e.g., B of Li₃BS₃) and the same doped composition may have a second dopant (or, second type of dopant) being a dopant or substitute for a second principal element (optionally, a non-Li principal element) of a composition (e.g., S of Li₃BS₃). As used herein, a dopant element may be present in the structure of the doped composition substitutionally (as a substitutional dopant element), interstitially (as an interstitial dopant element), or both substitutionally and interstitially. As used herein, a dopant element is preferably aliovalent with respect to the principal element it replaces or for which it is a substitute. For example, a dopant element for B (e.g., in Li₃BS₃) is preferably aliovalent with respect to B, such that said dopant element is a member of an element Group other than Group 13 of the Periodic Table of Elements (e.g., Si, being a member of Group 14). For example, a dopant element for S (e.g., in Li₃BS₃) is preferably aliovalent with respect to S, such that said dopant element is a member of an element Group other than Group 16 of the Periodic Table of Elements (e.g., Cl, being a member of Group 17). In some aspects, the material or composition thereof having the one or more dopants is characterized as a solid solution. In some aspects, the introduction of one or more dopants to a material or composition thereof obeys Vegard's law where the one or more dopants incorporate into the material's lattice or structure as a solid solution.

The term “amorphizing” refers to a process that reduces grain sizes (average, median, and/or bounds of a 95% confidence interval) of a material (or composition thereof), reduces crystallite sizes (average, median, and/or bounds of a 95% confidence interval) of a material (or composition thereof), increasing amorphous content of a material (or composition thereof), decreasing total crystallinity of a material (or composition thereof), and/or increasing an amount or concentration of defects in a material (or composition thereof). A defect generally refers to a crystallographic defect. As recognized by those skilled in the relevant art such as materials science or crystallography in particular, a defect may be a point defect, a line defect, a planar defect, and/or a bulk defect. A vacancy (or, “vacancy defect”), such as a vacancy of a principal element such as B in Li₃BS₃, is an example of a defect. A broken or dangling bond, which is optionally but not necessarily a result of a vacancy defect, is another example of a defect. Generally, but not necessarily, amorphizing refers to a process performed on a material after said material is formed or made. Thus, generally but not necessarily, amorphizing does not refer to the process of doping or making a doped composition (although doping may introduce defects such as interstitial defects), but rather to a separate or subsequent processing step performed on a material that has been formed. An example of an amorphizing process is ball milling, or any similar processes. In some aspects, the term amorphizing refers to a process that necessarily increases amorphous content of a material (or composition thereof) and decreases total crystallinity of the material (or composition thereof), while also optionally reducing grain sizes (average, median, and/or bounds of a 95% confidence interval) of the material (or composition thereof), optionally reducing crystallite sizes (average, median, and/or bounds of a 95% confidence interval) of the material (or composition thereof), and/or optionally increasing an amount or concentration of defects in the material (or composition thereof).

The term “ionic conductivity” is intended to be consistent with the term as it is readily known by one skilled in relevant arts, particularly in the art of semiconductors and/or solid state electrolytes, and refers the property of ionic conductivity as it would relate to the performance of a material or composition thereof as an ionically conductive solid state electrolyte in an electrochemical cell such as a battery. In some aspects, ionic conductivity particularly refers to ionic conductivity of Li⁺ ions in a material or a composition thereof. As used herein, unless explicitly otherwise stated, ionic conductivity of a material (or composition thereof) refers to ionic conductivity within or through the material, such as through a thickness or lateral dimension of the material (e.g., through the thickness of a thin film), instead of a surface ionic conductivity along a film's surface longitudinally. Unless otherwise explicitly stated, the term ionic conductivity refers to a combination of grain boundary transport of ions and bulk ionic conductivity. Preferably, but not necessarily, an ionic conductivity claimed herein is an average ionic conductivity, being an average of at least three repeated measurements. Further to the descriptions in Examples 1A-3 provided herein, useful techniques, assumptions, parameters, calculations, etc., for measuring ionic conductivity in materials disclosed herein is found in P. Vadhva, et al. (“Electrochemical Impedance Spectroscopy for All-Solid-State Batteries: Theory, Methods and Future Outlook”, first published in ChemElectroChem; Volume 8; Issue 11; 2021; Pages 1930-1947; DOI: 10.1002/celc.202100108), which is incorporated herein in its entirety.

The term “electronic conductivity” is intended to be consistent with the term as it is readily known by one skilled in relevant arts, particularly in the art of semiconductors and/or solid state electrolytes, and refers the property of electronic conductivity (conductivity or transport of electrons) as it would relate to the performance of a material or composition thereof as an ionically conductive (and preferably electronically insulating) solid state electrolyte in an electrochemical cell such as a battery. For clarity, electronic conductivity does not refer to nor include ionic conductivity. As used herein, unless explicitly otherwise stated, electronic conductivity of a material (or composition thereof) refers to electronic conductivity within or through the material, such as through a thickness or lateral dimension of the material (e.g., through the thickness of a thin film), instead of a surface electronic conductivity along a film's surface longitudinally. Unless otherwise explicitly stated, the term electronic conductivity may be inclusive of any and all possible mechanisms of electronic transport (i.e., transport/conductivity of electrons; e.g., including Poole-Frenkel emission, hopping conduction, ohmic conduction, space-charge-limited conduction, and/or grain-boundary-limited conduction). Further to the descriptions in Examples 1A-3 provided herein, useful techniques, assumptions, parameters, calculations, etc., for measuring electronic conductivity in materials disclosed herein is found in P. Vadhva, et al. (“Electrochemical Impedance Spectroscopy for All-Solid-State Batteries: Theory, Methods and Future Outlook”, published in ChemElectroChem; Volume 8; Issue 11; 2021; Pages 1930-1947; DOI: 10.1002/celc.202100108), which is incorporated herein in its entirety.

The term “electrochemical cell” refers to devices and/or device components that convert chemical energy into electrical energy or electrical energy into chemical energy. Electrochemical cells have two or more electrodes (e.g., positive and negative electrodes) and one or more electrolytes. For example, an electrolyte may be a fluid electrolyte or a solid electrolyte. In aspects disclosed herein, electrochemical cells comprise at least one solid state electrolyte (optionally but not necessarily also having a fluid electrolyte), the solid state electrolyte comprising a material or composition disclosed herein. The solid state electrolyte is an ionically conductive (e.g., for Li⁺ ions), and preferably electronically insulating to prevent electrical/electronic shorting between oppositely-charged electrodes within the electrochemical cell or battery. Reactions occurring at the electrode, such as sorption and desorption of a chemical species or such as an oxidation or reduction reaction, contribute to charge transfer processes in the electrochemical cell. Electrochemical cells include, but are not limited to, primary (non-rechargeable) batteries and secondary (rechargeable) batteries. In certain aspects, the term electrochemical cell includes metal hydride batteries, metal-air batteries, fuel cells, supercapacitors, capacitors, flow batteries, solid-state batteries, and catalysis or electrocatalytic cells (e.g., those utilizing an alkaline aqueous electrolyte). In some aspects, an electrochemical cell is a Li-ion or Li-ion based battery.

The term “gravimetric capacity”, consistent with the term as used in the art, particularly in the art of battery devices and electrochemistry, refers to amount of charge that can be stored per unit mass. The units are typically mAh/g or C/g. Generally, in the art, gravimetric capacity is normalized by the mass of active material in a cathode or anode, with the balance-of-plant ignored (carbon, binder, etc.) to allow for comparison between active materials. With respect to a battery, the capacity of the battery is normalized to the entire cell which includes all the “inactive” components like carbons, the current collectors, electrolyte, etc. Solid state electrolytes are normally reported as a way to enable Li metal anodes, which have a much higher gravimetric capacity than commercialized graphite anodes. For example, even though solid-state electrolytes are heavier/denser than liquid electrolytes, a solid-state battery could have higher capacity if the solid-state electrolyte is paired with a Li metal anode.

The term “stability”, as used herein in reference to a solid state electrolyte or a material, or composition thereof, that is a candidate solid state electrolyte generally refers to chemical and electrochemical stability (thermodynamic and kinetic) of the electrolyte or material, or composition thereof, with respect to reduction by a Li metal anode at voltages relevant to the operation of a battery having said electrolyte or material. Further to the descriptions in Examples 1A-3 provided herein, useful background, description, techniques, assumptions, parameters, calculations, etc., for determining stability of solid state electrolytes and materials that are candidate solid state electrolytes is found in H. Park, et al. (“Predicting Charge Transfer Stability between Sulfide Solid Electrolytes and Li Metal Anodes”, ACS Energy Lett. 2021, 6, 1, 150-157; DOI: 10.1021/acsenergylett.0c02372), which is incorporated herein in its entirety.

As used herein, total crystallinity refers to the sum of the wt. % of all crystal phases present in the material or a composition thereof. Optionally in any aspect disclosed herein, a material disclosed herein is characterized by a total crystallinity equal to or less than about 25% by weight (wt. %), optionally equal to or less than about 20 wt. %, optionally equal to or less than about 15 wt. %, optionally equal to or less than about 10 wt. %, optionally equal to or less than about 8 wt. %, optionally equal to or less than about 5 wt. %, optionally equal to or less than about 4 wt. %, optionally equal to or less than about 3 wt. %, optionally equal to or less than about 2 wt. %, optionally equal to or less than about 1 wt. %, optionally equal to or less than about 0.8 wt. %, optionally equal to or less than about 0.5 wt. %, optionally equal to or less than about 0.2 wt. %, optionally equal to or less than about 0.1 wt. %, optionally equal to or less than about 0.08 wt. %, optionally equal to or less than about 0.05 wt. %, optionally equal to or less than about 0.01 wt. %. The total crystallinity of a material or composition thereof can be determined through Rietveld quantitative analysis of X-ray diffraction (XRD) data measured from the material or a representative sample thereof. For example, the XRD may be measured using a sheet, film, pellet, powder, or such, of the material, for example. Optionally, XRD data is collected using a powder x-ray diffraction technique with a scan from 5 to 80 degrees, unless otherwise specified. For example, the Rietveld quantitative analysis method may employ a least squares method to model the XRD data and then determine the concentration of crystal phase(s) in the sample based on known lattice(s) and scale factor(s)s for the identified phase(s). However, it is understood that different methods and instrumentation for determining total crystallinity can also be employed.

In an embodiment, a composition or compound of the invention, such as an alloy or precursor to an alloy, is isolated or substantially purified. In an embodiment, an isolated or purified compound is at least partially isolated or substantially purified as would be understood in the art. In an embodiment, a substantially purified composition, compound or formulation of the invention has a chemical purity of 95%, optionally for some applications 99%, optionally for some applications 99.9%, optionally for some applications 99.99%, and optionally for some applications 99.999% pure.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, numerous specific details of the devices, device components and methods of the present invention are set forth in order to provide a thorough explanation of the precise nature of the invention. It will be apparent, however, to those of skill in the art that the invention can be practiced without these specific details.

The Li-ion all-solid-state battery (ASSB) is a promising template for next-generation energy storage. To commercialize Li-ion ASSBs, a suitable solid-state electrolyte is required. A solid-state electrolyte must exhibit a wide electrochemical stability window and ionic conductivity near that of traditional liquid electrolytes. Three compounds with near-liquid-electrolyte conductivity (˜10⁻² S cm⁻¹) have been discovered: Li₁₀GeP₂S₁₂ (LGPS), Li₆PS₅Br argyrodite, and a Li₇P₃S₁₁ glass ceramic. All three discovered electrolytes exhibit electrochemical instability against the Li anode, limiting application in commercial products. Li₃BS₃ is predicted to have a wide electrochemical stability window, sufficient for resisting electron injection from the Li anode.¹ However, the ionic conductivity of pure or intrinsic Li₃BS₃ is prohibitively low (10⁻⁷-10⁻⁶ S cm⁻¹).

In aspects herein, we present a method to significantly enhance the ionic conductivity of materials such as Li₃BS₃, which are candidates for solid state lithium ion conductivity electrolytes, through incorporation of Si and subsequent amorphization. Also disclosed here are ionically conductive materials, such as doped or substituted Li₃BS₃. For example, by substituting up to 5%, for example, of the B sites with Si, Li_3−xB_1−xSi_xS₃ achieves an ionic conductivity surpassing 10⁻⁵ S cm⁻¹ at room temperature. When the doped product is further amorphized, for example through continuous ball milling, the ionic conductivity is further enhanced to above 10⁻³ S cm⁻¹ at room temperature.

Pure or intrinsic Li₃BS₃ has been studied and characterized in the past. The pure structure exhibits an ionic conductivity in the range of 10⁻⁷-10⁻⁶ S cm⁻¹, which is unfavorably low for the material to be useful as a solid state lithium ion conductor. Ionic conductivity of pure/intrinsic Li₃BS₃ can be enhanced via extended ball milling to near 10⁻⁴ S cm⁻¹, 2 aspects disclosed herein include materials and associated methods demonstrating further significant enhancement in ionic conductivity of materials that are candidates for solid state lithium ion conductors (e.g., for use in a solid state electrolyte), such as Li₃BS₃.

In aspects, substitution of a principal element such as B, S, or both B and S in Li₃BS₃ with an aliovalent dopant element also reduces the amount of Li in the composition relative to the undoped composition. For example, in aspects, the relative amount of Li is reduced according to formula FX2: Li_3−x−yB_1−x[Q]_xS_3−y[G]_y, where Q (“first dopant”) is one or more (“first”) dopant elements aliovalent with respect to B, G (“second dopant”) is one or more (“second”) dopant elements each aliovalent with respect to S, x is a number (e.g., selected from range of 0.005 to 0.20) corresponding to the relative amount of substitution of B, and y is a number (e.g., selected from range of 0.005 to 0.20) corresponding to the relative amount of substitution of S. Generally, this reduction in Li occurs to maintain overall charge neutrality of the structure assuming formal oxidation states.

For example, aliovalent substitution of Si into the Li₃BS₃ lattice may introduce vacancies which can act as charge carrying defects. Aliovalent substitution for 5% of the B, for example, results in Li_2.95B_0.95Si_0.05S₃ which exhibits a room temperature ionic conductivity of 1.82·10⁻⁵ S cm⁻¹. In aspects, extended amorphization of the Li_2.95B_0.95Si_0.05S₃ further improves the ionic conductivity to between 1·10⁻³ and 3·10⁻³ S cm⁻¹. Thus, through aliovalent substitution and amorphization, in aspects, the ionic conductivity of Li₃BS₃ is improved to near that of conventional liquid electrolytes.

In aspects, doped materials and compositions thereof disclosed herein, such as amorphous Li_2.95B_0.95Si_0.05S₃ (a-Li_2.95B_0.95Si_0.05S₃), offer many unique advantages over most solid-state electrolyte candidates. The synthesis occurs at a relatively low temperature (˜800° C.) and pelletization can occur at room temperature. In some aspects, unlike most oxide candidates, doped materials and compositions thereof disclosed herein, such as a-Li_2.95B_0.95Si_0.05S₃, exhibit superb inter-grain conductivity without the need for a high-temperature grain-boundary sintering step. The precursor materials are also relatively inexpensive. For example, in comparing to LGPS, the a-Li_2.95B_0.95Si_0.05S₃ swaps Ge (˜$2400/kg) and P (˜$5/kg) for B (˜200/kg) and Si ($1/kg). Additionally, all four constituent elements have a low atomic mass, which is conducive to making ASSBs with high gravimetric capacity.

In some aspects, materials disclosed herein may be useful in a variety of aspects and applications beyond solid-state electrolytes. For example, the doped or substituted materials and compositions thereof disclosed herein, such as Li_2.95B_0.95Si_0.05S₃, may be employed as an artificial interphase on the Li anode surface. In such an application, doped materials and compositions thereof, such as Li_2.95B_0.95Si_0.05S₃, may facilitate ionic conduction while preventing the Li anode from reducing an adjacent SSE.

In some aspects, materials disclosed herein may also be employed as an additive for electrodes. In some aspects, materials disclosed herein may also be employed in glass electrolyte mixtures. In such applications, for example, doped materials and compositions thereof, such as Li_2.95B_0.95Si_0.05S₃, may serve either or both of the following roles: (1) improving electrochemical stability of the electrode/electrolyte and (2) improving ionic conductivity of the electrode/electrolyte.

REFERENCES CITED ABOVE

• 1. Park, H., Yu, S. & Siegel, D. J. Predicting Charge Transfer Stability between Sulfide Solid Electrolytes and Li Metal Anodes. ACS Energy Lett. 6, 150-157 (2021).
• 2. Kimura, T. et al. Characteristics of a Li₃BS₃ Thioborate Glass Electrolyte Obtained via a Mechanochemical Process. ACS Appl. Energy Mater. 5, 1421-1426 (2022).

The substituted or doped compositions disclosed herein generally have a low concentration or a low relative amount of one or more dopants. Preferably, a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is less than or equal to 30 at. %, optionally less than or equal to 28 at. %, optionally less than or equal to 25 at. %, optionally less than or equal to 22 at. %, optionally less than or equal to 21 at. %, optionally less than or equal to 20 at. %, optionally less than or equal to 19 at. %, optionally less than or equal to 18 at. %, optionally less than or equal to 17 at. %, optionally less than or equal to 16 at. %, optionally less than or equal to 15 at. %, optionally less than or equal to 14 at. %, optionally less than or equal to 13 at. %, optionally less than or equal to 12 at. %, optionally less than or equal to 11 at. %, optionally less than or equal to 10 at. %, optionally less than or equal to 9 at. %, optionally less than or equal to 8 at. %, optionally less than or equal to 7 at. %, optionally less than or equal to 6 at. %, optionally less than or equal to 5.0 at. %, optionally less than or equal to 4.5 at. %, optionally less than or equal to 4.0 at. %, optionally less than or equal to 3.5 at. %, optionally less than or equal to 3.0 at. %, optionally less than or equal to 2.7 at. %, optionally less than or equal to 2.5 at. %, optionally less than or equal to 2.3 at. %, optionally less than or equal to 2.1 at. %, optionally less than or equal to 2.0 at. %, optionally less than or equal to 1.9 at. %, optionally less than or equal to 1.7 at. %, optionally less than or equal to 1.5 at. %, optionally less than or equal to 1.3 at. %, optionally less than or equal to 1.0 at. %, optionally less than or equal to 0.8 at. %, optionally less than or equal to 0.7 at. %, optionally less than or equal to 0.6 at. %, optionally less than or equal to 0.5 at. %, optionally less than or equal to 0.4 at. %, optionally less than or equal to 0.3 at. %, optionally less than or equal to 0.2 at. %. Preferably, a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is greater than or equal to 0.1 at. % (optionally greater than or equal to 0.12%, optionally greater than or equal to 0.14%, optionally greater than or equal to 0.15%, optionally greater than or equal to 0.16%, optionally greater than or equal to 0.17%, optionally greater than or equal to 0.19%, optionally greater than or equal to 0.20%, optionally greater than or equal to 0.21%, optionally greater than or equal to 0.22%, optionally greater than or equal to 0.23%, optionally greater than or equal to 0.25%, optionally greater than or equal to 0.27%, optionally greater than or equal to 0.29%, optionally greater than or equal to 0.30%, optionally greater than or equal to 0.35%, optionally greater than or equal to 0.40%, optionally greater than or equal to 0.45%, optionally greater than or equal to 0.50%, optionally greater than or equal to 0.55%, optionally greater than or equal to 0.65%, optionally greater than or equal to 0.70%, optionally greater than or equal to 0.75%, optionally greater than or equal to 0.80%, optionally greater than or equal to 0.85%, optionally greater than or equal to 0.95%, optionally greater than or equal to 1.0%, optionally greater than or equal to 1.2%, optionally greater than or equal to 1.5%, optionally greater than or equal to 1.7%, optionally greater than or equal to 2.0%, optionally greater than or equal to 2.2%, optionally greater than or equal to 2.5%) and less than or equal to 30 at. % (optionally less than or equal to 28 at. %, optionally less than or equal to 25 at. %, optionally less than or equal to 22 at. %, optionally less than or equal to 21 at. %, optionally less than or equal to 20 at. %, optionally less than or equal to 19 at. %, optionally less than or equal to 18 at. %, optionally less than or equal to 17 at. %, optionally less than or equal to 16 at. %, optionally less than or equal to 15 at. %, optionally less than or equal to 14 at. %, optionally less than or equal to 13 at. %, optionally less than or equal to 12 at. %, optionally less than or equal to 11 at. %, optionally less than or equal to 10 at. %, optionally less than or equal to 9 at. %, optionally less than or equal to 8 at. %, optionally less than or equal to 7 at. %, optionally less than or equal to 6 at. %, optionally less than or equal to 5.0 at. %, optionally less than or equal to 4.5 at. %, optionally less than or equal to 4.0 at. %, optionally less than or equal to 3.5 at. %, optionally less than or equal to 3.0 at. %, optionally less than or equal to 2.7 at. %, optionally less than or equal to 2.5 at. %, optionally less than or equal to 2.3 at. %, optionally less than or equal to 2.1 at. %, optionally less than or equal to 2.0 at. %, optionally less than or equal to 1.9 at. %, optionally less than or equal to 1.7 at. %, optionally less than or equal to 1.5 at. %, optionally less than or equal to 1.3 at. %, optionally less than or equal to 1.0 at. %, optionally less than or equal to 0.8 at. %, optionally less than or equal to 0.7 at. %, optionally less than or equal to 0.6 at. %, optionally less than or equal to 0.5 at. %, optionally less than or equal to 0.4 at. %, optionally less than or equal to 0.3 at. %, optionally less than or equal to 0.2 at. %). Any value and range of total dopant concentration (concentration of the one or more dopants in a composition) between 0.1 at. % and 30 at. % is explicitly contemplated and disclosed herein. For example, optionally a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is selected from the range of 0.1 at. % to 20 at. %, optionally selected from the range of 0.1 at. % to 15 at. %, optionally selected from the range of 0.1 at. % to 10 at. %, optionally selected from the range of 0.1 at. % to 5 at. %, optionally selected from the range of 0.1 at. % to 4.0 at. %, optionally selected from the range of 0.1 at. % to 3.0 at. %, optionally selected from the range of 0.1 at. % to 2.5 at. %, optionally selected from the range of 0.1 at. % to 2.0 at. %, optionally selected from the range of 0.1 at. % to 1.5 at. %, optionally selected from the range of 0.1 at. % to 1.0 at. %, optionally selected from the range of 0.1 at. % to 0.95 at. %.

Preferably for some aspects or applications, a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is less than or equal to 30 mol. %, optionally less than or equal to 28 mol. %, optionally less than or equal to 25 mol. %, optionally less than or equal to 22 mol. %, optionally less than or equal to 21 mol. %, optionally less than or equal to 20 mol. %, optionally less than or equal to 19 mol. %, optionally less than or equal to 18 mol. %, optionally less than or equal to 17 mol. %, optionally less than or equal to 16 mol. %, optionally less than or equal to 15 mol. %, optionally less than or equal to 14 mol. %, optionally less than or equal to 13 mol. %, optionally less than or equal to 12 mol. %, optionally less than or equal to 11 mol. %, optionally less than or equal to 10 mol. %, optionally less than or equal to 9 mol. %, optionally less than or equal to 8 mol. %, optionally less than or equal to 7 mol. %, optionally less than or equal to 6 mol. %, optionally less than or equal to 5.0 mol. %, optionally less than or equal to 4.5 mol. %, optionally less than or equal to 4.0 mol. %, optionally less than or equal to 3.5 mol. %, optionally less than or equal to 3.0 mol. %, optionally less than or equal to 2.7 mol. %, optionally less than or equal to 2.5 mol. %, optionally less than or equal to 2.3 mol. %, optionally less than or equal to 2.1 mol. %, optionally less than or equal to 2.0 mol. %, optionally less than or equal to 1.9 mol. %, optionally less than or equal to 1.7 mol. %, optionally less than or equal to 1.5 mol. %, optionally less than or equal to 1.3 mol. %, optionally less than or equal to 1.0 mol. %, optionally less than or equal to 0.8 mol. %, optionally less than or equal to 0.7 mol. %, optionally less than or equal to 0.6 mol. %, optionally less than or equal to 0.5 mol. %, optionally less than or equal to 0.4 mol. %, optionally less than or equal to 0.3 mol. %, optionally less than or equal to 0.2 mol. %. Preferably, a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is greater than or equal to 0.1 mol. % (optionally greater than or equal to 0.12%, optionally greater than or equal to 0.14%, optionally greater than or equal to 0.15%, optionally greater than or equal to 0.16%, optionally greater than or equal to 0.17%, optionally greater than or equal to 0.19%, optionally greater than or equal to 0.20%, optionally greater than or equal to 0.21%, optionally greater than or equal to 0.22%, optionally greater than or equal to 0.23%, optionally greater than or equal to 0.25%, optionally greater than or equal to 0.27%, optionally greater than or equal to 0.29%, optionally greater than or equal to 0.30%, optionally greater than or equal to 0.35%, optionally greater than or equal to 0.40%, optionally greater than or equal to 0.45%, optionally greater than or equal to 0.50%, optionally greater than or equal to 0.55%, optionally greater than or equal to 0.65%, optionally greater than or equal to 0.70%, optionally greater than or equal to 0.75%, optionally greater than or equal to 0.80%, optionally greater than or equal to 0.85%, optionally greater than or equal to 0.95%, optionally greater than or equal to 1.0%, optionally greater than or equal to 1.2%, optionally greater than or equal to 1.5%, optionally greater than or equal to 1.7%, optionally greater than or equal to 2.0%, optionally greater than or equal to 2.2%, optionally greater than or equal to 2.5%) and less than or equal to 30 mol. % (optionally less than or equal to 28 mol. %, optionally less than or equal to 25 mol. %, optionally less than or equal to 22 mol. %, optionally less than or equal to 21 mol. %, optionally less than or equal to 20 mol. %, optionally less than or equal to 19 mol. %, optionally less than or equal to 18 mol. %, optionally less than or equal to 17 mol. %, optionally less than or equal to 16 mol. %, optionally less than or equal to 15 mol. %, optionally less than or equal to 14 mol. %, optionally less than or equal to 13 mol. %, optionally less than or equal to 12 mol. %, optionally less than or equal to 11 mol. %, optionally less than or equal to 10 mol. %, optionally less than or equal to 9 mol. %, optionally less than or equal to 8 mol. %, optionally less than or equal to 7 mol. %, optionally less than or equal to 6 mol. %, optionally less than or equal to 5.0 mol. %, optionally less than or equal to 4.5 mol. %, optionally less than or equal to 4.0 mol. %, optionally less than or equal to 3.5 mol. %, optionally less than or equal to 3.0 mol. %, optionally less than or equal to 2.7 mol. %, optionally less than or equal to 2.5 mol. %, optionally less than or equal to 2.3 mol. %, optionally less than or equal to 2.1 mol. %, optionally less than or equal to 2.0 mol. %, optionally less than or equal to 1.9 mol. %, optionally less than or equal to 1.7 mol. %, optionally less than or equal to 1.5 mol. %, optionally less than or equal to 1.3 mol. %, optionally less than or equal to 1.0 mol. %, optionally less than or equal to 0.8 mol. %, optionally less than or equal to 0.7 mol. %, optionally less than or equal to 0.6 mol. %, optionally less than or equal to 0.5 mol. %, optionally less than or equal to 0.4 mol. %, optionally less than or equal to 0.3 mol. %, optionally less than or equal to 0.2 mol. %). Any value and range of total dopant concentration (concentration of the one or more dopants in a composition) between 0.1 mol. % and 30 mol. % is explicitly contemplated and disclosed herein. For example, optionally a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is selected from the range of 0.1 mol. % to 20 mol. %, optionally selected from the range of 0.1 mol. % to 15 mol. %, optionally selected from the range of 0.1 mol. % to 10 mol. %, optionally selected from the range of 0.1 mol. % to 5 mol. %, optionally selected from the range of 0.1 mol. % to 4.0 mol. %, optionally selected from the range of 0.1 mol. % to 3.0 mol. %, optionally selected from the range of 0.1 mol. % to 2.5 mol. %, optionally selected from the range of 0.1 mol. % to 2.0 mol. %, optionally selected from the range of 0.1 mol. % to 1.5 mol. %, optionally selected from the range of 0.1 mol. % to 1.0 mol. %, optionally selected from the range of 0.1 mol. % to 0.95 mol. %.

Preferably for some aspects or applications, a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is less than or equal to 30 wt. %, optionally less than or equal to 28 wt. %, optionally less than or equal to 25 wt. %, optionally less than or equal to 22 wt. %, optionally less than or equal to 21 wt. %, optionally less than or equal to 20 wt. %, optionally less than or equal to 19 wt. %, optionally less than or equal to 18 wt. %, optionally less than or equal to 17 wt. %, optionally less than or equal to 16 wt. %, optionally less than or equal to 15 wt. %, optionally less than or equal to 14 wt. %, optionally less than or equal to 13 wt. %, optionally less than or equal to 12 wt. %, optionally less than or equal to 11 wt. %, optionally less than or equal to 10 wt. %, optionally less than or equal to 9 wt. %, optionally less than or equal to 8 wt. %, optionally less than or equal to 7 wt. %, optionally less than or equal to 6 wt. %, optionally less than or equal to 5.0 wt. %, optionally less than or equal to 4.5 wt. %, optionally less than or equal to 4.0 wt. %, optionally less than or equal to 3.5 wt. %, optionally less than or equal to 3.0 wt. %, optionally less than or equal to 2.7 wt. %, optionally less than or equal to 2.5 wt. %, optionally less than or equal to 2.3 wt. %, optionally less than or equal to 2.1 wt. %, optionally less than or equal to 2.0 wt. %, optionally less than or equal to 1.9 wt. %, optionally less than or equal to 1.7 wt. %, optionally less than or equal to 1.5 wt. %, optionally less than or equal to 1.3 wt. %, optionally less than or equal to 1.0 wt. %, optionally less than or equal to 0.8 wt. %, optionally less than or equal to 0.7 wt. %, optionally less than or equal to 0.6 wt. %, optionally less than or equal to 0.5 wt. %, optionally less than or equal to 0.4 wt. %, optionally less than or equal to 0.3 wt. %, optionally less than or equal to 0.2 wt. %. Preferably, a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is greater than or equal to 0.1 wt. % (optionally greater than or equal to 0.12%, optionally greater than or equal to 0.14%, optionally greater than or equal to 0.15%, optionally greater than or equal to 0.16%, optionally greater than or equal to 0.17%, optionally greater than or equal to 0.19%, optionally greater than or equal to 0.20%, optionally greater than or equal to 0.21%, optionally greater than or equal to 0.22%, optionally greater than or equal to 0.23%, optionally greater than or equal to 0.25%, optionally greater than or equal to 0.27%, optionally greater than or equal to 0.29%, optionally greater than or equal to 0.30%, optionally greater than or equal to 0.35%, optionally greater than or equal to 0.40%, optionally greater than or equal to 0.45%, optionally greater than or equal to 0.50%, optionally greater than or equal to 0.55%, optionally greater than or equal to 0.65%, optionally greater than or equal to 0.70%, optionally greater than or equal to 0.75%, optionally greater than or equal to 0.80%, optionally greater than or equal to 0.85%, optionally greater than or equal to 0.95%, optionally greater than or equal to 1.0%, optionally greater than or equal to 1.2%, optionally greater than or equal to 1.5%, optionally greater than or equal to 1.7%, optionally greater than or equal to 2.0%, optionally greater than or equal to 2.2%, optionally greater than or equal to 2.5%) and less than or equal to 30 wt. % (optionally less than or equal to 28 wt. %, optionally less than or equal to 25 wt. %, optionally less than or equal to 22 wt. %, optionally less than or equal to 21 wt. %, optionally less than or equal to 20 wt. %, optionally less than or equal to 19 wt. %, optionally less than or equal to 18 wt. %, optionally less than or equal to 17 wt. %, optionally less than or equal to 16 wt. %, optionally less than or equal to 15 wt. %, optionally less than or equal to 14 wt. %, optionally less than or equal to 13 wt. %, optionally less than or equal to 12 wt. %, optionally less than or equal to 11 wt. %, optionally less than or equal to 10 wt. %, optionally less than or equal to 9 wt. %, optionally less than or equal to 8 wt. %, optionally less than or equal to 7 wt. %, optionally less than or equal to 6 wt. %, optionally less than or equal to 5.0 wt. %, optionally less than or equal to 4.5 wt. %, optionally less than or equal to 4.0 wt. %, optionally less than or equal to 3.5 wt. %, optionally less than or equal to 3.0 wt. %, optionally less than or equal to 2.7 wt. %, optionally less than or equal to 2.5 wt. %, optionally less than or equal to 2.3 wt. %, optionally less than or equal to 2.1 wt. %, optionally less than or equal to 2.0 wt. %, optionally less than or equal to 1.9 wt. %, optionally less than or equal to 1.7 wt. %, optionally less than or equal to 1.5 wt. %, optionally less than or equal to 1.3 wt. %, optionally less than or equal to 1.0 wt. %, optionally less than or equal to 0.8 wt. %, optionally less than or equal to 0.7 wt. %, optionally less than or equal to 0.6 wt. %, optionally less than or equal to 0.5 wt. %, optionally less than or equal to 0.4 wt. %, optionally less than or equal to 0.3 wt. %, optionally less than or equal to 0.2 wt. %). Any value and range of total dopant concentration (concentration of the one or more dopants in a composition) between 0.1 wt. % and 30 wt. % is explicitly contemplated and disclosed herein. For example, optionally a total dopant concentration (concentration of the one or more dopants in a composition) in a material or composition thereof is selected from the range of 0.1 wt. % to 20 wt. %, optionally selected from the range of 0.1 wt. % to 15 wt. %, optionally selected from the range of 0.1 wt. % to 10 wt. %, optionally selected from the range of 0.1 wt. % to 5 wt. %, optionally selected from the range of 0.1 wt. % to 4.0 wt. %, optionally selected from the range of 0.1 wt. % to 3.0 wt. %, optionally selected from the range of 0.1 wt. % to 2.5 wt. %, optionally selected from the range of 0.1 wt. % to 2.0 wt. %, optionally selected from the range of 0.1 wt. % to 1.5 wt. %, optionally selected from the range of 0.1 wt. % to 1.0 wt. %, optionally selected from the range of 0.1 wt. % to 0.95 wt. %.

The substituted or doped compositions disclosed herein generally have only a small amount of a principal element substituted for or replaced with a dopant (the dopant being one or more elements aliovalent with respect to the substituted or replaced principal element). Optionally, the relative amount of any principal element of a composition that is substituted with a dopant is less than or equal to 20 at. %, optionally less than or equal to 19 at. %, optionally less than or equal to 18 at. %, optionally less than or equal to 17 at. %, optionally less than or equal to 16 at. %, optionally less than or equal to 15 at. %, optionally less than or equal to 14 at. %, optionally less than or equal to 13 at. %, optionally less than or equal to 12 at. %, optionally less than or equal to 11 at. %, optionally less than or equal to 10 at. %, optionally less than or equal to 9 at. %, optionally less than or equal to 8 at. %, optionally less than or equal to 7 at. %, optionally less than or equal to 6 at. %, optionally less than or equal to 5.0 at. %, optionally less than or equal to 4.5 at. %, optionally less than or equal to 4.0 at. %, optionally less than or equal to 3.5 at. %, optionally less than or equal to 3.0 at. %, optionally less than or equal to 2.7 at. %, optionally less than or equal to 2.5 at. %, optionally less than or equal to 2.3 at. %, optionally less than or equal to 2.1 at. %, optionally less than or equal to 2.0 at. %, optionally less than or equal to 1.9 at. %, optionally less than or equal to 1.7 at. %, optionally less than or equal to 1.5 at. %, optionally less than or equal to 1.3 at. %, optionally less than or equal to 1.0 at. %, optionally less than or equal to 0.8 at. %, optionally less than or equal to 0.7 at. %, optionally less than or equal to 0.6 at. %, optionally less than or equal to 0.5 at. %, optionally less than or equal to 0.4 at. %, optionally less than or equal to 0.3 at. %, optionally less than or equal to 0.2 at. %. Optionally, the relative amount of any principal element of a composition that is substituted with a dopant is greater than or equal to 0.1 at. % (optionally greater than or equal to 0.12%, optionally greater than or equal to 0.14%, optionally greater than or equal to 0.15%, optionally greater than or equal to 0.16%, optionally greater than or equal to 0.17%, optionally greater than or equal to 0.19%, optionally greater than or equal to 0.20%, optionally greater than or equal to 0.21%, optionally greater than or equal to 0.22%, optionally greater than or equal to 0.23%, optionally greater than or equal to 0.25%, optionally greater than or equal to 0.27%, optionally greater than or equal to 0.29%, optionally greater than or equal to 0.30%, optionally greater than or equal to 0.35%, optionally greater than or equal to 0.40%, optionally greater than or equal to 0.45%, optionally greater than or equal to 0.50%, optionally greater than or equal to 0.55%, optionally greater than or equal to 0.65%, optionally greater than or equal to 0.70%, optionally greater than or equal to 0.75%, optionally greater than or equal to 0.80%, optionally greater than or equal to 0.85%, optionally greater than or equal to 0.95%, optionally greater than or equal to 1.0%, optionally greater than or equal to 1.2%, optionally greater than or equal to 1.5%, optionally greater than or equal to 1.7%, optionally greater than or equal to 2.0%, optionally greater than or equal to 2.2%, optionally greater than or equal to 2.5%) and less than or equal to 20 at. % (optionally less than or equal to 19 at. %, optionally less than or equal to 18 at. %, optionally less than or equal to 17 at. %, optionally less than or equal to 16 at. %, optionally less than or equal to 15 at. %, optionally less than or equal to 14 at. %, optionally less than or equal to 13 at. %, optionally less than or equal to 12 at. %, optionally less than or equal to 11 at. %, optionally less than or equal to 10 at. %, optionally less than or equal to 9 at. %, optionally less than or equal to 8 at. %, optionally less than or equal to 7 at. %, optionally less than or equal to 6 at. %, optionally less than or equal to 5.0 at. %, optionally less than or equal to 4.5 at. %, optionally less than or equal to 4.0 at. %, optionally less than or equal to 3.5 at. %, optionally less than or equal to 3.0 at. %, optionally less than or equal to 2.7 at. %, optionally less than or equal to 2.5 at. %, optionally less than or equal to 2.3 at. %, optionally less than or equal to 2.1 at. %, optionally less than or equal to 2.0 at. %, optionally less than or equal to 1.9 at. %, optionally less than or equal to 1.7 at. %, optionally less than or equal to 1.5 at. %, optionally less than or equal to 1.3 at. %, optionally less than or equal to 1.0 at. %, optionally less than or equal to 0.8 at. %, optionally less than or equal to 0.7 at. %, optionally less than or equal to 0.6 at. %, optionally less than or equal to 0.5 at. %, optionally less than or equal to 0.4 at. %, optionally less than or equal to 0.3 at. %, optionally less than or equal to 0.2 at. %). Any value and range of the relative amount, of any principal element of a composition that is substituted with a dopant, between 0.1 at. % and 20 at. % is explicitly contemplated and disclosed herein. For example, optionally, the relative amount of any principal element of a composition that is substituted with a dopant is selected from the range of 0.1 at. % to 20 at. %, optionally selected from the range of 0.1 at. % to 15 at. %, optionally selected from the range of 0.1 at. % to 10 at. %, optionally selected from the range of 0.1 at. % to 5 at. %, optionally selected from the range of 0.1 at. % to 4.0 at. %, optionally selected from the range of 0.1 at. % to 3.0 at. %, optionally selected from the range of 0.1 at. % to 2.5 at. %, optionally selected from the range of 0.1 at. % to 2.0 at. %, optionally selected from the range of 0.1 at. % to 1.5 at. %, optionally selected from the range of 0.1 at. % to 1.0 at. %, optionally selected from the range of 0.1 at. % to 0.95 at. %.

Optionally, the relative amount of any principal element of a composition that is substituted with a dopant is less than or equal to 20 mol. %, optionally less than or equal to 19 mol. %, optionally less than or equal to 18 mol. %, optionally less than or equal to 17 mol. %, optionally less than or equal to 16 mol. %, optionally less than or equal to 15 mol. %, optionally less than or equal to 14 mol. %, optionally less than or equal to 13 mol. %, optionally less than or equal to 12 mol. %, optionally less than or equal to 11 mol. %, optionally less than or equal to 10 mol. %, optionally less than or equal to 9 mol. %, optionally less than or equal to 8 mol. %, optionally less than or equal to 7 mol. %, optionally less than or equal to 6 mol. %, optionally less than or equal to 5.0 mol. %, optionally less than or equal to 4.5 mol. %, optionally less than or equal to 4.0 mol. %, optionally less than or equal to 3.5 mol. %, optionally less than or equal to 3.0 mol. %, optionally less than or equal to 2.7 mol. %, optionally less than or equal to 2.5 mol. %, optionally less than or equal to 2.3 mol. %, optionally less than or equal to 2.1 mol. %, optionally less than or equal to 2.0 mol. %, optionally less than or equal to 1.9 mol. %, optionally less than or equal to 1.7 mol. %, optionally less than or equal to 1.5 mol. %, optionally less than or equal to 1.3 mol. %, optionally less than or equal to 1.0 mol. %, optionally less than or equal to 0.8 mol. %, optionally less than or equal to 0.7 mol. %, optionally less than or equal to 0.6 mol. %, optionally less than or equal to 0.5 mol. %, optionally less than or equal to 0.4 mol. %, optionally less than or equal to 0.3 mol. %, optionally less than or equal to 0.2 mol. %. Optionally, the relative amount of any principal element of a composition that is substituted with a dopant is greater than or equal to 0.1 mol. % (optionally greater than or equal to 0.12%, optionally greater than or equal to 0.14%, optionally greater than or equal to 0.15%, optionally greater than or equal to 0.16%, optionally greater than or equal to 0.17%, optionally greater than or equal to 0.19%, optionally greater than or equal to 0.20%, optionally greater than or equal to 0.21%, optionally greater than or equal to 0.22%, optionally greater than or equal to 0.23%, optionally greater than or equal to 0.25%, optionally greater than or equal to 0.27%, optionally greater than or equal to 0.29%, optionally greater than or equal to 0.30%, optionally greater than or equal to 0.35%, optionally greater than or equal to 0.40%, optionally greater than or equal to 0.45%, optionally greater than or equal to 0.50%, optionally greater than or equal to 0.55%, optionally greater than or equal to 0.65%, optionally greater than or equal to 0.70%, optionally greater than or equal to 0.75%, optionally greater than or equal to 0.80%, optionally greater than or equal to 0.85%, optionally greater than or equal to 0.95%, optionally greater than or equal to 1.0%, optionally greater than or equal to 1.2%, optionally greater than or equal to 1.5%, optionally greater than or equal to 1.7%, optionally greater than or equal to 2.0%, optionally greater than or equal to 2.2%, optionally greater than or equal to 2.5%) and less than or equal to 20 mol. % (optionally less than or equal to 19 mol. %, optionally less than or equal to 18 mol. %, optionally less than or equal to 17 mol. %, optionally less than or equal to 16 mol. %, optionally less than or equal to 15 mol. %, optionally less than or equal to 14 mol. %, optionally less than or equal to 13 mol. %, optionally less than or equal to 12 mol. %, optionally less than or equal to 11 mol. %, optionally less than or equal to 10 mol. %, optionally less than or equal to 9 mol. %, optionally less than or equal to 8 mol. %, optionally less than or equal to 7 mol. %, optionally less than or equal to 6 mol. %, optionally less than or equal to 5.0 mol. %, optionally less than or equal to 4.5 mol. %, optionally less than or equal to 4.0 mol. %, optionally less than or equal to 3.5 mol. %, optionally less than or equal to 3.0 mol. %, optionally less than or equal to 2.7 mol. %, optionally less than or equal to 2.5 mol. %, optionally less than or equal to 2.3 mol. %, optionally less than or equal to 2.1 mol. %, optionally less than or equal to 2.0 mol. %, optionally less than or equal to 1.9 mol. %, optionally less than or equal to 1.7 mol. %, optionally less than or equal to 1.5 mol. %, optionally less than or equal to 1.3 mol. %, optionally less than or equal to 1.0 mol. %, optionally less than or equal to 0.8 mol. %, optionally less than or equal to 0.7 mol. %, optionally less than or equal to 0.6 mol. %, optionally less than or equal to 0.5 mol. %, optionally less than or equal to 0.4 mol. %, optionally less than or equal to 0.3 mol. %, optionally less than or equal to 0.2 mol. %). Any value and range of the relative amount, of any principal element of a composition that is substituted with a dopant, between 0.1 mol. % and 20 mol. % is explicitly contemplated and disclosed herein. For example, optionally, the relative amount of any principal element of a composition that is substituted with a dopant is selected from the range of 0.1 mol. % to 20 mol. %, optionally selected from the range of 0.1 mol. % to 15 mol. %, optionally selected from the range of 0.1 mol. % to 10 mol. %, optionally selected from the range of 0.1 mol. % to 5 mol. %, optionally selected from the range of 0.1 mol. % to 4.0 mol. %, optionally selected from the range of 0.1 mol. % to 3.0 mol. %, optionally selected from the range of 0.1 mol. % to 2.5 mol. %, optionally selected from the range of 0.1 mol. % to 2.0 mol. %, optionally selected from the range of 0.1 mol. % to 1.5 mol. %, optionally selected from the range of 0.1 mol. % to 1.0 mol. %, optionally selected from the range of 0.1 mol. % to 0.95 mol. %.

Optionally, the relative amount of any principal element of a composition that is substituted with a dopant is less than or equal to 20 wt. %, optionally less than or equal to 19 wt. %, optionally less than or equal to 18 wt. %, optionally less than or equal to 17 wt. %, optionally less than or equal to 16 wt. %, optionally less than or equal to 15 wt. %, optionally less than or equal to 14 wt. %, optionally less than or equal to 13 wt. %, optionally less than or equal to 12 wt. %, optionally less than or equal to 11 wt. %, optionally less than or equal to 10 wt. %, optionally less than or equal to 9 wt. %, optionally less than or equal to 8 wt. %, optionally less than or equal to 7 wt. %, optionally less than or equal to 6 wt. %, optionally less than or equal to 5.0 wt. %, optionally less than or equal to 4.5 wt. %, optionally less than or equal to 4.0 wt. %, optionally less than or equal to 3.5 wt. %, optionally less than or equal to 3.0 wt. %, optionally less than or equal to 2.7 wt. %, optionally less than or equal to 2.5 wt. %, optionally less than or equal to 2.3 wt. %, optionally less than or equal to 2.1 wt. %, optionally less than or equal to 2.0 wt. %, optionally less than or equal to 1.9 wt. %, optionally less than or equal to 1.7 wt. %, optionally less than or equal to 1.5 wt. %, optionally less than or equal to 1.3 wt. %, optionally less than or equal to 1.0 wt. %, optionally less than or equal to 0.8 wt. %, optionally less than or equal to 0.7 wt. %, optionally less than or equal to 0.6 wt. %, optionally less than or equal to 0.5 wt. %, optionally less than or equal to 0.4 wt. %, optionally less than or equal to 0.3 wt. %, optionally less than or equal to 0.2 wt. %. Optionally, the relative amount of any principal element of a composition that is substituted with a dopant is greater than or equal to 0.1 wt. % (optionally greater than or equal to 0.12%, optionally greater than or equal to 0.14%, optionally greater than or equal to 0.15%, optionally greater than or equal to 0.16%, optionally greater than or equal to 0.17%, optionally greater than or equal to 0.19%, optionally greater than or equal to 0.20%, optionally greater than or equal to 0.21%, optionally greater than or equal to 0.22%, optionally greater than or equal to 0.23%, optionally greater than or equal to 0.25%, optionally greater than or equal to 0.27%, optionally greater than or equal to 0.29%, optionally greater than or equal to 0.30%, optionally greater than or equal to 0.35%, optionally greater than or equal to 0.40%, optionally greater than or equal to 0.45%, optionally greater than or equal to 0.50%, optionally greater than or equal to 0.55%, optionally greater than or equal to 0.65%, optionally greater than or equal to 0.70%, optionally greater than or equal to 0.75%, optionally greater than or equal to 0.80%, optionally greater than or equal to 0.85%, optionally greater than or equal to 0.95%, optionally greater than or equal to 1.0%, optionally greater than or equal to 1.2%, optionally greater than or equal to 1.5%, optionally greater than or equal to 1.7%, optionally greater than or equal to 2.0%, optionally greater than or equal to 2.2%, optionally greater than or equal to 2.5%) and less than or equal to 20 wt. % (optionally less than or equal to 19 wt. %, optionally less than or equal to 18 wt. %, optionally less than or equal to 17 wt. %, optionally less than or equal to 16 wt. %, optionally less than or equal to 15 wt. %, optionally less than or equal to 14 wt. %, optionally less than or equal to 13 wt. %, optionally less than or equal to 12 wt. %, optionally less than or equal to 11 wt. %, optionally less than or equal to 10 wt. %, optionally less than or equal to 9 wt. %, optionally less than or equal to 8 wt. %, optionally less than or equal to 7 wt. %, optionally less than or equal to 6 wt. %, optionally less than or equal to 5.0 wt. %, optionally less than or equal to 4.5 wt. %, optionally less than or equal to 4.0 wt. %, optionally less than or equal to 3.5 wt. %, optionally less than or equal to 3.0 wt. %, optionally less than or equal to 2.7 wt. %, optionally less than or equal to 2.5 wt. %, optionally less than or equal to 2.3 wt. %, optionally less than or equal to 2.1 wt. %, optionally less than or equal to 2.0 wt. %, optionally less than or equal to 1.9 wt. %, optionally less than or equal to 1.7 wt. %, optionally less than or equal to 1.5 wt. %, optionally less than or equal to 1.3 wt. %, optionally less than or equal to 1.0 wt. %, optionally less than or equal to 0.8 wt. %, optionally less than or equal to 0.7 wt. %, optionally less than or equal to 0.6 wt. %, optionally less than or equal to 0.5 wt. %, optionally less than or equal to 0.4 wt. %, optionally less than or equal to 0.3 wt. %, optionally less than or equal to 0.2 wt. %). Any value and range of the relative amount, of any principal element of a composition that is substituted with a dopant, between 0.1 wt. % and 20 wt. % is explicitly contemplated and disclosed herein. For example, optionally, the relative amount of any principal element of a composition that is substituted with a dopant is selected from the range of 0.1 wt. % to 20 wt. %, optionally selected from the range of 0.1 wt. % to 15 wt. %, optionally selected from the range of 0.1 wt. % to 10 wt. %, optionally selected from the range of 0.1 wt. % to 5 wt. %, optionally selected from the range of 0.1 wt. % to 4.0 wt. %, optionally selected from the range of 0.1 wt. % to 3.0 wt. %, optionally selected from the range of 0.1 wt. % to 2.5 wt. %, optionally selected from the range of 0.1 wt. % to 2.0 wt. %, optionally selected from the range of 0.1 wt. % to 1.5 wt. %, optionally selected from the range of 0.1 wt. % to 1.0 wt. %, optionally selected from the range of 0.1 wt. % to 0.95 wt. %.

CERTAIN ASPECTS AND EMBODIMENTS

Various aspects are contemplated and disclosed herein, several of which are set forth in the paragraphs below. It is explicitly contemplated and disclosed that any aspect or portion thereof can be combined to form an aspect. In addition, it is explicitly contemplated and disclosed that: any reference to Aspect 1 includes reference to Aspects 1a, 1b, 1c, 1d, 1e, 1f, 1g, 1h, 1i, 1j, 1k, and/or 11, and any combination thereof; any reference to Aspect 3 includes reference to Aspects 3a, 3b, and/or 3c; and so on (i.e., any reference to an aspect includes reference to that aspect's lettered versions). Moreover, the terms “any preceding aspect” and “any one of the preceding aspects” means any aspect that appears prior to the aspect that contains such phrase (for example, the sentence “Aspect 15: The material, device, electrolyte, or method of any preceding Aspect . . . ” means that any Aspect prior to Aspect 15 is referenced, including letter versions, including aspects 1a through 14b). For example, it is contemplated and disclosed that, optionally, any composition, method, or formulation of any the below aspects may be useful with or combined with any other aspect provided below. Further, for example, it is contemplated and disclosed that any embodiment or aspect described above may, optionally, be combined with any of the below listed aspects.

• • Aspect 1a: A material comprising:
  • a lithium thioborate composition characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 1b: A device comprising:
  • a material, the material comprising:
  • a lithium thioborate composition characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 1c: A solid state electrolyte comprising:
  • a lithium thioborate composition characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 1d: A method of making a material, the method comprising:
  • combining a plurality of precursors comprising lithium, boron, sulfur, and at least one of a first dopant and a second dopant; and heating the combined plurality of precursors to form the material having a lithium thioborate composition;
  • wherein the lithium thioborate composition is characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is the first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is the second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 1e: An electrolyte comprising:
  • a lithium solid state electrolyte comprising Li, one or more principal elements (optionally, non-Li principal elements), and at least one dopant;
  • wherein the dopant substitutes for a portion of the one of the one or more principal elements (optionally, non-Li principal elements) of the lithium solid state electrolyte and is aliovalent with the respective substituted principal elements (optionally, non-Li principal elements);
  • wherein the ionic conductivity of the lithium solid state electrolyte is greater than or equal to 1·10⁻⁵ S/cm at 25° C.
  • Aspect 1f: A doped lithium solid state electrolyte comprising:
  • a doped inorganic composition having at least one dopant;
  • wherein the doped composition has up to 20 at. % (optionally up to 15 at. %, optionally up to 12 at. %, optionally up to 10 at. %, optionally up to 8 at. %, optionally up to 5 at. %, optionally up to 3 at. %, optionally up to 2 at. %, optionally up to 1 at. %, optionally up to 0.9 at. %, optionally up to 0.8 at. %, optionally up to 0.7 at. %, optionally up to 0.5 at. %) of one or more principal elements (optionally, non-Li principal elements) substituted with the at least one dopant relative to a reference composition of a reference lithium solid state electrolyte;
  • wherein each dopant is one or more elements each aliovalent with the respective substituted principal element (optionally, a non-Li principal element);
  • wherein the presence of the one or more dopants provides for an ionic conductivity greater than or equal to 1·10⁻⁵ S/cm at 25° C.
  • Aspect 1g: A method for increasing an ionic conductivity of a reference lithium solid state electrolyte, the method comprising:
  • forming a doped lithium solid state electrolyte having a doped composition;
  • wherein the reference lithium solid state electrolyte has a reference composition, and wherein the doped composition has up to 20 at. % (optionally up to 15 at. %, optionally up to 12 at. %, optionally up to 10 at. %, optionally up to 8 at. %, optionally up to 5 at. %, optionally up to 3 at. %, optionally up to 2 at. %, optionally up to 1 at. %, optionally up to 0.9 at. %, optionally up to 0.8 at. %, optionally up to 0.7 at. %, optionally up to 0.5 at. %) of one or more principal elements (optionally, non-Li principal elements) substituted with at least one dopant relative to the reference composition;
  • wherein each element of the at least one dopant is aliovalent with respect to the respective substituted principal element (optionally, a non-Li principal element); and
  • wherein the doped lithium solid state electrolyte has a greater ionic conductivity than the reference lithium solid state electrolyte by a factor of at least 2 (optionally at least 3, optionally at least 4, optionally at least 5, optionally at least 6, optionally at least 7, optionally at least 8, optionally at least 9, optionally at least 10, optionally at least 11, optionally at least 12, optionally at least 13, optionally at least 14, optionally at least 15, optionally at least 18, optionally at least 20, optionally at least 21, optionally at least 22, optionally at least 23, optionally at least 24, optionally at least 25, optionally at least 50, optionally at least 75, optionally at least 100, optionally at least 125, optionally at least 150, optionally at least 175, optionally at least 200, optionally at least 300, optionally at least 400, optionally at least 500, optionally at least 600, optionally at least 700, optionally at least 800, optionally at least 900, optionally at least 1000, optionally at least 1100, optionally at least 1200, optionally at least 1300, optionally at least 1400).
  • Aspect 1h: The material, device, electrolyte, or method of Aspect 1, wherein z is greater than 0 and less than 1 (optionally less than or equal to 0.50, optionally less than or equal to 0.45, optionally less than or equal to 0.40, optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025).

The material, device, electrolyte, or method of Aspect 1, wherein z is greater than 0 and less than 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025).

• • Aspect 1j: The material, device, electrolyte, or method of Aspect 1, wherein the material or the composition thereof is a solid solution.
  • Aspect 1k: Any material or composition disclosed herein, such as any of those disclosed in Examples 1A and 1B, optionally further doped/substituted and/or optionally amorphized.
  • Aspect 11: The material, device, electrolyte, or method of Aspect 1, wherein z is greater than 0 and less than 0.15.
  • Aspect 2: The material, device, electrolyte, or method of any preceding Aspect, having a greater ionic conductivity than that of an undoped stoichiometric Li₃BS₃ material by a factor of at least 2 (optionally at least 3, optionally at least 4, optionally at least 5, optionally at least 6, optionally at least 7, optionally at least 8, optionally at least 9, optionally at least 10, optionally at least 11, optionally at least 12, optionally at least 13, optionally at least 14, optionally at least 15, optionally at least 18, optionally at least 20, optionally at least 21, optionally at least 22, optionally at least 23, optionally at least 24, optionally at least 25, optionally at least 50, optionally at least 75, optionally at least 100, optionally at least 125, optionally at least 150, optionally at least 175, optionally at least 200, optionally at least 300, optionally at least 400, optionally at least 500, optionally at least 600, optionally at least 700, optionally at least 800, optionally at least 900, optionally at least 1000, optionally at least 1100, optionally at least 1200, optionally at least 1300, optionally at least 1400) at 25° C., wherein the undoped stoichiometric Li₃BS₃ material is free of Q and G.
  • Aspect 3a: The material, device, electrolyte, or method of any preceding Aspect being characterized by an ionic conductivity (such as average ionic conductivity) greater than 6·10⁻⁶ S/cm (optionally greater than or equal to 7·10⁻⁶ S/cm, optionally greater than or equal to 8·10⁻⁶ S/cm, optionally greater than or equal to 9·10⁻⁶ S/cm, optionally greater than or equal to 1.0·10⁻⁵ S/cm, optionally greater than or equal to 1.2·10⁻⁵ S/cm, optionally greater than or equal to 1.4·10⁻⁵ S/cm, optionally greater than or equal to 1.5·10⁻⁵ S/cm, optionally greater than or equal to 1.6·10⁻⁵ S/cm, optionally greater than or equal to 1.9·10⁻⁵ S/cm, optionally greater than or equal to 2.0·10⁻⁵ S/cm, optionally greater than or equal to 2.5·10⁻⁵ S/cm, optionally greater than or equal to 3.0·10⁻⁵ S/cm, optionally greater than or equal to 3.5·10⁻⁵ S/cm, optionally greater than or equal to 4.0·10⁻⁵ S/cm, optionally greater than or equal to 4.5·10⁻⁵ S/cm, optionally greater than or equal to 5.0·10⁻⁵ S/cm, optionally greater than or equal to 5.5·10⁻⁵ S/cm, optionally greater than or equal to 6.0·10⁻⁵ S/cm, optionally greater than or equal to 6.5·10⁻⁵ S/cm, optionally greater than or equal to 7.0·10⁻⁵ S/cm, optionally greater than or equal to 7.5·10⁻⁵ S/cm, optionally greater than or equal to 8.0·10⁻⁵ S/cm, optionally greater than or equal to 8.5·10⁻⁵ S/cm, optionally greater than or equal to 9.0·10⁻⁵ S/cm, optionally greater than or equal to 9.5·10⁻⁵ S/cm, optionally greater than or equal to 1.0·10⁻⁴ S/cm, optionally greater than or equal to 1.2·10⁻⁴ S/cm, optionally greater than or equal to 1.5·10⁻⁴ S/cm, optionally greater than or equal to 1.7·10⁻⁴ S/cm, optionally greater than or equal to 1.9·10⁻⁴ S/cm, optionally greater than or equal to 2.0·10⁻⁴ S/cm, optionally greater than or equal to 2.5·10⁻⁴ S/cm, optionally greater than or equal to 3.0·10⁻⁴ S/cm, optionally greater than or equal to 3.5·10⁻⁴ S/cm, optionally greater than or equal to 4.0·10⁻⁴ S/cm, optionally greater than or equal to 4.5·10⁻⁴ S/cm, optionally greater than or equal to 5.0·10⁻⁴ S/cm, optionally greater than or equal to 5.5·10⁻⁴ S/cm, optionally greater than or equal to 6.0·10⁻⁴ S/cm, optionally greater than or equal to 6.5·10⁻⁴ S/cm, optionally greater than or equal to 7.0·10⁻⁴ S/cm, optionally greater than or equal to 7.5·10⁻⁴ S/cm, optionally greater than or equal to 8.0·10⁻⁴ S/cm, optionally greater than or equal to 8.5·10⁻⁴ S/cm, optionally greater than or equal to 9.0·10⁻⁴ S/cm, optionally greater than or equal to 9.3·10⁻⁴ S/cm, optionally greater than or equal to 9.5·10⁻⁴ S/cm, optionally greater than or equal to 9.7·10⁻⁴ S/cm, optionally greater than or equal to 1.0·10⁻³ S/cm, optionally greater than or equal to 1.1·10⁻³ S/cm, optionally greater than or equal to 1.2·10⁻³ S/cm, optionally greater than or equal to 1.5·10⁻³ S/cm, optionally greater than or equal to 1.6·10⁻³ S/cm, optionally greater than or equal to 1.7·10⁻³ S/cm, optionally greater than or equal to 1.8·10⁻³ S/cm, optionally greater than or equal to 1.9·10⁻³ S/cm, optionally greater than or equal to 2.0·10⁻³ S/cm, optionally greater than or equal to 2.1·10⁻³ S/cm, optionally greater than or equal to 2.2·10⁻³ S/cm, optionally greater than or equal to 2.5·10⁻³ S/cm, optionally greater than or equal to 2.7·10⁻³ S/cm, optionally greater than or equal to 2.9·10⁻³ S/cm, optionally greater than or equal to 3.0·10⁻³ S/cm, optionally greater than or equal to 3.1·10⁻³ S/cm) at 25° C.
  • Aspect 3b: The material, device, electrolyte, or method of any preceding Aspect being characterized by an ionic conductivity (such as average ionic conductivity) selected from the range of 6·10⁻⁶ S/cm to 5·10⁻² S/cm, and wherein any value and range of ionic conductivity therebetween is explicitly contemplated and disclosed herein. Aspect 3c: The material, device, electrolyte, or method of any preceding Aspect being characterized by an ionic conductivity (such as average ionic conductivity) selected from the range of 6·10⁻⁶ S/cm to 1·10⁻² S/cm, optionally selected from the range of 1·10⁻⁴ S/cm to 1·10⁻² S/cm, optionally selected from the range of 5·10⁻⁴ S/cm to 1·10⁻² S/cm, optionally selected from the range of 1·10⁻³ S/cm to 1·10⁻² S/cm.
  • Aspect 4a: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by the ratio Q/(B+Q) being greater than 0.001 and less than 0.20, and wherein any value and range therebetween is explicitly contemplated and disclosed herein. Aspect 4b: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by the ratio Q/(B+Q) being selected from the range of 0.01 to 0.20, optionally selected from the range of 0.02 to 0.20, optionally selected from the range of 0.01 to 0.15, optionally selected from the range of 0.01 to 0.12, optionally selected from the range of 0.02 to 0.10.
  • Aspect 5: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by the ratio Q/(B+Q) being greater than 0.020 and less than 0.075.
  • Aspect 6a: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is one or more Group 14 elements and/or one or more metal elements such as transition metal elements. Aspect 6b: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is one or more Group 14 elements. Aspect 6c: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is one Group 14 element. Aspect 6d: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is one or more metal elements, such as one or more transition metal elements.
  • Aspect 7a: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is Si, Ge, Sn, and/or Zr. Aspect 7b: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is Si and/or Ge. Aspect 7c: The material, device, electrolyte, or method of any preceding Aspect, wherein Q comprises Si. Aspect 7d: The material, device, electrolyte, or method of any preceding Aspect, wherein Q is Si.
  • Aspect 8a: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by the ratio G/(S+G) being greater than 0.001 and less than 0.20, and wherein any value and range therebetween is explicitly contemplated and disclosed herein. Aspect 8b: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by the ratio Q/(B+Q) being selected from the range of 0.01 to 0.20, optionally selected from the range of 0.02 to 0.20, optionally selected from the range of 0.01 to 0.15, optionally selected from the range of 0.01 to 0.12, optionally selected from the range of 0.02 to 0.10.
  • Aspect 9: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by the ratio G/(S+G) being greater than 0.020 and less than 0.2, and wherein any value and range therebetween is explicitly contemplated and disclosed herein.
  • Aspect 10a: The material, device, electrolyte, or method of any preceding Aspect, wherein G is one or more Group 17 (halogen) elements. Aspect 10b: The material, device, electrolyte, or method of any preceding Aspect, wherein G is one Group 17 (halogen) element.
  • Aspect 11a: The material, device, electrolyte, or method of any preceding Aspect, wherein G is Cl and/or Br. Aspect 11 b: The material, device, electrolyte, or method of any preceding Aspect, wherein G comprises Cl. Aspect 11c: The material, device, electrolyte, or method of any preceding Aspect, wherein G is Cl.
  • Aspect 12a: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by formula FX2, FX3, or FX4:

Li_3−x−yB_1−x[Q]_xS_3−y[G]_y  (FX2);

Li_3−xB_1−x[Q]_xS₃  (FX3);

Li_3−yB₁S_3−y[G]_y  (FX4); wherein:

• • x is selected from the range of 0.005 (optionally 0.007, optionally 0.009, optionally 0.01, optionally 0.015, optionally 0.02, optionally 0.025, optionally 0.03, optionally 0.035, optionally 0.04, optionally 0.045, optionally 0.05, optionally 0.055, optionally 0.06) to 0.20 (optionally 0.19, optionally 0.18, optionally 0.17, optionally 0.16, optionally 0.15, optionally 0.14, optionally 0.13, optionally 0.12, optionally 0.11, optionally 0.10, optionally 0.09, optionally 0.08, optionally 0.07, optionally 0.06); and
  • y is selected from the range of 0.005 (optionally 0.007, optionally 0.009, optionally 0.01, optionally 0.015, optionally 0.02, optionally 0.025, optionally 0.03, optionally 0.035, optionally 0.04, optionally 0.045, optionally 0.05, optionally 0.055, optionally 0.06) to 0.20 (optionally 0.19, optionally 0.18, optionally 0.17, optionally 0.16, optionally 0.15, optionally 0.14, optionally 0.13, optionally 0.12, optionally 0.11, optionally 0.10, optionally 0.09, optionally 0.08, optionally 0.07, optionally 0.06). Therefore, in Aspect 12, the variable z of claim 1 is equal to or approximately equal to x (in FX3), y (in FX4), or x+y (in FX2).
  • Aspect 12b: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by formula FX3; and wherein x is greater than 0 and less than or equal to 0.05, y is 0, and z is equal to or approximately equal to x.
  • Aspect 13a: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by formula FX3; and wherein x is greater than 0.025 (optionally greater than 0.03, optionally greater than 0.04) and less than or equal to 0.05 (optionally less than or equal to 0.06), y is 0, and z is equal to or approximately equal to x. Aspect 13b: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is characterized by formula FX3; and wherein x is about 0.05, y is 0, and z is equal to or approximately equal to x.
  • Aspect 14a: The material, device, electrolyte, or method of any preceding Aspect, wherein the material or the composition thereof is amorphous or substantially amorphous. Aspect 14b: The material, device, electrolyte, or method of any preceding Aspect, wherein the material or the composition thereof is has a total crystallinity less than 50 wt. %. Aspect 14c: The material, device, electrolyte, or method of any preceding Aspect, wherein the material or the composition thereof is has a total crystallinity less than or equal to about 35 wt. %, optionally less than or equal to about 30 wt. %, optionally less than or equal to about 25 wt. %, optionally less than or equal to about 20 wt. %, optionally less than or equal to about 15 wt. %, optionally equal to or less than about 10 wt. %, optionally equal to or less than about 8 wt. %, optionally equal to or less than about 5 wt. %, optionally equal to or less than about 4 wt. %, optionally equal to or less than about 3 wt. %, optionally equal to or less than about 2 wt. %, optionally equal to or less than about 1 wt. %, optionally equal to or less than about 0.8 wt. %, optionally equal to or less than about 0.5 wt. %, optionally equal to or less than about 0.2 wt. %, optionally equal to or less than about 0.1 wt. %, optionally equal to or less than about 0.08 wt. %, optionally equal to or less than about 0.05 wt. %, optionally equal to or less than about 0.01 wt. %.
  • Aspect 15: The material, device, electrolyte, or method of any preceding Aspect, being characterized by an ionic conductivity greater than or equal to 1·10⁻⁵ S/cm at 25° C.
  • Aspect 16: The material, device, electrolyte, or method of any preceding Aspect, being characterized by an ionic conductivity greater than or equal to 1·10⁻³ S/cm at 25° C.
  • Aspect 17: The material, device, electrolyte, or method of any preceding Aspect, being characterized by an ionic conductivity selected from the range of 1·10⁻⁵ S/cm to 1·10⁻² at 25° C.
  • Aspect 18: The material, device, electrolyte, or method of any preceding Aspect, being characterized by an electronic conductivity less than 5·10⁻¹⁰ S/cm (optionally less than or equal to about 4.8·10⁻¹⁰ S/cm, optionally less than or equal to about 4.5·10⁻¹⁰ S/cm, optionally less than or equal to about 4.3·10⁻¹⁰ S/cm, optionally less than or equal to about 4.1·10⁻¹⁰ S/cm, optionally less than or equal to about 4.0·10⁻¹⁰ S/cm, optionally less than or equal to about 3.8·10⁻¹⁰ S/cm, optionally less than or equal to about 3.5·10⁻¹⁰ S/cm, optionally less than or equal to about 3.2·10⁻¹⁰ S/cm, optionally less than or equal to about 3.0·10⁻¹⁰ S/cm, optionally less than or equal to about 2.0·10⁻¹⁰ S/cm, optionally less than or equal to about 1.0·10⁻¹⁰ S/cm) at 25° C.
  • Aspect 19: The material, device, electrolyte, or method of any preceding Aspect, being characterized by an activation energy (E_a) for an ionic conductivity of less than or equal to about 500 meV (optionally less than or equal to about 475 meV, optionally less than or equal to about 450 meV, optionally less than or equal to about 425 meV, optionally less than or equal to about 400 meV, optionally less than or equal to about 375 meV, optionally less than or equal to about 350 meV, optionally less than or equal to about 325 meV, optionally less than or equal to about 300 meV, optionally less than or equal to about 275 meV, optionally less than or equal to about 250 meV, optionally less than or equal to about 225 meV, optionally less than or equal to about 200 meV, optionally less than or equal to about 175 meV) when its temperature-dependent ionic conductivity is fit to equation EQ1:

$\begin{array}{cc}\sigma =\frac{{\sigma }_0}{T}{e}^{\frac{-E_a}{k_{B}T}};& \left(\mathrm{EQ1}\right)\end{array}$

wherein:

• • σ is the ionic conductivity;
  • σ₀ is a conductivity prefactor;
  • T is temperature;
  • k_B is the Boltzmann's constant; and
  • E_a is the activation energy for ionic conductivity.
  • Aspect 20: A device comprising the material of any of the preceding Aspects.
  • Aspect 21: The device of Aspect 20 being an electrochemical cell.
  • Aspect 22: The device of Aspect 21, being a rechargeable lithium battery.
  • Aspect 23: The device of Aspect 21 or 22 having a solid state electrolyte comprising the material of any one of the preceding claims.
  • Aspect 24: The device of Aspect 21, 22, or 23 having a coating on a Li anode, the coating comprising the material of any one of the preceding claims.
  • Aspect 25: A device comprising:
  • a material, the material comprising:
  • a lithium thioborate composition characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 26: The device of Aspect 25 being an electrochemical cell.
  • Aspect 27: The device of Aspect 26, wherein the electrochemical cell comprises a solid state electrolyte having the material.
  • Aspect 28: The device of Aspect 26 or 27, being a rechargeable lithium battery.
  • Aspect 29: A solid state electrolyte comprising:
  • a lithium thioborate composition characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 30: A method of making a material, the method comprising:
  • combining a plurality of precursors comprising lithium, boron, sulfur, and at least one of a first dopant and a second dopant; and
  • heating the combined plurality of precursors to form the material having a lithium thioborate composition;
  • wherein the lithium thioborate composition is characterized by formula FX1:

Li_3−z[B+Q]₁[S+G]₃  (FX1);

• • wherein Q is the first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;
  • wherein G is the second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;
  • wherein z is 0 or a number greater than 0 and less than or equal to 0.40 (optionally less than or equal to 0.35, optionally less than or equal to 0.30, optionally less than or equal to 0.25, optionally less than or equal to 0.20, optionally less than or equal to 0.18, optionally less than or equal to 0.16, optionally less than or equal to 0.15, optionally less than or equal to 0.13, optionally less than or equal to 0.11, optionally less than or equal to 0.10, optionally less than or equal to 0.09, optionally less than or equal to 0.08, optionally less than or equal to 0.07, optionally less than or equal to 0.06, optionally less than or equal to 0.05, optionally less than or equal to 0.04, optionally less than or equal to 0.03, optionally less than or equal to 0.025); and
  • wherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.
  • Aspect 31: The method of Aspect 30 further comprising amorphizing the material to increase its ionic conductivity.
  • Aspect 32a: The method of Aspect 31, wherein the step of amorphizing comprises reducing grain sizes of the lithium thioborate composition, increasing amorphous content of the lithium thioborate composition, decreasing a total crystallinity of the lithium thioborate composition, and/or increasing a concentration of defects in the lithium thioborate composition. Aspect 32b: The method of Aspect 31, wherein the step of amorphizing comprises increasing amorphous content of the lithium thioborate composition and decreasing a total crystallinity of the lithium thioborate composition.
  • Aspect 33: The method of any of Aspects 30-32, wherein the plurality of precursors comprises a lithium-containing precursor, a boron-containing precursor, and a sulfur-containing precursor.
  • Aspect 34: The method of any of Aspects 30-33, wherein the step of combining comprises mixing and/or milling.
  • Aspect 35: The method of any of Aspects 30-34, wherein the step of heating comprises melting the plurality of precursors at a temperature less than 1500° C. (optionally less than or equal to 1400° C., optionally less than or equal to 1300° C., optionally less than or equal to 1200° C., optionally less than or equal to 1100° C., optionally less than or equal to 1000° C., optionally less than or equal to 975° C., optionally less than or equal to 950° C., optionally less than or equal to 900° C., optionally less than or equal to 875° C., optionally less than or equal to 850° C., optionally less than or equal to 825° C., optionally less than or equal to 800° C.) to form a melt comprising lithium, boron, sulfur, and at least of the first dopant and the second dopant.
  • Aspect 36: The method of Aspect 35, wherein the step of heating further comprises cooling the melt thereby forming the material as a solid.
  • Aspect 37: An electrolyte comprising:
  • a lithium solid state electrolyte comprising Li, one or more principal elements (optionally, non-Li principal elements), and at least one dopant;
  • wherein the dopant substitutes for a portion of the one of the one or more principal elements (optionally, non-Li principal elements) of the lithium solid state electrolyte and is aliovalent with the respective substituted principal elements (optionally, non-Li principal elements);
  • wherein the ionic conductivity of the lithium solid state electrolyte is greater than or equal to 1·10⁻⁵ S/cm (optionally selected from the range of 1·10⁻⁵ S/cm to 5·10⁻² S/cm) at 25° C.
  • Aspect 38: The electrolyte of Aspect 37, wherein the lithium solid state electrolyte is obtained from doping (or forming a doped or substituted variation of) a material characterized by formula FX5, FX6, FX7, FX8, FX9, FX10, FX11, FX12, or FX13:

Li₃VS₄  (FX5);

Na₃Li₃Al₂F₁₂  (FX6);

Li₂Te  (FX7);

LiAlTe₂  (FX8);

LiInTe₂  (FX9);

Li₆MnS₄  (FX10);

LiGaTe₂  (FX11);

KLi₆TaO₆  (FX12); or

Li₃CuS₂  (FX13).

• • Aspect 39: A doped lithium solid state electrolyte comprising:
  • a doped inorganic composition having at least one dopant;
  • wherein the doped composition has up to 20 at. % (optionally up to 15 at. %, optionally up to 12 at. %, optionally up to 10 at. %, optionally up to 8 at. %, optionally up to 5 at. %, optionally up to 3 at. %, optionally up to 2 at. %, optionally up to 1 at. %, optionally up to 0.9 at. %, optionally up to 0.8 at. %, optionally up to 0.7 at. %, optionally up to 0.5 at. %) of one or more principal elements (optionally, non-Li principal elements) substituted with the at least one dopant relative to a reference composition of a reference lithium solid state electrolyte;
  • wherein each dopant is one or more elements each aliovalent with the respective substituted principal element (optionally, a non-Li principal element);
  • wherein the presence of the one or more dopants provides for an ionic conductivity greater than or equal to 1·10⁻⁵ S/cm at 25° C.
  • Aspect 40: The material of Aspect 39, wherein the doped inorganic composition has up to 10 at. % of each of the one or more principal element (optionally, a non-Li principal element) substituted with a respective dopant.
  • Aspect 41: The method of Aspect 39 or 40, wherein the doped composition has up to 10 at. % of a cationic principal element, such as B, (optionally, a non-Li principal element) substituted with a first dopant, the first dopant being one or more elements each aliovalent with respect to said cationic principal element (optionally, a non-Li principal element).
  • Aspect 42: The method of any of Aspects 39-41, wherein the doped composition has up to 10 at. % of an anionic principal element, such as S, (optionally, a non-Li principal element) substituted with a second dopant, the second dopant being one or more elements each aliovalent with respect to said anionic principal element (optionally, a non-Li principal element).
  • Aspect 43: The material of any of Aspects 39-42, wherein the presence of the one or more dopants provides for the doped lithium solid state electrolyte having an ionic conductivity greater than that of the reference lithium solid state electrolyte by a factor of at least 2 (optionally at least 3, optionally at least 4, optionally at least 5, optionally at least 6, optionally at least 7, optionally at least 8, optionally at least 9, optionally at least 10, optionally at least 11, optionally at least 12, optionally at least 13, optionally at least 14, optionally at least 15, optionally at least 18, optionally at least 20, optionally at least 21, optionally at least 22, optionally at least 23, optionally at least 24, optionally at least 25, optionally at least 50, optionally at least 75, optionally at least 100, optionally at least 125, optionally at least 150, optionally at least 175, optionally at least 200, optionally at least 300, optionally at least 400, optionally at least 500, optionally at least 600, optionally at least 700, optionally at least 800, optionally at least 900, optionally at least 1000, optionally at least 1100, optionally at least 1200, optionally at least 1300, optionally at least 1400).
  • Aspect 44: The material of any of Aspects 39-43, wherein the reference composition is characterized by formula FX5, FX6, FX7, FX8, FX9, FX10, FX11, FX12, or FX13:

Li₃VS₄  (FX5);

Na₃Li₃Al₂F₁₂  (FX6);

Li₂Te  (FX7);

LiAlTe₂  (FX8);

LiInTe₂  (FX9);

Li₆MnS₄  (FX10);

LiGaTe₂  (FX11);

KLi₆TaO₆  (FX12); or

Li₃CuS₂  (FX13).

• • Aspect 45: A method for increasing an ionic conductivity of a reference lithium solid state electrolyte, the method comprising:
  • forming a doped lithium solid state electrolyte having a doped composition;
  • wherein the reference lithium solid state electrolyte has a reference composition, and wherein the doped composition has up to 20 at. % (optionally up to 15 at. %, optionally up to 12 at. %, optionally up to 10 at. %, optionally up to 8 at. %, optionally up to 5 at. %, optionally up to 3 at. %, optionally up to 2 at. %, optionally up to 1 at. %, optionally up to 0.9 at. %, optionally up to 0.8 at. %, optionally up to 0.7 at. %, optionally up to 0.5 at. %) of one or more principal elements (optionally, non-Li principal elements) substituted with at least one dopant relative to the reference composition;
  • wherein each element of the at least one dopant is aliovalent with respect to the respective substituted principal element (optionally, a non-Li principal element); and
  • wherein the doped lithium solid state electrolyte has a greater ionic conductivity than the reference lithium solid state electrolyte by a factor of at least 2 (optionally at least 3, optionally at least 4, optionally at least 5, optionally at least 6, optionally at least 7, optionally at least 8, optionally at least 9, optionally at least 10, optionally at least 11, optionally at least 12, optionally at least 13, optionally at least 14, optionally at least 15, optionally at least 18, optionally at least 20, optionally at least 21, optionally at least 22, optionally at least 23, optionally at least 24, optionally at least 25, optionally at least 50, optionally at least 75, optionally at least 100, optionally at least 125, optionally at least 150, optionally at least 175, optionally at least 200, optionally at least 300, optionally at least 400, optionally at least 500, optionally at least 600, optionally at least 700, optionally at least 800, optionally at least 900, optionally at least 1000, optionally at least 1100, optionally at least 1200, optionally at least 1300, optionally at least 1400).
  • Aspect 46: The method of Aspect 45, wherein the doped composition has up to 10 at. % of a cationic principal element (optionally, a non-Li principal element) substituted with a first dopant, the first dopant being one or more elements each aliovalent with respect to said cationic principal element (optionally, a non-Li principal element).
  • Aspect 47: The method of Aspect 45 or 46, wherein the doped composition has up to 10 at. % of an anionic principal element (optionally, a non-Li principal element) substituted with a second dopant, the second dopant being one or more elements each aliovalent with respect to said anionic principal element (optionally, a non-Li principal element).
  • Aspect 48: The method of any of Aspects 45-47, wherein the step of forming comprises amorphizing the material to increase its ionic conductivity.
  • Aspect 49a: The method of Aspect 48, wherein the step of amorphizing comprises reducing grain sizes of the lithium thioborate composition, increasing amorphous content of the lithium thioborate composition, and/or increasing a concentration of defects in the lithium thioborate composition. Aspect 49b: The method of Aspect 48, wherein the step of amorphizing comprises increasing amorphous content of the lithium thioborate composition and decreasing a total crystallinity of the lithium thioborate composition.
  • Aspect 50: The method of any of Aspects 45-49, wherein the reference lithium solid state electrolyte and the doped lithium solid state electrolyte are inorganic materials.
  • Aspect 51a: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is further doped with the O (oxygen) such that the lithium borate composition further comprises O. Aspect 51b: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition is further doped with the O (oxygen) such that the lithium borate composition further comprises O being greater than 0 at. % but less than 0.3 at. % O, optionally less than 0.2 at. % O, optionally less than or equal to 0.1 at. % O, optionally less than or equal to 0.08 at. % O, optionally less than or equal to 0.06 at. % O, optionally less than or equal to 0.05 at. % O, optionally less than or equal to 0.03 at. % O, optionally less than or equal to 0.02 at. % O, optionally less than or equal to 0.01 at. % O).
  • Aspect 52a: The material, device, electrolyte, or method of any preceding Aspect other than Aspect 51, wherein the composition is free of O (oxygen) such that the content of O is less than that measurable (e.g., below noise/background level) by techniques known in the art. Aspect 52b: The material, device, electrolyte, or method of any preceding Aspect other than Aspect 51, wherein the composition is free of O (oxygen) or the content of O is less than 0.01 at. %, optionally less than 0.009 at. %.
  • Aspect 53: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition comprises both ionic and covalent bonding. Optionally, for example, assuming the Li—S correlations are ionic and the B—S correlations are covalent, the composition may have about 80% ionic bonding and about 20% covalent bonding.
  • Aspect 54: The material, device, electrolyte, or method of any preceding Aspect, wherein the composition comprises a vacancy defect concentration about equal to z (where z is approximately x+y).

The invention can be further understood by the following non-limiting examples.

Overview of Examples 1-3: Despite ongoing efforts to identify high-performance electrolytes for solid-state Li-ion batteries, thousands of prospective Li-containing structures remain unexplored. Here, we employ a semi-supervised learning approach to expedite identification of superionic conductors. We screen 180 unique descriptor representations and use agglomerative clustering to cluster ˜26,000 Li-containing structures. The clusters are then labeled with experimental ionic conductivity data to assess the fitness of the descriptors. By inspecting clusters containing the highest conductivity labels, we identify 212 promising structures that are further screened using bond valence site energy and nudged elastic band calculations. Li₃BS₃ is identified as a potential high-conductivity material and selected for experimental characterization. With sufficient defect engineering, we show that Li₃BS₃ is a superionic conductor with room temperature ionic conductivity greater than 1 mS cm⁻¹. While the semi-supervised method shows promise for identification of superionic conductors, the results illustrate a continued need for descriptors that explicitly encode for defects.

Example 1A: Semi-Supervised Machine Learning Approach for Identification of Candidate Solid State Li-ion Conductors or Lithium Solid State Electrolytes

Identifying new materials that could improve solid-state ion battery prospects is an ongoing challenge. The search for an ideal solid-state Li electrolyte is a prime example. Research has focused on eight classes of materials: LISICON-type structures, argyrodites, garnets, NASICON-type structures, Li-nitrides, Li-hydrides, perovskites, and Li-halides¹. However, only three compounds with near-liquid-electrolyte conductivity (˜10⁻² S cm⁻¹) have been discovered: Li₁₀GeP₂S₁₂ (LGPS)², Li₆PS₅Br argyrodite³, and Li₇P₃S₁₁ ceramic-glass^1,4. Although promising discoveries, all three high-conductivity structures are unstable against the Li anode^5-10. While investigations to limit instability are ongoing^11,12, identification of additional superionic structures is desirable. Discovery of new structures that support superionic conductivity improves the odds of identifying or engineering a stable electrode|SSE interface. For example, engineering solutions that fail to stabilize the Li|argyrodite interface may prove more successful when applied to not-yet-discovered superionic conductors. Discovery of new superionic conductors may also enable stable architectures via multi-electrolyte approaches which have been proposed as more promising than single-electrolyte architectures for achieving stability against Li metal and cathode materials¹³. High-performing structures that enable new battery chemistries may exist outside of the eight classes. However, exploration under the traditional Edisonian approach prioritizes small perturbations to well-known variable spaces.

Machine learning (ML) is a promising tool for expediting the discovery of useful solid-state materials. By describing prospective materials with physically meaningful descriptors, ML models can identify high-dimensional patterns in large datasets that are not readily apparent^14-20. Ongoing descriptor engineering^21-26 has enabled discovery of battery components^27,28, electrocatalysts^15,29, photovoltaic components^16,30, piezoelectrics³¹, new metallic glasses¹⁴ and new alloys³². However, application of ML for discovery of SSEs and other emerging technologies can be challenging. Supervised ML approaches require empirical data for use as “labels”. For example, graph neural network (GNN) approaches have been successful in many domains but generally require thousands to tens of thousands of labels to avoid overfitting³³. By contrast, relatively few SSEs have been experimentally characterized compared to the ˜26,000 known Li-containing structures^19,34-36. Characterized materials often exhibit ill-defined properties owing to the variety of synthetic approaches and non-standardized testing methods³⁷. Well-performing materials often contain charge-carrying defects that are not explicitly characterized or reported³⁸. Negative examples, i.e. materials with undesirable properties, are useful for ML models but are seldom reported.

Semi-supervised ML can guide synthetic prioritization of SSEs by overcoming the issues associated with label scarcity. Supervised ML requires labels because it infers correlation functions by mapping the input descriptors to the labels³⁹. Semi-supervised ML prioritizes comparison of descriptors to identify relationships between the descriptors in a dataset^36,39. The input compositions are clustered (or grouped) by comparison of descriptors using a similarity metric. The clustering process does not consider labels, and thus circumvents the need for abundant labels. The resultant clusters can be labeled ex post facto to examine correlation between the descriptor and a physical property of interest. For semi-supervised ML, ideal descriptors result in a set of clusters where each cluster has similar labels and thus the label variance is minimized. Promising synthetic targets may then be identified by their membership in clusters that contain desirable labels.

A key insight of this work is that semi-supervised ML can be used to rank descriptors in terms of their correlation to physical properties of interest. Descriptors are representations of the input materials that encode the chemistry, composition, structure, and/or other system properties. An ideal descriptor should be a unique representation, a continuous function of the structure, exhibit rotational/translational invariance, and be readily comparable across all structures in the dataset^24-26. Recently, Zhang et al. demonstrated that a modified X-Ray diffraction (mXRD) descriptor lead to favorable clustering for Li SSEs³⁴. By labeling the resultant clusters with experimental room-temperature Li-ion conductivities, they identified 16 prospective fast-ion conductors. However, an ideal descriptor is not known a priori, and no comprehensive descriptor screening has yet been pursued for correlation with SSE properties. Descriptor screening is desirable for both experimentalists and computationalists. For experimentalists, ranking of descriptors affords insight into what aspects of materials are most correlated with target properties. For computationalists, descriptors rankings enable improved regression and supervised learning models by guiding the selection of input representation(s). Descriptor transformations for inorganic structures have been curated in a variety of software packages, including: Matminer²⁴, Dscribe²⁵, SchNet⁴⁰, and Aenet⁴¹

Herein, we employ hierarchical agglomerative clustering to screen many descriptors, without assuming correlation to ionic conductivity. The performance of 20 descriptors is assessed for semi-supervised identification of Li SSEs. Each descriptor is paired with 9 structural simplification strategies, yielding a total of 180 unique representations per input structure. The approach is applied to a dataset of ˜26,000 Li-containing phases, encompassing all Li-containing structures contained in the Inorganic Crystal Structure Database (ICSD—v.4.4.0) and the Materials Project (MP—v.2020.09.08) database (FIG. 1). A set of 220 experimental room temperature ionic conductivities (σ_{25° C.}) are aggregated from literature reports and used as labels. Experimental labels are selected because they may bias models towards identifying structures that are synthetically tractable and processable. Descriptors that encode the spatial environment are found to be most correlated with the ionic conductivity labels. Whereas descriptors that encode the electronic, compositional, or bonding environment have less predictive power. For the structural descriptors, simplifications that neglect the mobile ion perform best. The descriptor screening results suggest that ionic conductivity is most sensitive to the spatial environment of the framework lattice.

Using the descriptors, the semi-supervised approach can identify potential fast solid-state Li-ion conductors. By selecting structures in clusters containing high conductivity labels, the ˜26,000 input structures are down selected to just 212 promising structures. Practical considerations, a semi-empirical bond valence site energy (BVSE) method,⁴² and the Nudged Elastic Band (NEB) method are employed to rank the structures. From the ten highest ranking structures, Li₃BS₃ is selected for model validation. Synthesis of pure Li₃BS₃ yields a poor conductor. However, by employing defect engineering strategies we demonstrate that Li₃BS₃ is a superionic conductor with an ionic conductivity greater than 10⁻³ S cm⁻¹.

Screening Simplification-Descriptor Combinations:

A set of 20 descriptors is selected for screening the semi-supervised learning approach (Table 1). The descriptors generally encode four types of information: the spatial environment, the chemical bonding environment, the electronic environment, and composition. All descriptors are implemented in Python using the Matminer²⁴ or Dscribe²⁵ libraries. The code is published to a github repository and is available for download (https://github.com/FALL-ML/materials-discovery). Zhang et al. illustrated that structure simplification prior to learning can produce lower variance outcomes³⁴. Their mXRD descriptor was found to work best with removal of all cations, all the anions replaced by a single representative anion, and the structure volume scaled to 40 ų per anion. Inspired by the previous success in using structure simplification, we screen eight structure simplifications in addition to the unperturbed structure. For simplifications the following categories of atoms are replaced with a representative specie: (1) Cations are represented as Al, (2) Anions are represented as S, (3) Mobile ions are represented as Li, and (4) Neutral atoms are represented as Mg. Categories of atom are removed as to yield the four simplifications: CAMN (all atoms retained), CAN (mobile ions removed), AM (cations and neutral atoms removed), and A (only anions retained). Four additional simplifications are formed by scaling each lattice volume to 40 ų per anion: CAMN-40, CAN-40, AM-40, and A-40.

TABLE 1
The descriptors used for agglomerative clustering. Descriptor vectors are attained
by simplifying the input structures and then applying the descriptor transformation.
In total, 180 unique descriptor vectors are screened for each structure.
Descriptor	Descriptor Description	Refs
Bond Fraction	“Bag of bonds” approach described in Hansen et. al. wherein	43
	pairwise nuclear charges and distances are encoded.
Band Center	Estimation of band center from constituent atoms'	44
	electronegativity values described by Butler et al.
Crystal Structure Analysis by	Calculation of the largest sphere that can pass through the	45
Voronoi Decomposition	lattice-sans-mobile-ion using Voronoi decomposition of
(CAVD)	structures.
Chemical Ordering	Warren-Cowley-like ordering method to determine how different	46
	the structure's ordering is from random.
Density Features	Calculates density, volume per atom, and the packing fraction.	47
Electronegativity Difference	Composition weighted calculation of the electronegativity	48
	difference between cations and anions.
Ewald Energy	Sum of coulomb interaction energies across all lattice sites	49
	described by Ewald et al.
Global Instability Index	Averaged square root of the sum of squared differences over
	the bond valence sums.
Jarvis	Diverse set of descriptors from the Jarvis-ML library.	50
Maximum Packing Efficiency	A measure of the void space within the unit cell.	46
Meredig	Composite descriptor from Meredig et al.	51
Modified XRD (mXRD)	Powder diffraction pattern calculated using Bragg's law.	47
Orbital Field Matrix	Descriptor that encodes the distribution of valence shell	52
	electrons for each input structure.
Oxidation States	Concentration weighted oxidation state statistics.	48
Radial Distribution Function	Radial distribution function for each structure.	47
Sine Coulomb Matrix	Coulomb matrix for periodic lattices, developed by Faber et al.	53,54
Smooth Overlap of Atomic	Geometric encoder that is rotationally/transitionally invariant	25
Positions (SOAP)	through use of spherical harmonics and radial basis functions.
	Atoms are represented by a smeared gaussian.
Structural Complexity	The Shannon information entropy for a given structure.	55
Structure Variance	Bond length and atomic volume variance for each structure.	46
Valence Orbital	Structure averaged number of valence electrons in each orbital.	48,56
Control	A control descriptor is not explicitly used. Instead, clustering
	outcomes are randomly assigned. For composite intracluster
	variance calculations, 100 control iterations are averaged.

Agglomerative clustering is performed on all Li-containing structures from the ICSD and MP repositories. Agglomerative clustering is a “bottom-up” approach to clustering where each structure starts in its own cluster of one. Clusters are merged according to Ward's Minimum Variance criterion in Euclidean space, which minimizes the global descriptor variance⁵⁷.

$W=\sum _{k=1}^{n_c}\sum _{i\in C_k}{\left[d_i-{\overline{d}}_k\right]}^2$

where n_C is the number of clusters in a set, C_k is cluster k, di is a descriptor representation for structure i, and d_k is the average descriptor representation in cluster k. Each cluster merger results in the lowest variance set of clusters, relative to all other possible mergers. Other common linkage criteria (average, complete, and single linkages) and metrics (I1, I2, manhatten, cosine) were screened but are found to result in clustering outcomes with larger W. For each simplification-descriptor combination, all clustering sets from 2-300 are computed. Physically relevant labels are applied to the resultant clustering sets to assess how well each simplification-descriptor combination performs. To compare between the 180 different simplification-descriptions combinations, the data is labeled with 155 experimental room temperature conductivity (σ_RT) values aggregated from the literature reports (see Example 1B: sections I-IV). A secondary label set is also screened, comprised of 6845 activation energies (E_a) computationally generated using a bond valence energy approach (see Example 1B: section V).

An ideal simplification-descriptor combination results in clustering where each cluster contains labels with similar σ_RT values. Ward's minimum variance method is applied to the conductivity labels as a measure of clustering efficacy:

$W_{\sigma }=\sum _{k=1}^{n_c}\sum _{i\in C_k}{\left[{\log \left({\sigma }_{RT}\right)}_i-{\stackrel{\_}{\log \left({\sigma }_{RT}\right)}}_k\right]}^2$

where n_C is the number of clusters in a set, C_k is cluster k, and log(σ_RT)_kdenotes the mean for all labels in cluster k. Since clusters containing only one label effectively drop out of the W_σ calculation, a frozen-state strategy is employed when needed (see Example 1B: section IV). Each descriptor's W_σ results are shown in FIG. 2 for the first 50 clustering outcomes (i.e. the W_σ is shown for each set of 2, 3, . . . , 49, and 50 clusters). For simplicity, only the best-performing simplification-descriptor combination is shown for each descriptor.

Using σ_{25° C.} labels, the best semi-supervised ML performance is attained when using the SOAP descriptor. SOAP is a spatial descriptor that employs smeared gaussians to represent atomic positions for each crystal structure²⁵. Predictions using the SOAP descriptor have exhibited similar performance to state-of-the-art graph neural networks (GCNs) on a variety of materials science datasets⁵⁸. Optimization of SOAP hyper-parameters (radial cutoff, number of radial basis functions, degree of spherical harmonics) is explored in section VI of the supplemental information. SOAP is found to perform best when combined with the CAN structure simplification. That is, the simplification where the mobile Li atoms are removed, and the remaining atoms are simplified into three representative species: cations, anions, and neutral atoms. SOAP outperforms all other descriptors for all depths of clustering. The SOAP descriptor can be modestly improved (2-3% decrease in W_Q) by mixing with other descriptors to make a 2^nd order SOAP descriptor (see Example 1B: section VI).

Semi-Supervised Identification of Prospective Li-Ion Conductors:

Agglomerative clustering with the 2^nd order SOAP descriptor is used to identify prospective ionic conductors. W_σ minimization is prioritized over W_Ea minimization because E_a alone is not necessarily a good predictor of conductivity; σ_{25° C.} may be affected by properties including the ionic carrier concentration, hopping attempt frequency, and the presence of concerted migration modes⁵⁹. The agglomerative dendrogram for the 2^nd order SOAP is shown in FIG. 3, with the label densities plotted below. The agglomerative dendrogram is depicted to 241 clusters, after which the W_Q does not appreciably decrease. To facilitate discussion, an arbitrary cutoff is placed to yield 9 large clusters. The results show that although cluster #2 contains only 15% of the input structures, it accounts for over half of the high-conductivity (σ_{25° C.}>10⁻⁵ S cm⁻¹) labels. By the 17^th clustering step, the densest cluster accounts for 6.2% of the structures while containing over half (52%) of the high-conductivity labels.

Candidates for next-generation SSEs can be identified by evaluating clusters that either contain or are near high conductivity labels. Clusters #2, #4, and #7 are promising because they account for 85% of the high σ_{25° C.} labels. However, targeting these clusters would necessitate screening thousands of structures. Instead, we search from the 241^st cluster depth, targeting all clusters that contain or are directly adjacent (i.e. the nearest cluster in the Euclidean feature space) to high σ_{25° C.} labels. The promising structures are further screened using calculated stability (E vs. E_hull) and band gap (E_g) properties from the Materials Project, and the BVSE E_a values. We select the structures that have (1) an E_hull of 70 meV or lower,⁶⁰ (2) an E_g of at least 1 eV, and (3) a BVSE-calculated E_a below a conservative 0.6 eV. We note that while a true E_g value of 1 eV would be problematic for an SSE, the bandgaps reported on Materials Project are typically underestimated by about 40%⁶¹. The approach identifies 212 structures as prospective ionic conductors. Climbing image nudged elastic band (CI-NEB) is employed to calculate the E_a for Li-ion hopping on the ten materials with the lowest BVSE-calculated E_a and an E_hull of 0 eV. The CI-NEB functionals and parameters can be found in the supporting information section VII. The top 10 prospective structures are tabulated in Table 2.

TABLE 2
The top 10 prospective structures from the semi-supervised learning model as
ranked by BVSE−calculated Ea. Structures in or directly adjacent to high-
conductivity clusters were identified as promising. The list of promising structures was then
further simplified by removing structures with Materials Project reported Ehull values greater
than 0 V and Eg values less than 1 eV. To rank the remaining structures, the Ea
was calculated using BVSE and NEB approaches.
	E vs. Ehull	Eg	Ea—calc (meV)
compound	space group	MP_ID	ICSD_ID	(eV/atom)	(eV)	BVSE	NEB
Li3VS4	P43m (#215)	mp-760375		0	1.88	160	390
Na3Li3Al2F12	Ia3d (#230)	mp-6711	9923	0	7.85	230	340
Li2Te	Fm3m (#225)	mp-2530	60434	0	2.49	260	320
LiAlTe2	I42d (#122)	mp-4586	280226	0	2.46	260	310
LiInTe2	I42d (#122)	mp-20782	658016	0	1.49	270	450
Li6MnS4	P42/nmc (#137)	mp-756490		0	1.55	270	466
LiGaTe2	I42d (#122)	mp-5048	162555	0	1.59	270	340
Li3BS3	Pnma (#62)	mp-5614	380104	0	2.89	280	260
KLi6TaO6	R3m (#166)	mp-9059	73159	0	4.27	300	404
Li3CuS2	Ibam (#72)	mp-1177695		0	2.03	310	440

The CI-NEB calculations generally agree with the BVSE calculated E_a values, suggesting favorable activation energies (<500 meV). Discrepancies between the two values may arise because BVSE does not allow framework ions to relax during Li⁺ migration and does not account for repulsive interactions between atoms of the mobile ion species. BVSE also does not capture cooperative conduction mechanisms or those involving the so-called paddlewheel effect. Despite these limitations, we note that the model identifies numerous diverse structures beyond those routinely explored. Table 1 includes four tellurides, a vanadium sulfide, and multiple transition-metal-containing structures. Of the structures in Table 1, 70% avoid the space groups for the best-performing SSEs discovered to date: LPS (62), LGPS (137), the argyrodites (216), and LLZO (230).

Data Processing and Semi-Supervised Learning:

The ˜26,000 input compositions are exported from the Inorganic Crystalline Structure Database (ICSD v. 4.4.0) and Material's Project (MP—v.2020.09.08) as crystallographic information files (.cif). All structures containing Li are imported. Although transition metals could produce undesirable redox activity, transition metal containing structures are not screened out. Some of the best-performing SSEs contain transition metals (e.g. LLZO and LLTO). Entries that existed in both ICSD and MP are merged. Data manipulations and structure simplifications are performed using the Python libraries NumPy (v1.19.1), Pandas (v1.0.5), ASE (v3.19.1), and Pymatgen (v2020.8.3). Descriptor transformations are performed using the Python libraries Pymatgen (v2020.8.3), Matminer (v0.6.3), and Dscribe. Agglomerative hierarchical clustering is performed using the Python library scipy (v1.5.0). All code has been successfully executed on a custom-built CPU with an AMD Ryzen Threadripper 3990x Processor and 256 GB of RAM, in Ubuntu 20.04 running on Windows Subsystem for Linux 2. All code is made available on the github (https://github.com/FALL-ML/materials-discovery).

CI-NEB:

Migration barriers for Li ion hopping are evaluated with the Climbing Image—Nudged Elastic Band (CI-NEB) method as implemented in the QuantumESPRESSO PWneb software package^81-84. Density-functional theory (DFT) calculations are performed using the Perdew-Burke-Ernzerfof (PBE) generalized gradient approximation functional and projector-augmented wave (PAW) sets^85,86. Convergence testing for the kinetic-energy cutoff of the plane-wave basis and the k-point sampling is performed for each structure to ensure an accuracy of 1 meV per atom. The lattice parameters and atomic positions of the as-retrieved structure are optimized. Supercells are created for each structure that are a minimum of 10 Å in each lattice direction to minimize interactions between periodic images of the mobile ion. To study the migration barrier in the dilute limit, a single Li vacancy is created in the boundary endpoint structures of each studied pathway. A uniform background charge is used to balance excess charge. Each boundary configuration is relaxed until the force on each atom is less than 3×10⁻⁴ eV/Å. Images are created by linearly interpolating framework atomic positions between the initial and final boundary configurations. The initial pathway for the mobile ion is generated from the BVSE output minimum energy pathway to promote faster convergence of the NEB calculation. An NEB force convergence threshold of 0.05 eV/Å is used. The calculation is first converged using the default NEB algorithm and then restarted with the CI scheme to allow for the maximum energy of the pathway to be determined.

Example 1B: Additional Aspects and Details for Semi-Supervised Machine Learning Approach for Identification of Candidate Solid State Li-ion Conductors or Lithium Solid State Electrolytes

Section I. Digitized Labels for Lithium-Ion Conductors: RT Conductivity, Activation Energy, and Corresponding ICSD Identifier

Data labels for the semi-supervised learning approach were ultimately digitized from over 300 literature publications. Many more publications were initially examined. The stepwise decision chart below was used as a guide for deciding what data to digitize. Room temperature conductivity data was only digitized if it originated from an equivalent circuit fit (where a blocking feature was clearly present) or if calculated from NMR. DC techniques were categorically discounted because they cannot differentiate between electronic and ionic conductivity.

All of the digitized data is presented in the subsequent tableI. Activation energies were also digitized when available. The activation energies were not used in the manuscript but are still presented here to aid future machine learning endeavors. The digitized data was manually matched with the appropriate ICSD ID, so that the crystallographic information file (.cif) can be downloaded.

	σ25° C.	Ea	Space	Space	Other
Compound	(S cm−1)	(eV)	Group	Group #	names	ICSD	Citation
LiAlSi3O8	1.30E−10		C1	2		81980	1
LiSn2(PO4)3	2.04E−9		P1	2		83832	2
Li7BiO6	8.80E−07	0.58	P1	2		155950	3
Li7SbO6	6.70E−08	0.7	P1	2		413370	3
Li7P3S11	1.70E−02	0.17	P1	2		157654	4
Li7P3S11	3.2E−3	0.124	P1	2		157654	5
LiV(PO4)F	8.1E−7	0.23	P1	2		183876	6
Li2B3PO8	5.80E−15	0.76	P1	2		248343	7
Li3BP2O8	9.60E−12	0.62	P1	2		248343	7
Li2NaBP2O8	4.40E−18	1.21	P1	2		291512	7
Li4P2O7	<1E−10	1.617	P1	2		248414	8
LiMgSO4F	5.40E−08	0.54	P1	2		281119	9
Li6CuB4O10	1.00E−13	0.92	P1	2	β-Li6CuB4O10	4819	10
Li0.91Hf2.022(PO4)3	<1E−10	0.47	C1	2			11
Li7P3S11	8.6E−3	0.29	P1	2			12
Li2ZnGeO4	1.00E−07	0.4	Pc	7		34362	13
Li3.8Ge0.8P0.2S4	1.78E−6	0.47	P21/m	11			14
Li3.6Ge0.6P0.4S4	1.75E−4	0.34	P21/m	11			14
Li3.4Ge0.4P0.6S4	6.54E−4	0.28	P21/m	11			14
Li3.35Ge0.35P0.65S4	1.54E−3	0.23	P21/m	11			14
Li3.3Ge0.3P0.7S4	1.74E−3	0.22	P21/m	11			14
Li3.25Ge0.25P0.75S4	2.2E−03	0.207	P21/m	11			14
Li3.2Ge0.2P0.8S4	5.55E−4	0.27	P21/m	11			14
Li4SiS4	5.00E−08	0.56	P21/m	11		59708	15
Li7.22Si1.5P0.5O8	1.64E−7	0.48	P21/m	11		238602	16
Li4SiO4	5.00E−10	0.55	P21/m	11		238603	17
Li4SiS4	1.59E−8	0.56	P21/m	11			18
Li3.8Si0.8P0.2S4	8.11E−7	0.37	P21/m	11			18
Li3.6Si0.6P0.4S4	7.19E−5	0.34	P21/m	11			18
Li3.5Si0.5P0.5S4	1.66E−4	0.34	P21/m	11			18
Li3.4Si0.4P0.6S4	6.62E−4	0.29	P21/m	11			18
Li3.3Si0.3P0.7S4	1.02E−5	0.36	P21/m	11			18
Li3.2Si0.2P0.8S4	3.20E−6	0.37	P21/m	11			18
Li4SiS4	1.62E−8	0.56	P21/m	11			18
Li3.8Si0.8P0.2S4	8.07E−7	0.37	P21/m	11			18
Li3.6Si0.6P0.4S4	7.11E−5	0.34	P21/m	11			18
Li3.5Si0.5P0.5S4	1.61E−4	0.34	P21/m	11			18
Li3.4Si0.4P0.6S4	6.49E−4	0.29	P21/m	11			18
Li3.3Si0.3P0.7S4	9.84E−6	0.36	P21/m	11			18
Li3.2Si0.2P0.8S4	3.05E−6	0.37	P21/m	11			18
Li3.1P0.9Si0.1O4	7.47E−8		P21/m	11			19
Li3.5P0.5Si0.5O4	2.89E−6		P21/m	11			19
Li3.9P0.1Si0.9O4	1.99E−8		P21/m	11			19
Li3.7P0.3Si0.7O4	3.84E−7		P21/m	11		35168	19
Li3InCl6	2.04E−3	0.35	C2/m	12		89617	20
Li2P2S6	7.80E−11	0.48	C2/m	12		253894	21
Li0.6[Li0.2Sn0.8S2]	1.2E−4	0.17	C2/m	12			22
Li3(Mo8S8O8(OH)8(HWO5(H2O)))*(H2O)18	3.8E−7	0.62	C2/m	12		412011	23
Li17Sb13S28	1.05E−9	0.4	C2/m	12		429902	24
Li3InBr6	9.04E−4		C2/m	12			25
Li3YBr6	1.92E−3	0.37	C2/m	12			26
Li0.84Sn0.79S2	1.2E−4	0.17	C2/m	12			27
LiAlSi4O10	1.01E−10		P2/c	13		194284	1
LiPO3	1.00E−09		P2/c	13		51630	28
LiGaBr4	7.00E−6	0.54	P21/c	14		61337	25
Li2SO4	1.40E−14	1.1	P21/c	14		2512	29
Li3BO3	7.40E−11	0.63	P21/c	14		9105	30
Li6Ge2O7	8.50E−07	0.43	P21/c	14		31050	31
LiAlCl4	1.00E−06	0.47	P21/c	14		35275	32
LiYO2	1.80E−08	0.72	P21/c	14		45511	33
LiBO2	1.00E−08	0.71	P21/c	14		200891	34
LiClC3H7NO	1.6E−4	0.881	P21/c	14		238683	35
LaLiO2	<1E−10	0.92	P21/c	14		239278	36
(La0.9Sr0.1)LiO2	6.29E−10	0.62	P21/c	14		239279	36
La(Li0.76Mg0.08)O2	7.27E−10	0.66	P21/c	14		239280	36
Li2.5V2(PO4)3	1.9E−7		P21/c	14		240269	37
Li4Zn(PO4)2	<1E−10	1.3	P21/c	14	α-Li4Zn(PO4)2	255464	38
LiSbO2	<1E−10	0.88	P21/c	14		262075	39
Li2Sr2Al(PO4)3	<1E−10	1.02	P21/c	14		431319	40
Li2ZrO3	6.10E−10	0.78	C2/c	15		94894	33
Li6Zr2O7	5.20E−10	0.68	C2/c	15		73835	41
Li3AlF6	5.00E−07	0.54	C2/c	15		85171	42
Li2SnS3	1.50E−05	0.59	C2/c	15		251656	43
LiTa2PO8	1.6E−3	0.32	C2/c	15		267438	44
LiBaP2O7	1.00E−10		C2/c	15		280927	45
Li3Na5(TiS4)2	8.80E−06	0.4	C2/c	15		391258	46
LiGd(PO3)4	<1E−10	1.7	C2/c	15		416442	47
LiVO3	2.048E−9		C2/c	15		51443	48
Li2CrCl4	<1E−10	1.22	C2/c	15		202627	49
Li3ErI6	9.92E−5	0.37	C2/c	15			50
Li3.7Zn0.7Ga0.3(PO4)2	<1E−10	0.91	P212121	19	β′-	255466	38
					Li3.7Zn0.7Ga0.3(PO4)2
Li3SbS4	1.5E−6	0.518	Pmn21	31		8407	51
Li3PS4	2.60E−07	0.49	Pmn21	31	γ-Li3PS4	180318	52
LiGaO2	2.40E−14	0.86	Pna21	33		18152	53
LiB6OgF	5.40E−24	1.38	Pna21	33		420286	54
Li3SbS3	1.00E−07	0.4	Pna21	33		424834	55
LiSi2N3	6.17E−08	0.64	Cmc21	36		34118	56
Li2(PO2N)	<1E−10	0.57	Cmc21	36		188493	57
LiGa2GeS6	3.80E−08	0.47	Fdd2	43		254406	58
La0.64Li0.08TiO3	3.35E−4		Pmmm	47		92228	59
La0.62Li0.14TiO3	4.42E−4		Pmmm	47		92231	59
La0.595Li0.215TiO3	8.53E−4		Pmmm	47		92234	59
Li0.4Na0.1La0.5Nb2O6	9.92E−6		Pmmm	47		180629	60
Li0.3Na0.2La0.5Nb2O6	1.11E−5		Pmmm	47		180630	60
Li0.2Na0.3La0.5Nb2O6	1.18E−5		Pmmm	47		180631	60
Li0.1Na0.4La0.5Nb2O6	1.21E−5		Pmmm	47		180632	60
Li0.07Na0.43La0.5Nb2O6	1.23E−5		Pmmm	47		180633	60
Li0.04Na0.46La0.5Nb2O6	5.91E−6		Pmmm	47		180634	60
Li0.02Na0.48La0.5Nb2O6	3.99E−6		Pmmm	47		180635	60
(Ag0.33Li0.67)0.27La0.57TiO3	1E−4	0.30	Pmmm	47			61
(Ag0.5Li0.5)0.27La0.57TiO3	2.3E−5	0.28	Pmmm	47			61
(Ag0.67Li0.33)0.27La0.57TiO3	2E−7	0.37	Pmmm	47			61
Pr0.56Li0.34TiO3.01	1E−6	0.47	Pmmm	47			62
Nd0.55Li0.34TiO3	8E−7	0.53	Pmmm	47			62
Li0.09La0.77TiO3	1.23E−4		Pmmm	47			63
Li0.15La0.72TiO3	4.14E−4		Pmmm	47			63
Li0.24La0.65TiO3	5.77E−4		Pmmm	47			63
Li0.12La0.75TiO3	2.38E−4		Pmmm	47			63
Li0.16La0.7TiO3	5.21E−4		Pmmm	47			63
Li0.23La0.7TiO3	5.26E−4		Pmmm	47			63
Li5AlO4	5.00E−10	0.99	Pmmn	59		16229	64
Li14Nd5(Si11N19O5)O2F2	1.7E−10	0.69	Pmmn	59		262923	65
Li5GaO4	5.00E−09	0.71	Pbca	61	α-Li5GaO4	9082	64
Li2SiN2	1.60E−07		Pbca	61		420126	66
Li6.5O8P1.5Si0.5	4.49E−07	0.44	Pnma	62		238600	16
Li3.4Si0.7S0.3O4	4.21E−7		Pnma	62		47145	67
Li3.2Si0.6S0.4O4	1.32E−6		Pnma	62			67
Li3.1Si0.55S0.45O4	3.14E−7		Pnma	62			67
Li6.6SiPO8	1.48E−7	0.49	Pnma	62		238601	16
Li4.2Si0.8Al0.2S4	2.40E−8	0.53	Pnma	62			18
Li4.4Si0.6Al0.4S4	3.04E−8	0.52	Pnma	62			18
Li4.6Si0.4Al0.6S4	1.45E−8	0.52	Pnma	62			18
Li4.8Si0.2Al0.8S4	2.25E−7	0.52	Pnma	62			18
Li3.8Si0.8Al0.2S4	2.38E−8	0.53	Pnma	62			18
Li3.6Si0.6Al0.4S4	3.06E−8	0.52	Pnma	62			18
Li3.4Si0.4Al0.6S4	1.45E−8	0.52	Pnma	62			18
Li3.2Si0.2Al0.8S4	2.28E−7	0.52	Pnma	62			18
Li4Zn(PO4)2	<1E−10	1.1	Pnma	62	β-Li4Zn(PO4)2	255465	38
Li3.5Zn0.5Ga0.5(PO4)2	<1E−10	1.02	Pnma	62	β-Li3.5Zn0.5Ga0.5(PO4)2	255468	38
Li3PS4	1.60E−04	0.36	Pnma	62	β-Li3PS4	180319	52
Li3PO4	<1E−10	1.14	Pnma	62	γ-Li3PO4	20208	68
Li3PS4	3.00E−7		Pnma	62	γ-Li3PS4	35018	69
Li2.88PO3.73N0.14	1.4E−13	0.97	Pnma	62		79426	70
Li3PO4	4.2E−18	1.24	Pnma	62	γ-Li3PO4	79427	70
Li4GeS4	2E−7	0.53	Pnma	62		92200	71
Li14Zn(GeO4)4	1.00E−06	0.24	Pnma	62		100169	72
Li3.75Ge0.75V0.25O4	5.66E−6		Pnma	62		150918	73
Li3.70Ge0.85W0.15O4	3.80E−5		Pnma	62		150920	73
Li0.2Ca0.4TaO3	3.53E−9	0.54	Pnma	62		151936	74
Li0.2(Ca0.36Sr0.04)TaO3	9.2E−9		Pnma	62		151937	74
Li2Mg2(MoO4)3	<1E−10	0.71	Pnma	62		170956	75
Li4SnSe4	2E−5	0.45	Pnma	62		193768	76
Li(BH4)	1E−8		Pnma	62		239763	77
LiZnSO4F	2.80E−05	0.2455	Pnma	62		261343	78
Li4GeS4	2.00E−07	0.53	Pnma	62		290831	79
Li4SnS4	7.0E−5	0.29	Pnma	62		290832	80
Li2ZnI4	4.00E−08	0.58	Pnma	62		402062	81
Pr0.53Li0.41TiO3	0.84E−7	0.462	Pnma	62			82
Pr0.54Li0.38TiO3	1.18E−6	0.452	Pnma	62			82
Pr0.55Li0.35TiO3	1.51E−6	0.441	Pnma	62			82
Pr0.56Li0.32TiO3	1.91E−6	0.437	Pnma	62			82
Pr0.57Li0.29TiO3	2.86E−6	0.429	Pnma	62			82
Pr0.58Li0.26TiO3	3.87E−6	0.421	Pnma	62			82
Pr0.59Li0.23TiO3	3.40E−6	0.425	Pnma	62			82
Li2.5Y0.5Zr0.5Cl6	1.4E−3	0.33	Pnma	62			83
Li2.633Er0.633Zr0.367Cl6	1.1E−3	0.35	Pnma	62			83
Li3.33Ge0.33V0.67O4	6.94E−6		Pnma	62			84
Li3.6Ge0.6V0.4O4	1.97E−5	0.44	Pnma	62			84
Li3.75Ge0.75V0.25O4	1.08E−5		Pnma	62			84
Li3.5Ge0.5V0.5O4	1.77E−5		Pnma	62		66576	84
Li3.87Sn0.87As0.13S4	1.48E−5	0.39	Pnma	62			85
Li3.855Sn0.855As0.145S4	1.31E−4	0.35	Pnma	62			85
Li3.85Sn0.85As0.15S4	2.08E−4	0.31	Pnma	62			85
Li3.84Sn0.84As0.16S4	5.85E−4	0.29	Pnma	62			85
Li3.83Sn0.83As0.17S4	1.39E−3	0.21	Pnma	62			85
Li3.825Sn0.825As0.175S4	5.18E−4	0.27	Pnma	62			85
Li3.82Sn0.82As0.18S4	2.83E−4	0.35	Pnma	62			85
Li3.8Sn0.8As0.2S4	1.06E−4	0.4	Pnma	62			85
Li3.75Sn0.75As0.25S4	3.69E−6	0.48	Pnma	62			85
Nd0.54Li0.36TiO3	3.42E−8	0.50	Pnma	62		81047	86
Pr0.51Li0.39TiO2.96	5.34E−7	0.44	Pnma	62		81048	86
Sm0.52Li0.38TiO2.97	2E−7	0.64	Pnma	62			62
Li4GeO4	2.80E−10	0.73	Cmcm	63		18096	87
LiCl*H2O	1E−8	0.777	Cmcm	63		281198	88
Li2MgBr4	7.80E−10	0.77	Cmmm	65		73276	89
Li0.22La0.60TiO3	4.8E−4	0.391	Cmmm	65			90
Li0.18La0.61TiO3	2.0E−4	0.432	Cmmm	65		99398	90
LiBiO2	3.80E−08	0.1	Ibam	72		46022	30
Li2.5Zn0.25PS4	8.40E−4		I4	82			69
LiZnPS4	5.4E−8		I4	82		95785	69
Li2Zn0.5PS4	1.30E−4	0.22	I4	82		264462	69
(Li1.69Zn0.66)PS4	1.30E−4	0.181	I4	82		264462	69
Li1.5Zn0.75PS4	1.65E−5	0.25	I4	82		264463	69
(Li1.19Zn0.9)PS4	0.65E−5	0.25	I4	82		264463	69
(Li0.5Ce0.5)(MoO4)	1.3E−8	0.4	I41/a	88		186450	91
(Li0.5Ce0.25Pr0.25)(MoO4)	1E−9	0.5	I41/a	88		186451	91
(Li0.5Ce0.25Sm0.25)(MoO4)	1.8E−10	0.5	I41/a	88		186452	91
Li2TeO4	<1E−10	1.129	P4122	91		1485	92
Li3BN2	1.60E−10	0.67	P42212	94	α-Li3BN2	655673	93
Li2B4O7	1.00E−10		I41cd	110		65930	94
LiY(BH4)4	1.26E−6		P42c	112		239762	77
LiPN2	1.6E−7	0.40	I42d	122		66007	95
La0.565Li0.305TiO3	9.57E−4		P4/mmm	123		92235	59
La0.5Li0.5TiO3	9.25E−4	0.39	P4/mmm	123		92236	59
Li0.33La0.5TiO3	1E−3	0.15	P4/mmm	123		82671	96
Li0.27La0.57TiO3	3.4E−4	0.38	P4/mmm	123			61
La0.61Li0.18TiO3	4.12e-4		P4/mmm	123			97
La0.55Li0.36TiO3	6.88E−4	0.35	P4/mmm	123			97
La0.54Li0.39TiO3	6.51E−4		P4/mmm	123			97
La0.52Li0.45TiO3	5.01E−4		P4/mmm	123		50434	97
La0.58Li0.27TiO3	5.99E−4		P4/mmm	123		82672	97
La0.56Li0.33TiO3	6.68E−4		P4/mmm	123		504435	97
Li0.31La0.63TiO3	4.11E−4		P4/mmm	123			63
Li0.39La0.59TiO3	8.83E−4		P4/mmm	123			63
Li0.49La0.55TiO3	9.39E−4		P4/mmm	123			63
Li0.68La0.49TiO3	1.03E−3		P4/mmm	123			63
Li0.24La0.65TiO3	9.57E−4		P4/mmm	123			63
Li0.33La0.58TiO3	8.93E−4		P4/mmm	123			63
Li0.36La0.55TiO3	9.34E−4		P4/mmm	123			63
Li0.42La0.52TiO3	8.47E−4		P4/mmm	123			63
Li0.29La0.57TiO3	4.4E−5	0.453	P4/mmm	123			90
La0.56Li0.33TiO3	1.65E−4	0.41	P4/mmm	123			98
La0.56Li0.33TiO3-5 wt % Al2O3	1.66E−4	0.24	P4/mmm	123			98
La0.56Li0.33TiO3-10 wt % Al2O3	9.33E−4	0.17	P4/mmm	123			98
La0.56Li0.33TiO3-15 wt % Al2O3	9.56E−5	0.50	P4/mmm	123			98
Li(LaTiO4)	<1E−10	0.83	P4/nmm Z	129		91843	99
Li(NdTiO4)	<1E−10	0.87	P4/nmm Z	129		91844	99
La0.65Li0.05(Mg0.5W0.5)O3	1.8E−7	0.46	P4/nmm	129		151900	100
La0.63Li0.11(Mg0.5W0.5)O3	6.8E−6	0.38	P4/nmm	129		151901	100
La0.62Li0.14(Mg0.5W0.5)O3	1.2E−5	0.37	P4/nmm	129		151902	100
Li4PS4I	1.2E−4	0.37	P4/nmm Z	129		432169	101
Li9.75Sn0.75P2.25S12	3.57E−3		P42/nmc S	137
Li6ZnO4	9.40E−09	0.61	P42/nmc	137		62137	64
Li9.42Si1.02P2.1S9.96O2.04	1.1E−4	0.238	P42/nmc	137			102
Li9.54Si1.74P1.44S11.7Cl0.3	2.53E−2	0.238	P42/nmc	137			102
Li10GeP2S11.7O0.3	1.15E−2	0.155	P42/nmc	137			102
Li10(Si0.5Sn0.5)P2S12	4.28E−3	0.29	P42/nmc	137			102
Li9P3S9O3	4.27E−5	0.311	P42/nmc	137			103
Li10.05Ge1.05P1.95S12	1.22E−2	0.28	P42/nmc4	137			104
Li10.2Ge1.2P1.8S12	1.32E−2		P42/nmc4	137			104
Li10.5Ge1.5P1.5S12	1.10E−2		P42/nmc4	137			104
Li10GePS12	1.21E−2		P42/nmc	137		188887	104
Li10.35Ge1.35P1.65S12	1.44E−2	0.269	P42/nmc S	137		193947	104
Li3.475Si0.475P0.525S4	5.27E−3		P42/nmc	137			105
Li3.45Si0.45P0.55S4	6.73E−3	0.27	P42/nmc	137			105
Li3.425Si0.425P0.575S4	5.65E−3		P42/nmc	137			105
Li3.4Si0.4P0.6S4	4.21E−3		P42/nmc	137			105
Li3.335Sn0.33P0.67S4	3.73E−3		P42/nmc	137			105
Li3.3Sn0.3P0.7S4	3.65E−3		P42/nmc	137			105
Li3.285Sn0.28P0.72S4	4.36E−3		P42/nmc	137			105
Li3.27Sn0.27P0.73S4	4.96E−3		P42/nmc	137			105
Li3.26Sn0.26P0.74S4	4.53E−3		P42/nmc	137			105
Li3.25Sn0.25P0.75S4	3.6E−3		P42/nmc	137			105
Li10SiP2S12	2.3E−3	0.196	P42/nmc	137			106
Li10SnP2S12	7E−3	0.27	P42/nmc C	137		193755	107
Li10GeP2S12	2.46E−2	0.274	P42/nmc	137		241439	108
Li10(Ge0.776Sn0.224)P2S12	1.41E−2	0.276	P42/nmc	137		255748	108
Li10SnP2S12	3.98E−3	0.305	P42/nmc	137		255750	108
Li10(Ge0.416Sn0.584)P2S12	7.43E−3	0.285	P42/nmc	137		255757	108
Li10.35Si1.35P1.65S12	6.5E−3		P42/nmc S	137		252037	109
Li9.81Sn0.81P2.19S12	5.5E−3		P42/nmc	137		252040	109
Li10GeP2S12	1.20E−02	0.25	P42/nmc	137		255749	110
Li10.2Si1.2P1.8S12	4.16E−3		P42/nmc S	137			111
Li10.275Si1.275P1.725S12	5.61E−3		P42/nmc S	137			111
Li10.35Si1.35P1.65S12	6.68E−3		P42/nmc S	137			111
Li10.425Si1.425P1.575S12	5.22E−3		P42/nmc S	137			111
Li10GeP2S12	1.21E−2		P42/nmc S	137			111
Li10.05Ge1.05P1.95S12	1.25E−2		P42/nmc S	137			111
Li10.2Ge1.2P1.8S12	1.36E−2		P42/nmc S	137			111
Li10.35Ge1.35P1.65S12	1.41E−2		P42/nmc S	137			111
Li10.5Ge1.5P1.5S12	1.09E−2		P42/nmc S	137			111
Li9.79Sn0.79P2.21S12	4.56E−3		P42/nmc S	137			111
Li9.81Sn0.81P2.19S12	4.98E−3		P42/nmc S	137			111
Li9.87Sn0.87P2.13S12	4.32E−3		P42/nmc S	137			111
Li9.9Sn0.9P2.1S12	3.66E−3		P42/nmc S	137			111
Li10SnP2S12	3.65E−3		P42/nmc S	137			111
Li10.2(Sn0.2Si0.8)1.2P1.8S12	7.82E−3		P42/nmc S	137		5667	111
Li10.5(Sn0.2Si0.8)1.5P1.5S12	8.79E−3		P42/nmc S	137		5668	111
Li10.35(Sn0.2Si0.8)1.35P1.65S12	1.08E−2		P42/nmc S	137		5669	111
Li10.35(Sn0.27Si1.08)P1.65S12	1.1E−3	0.197	P42/nmc S	137		257946	111
Li10.2(Sn0.2Si0.8)1.2P1.8S12	2.69E−3		P42/nmc S	137		257948	111
Li10GeP2S12	1.43E−3	0.24	P42/nmc S	137			112
Li9.8Ba0.1GeP2S12	5.61E−4		P42/nmc S	137			112
Li9.6Ba0.2GeP2S12	5.72E−4		P42/nmc S	137			112
Li9.4Ba0.3GeP2S12	7.07E−4	0.29	P42/nmc S	137			112
Li9.2Ba0.4GeP2S12	3.16E−4		P42/nmc S	137			112
Li9Ba0.5GeP2S12	9.98E−5		P42/nmc S	137			112
Li10GeP2S12	5.0E−3	0.35	P42/nmc	137			113
LiIaNb2O7	<1E−8		I4/mmm	139		72566	114
Li4Sr3Nb5.77Fe0.23O19.77	<1E−10		I4/mmm	139		87823	115
Li4Sr3Nb6O20	<1E−10		I4/mmm	139		87824	115
Li4Sr3.056Nb6O20	<1E−10	0.74	I4/mmm	139		109168	115
LiScO2	1.00E−12	0.87	I41/amd	141		36124	33
r-LiAlO2	1.10E−12	0.97	I41/amd	141		99517	33
Li3BN2	8.70E−08	0.55	I41/amd	141	β-Li3BN2	155126	93
Li4SrN2	2.30E−13	0.9	I41/amd	141		87413	116
LiScO2	<1E−10	1.047	I41/amd	141		257819	117
Li0.9SC0.9Zr0.1O2	<1E−10	0.912	I41/amd	141		257820	117
Li7La3HfO12	9.85E−7	0.53	I41/acdZ	142	“tetragonal-LLHO”	174202	118
Li7LasZr2O12	1.63E−6	0.54	I41/acdZ	142	“tetraganol-LLZO”	183684	119
Li7La3Zr2O12	5E−7	0.59	I41/acdZ	142			120
Li7La3Zr2O12	9.9E−6	0.43	I41/acdZ	142		238687	121
LiGaSiO4	3.00E−16	0.9	R3H	146		65125	122
LiGa0.5Al0.5GeO4	<1E−10	1.06	R3H	146		257740	123
LiAlGeO4	<1E−10	0.97	R3H	146		257741	123
LiGaGeO4	<1E−10	1.12	R3	148		257739	123
LiTi2(PO4)3	1.61E−4	0.21	R3	148			124
Li1.2Ti1.8Al0.2(PO4)3	4.82E−3	0.18	R3	148			124
LiNaSO4	8.80E−10		P31c	159		14364	125
Li3.333Mg0.333P2S6	8.20E−8	0.517	P31m	162		95606	126
Li2.667Mg0.667P2S6	4.00E−06	0.46	P31m	162		95607	126
Li4P2S6	2.38E−07	0.29	P31m	162		242170	127
Li4P2S6	1.6E−10	0.48	P31m	162			128
Li3YCl6	5.39E−4	0.40	P3m1	164			26
Li3ErCl6	3.3E−4	0.41	P3m1	164		50151	129
Li4.4Al0.4Ge0.6S4	4.33E−5	0.38	P3m1	164		235201	130
Li4.4Al0.4Sn0.6S4	3.6E−6	0.15	P3m1	164		235207	130
Li5NCl2	1.20E−06	0.5	R3m	166		84763	131
LiHf2(PO4)3	2.833E−7		R3cH	167			2
LiZr2(PO4)3	2.96E−10		R3cH	167		201935	2
LiGe2(PO4)3	3.33E−7		R3cH	167		263767	2
Li1.1Ti1.9Sc0.1(PO4)3	3.89E−4	0.3	R3cH	167			132
Li1.2Ti1.8Sc0.2(PO4)3	2.51E−3	0.25	R3cH	167			132
Li1.3Ti1.7Sc0.3(PO4)3	7.91E−4	0.28	R3cH	167			132
Li1.4Ti1.6Sc0.4(PO4)3	1.99E−4	0.31	R3cH	167			132
Li1.5Ti1.5Sc0.5(PO4)3	9.74E−5	0.32	R3cH	167			132
LiTi2(PO4)3	7.61E−6	0.38	R3cH	167		95979	132
LiGe2(PO4)3	4.83E−9	0.654	R3cH	167		69763	133
Li1.2Al0.2Ge1.8(PO4)3	4.83E−5	0.387	R3cH	167		263760	133
Li1.4A10.4Ge1.6(PO4)3	1.88E−4	0.407	R3cH	167		263762	133
Li1.5A10.5Ge1.5(PO4)3	3.36E−4	0.426	R3cH	167		263763	133
Li1.7Al0.7Ge1.3(PO4)3	2.64E−4	0.450	R3cH	167		263765	133
Li1.8Al0.8Ge1.2(PO4)3	1.37E−4	0.429	R3cH	167		263766	133
LiTi2(PO4)3	1.0E−4		R3cH	167			134
Li1.2Ti2Si0.2P2.8O12	8.6E−5		R3cH	167			134
Li1.3Ti2Si0.3P2.7O12	3.2E−4		R3cH	167			134
Li1.4Ti2Si0.4P2.6O12	1.5E−4		R3cH	167			134
Li1.5Ti2Si0.5P2.5O12	9.6E−5		R3cH	167			134
Li1.3Al0.3Ti1.7(PO4)3	3E−3		R3cH	167			134
Li1.4Al0.4Ti1.6(PO4)3	3.88E−4		R3cH	167			134
Li1.5Al0.5Ti1.5(PO4)3	2.48E−4		R3cH	167			134
Li1.2Cr0.2Ti1.8(PO4)3	1.82E−5		R3cH	167			134
Li1.3Cr0.3Ti1.7(PO4)3	3.51E−5		R3cH	167			134
Li1.4Cr0.4Ti1.6(PO4)3	1.49E−4		R3cH	167			134
Li1.5Cr0.5Ti1.5(PO4)3	3.86E−4		R3cH	167			134
Li1.6Cr0.6Ti1.4(PO4)3	1.26E−4		R3cH	167			134
Li1.7Cr0.7Ti1.3(PO4)3	8.05E−6		R3cH	167			134
Li1.2Ga0.2Ti1.8(PO4)3	1.62E−4		R3cH	167			134
Li1.3Ga0.3Ti1.7(PO4)3	2.61E−4		R3cH	167			134
Li1.4Ga0.4Ti1.6(PO4)3	1.28E−4		R3cH	167			134
Li1.5Ga0.5Ti1.5(PO4)3	1.22E−4		R3cH	167			134
Li1.2Fe0.2Ti1.8(PO4)3	1.80E−4		R3cH	167			134
Li1.3Fe0.3Ti1.7(PO4)3	2.46E−4		R3cH	167			134
Li1.4Fe0.4Ti1.6(PO4)3	3.92E−4		R3cH	167			134
Li1.2Sc0.2Ti1.8(PO4)3	6.90E−4		R3cH	167			134
Li1.3Sc0.3Ti1.7(PO4)3	7.03E−4		R3cH	167			134
Li1.4Sc0.4Ti1.6(PO4)3	5.15E−4		R3cH	167			134
Li1.5Sc0.5Ti1.5(PO4)3	2.53E−4		R3cH	167			134
Li1.2In0.2Ti1.8(PO4)3	3.90E−4		R3cH	167			134
Li1.3In0.3Ti1.7(PO4)3	3.93E−4		R3cH	167			134
Li1.4In0.4Ti1.6(PO4)3	3.02E−4		R3cH	167			134
Li1.5In0.5Ti1.5(PO4)3	2.04E−4		R3cH	167			134
Li1.2La0.2Ti1.8(PO4)3	8.00E−5		R3cH	167			134
Li1.3La0.3Ti1.7(PO4)3	5.23E−4		R3cH	167			134
Li1.4La0.4Ti1.6(PO4)3	4.98E−4		R3cH	167			134
Li1.5La0.5Ti1.5(PO4)3	2.81E−4		R3cH	167			134
Li1.5Fe0.5Ti1.5(PO4)3	1.74E−4		R3cH	167		55751	134
Li0.87Hf2.032P3O12	1.29E−05	0.33	R3cH	167		83501	134
Li1.2Al0.2Ti1.8(PO4)3	5.95E−4		R3cH	167		427621	134
Li(Ti1.4Sn0.6)(PO4)3	2.28E−5	0.32	R3cH	167		183672	135
Li(Ti0.6Sn1.4)(PO4)3	9.42E−6		R3cH	167		183676	135
Li(Ti0.4Sn1.6)(PO4)3	3.15E−6		R3cH	167		183677	135
Li1.15Y0.15Zr1.85(PO4)3	1.4E−4	0.39	R3cH	167		191891	136
LiZr2(PO4)3	1E−9	0.76	R3cH	167		201935	137
Li1.3(Al0.3Ti1.7)(PO4)3	8.02E−7		R3cH	167		253240	138
Li1.3(Al0.23Ga0.07Ti1.7)(PO4)3	4.46E−6		R3cH	167		253241	138
Li1.3(Al0.23Sc0.07Ti1.7)(PO4)3	1.94E−7		R3cH	167		253242	138
Li1.3(Al0.23Y0.07Ti1.7)(PO4)3	3.84E−8		R3cH	167		253243	138
Li1.3Al0.3Ti1.7(PO4)3	7E−4		R3cH	167		257190	139
LiZr2(PO4)3	8.5E−5		R3cH	167			140
Li1.025Y0.025Zr1.975(PO4)3	1.28E−4		R3cH	167			140
Li1.05Y0.05Zr1.95(PO4)3	1.3E−4		R3cH	167			140
Li1.1Y0.1Zr1.9(PO4)3	1.0E−4		R3cH	167			140
Li1.1Al0.1Ge1.9(PO4)3	1.29E−5		R3cH	167			140
Li1.2Al0.2Ge1.8(PO4)3	1.89E−5	0.46	R3cH	167			140
Li1.3Al0.3Ge1.7(PO4)3	1.91E−4		R3cH	167			140
Li1.4Al0.4Ge1.6(PO4)3	3.17E−4	0.37	R3cH	167			140
Li1.5Al0.5Ge1.5(PO4)3	3.45E−4		R3cH	167			140
Li1.6Al0.6Ge1.4(PO4)3	3.94E−4	0.37	R3cH	167			140
Li1.7Al0.7Ge1.3(PO4)3	2.75E−4		R3cH	167			140
Li1.8Al0.8Ge1.2(PO4)3	1.23E−4	0.43	R3cH	167			140
LiGe2(PO4)3	3.12E−9	0.60	R3cH	167			141
Li0.86Hf2.035(PO4)3	9.2E−8	0.48	R3cH	167			11
Li1.7Al0.3Ti1.6(PO4)3	5E−5		R3cH	167			142
Li1.2In0.2Ti1.8(PO4)3	8.22E−5	0.32	R3cH	167			143
Li1.3Al0.2Sc0.1Ti1.7(PO4)3	9.72E−4	0.25	R3cH	167			144
Li1.3Al0.15Sc0.15Ti1.7(PO4)3	1.24E−3	0.23	R3cH	167			144
Li1.3Al0.1Sc0.2Ti1.7(PO4)3	4.29E−4	0.26	R3cH	167			144
Li1.3Sc0.3Ti1.7(PO4)3	4.52E−4	0.25	R3cH	167			144
Li1.3Al0.3Ti1.7(PO4)3	1.13E−3	0.23	R3cH	167		257190	144
LiTi(PO4)3	6E−5	0.33	R3c	167			145
Li1.05Al0.05Ti0.95(PO4)3	1.1E−3	0.31	R3c	167			145
Li1.1Al0.1Ti0.9(PO4)3	6.7E−4	0.32	R3c	167			145
Li1.2Al0.2Ti0.8(PO4)3	4.0E−3	0.31	R3c	167			145
Li1.3Al0.3Ti0.7(PO4)3	6.2E−3	0.30	R3c	167			145
Li1.4Al0.4Ti0.6(PO4)3	3.3E−3	0.29	R3c	167			145
Li1.05Cr0.05Ti0.95(PO4)3	1.8E−4	0.33	R3c	167			145
Li1.1Cr0.1Ti0.9(PO4)3	2.6E−4	0.32	R3c	167			145
Li1.2Cr0.2Ti0.8(PO4)3	4.3E−4	0.31	R3c	167			145
Li1.3Cr0.3Ti0.7(PO4)3	2.9E−4	0.32	R3c	167			145
Li1.05Fe0.05Ti0.95(PO4)3	1.3E−4	0.34	R3c	167			145
Li1.1Fe0.1Ti0.9(PO4)3	6.3E−4	0.34	R3c	167			145
Li1.2Fe0.2Ti0.8(PO4)3	1.4E−3	0.32	R3c	167			145
Li1.3Fe0.3Ti0.7(PO4)3	2.3E−3	0.31	R3c	167			145
Li1.5Fe0.5Ti0.5(PO4)3	2.7E−4	0.32	R3c	167			145
LiGe2(PO4)3	3.37E−7	0.38	R3c	167			146
Li1.3Al0.3Ge1.7(PO4)3	1.42E−4	0.37	R3c	167			146
Li1.7Al0.7Ge1.3(PO4)3	2.04E−4		R3c	167			146
Li1.3Cr0.3Ge1.7(PO4)3	8.87E−5	0.39	R3c	167			146
Li1.5Cr0.5Ge1.5(PO4)3	1.21E−4	0.37	R3c	167			146
Li1.7Cr0.7Ge1.3(PO4)3	2.46E−5		R3c	167			146
Li1.3Ga0.3Ge1.7(PO4)3	4.47E−5	0.38	R3c	167			146
Li1.5Ga0.5Ge1.5(PO4)3	2.01E−5		R3c	167			146
Li1.3Fe0.3Ge1.7(PO4)3	2.99E−5	0.39	R3c	167			146
Li1.5Fe0.5Ge1.5(PO4)3	2.56E−5		R3c	167			146
Li1.3Sc0.3Ge1.7(PO4)3	5.59E−5		R3c	167			146
Li1.3In0.3Ge1.7(PO4)3	9.22E−6		R3c	167			146
Li1.5In0.5Ge1.5(PO4)3	5.81E−6		R3c	167			146
Li1.5Al0.5Ge1.5(PO4)3	2.86E−4	0.38	R3c	167		263764	146
LiIO3	1.90E−07		P63	173		35473	147
Li9Mg3(PO4)4F3	<1E−10	0.835	P63	173		426103	148
Pb6.12Ca1.9Li1.96(PO4)6	<1E−10	1.05	P63/m	176		59615	149
LiNdSiO4	<1E−10		P63/m	176			150
LiDySiO4	<1E−10		P63/m	176			150
Li2La8Si6O25	<1E−10		P63/m	176			150
Li3La7Si6O24	<1E−10		P63/m	176			150
Li0.284Sm4.512Si3O12.91	<1E−10		P63/m	176		83279	150
LiLa9Si6O26	<1E−10		P63/m	176		291218	150
LiEu9Si6O26	<1E−10		P63/m	176		291220	150
LiAlSiO4	2.00E−09	0.68	P6422	181		55665	151
Li3(NH2)2I	1E−5	0.58	P63mc	186		167528	152
Ba3LiTa5ZrSi4O26	<1E−10	0.79	P62m	189		239277	153
Li3N	1.2E−3	0.25	P6/mmm	191		26540	154
Li3N	3.00E−04	0.26	P6/mmm	191		156894	155
Fe2Na2K(Li3Si12O30)	<1E−10	1.22	P6/mcc	192		235750	156
Li3P	7.03E−4	0.18	P63/mmc	194		642223	157
Li5.5K0.25La2.75Nb2O12	3.19E−3	0.49	I213	199			158
Li5.5La3Nb1.75In0.25O12	8.07E−3	0.49	I213	199			158
Li6BaLa2Nb2O12	6E−6	0.44	I213	199			159
Li5La3Nb2O12	8E−6	0.43	I213	199		54865	159
(K0.1Li0.9)(SbO3)	1.36E−8		Pn3Z	201		200984	160
Li8GeP4	1.8E−5	0.435	Pa3	205	α-Li8GeP4	235184	161
Li8SiP4	4.5E−5	0.404	Pa3	205		235186	161
Li3AlN2	5.00E−08	0.45	Ia3	206		257464	162
Li2MgTi3O8	<1E−10	0.71	P4332	212		86165	163
Li2CoTi3O8	<1E−10	1.33	P4332	212		86166	163
Li2CoGe3O8	<1E−10	1.49	P4332	212		86167	163
Li2ZnGe3O8	<1E−10	2.14	P4332	212		86169	163
(Li0.61Mg0.39)(Li0.46Mg0.005Ti0.035)Ti1.5O4	6.56E−10	0.685	P4332	212		168144	164
(Li0.55Mg0.45)(Li0.445Mg0.055)Ti1.5O4	1.53E−11	0.786	P4332	212		168145	164
Li5NI2	4.00E−6		F43m	216		16800	165
Li2VCl4	6.95E−6		F43m	216		74959	166
Li6PS5Cl0.25Br0.75	1.86E−3	0.328	F43m	216			167
Li6PS5Cl	2.05E−3	0.452	F43m	216		259200	167
Li6PS5Cl0.5Br0.5	3.33E−3	0.367	F43m	216		259201	167
Li6PS5Br	1.15E−3	0.303	F43m	216		259202	167
Li6PS5Br0.5I0.5	2.62E−5	0.312	F43m	216		259203	167
Li6PS5I	1.3E−6	0.383	F43m	216		259204	167
Li6PS5Cl0.75Br0.25	2.26E−3	0.408	F43m	216		259206	167
Li6PS5Br0.75I0.25	1.12E−4	0.321	F43m	216		259209	167
Li6PS5Br0.25I0.75	4.72E−6	0.351	F43m	216		259211	167
Li6PS5Br	7.01E−4	0.194	F43m	216		234584	168
Li6.025P0.975Si0.025S5Br	8.78E−4	0.196	F43m	216		234585	168
Li6.05P0.95Si0.05S5Br	4.37E−4	0.173	F43m	216		234586	168
Li6.075P0.925Si0.075S5Br	8.73E−4	0.178	F43m	216		234587	168
Li6.1P0.95Si0.1S5Br	7.99E−4	0.22	F43m	216		234588	168
Li6.125P0.875Si0.125S5Br	9.02E−4	0.189	F43m	216		234589	168
Li6.175P0.825Si0.175S5Br	9.31E−4	0.142	F43m	216		234591	168
Li6.2P0.8Si0.2S5Br	1.69E−3	0.25	F43m	216		234592	168
Li6.225P0.775Si0.225S5Br	1.08E−3	0.248	F43m	216		234593	168
Li6.25P0.75Si0.25S5Br	1.41E−3	0.223	F43m	216		234594	168
Li6.3P0.7Si0.3S5Br	1.65E−3	0.236	F43m	216		234595	168
Li6.35P0.65Si0.35S5Br	2.34E−3	0.142	F43m	216		234596	168
Li6.5P0.5Si0.5S5Br	2.19E−3	0.27	F43m	216		234597	168
Li7Ge3PS12	1.1E−4	0.259	F43m	216		258187	169
Li6B0.9PH3.6S4.9	1.8E−3	0.166	F43m	216		264526	170
Li6PS5Cl	1.30E−03	0.33	F43m	216			171
Li6PS5Br	2.77E−3	0.31	F43m	216		267193	172
Li6P(S4.9Se0.1)Br	3.20E−3	0.33	F43m	216		267194	172
Li6P(S4.8Se0.2)Br	3.92E−3	0.34	F43m	216		267195	172
Li6P(S4.7Se0.3)Br	3.62E−3	0.33	F43m	216		267196	172
Li6P(S4.6Se0.4)Br	3.64E−3	0.33	F43m	216		267197	172
Li6P(S4.5Se0.5)Br	2.68E−3	0.34	F43m	216		267198	172
Li6P(S4.4Se0.6)Br	2.78E−3	0.34	F43m	216		267199	172
Li6P(S4.3Se0.7)Br	3.01E−3	0.35	F43m	216		267200	172
Li6P(S4.2Se0.8)Br	3.48E−3	0.34	F43m	216		267201	172
Li6P(S4.1Se0.9)Br	3.82E−3	0.34	F43m	216		267202	172
Li6P(S4Se)Br	3.61E−3	0.34	F43m	216		267203	172
Li6PO5Cl	5.54E−10	0.66	F43m	216		421479	173
Li6PS5Br	3.2E−5	0.32	F43m	216		234598	174
Li6PS5Cl	3.3E−5	0.38	F43m	216		259205	174
Li6PS5I	2.2E−4	0.26	F43m	216		259212	174
Li6PS5I	1.26E−6	0.38	F43m	216			175
Li6P0.92Ge0.08S5I	9.02E−6	0.39	F43m	216			175
Li6P0.85Ge0.15S5I	3.99E−5	0.36	F43m	216			175
Li6P0.75Ge0.25S5I	3.26E−5	0.36	F43m	216			175
Li6P0.74Ge0.26S5I	1.51E−4	0.30	F43m	216			175
Li6P0.64Ge0.36S5I	6.58E−4	0.24	F43m	216			175
Li6P0.53Ge0.47S5I	1.52E−3	0.24	F43m	216			175
Li6P0.48Ge0.52S5I	1.83E−3	0.23	F43m	216			175
Li6P0.31Ge0.69S5I	5.16E−3	0.24	F43m	216			175
Li6P0.21Ge0.79S5I	5.41E−3	0.25	F43m	216			175
Li6PS5Cl	1.31E−6	0.38	F43m	216			176
Li6PS5Br	2.41E−5	0.16	F43m	216		259208	176
Li6PS5I	4.1E−7	0.32	F43m	216		418489	176
Li6PS5I	9.24E−5		F43m	216			177
Li6.1P0.9Sn0.1S5I	1.61E−4		F43m	216			177
Li6.2P0.8Sn0.2S5I	2.32E−4		F43m	216			177
Li6.25P0.75Sn0.25S5I	2.92E−4		F43m	216			177
Li6.3P0.7Sn0.3S5I	3.06E−4		F43m	216			177
Li6.5P0.5Sn0.5S5I	2.35E−4		F43m	216			177
Li6.4P0.6Ge0.4S5I	2.51E−4		F43m	216			177
Li6.45P0.55Ge0.45S5I	3.65E−4		F43m	216			177
Li6.5P0.5Ge0.5S5I	5.42E−4		F43m	216			177
Li6.55P0.45Ge0.55S5I	4.11E−4		F43m	216			177
Li6.6P0.4Ge0.6S5I	2.74E−4		F43m	216			177
Li6.8P0.2Ge0.8S5I	5.21E−5		F43m	216			177
LiCe(BH4)3Cl	1.03E−4		I43m	217		185218	178
Li7PN4	1.60E−07	0.4	P43n	218		69017	95
β-Li8GeP4	8.6E−5	0.394	P43n	218	β-Li8GeP4	235185	161
Li4B7O12Cl	2.4E−5		F43c	219		1125	179
Fe0.16La2.95Li5.68Zr2O12	9.35E−4	0.29	I43d	220		431391	180
Fe0.19La2.95Li5.57Zr2O12	1.38E−3	0.28	I43d	220		431392	180
Li3ClO	2.5E−2		Pm3m	221			181
Li2.99Ba0.005Cl0.5I0.5	2.5E−3	0.06	Pm3m	221			181
Li0.31La0.63((Ti0.9Co0.1)O3	2.60E−4		Pm3m	221		151533	182
(La0.49Li0.461Sr0.049)(TiO3)	7.09E−4	0.33	Pm3m	221		190825	183
(La0.46Li0.429Sr0.111)(TiO3)	1.97E−4	0.33	Pm3m	221		190826	183
(La0.402Li0.368Sr0.230)(TiO3)	2.87E−5	0.36	Pm3m	221		190827	183
Li2(OH)0.9F0.1Cl	3.86E−5	0.52	Pm3m	221			184
Li2(OH)Br	1.20E−6	0.75	Pm3m	221		200874	184
Li9NS3	8.30E−07	0.52	Pm3m	221		240749	185
(La0.55Li0.45)(Ti0.9Al0.1)O3	1.51E−3		Pm3m	221		254045	186
(La0.6Li0.4)(Ti0.8Al0.2)O3	5.68E−4		Pm3m	221		254046	186
(La0.65Li0.35)(Ti0.7Al0.3)O3	1.61E−4		Pm3m	221		254047	186
(La0.7Li0.3)(Ti0.6Al0.4)O3	1.04E−7		Pm3m	221		254048	186
(Li0.16Sr0.69)(Ga0.25Ta0.75)O3	3.69E−6	0.359	Pm3m	221		291520	187
Li0.375Sr0.4375Zr0.25Ta0.75O3	2.0E−4	0.26	Pm3m	221			188
Li0.25Sr0.625Ta0.5Zr0.5O3	3.34E−7	0.42	Pm3m	221			188
Li0.375Sr0.4375Hf0.25Ta0.75O3	3.8E−4	0.36	Pm3m	221			189
Li0.375Sr0.4375Zr0.25Nb0.75O3	2.00E−5	0.26	Pm3m	221			190
Li0.25Sr0.625Zr0.5Nb0.5O3	2.75E−7	0.36	Pm3m	221			190
Li2.99Ba0.005ClO	2.5E−2	0.13	Pm3m	221			191
Li2.99Ba0.005Cl0.5I0.5O	3.37E−3		Pm3m	221			191
Sm0.5Li0.42TiO2.96	3.93E−10	0.58	Pm3m	221			86
La0.52Li0.35TiO2.96	9.11E−4	0.32	Pm3m	221			86
La0.61Li0.15TiO3	2.06E−4		Pm3m	221			192
La0.58Li0.24TiO3	7.22E−4		Pm3m	221			192
La0.55Li0.33TiO3	1.58E−3		Pm3m	221			192
La0.54Li0.36TiO3	9.79E−3		Pm3m	221			192
La0.52Li0.42TiO3	7.21E−4		Pm3m	221			192
La0.5Sr0.06Li0.06TiO3	1.13E−5	0.37	Pm3m	221			193
La0.56Sr0.1Li0.1TiO3	1.37E−5	0.37	Pm3m	221			193
La0.51Sr0.15Li0.15TiO3	5.3E−5	0.38	Pm3m	221			193
La0.41Sr0.25Li0.25TiO3	7.64E−5	0.35	Pm3m	221			193
La0.385Sr0.275Li0.275TiO3	6.04E−5	0.37	Pm3m	221			193
La0.36Sr0.3Li0.3TiO3	1.92E−5	0.35	Pm3m	221			193
La0.61Li0.18TiO3	2.09E−4		Pm3m	221			97
La0.58Li0.27TiO3	8.32E−4		Pm3m	221			97
La0.56Li0.33TiO3	1.30E−3		Pm3m	221			97
La0.55Li0.36TiO3	1.54E−3	0.33	Pm3m	221			97
La0.54Li0.39TiO3	1.25E−3		Pm3m	221			97
La0.52Li0.45TiO3	7.85E−4		Pm3m	221			97
La0.51Li0.34TiO2.94	7E−5	0.36	Pm3m	221			62
Li3OBr	1.10E−06	0.74	Pm3m	221		67265	194, 195
Li7.2N1.6Cl2.4	8.4E−7	0.49	Fm3m	225		49646	131
Li6NI3	3.70E−06		Fm3m	225		83380	165
Li0.19La0.67(Ti0.9Co0.1)O3	1.08E−4		Fm3m	225		151535	182
Li6NBr3	1.00E−08	0.69	Fm3m	225		84091	196
LiI	1E−7		Fm3m	225		414244	197
Li(Li0.34Ti1.66)O4	6.03E−8	0.506	Fd3m	227		168137	164
(Li0.916Mg0.084)(Li0.352Mg0.016Ti1.634)O4	1.73E−8	0.564	Fd3m	227		168139	164
(Li0.826Mg0.174)(Li0.374Mg0.026Ti1.60)O4	4.24E−9	0.615	Fd3m	227		168141	164
(Li0.74Mg0.26)(Li0.40Mg0.04Ti1.56)O4	1.51E−9	0.639	Fd3m	227		168142	164
Li2MnCl4	4.79E−6		Fd3m	227		69678	166
Li2MgCl4	6.24E−7		Fd3m	227		74957	166
Li1.9Mn0.9Ga0.1Cl4	2.37E−7		Fd3m	227		50305	198
Li1.65Mn0.65In0.35Cl4	9.9E−8		Fd3m	227		50306	198
LiCdCl4	5.80E−07	0.44	Fd3m	227		74958	199
LiSrNb2O6F	<1E−10	0.604	Fd3m	227		236009	200
LiSrTa2O6F	<1E−10	0.604	Fd3m	227		236010	200
LiSr0.9Nb2O6F0.8	<1E−10	0.709	Fd3m	227		236011	200
LiSr0.9Ta2O6F0.8	<1E−10	0.76	Fd3m	227		236012	200
Li1.1SrNb1.9Zr0.1O6F	<1E−10	0.622	Fd3m	227		236013	200
Li1.1SrTa1.9Zr0.1O6F	<1E−10	0.693	Fd3m	227		236014	200
Li6SrLa2Nb2O12	4.2E−6	0.5	Ia3d	230		157628	159
Li6CaLa2Nb2O12	1.6E−6	0.55	Ia3d	230		161386	159
Li5.25Ba0.25La2.75Ta2O12	6.03E−6	0.479	Ia3d	230			201
Li5.5Ba0.5La2.5Ta2O12	1.35E−5	0.455	Ia3d	230			201
Li6.25Ba1.25La1.75Ta2O12	5.05E−5	0.395	Ia3d	230			201
Li6.5Ba1.5La1.5Ta2O12	3.2E−5	0.402	Ia3d	230			201
Li6.75Ba1.75La1.25Ta2O12	1.25E−5	0.418	Ia3d	230			201
Li7Ba2LaTa2O12	3.00E−6	0.442	Ia3d	230			201
Li5La3Ta2O12	4.33E−6	0.50	Ia3d	230		154400	201
Li6BaLa2Ta2O12	3.02E−5	0.419	Ia3d	230		237201	201
Li7La3Zr1.89Al0.15O12	3.4E−4	0.334	Ia3d	230			202
Li7.06La3Y0.06Zr1.94O12	9.56E−4	0.26	Ia3d	230			203
Li6.25La3Zr2Ga0.25O12	3.5E−4		Ia3d	230			204
Li7La3Zr2O12	1.2E−4		Ia3d	230			205
Li6.8La3Zr1.8Ta0.2O12	2.8E−4		Ia3d	230			205
Li6.6La3Zr1.6Ta0.4O12	7.3E−4		Ia3d	230			205
Li6.5La3Zr1.5Ta0.5O12	9.2E−4		Ia3d	230			205
Li6.4La3Zr1.4Ta0.6O12	1.0E−3	0.35	Ia3d	230			205
Li6.2La3Zr1.2Ta0.8O12	3.2E−4		Ia3d	230			205
Li6La3ZrTaO12	1.6E−4		Ia3d	230			205
Li7La3Zr2O12	1.2E−4		Ia3d	230			205
Li6.8La3Zr1.8Ta0.2O12	2.8E−4		Ia3d	230			205
Li6.6La3Zr1.6Ta0.4O12	7.3E−4		Ia3d	230			205
Li6.5La3Zr1.5Ta0.5O12	9.2E−4		Ia3d	230			205
Li6.4La3Zr1.4Ta0.6O12	1E−3	0.35	Ia3d	230			205
Li6.2La3Zr1.2Ta0.8O12	3.2E−4		Ia3d	230			205
Li6La3ZrTaO12	1.6E−4		Ia3d	230			205
Li6.8LasZr1.8Ta0.2O12	7.8E−4		Ia3d	230			206
Li6.75La3Zr1.75Ta0.25O12	8.8E−4		Ia3d	230			206
Li6.65La3Zr1.65Ta0.35O12	7.7E−4		Ia3d	230			206
Li6.6La3Zr1.6Ta0.4O12	7.2E−4		Ia3d	230			206
Li6.55La3Zr1.55Ta0.45O12	6.9E−4		Ia3d	230			206
Li6La3ZrTaO12	4.4E−4		Ia3d	230			206
Li5La3Ta2O12	1.6E−4		Ia3d	230			206
Li6.7La3Zr1.7Ta0.3O12	9.6E−4	0.37	Ia3d	230			206
Li6.5La3Zr1.5Ta0.5O12	6.7E−4		Ia3d	230		183686	206
Li6.05Ga0.25La3Zr2O11.8F0.2	1.28E−3	0.28	Ia3d	230			207
Li5.72Al0.26La3Zr1.5W0.25O12	4.9E−4	0.35	Ia3d	230			208
Li6.8La3Zr1.9Mo0.1O12	8.00E−5	0.46	Ia3d	230			209
Li6.6La3Zr1.8Mo0.2O12	3.11E−4	0.48	Ia3d	230			209
Li6.4La3Zr1.7Mo0.3O12	3.69E−4	0.49	Ia3d	230			209
Li6.2La3Zr1.6Mo0.4O12	3.40E−4	0.48	Ia3d	230			209
Li6.5La3Zr1.75Mo0.25O12	3.33E−4	0.39	Ia3d	230		239128	209
Li6.75La3Zr1.875Te0.125O12	3.30E−4	0.41	Ia3d	230			210
Li6.5La3Zr1.75Te0.25O12	1.02E−3	0.38	Ia3d	230			210
Li6.375La3Zr1.375Nb0.625O12	1.37E−3	0.25	Ia3d	230			211
Li5La3Ta2O12	1.2E−6	0.56	Ia3d	230		154400	212
Li5La3Nb2O12	1E−5	0.43	Ia3d	230		171171	212
Li5La3Bi2O12	4.00E−05	0.47	Ia3d	230		158372	213
Li6La2SrBi2O12	5.20E−05	0.43	Ia3d	230		158373	213
Li5Nd3Sb2O12	1.3E−7	0.67	Ia3d	230		159426	214
Li4Nd3TeSbO12	1.96E−6	0.64	Ia3d	230		159732	215
Li5La3Sb2O12	8.2E−6	0.51	Ia3d	230		161342	216
Li6SrLa2Sb2O12	6.6E−6	0.54	Ia3d	230		161343	216
Li6(La2Ca)(NbO6)2	1.33E−6		Ia3d	230		161386	217
Li6(La2Sr)(NbO6)2	3.69E−6		Ia3d	230		161387	217
Li6CaLa2Ta2O12	2.2E−6	0.5	Ia3d	230		163860	218
Li6BaLa2Ta2O12	1.3E−5	0.44	Ia3d	230		163861	218
Li6.15La3Zr1.75Ta0.25Ga0.2O12	4.1E−4	0.27	Ia3d	230			219
Li6.15La3Zr1.75Ta0.25Al0.2O12	3.7E−4	0.30	Ia3d	230			219
Li6.75La3Zr1.75Ta0.25O12	8.7E−4	0.22	Ia3d	230		183873	219
Li6.16Al0.28La3Zr2O12	6.1E−4	0.34	Ia3d	230		185539	220
Li7La3Zr2O12	1.97E−6	0.49	Ia3d	230			221
Li7La3Zr2O12-0.5 wt % Al	1.58E−4		Ia3d	230			221
Li7La3Zr2O12-0.9 wt % Al	3.2E−4	0.34	Ia3d	230			221
Li6.06Al0.2LasZr2O12	4E−4	0.34	Ia3d	230		185539	221
Li6BaLa2Ta2O12	2.45E−5	0.40	Ia3d	230		185602	222
Nd3Zr2Al0.5Li5.5O12	3.9E−5	0.56	Ia3d	230		189530	223
(Li6.26Al0.24)La3Zr2O12	3.1E−4	0.33	Ia3d	230		195182	224
Li6La3Nb1.5Y0.5O12	1.88E−4		Ia3d	230		237141	225
Li5.2La3Nb1.9Y0.1O12	6.39E−5		Ia3d	230		237143	225
Li5.4La3Nb1.8Y0.2O12	6.74E−5		Ia3d	230		237144	225
Li6.5La3Nb1.75Y0.25O12	9.18E−5		Ia3d	230		237145	225
Li6.5La3Nb1.25Y0.75O12	3.43E−4		Ia3d	230		237146	225
Li6Ba0.5Sr0.5La2Ta2O12	7.1E−6	0.45	Ia3d	230		237199	226
Li6SrLa2Ta2O12	5.4E−6	0.45	Ia3d	230		237200	226
Li6BaLa2Ta2O12	1.5E−5	0.47	Ia3d	230		237201	226
Li6CaLa2Ta2O12	2.2E−6	0.47	Ia3d	230		237202	226
Li6BaLa2Ta2O12	4E−5	0.4	Ia3d	230			227
Li6SrLa2Ta2O12	7E−6	0.5	Ia3d	230			227
Li6SrLa2Ta2O12	7E−6	0.5	Ia3d	230		237200	227
Li6BaLa2Ta2O12	4E−5	0.4	Ia3d	230		237201	227
Li5.74La3Zr1.5Ta0.5O12	9.03E−4	0.435	Ia3d	230		239663	228
La3Li5.08Ta1.51Zr0.39O12	1.03E−4	0.536	Ia3d	230		239664	228
Li51.2Al1.6La24Zr16O96	2.54E−4	0.36	Ia3d	230		241475	229
Li49.6Al1.6La24Zr14.4Ta1.6O96	6.14E−4	0.29	Ia3d	230		241476	229
Li6.5La3Hf1.5Ta0.5O12	4.0E−4	0.40	Ia3d	230		258921	230
Li6.5La3Sn1.5Ta0.5O12	1.9E−4	0.45	Ia3d	230		258922	230
Li5La3Ta2O12	1.59E−5		Ia3d	230		259164	231
Li5.3La3Ta1.85Sm0.15O12	7.11E−6		Ia3d	230		259165	231
Li5.5La3Ta1.75Sm0.25O12	5.17E−6		Ia3d	230		259166	231
Li5.70La3Ta1.65Sm0.35O12	2.15E−5		Ia3d	230		259167	231
Li5.90La3Ta1.55Sm0.45O12	1.18E−5		Ia3d	230		259168	231
Li6.10La3Ta1.45Sm0.55O12	1.40E−5		Ia3d	230		259169	231
Li7La3Zr2O12	5.69E−04	0.36	Ia3d	230	“cubic LLZO”	422259	232
Li5La3Nb2O12	4.99e-6		Ia3d	230			233
Li5La3Nb1.95Y0.05O12	1.32E−5		Ia3d	230			233
Li5La3Nb1.9Y0.1O12	1.43E−5		Ia3d	230			233
Li5La3Nb1.85Y0.15O12	5.85E−6		Ia3d	230			233
Li5La3Nb1.8Y0.2O12	9.05E−6		Ia3d	230			233
Li5La3Nb1.75Y0.25O12	9.42E−6		Ia3d	230			233
Li6.24La3Zr2Al0.24O11.98	4.0E−4	0.26	Ia3d	230			234
Li7La3Zr2O12—0.3Ga	3.8E−5	0.37	Ia3d	230			235
Li7La3Zr2O12—0.4Ga	4.4E−5	0.36	Ia3d	230			235
Li7La3Zr2O12—0.5Ga	8.9E−5	0.36	Ia3d	230			235
Li7La3Zr2O12—Ga	5.4E−4	0.32	Ia3d	230			235
La3Zr2Ga0.5Li5.5O12	1E−4		Ia3d	230			236
Li6.8La3Zr1.8Sb0.2O12	5.9E−5	0.39	Ia3d	230			237
Li6.6La3Zr1.6Sb0.4O12	7.7E−4	0.34	Ia3d	230			237
Li6.4La3Zr1.4Sb0.6O12	6.6E−4	0.36	Ia3d	230			237
Li6.2La3Zr1.2Sb0.8O12	4.5E−4	0.37	Ia3d	230			237
Li6La3ZrSbO12	2.6E−4	0.38	Ia3d	230			237
Li6.5La3Zr1.75Te0.25O12—0.07Al	4E−4	0.33	Ia3d	230			238
Li6.65La2.75Ba0.25Zr1.4Ta0.5Nb0.1O12	5.27E−4	0.26	Ia3d	230			239
Li6.4La3Zr1.4Ta0.6O12	7.24E−4	0.24	Ia3d	230			239
Li6.4La3Zr1.4Ta0.5Nb0.1O12	4.44E−4	0.27	Ia3d	230			239
Li6.4La3Zr1.4Ta0.4Nb0.2O12	4.55E−4	0.28	Ia3d	230			239
Li6.4La3Zr1.4Ta0.3Nb0.3O12	6.06E−4	0.26	Ia3d	230			239
Li7La3Zr2O12	1.74E−4	0.26	Ia3d	230			239
Li3Nd3Te2O12	<1E−10	1.22	Ia3d	230			240
Li7.131La3Zr2O12Al0.244	7.73E−5		Ia3d	230			241
Li6.949La3Zr2O12Al0.262	2.25E−4		Ia3d	230			241
Li6.835La3Zr2O12Al0.231	2.20E−4		Ia3d	230			241
Li6.660La3Zr2O12Al0.258	1.51E−4		Ia3d	230			241
Li6.75La3Zr1.75Ta0.25O12	4.1E−4	0.42	Ia3d	230			121
Li6.5La3Zr1.5Ta0.5O12	6.1E−4	0.4	Ia3d	230			121
Li6La3ZrTaO12	2.1E−4	0.42	Ia3d	230			121
Li3Gd3Te2O12	<1E−10		Ia3d	230			242
Li3Tb3Te2O12	<1E−10		Ia3d	230			242
Li3Er3Te2O12	<1E−10		Ia3d	230			242
Li3Lu3Te2O12	<1E10		Ia3d	230			242
Li2S*P2S5	3.2E−03						4
0.7Li2S—0.3P2S5	5.4E−5						4
Li3.8Ge0.8P0.2S4	1.75E−6	0.466					14
Li3.6Ge0.6P0.4S4	1.74E−4	0.339					14
Li3.4Ge0.4P0.6S4	6.53E−4	0.275					14
Li3.35Ge0.35P0.65S4	1.53E−3	0.229					14
Li3.3Ge0.3P0.7S4	1.76E−3	0.221					14
Li3.2Ge0.2P0.8S4	5.57E−4	0.275					14
Li2.9Ca0.05InBr6	2.16E−4						25
Li2.86Ca0.07InBr6	4.04E−4						25
Li2.8Ca0.1InBr6	3.00E−4						25
Li2.7Ca0.15InBr6	6.97E−5						25
Li3.9Zn0.05GeS4	2.72E−7	0.517					71
Li3.8Zn0.1GeS4	9.95E−8	0.545					71
Li3.6Zn0.2GeS4	5.90E−8	0.539					71
Li7GeS3	9.7E−9						71
Li7ZnGeS4	1.4E−9						71
Li9.6P3S12	1.2E−3	0.259					102
Li1.3Al0.3Ge1.7(PO4)3	8.24E−5	0.386					133
Li1.6Al0.6Ge1.4(PO4)3	2.84E−4	0.430					133
LiTi2(PO4)3—0.2Li2O	2.4E−4						134
LiTi2(PO4)3—0.3Li2O	1.5E−3						134
LiTi2(PO4)3—0.4Li2O	1.3E−4						134
Li1.3Al0.3Ti1.7(PO4)3—0.3Li2O	3.5E−4						134
LiTi2(PO4)3—0.1Li4P2O7	1.6E−4						134
Li1.4Al0.4Ti1.6(PO4)3	3.38E−3	0.30			LATP		243
Li1.2Ge0.2Ti1.8(PO4)3	7.94E−5	0.27			LAGP		243
Li1.5Ge0.5Ti1.5(PO4)3	1.90E−4	0.33			LAGP		243
Li1.2Al0.2Ti1.8(PO4)3	3.38E−3	0.28			LATP	427619	243
Li3ClO	0.85E−3	0.26					194
Li3C10.5Br0.50	1.94E−3	0.18					194
Li3OCl	1.47E−4	0.26					194
Li3OCl0.5Br0.5	9.49E−4	0.18					194
Li6.6La2.6Ce0.4Zr2O12	1.44E−5	0.48					244
Li1.4Al0.4Ti1.6(PO4)3	1.1E−03						245
80Li2S * 20P2S5	7.2E−04						246
0.8Li2S—0.2P2S5	7.2E−4						246
0.75Li2S—0.25P2S5	2.8E−4						246
Li2S*P2S5*P2S3	5.4E−03						247
Li7S*P2S5*Li3N	1.4E−03						248
Li7La3Nb1.9Y0.1O12	1.44E−5	0.55					233
Li7La3Zr2O12	2.35E−4	0.339					249
Li6.88La3Zr1.88Nb0.12O12	5.99E−4	0.319					249
Li6.75La3Zr1.75Nb0.25O12	7.71E−4	0.3					249
Li6.62La3Zr1.62Nb0.38O12	4.41E−4	0.31					249
Li6.5La3Zr1.5Nb0.5O12	2.98E−4	0.319					249
Li6La3ZrNbO12	1.50E−4	0.42					249
Li5La3Nb2O12	3E−5	0.44					249
Li7La3Hf2O12	2.4E−4	0.29					250
Li7GePS8	7E−3	0.22					251
Li10(Ge0.95Si0.05)P2S12	8.63E−3	0.251					252
Li10(Ge0.9Si0.1)P2S12	8.07E−3	0.26					252
Li10(Ge0.8Si0.2)P2S12	7.28E−3	0.261					252
Li10(Ge0.7Si0.3)P2S12	5.82E−3	0.265					252
Li10(Ge0.6Si0.4)P2S12	5.24E−3	0.28					252
Li10(Ge0.5Si0.5)P2S12	4.2E−3	0.284					252
Li10(Ge0.2Si0.8)P2S12	4.81E−3	0.269					252
Li10(Ge0.95Sn0.05)P2S12	7.8E−3	0.254					252
Li10(Ge0.9Sn0.1)P2S12	7.53E−3	0.256					252
Li10(Ge0.8Sn0.2)P2S12	7.06E−3	0.252					252
Li10(Ge0.7Sn0.3)P2S12	6.49E−3	0.254					252
Li10(Ge0.5Sn0.5)P2S12	6.17E−3	0.249					252
Li10(Ge0.4Sn0.6)P2S12	5.76E−3	0.265					252
Li10(Ge0.3Sn0.7)P2S12	5.56E−3	0.261					252
Li10(Ge0.2Sn0.8)P2S12	4.77E−3	0.269					252
0.5(Li2O) * 0.5(P2O5)	1.1E−9	0.71					253
0.58(Li2O) * 0.5(P2O5)	2E−8	0.60					253
0.6(Li2O) * 0.5(P2O5)	3E−8	0.61					253
0.63(Li2O) * 0.5(P2O5)	1.3E−7	0.56					253
0.66(Li2O) * 0.5(P2O5)	2.3E−7	0.55					253
0.7(Li2O) * 0.5(P2O5)	3E−7	0.57					253
0.2(Li2S) 0.8(GeS2)	1.1E−7	0.52					253
0.3(Li2S) 0.7(GeS2)	9.3E−7	0.48					253
0.4(Li2S) 0.6(GeS2)	2.9E−6	0.42					253
0.5(Li2S) 0.5(GeS2)	3.3E−5	0.35					253
0.6(Li2S) 0.4(GeS2)	9.2E−5	0.32					253
0.63(Li2S) 0.37(GeS2)	1.5E−4	0.34					253
0.66(Li2S) 0.34(GeS2)	1.0E−4	0.37					253
0.7(Li2S) 0.3(GeS2)	1.2E−4	0.34					253
Li2O—P2O5	1.1E−9	0.71					253
0.58Li2O—0.42P2O5	2.0E−8	0.60					253
0.6Li2O—0.4P2O5	3.0E−8	0.61					253
0.63Li2O—0.37P2O5	1.3E−7	0.56					253
0.66Li2O—0.34P2O5	2.3E−7	0.55					253
0.7Li2O—0.3P2O5	3.0E−7	0.57					253
0.2Li2S—0.8GeS2	1.1E−7	0.52					253
0.3Li2S—0.7GeS2	9.3E−7	0.48					253
0.4Li2S—0.6GeS2	2.9E−6	0.42					253
0.5Li2S—0.5GeS2	3.3E−5	0.35					253
0.6Li2S—0.4GeS2	9.2E−5	0.32					253
0.63Li2S—0.37GeS2	1.5E−4	0.34					253
0.66Li2S—0.34GeS2	1.0E−4	0.37					253
0.7Li2S—0.3GeS2	1.2E−4	0.34					253
Li6.55La3Zr2Ga0.15O12	1.3E−3	0.3					254
Li6.40La3Zr2Ga0.2O12	9E−4	0.3					254
Li6.10La3Zr2Ga0.25O12	7E−5	0.3					254
Li6.8La3Zr1.8Sb0.2O12	5.9E−5	0.39					255
Li6.6La3Zr1.6Sb0.4O12	7.7E−4	0.34					255
Li6.4La3Zr1.4Sb0.6O12	6.6E−4	0.36					255
Li6.2La3Zr1.2Sb0.8O12	4.5E−4	0.37					255
Li6La3ZrSbO12	2.6E−4	0.38					255
Li(In0.62Li1.38)Br3.92	4.9E−6	0.58					256
Li3InBr6	1.77E−4						257
Li3InBr4Cl2	7.58E−6						257
Li3InBr3Cl3	1.14E−4						257
Li3InBr2.5Cl3.5	3.60E−6						257
Li3InBr2Cl4	6.89E−8						257
Li1.8Mg1.1Cl4	1.52E−6						258
Li1.6Mg1.2Cl4	3.07E−6						258
Li1.34Mg1.33Cl4	3.07E−6						258
Li1.9Mn1.05Cl4	4.61E−6						258
Li1.72Mn1.14Cl4	3.62E−6						258
Li1.6Mn1.2Cl4	1.45E−5						258
Li1.52Mn1.24Cl4	1.85E−5						258
Li1.34Mn1.33Cl4	9.57E−6						258
Li1.94Cl1.03Cl4	2.56E−6						258
Li1.90Cd1.05Cl4	3.50E−6						258
Li2OHBrF	7.10E−7						259
Li2OHBr0.99F0.01	9.16E−7						259
Li2OHBr0.98F0.02	1.11E−6						259
Li2OHBr0.95F0.05	6.75E−7						259
Li2OHBr0.9F0.1	6.80E−7						259
Li2OHBr0.8F0.2	5.44E−7						259
Li3(OH)2Cl	2.72E−8	0.88					260
Li5(OH)3Cl2	2.52E−8	0.75					260
Li2OHCl	4.28E−8	0.56					260
Li5(OH)2Cl3	1.48E−7	0.49					260
Li3OHCl2	8.92E−8	0.67					260
Li3.7Zn0.15GeO4	4.63E−7						261
Li3.5Zn0.25GeO4	2.42E−7						261
Li3.1Zn0.45GeO4	9.89E−8						261
Li2.8Zn0.6GeO4	1.27E−7						261
Li2.6Zn0.7GeO4	5.79E−8						261
Li2.3Zn0.85GeO4	4.23E−9						261
Li7La2.75Ca0.25Zr1.75Nb0.25O12	2.2E−4	0.35					262
Li1.5Cr0.5Ti1.5(PO4)3	1.98E−4	0.29					263
Li3V2(PO4)3	2.09E−7						263
Li3V1.8Al0.2(PO4)3	1.88E−6						263
Li3V1.6Al0.4(PO4)3	6.21E−6						263
Li3V1.4Al0.6(PO4)3	9.34E−7						263
Li7P2.9Mn0.1S10.7I0.3	5.6E−3	0.22					264
0.3 Li2S * 0.7 SiS2	1.6E−6	0.46					265
0.4 Li2S * 0.6 SiS2	2.8E−5	0.38					265
0.5 Li2S * 0.5 SiS2	1.0E−4	0.32					265
0.6 Li2S * 0.4 SiS2	5.0E−4	0.25					265
(2Li2S—P2S5)	1.12E−4						266
(2Li2S—P2S5)0.85(LiI)0.15	2.35E−4						266
(2Li2S—P2S5)0.75(LiI)0.25	3.96E−4						266
(2Li2S—P2S5)0.60(LiI)0.40	7.60E−4						266
(2Li2S—P2S5)0.55(LiI)0.45	1.12E−3						266
0.14SiS2—0.09P2S5—0.47Li2S—0.30LiI	1.32E−3	0.34					267
0.26B2S3—0.3Li2S—0.44LiI	1.57E−3	0.3					268
0.26B2S3—0.31Li2S—0.43LiI	7.99E−4	0.33					268
0.27B2S3—0.32Li2S—0.41LiI	4.25E−4	0.35					268
0.5SiS2—0.5Li2S	1.5E−4	0.34					269
0.1LiBr—0.45SiS2—0.45Li2S	1.9E−4	0.30					269
0.2LiBr—0.4SiS2—0.4Li2S	2.1E−4	0.33					269
0.25LiBr—0.38SiS2—0.38Li2S	2.4E−4	0.31					269
0.3LiBr—0.3SiS2—0.35Li2S	3.2E−4	0.33					269
0.35LiBr—0.33SiS2—0.33Li2S	2.3E−4	0.38					269
0.4LiBr—0.3SiS2—0.3Li2S	1.1E−4	0.42					269
SiS2—Li2S	1.20E−4	0.35					270
0.9(SiS2—Li2S)—0.1LiCl	1.84E−4	0.34					270
0.8(SiS2—Li2S)—0.2LiCl	2.35E−4	0.33					270
0.75(SiS2—Li2S)—0.25LiCl	2.66E−4	0.35					270
0.7(SiS2—Li2S)—0.3LiCl	2.33E−4	0.35					270
0.65(SiS2—Li2S)—0.35LiCl	1.78E−4	0.36					270
0.6(SiS2—Li2S)—0.4LiCl	0.93E−4	0.34					270
(0.4SiS2—0.6Li2S)	5.3E−4	0.33					271
0.9(0.4SiS2—0.6Li2S)—0.1LiI	6.5E−4	0.31					271
0.8(0.4SiS2—0.6Li2S)—0.2LiI	7.7E−4	0.30					271
0.7(0.4SiS2—0.6Li2S)—0.3LiI	1.15E−3	0.29					271
0.6(0.4SiS2—0.6Li2S)—0.4LiI	1.78E−3	0.28					271
0.55(0.4SiS2—0.6Li2S)—0.45LiI	1.41E−3	0.29					271
0.24SiS2—0.36Li2S—0.4LiI	1.8E−3	0.28					272
0.28SiS2—0.42Li2S—0.30LiI	1.8E−3	0.31					273
0.14SiS2—0.09P2S5—0.47Li2S—0.30LiI	2.1E−3	0.34					273
0.27SiS2—0.03Al2S3—0.30Li2S—0.40LiI	1.2E−3	0.34					273
0.21SiS2—0.09B2S3—0.30Li2S—0.40LiI	1.7E−3	0.30					273
0.30Li2S—0.7GeS2	4.4E−7	0.63					274
0.40Li2S—0.60GeS2	3.2E−6	0.52					274
0.50Li2S—0.50GeS2	4.0E−5	0.51					274
0.3Li2S—0.7P2S5	1.7E−2	0.18					275
0.7Li2S—0.3P2S5	3.2E−3	0.12					276
0.6Li2S—0.4P2S5	1.5E−4	0.31					277
0.95(0.6Li2S—0.4SiS2)—0.05Li4SiO4	1.58E−3	0.34					278
0.9(0.6Li2S—0.4SiS2)—0.1Li4SiO4	4.34E−4	0.37					278
0.8(0.6Li2S—0.4SiS2)—0.2Li4SiO4	1.59E−4	0.43					278
0.95(0.6Li2S—0.4SiS2)—0.05Li3PO4	8.68E−4	0.35					278
0.7(0.6Li2S—0.4SiS2)—0.3Li3PO4	2.08E−5	0.46					278
0.6(0.6Li2S—0.4SiS2)—0.4Li3PO4	5.33E−6	0.51					278
0.95(0.6Li2S—0.4SiS2)—0.05Li4GeO4	1.19E−3	0.28					278
0.9(0.6Li2S—0.4SiS2)—0.1Li4GeO4	3.18E−4	0.35					278
0.85(0.6Li2S—0.4SiS2)—0.15Li4GeO4	1.14E−4	0.40					278
0.95(0.6Li2S—0.4SiS2)—0.05Li3BO3	1.44E−3	0.33					278
0.93(0.6Li2S—0.4SiS2)—0.07Li3BO3	3.84E−4	0.35					278
0.85(0.6Li2S—0.4SiS2)—0.15Li3BO3	3.42E−4	0.36					278
0.75(0.6Li2S—0.4SiS2)—0.25Li3BO3	7.06E−5	0.38					278
0.95(0.6Li2S—0.4SiS2)—0.05Li3AlO3	1.31E−3	0.31					278
0.94(0.6Li2S—0.4SiS2)—0.06Li3AlO3	6.83E−4	0.34					278
0.92(0.6Li2S—0.4SiS2)—0.08Li3AlO3	4.04E−4	0.34					278
0.825(0.6Li2S—0.4SiS2)—0.175Li3AlO3	1.31E−4	0.36					278
0.975(0.6Li2S—0.4SiS2)—0.025Li3GaO3	6.82E−4	0.31					278
0.95(0.6Li2S—0.4SiS2)—0.05Li3GaO3	3.25E−4	0.32					278
0.92(0.6Li2S—0.4SiS2)—0.08Li3GaO3	3.03E−4	0.35					278
0.89(0.6Li2S—0.4SiS2)—0.11Li3GaO3	1.13E−4	0.38					278
0.97(0.6Li2S—0.4SiS2)—0.03Li3InO3	3.09E−4	0.34					278
0.95(0.6Li2S—0.4SiS2)—0.05Li3InO3	3.25E−4	0.35					278
0.9(0.6Li2S—0.4SiS2)—0.1Li3InO3	6.84E−5	0.40					278
0.95(0.6Li2S—0.4SiS2)—0.05Li4SiO4	1.54E−3	0.38					279
0.9(0.6Li2S—0.4SiS2)—0.1Li4SiO4	4.39E−4	0.40					279
0.95(0.6Li2S—0.4SiS2)—0.05Li2SO4	4.53E−4	0.41					279
0.9(0.6Li2S—0.4SiS2)—0.1Li2SO4	4.70E−5	0.45					279
0.5Li2O—0.1TiO2—0.4P2O5	5.67E−8	0.56					280
0.5025Li2O—0.0025Al2O3—0.095TiO2—0.4P2O5	1.56E−8	0.55					280
0.505Li2O—0.005Al2O3—0.09TiO2—0.4P2O5	1.78E−7	0.50					280
0.5075Li2O—0.0075Al2O3—0.085TiO2—0.4P2O5	2.51E−7	0.57					280
0.51Li2O—0.01Al2O3—0.08TiO2—0.4P2O5	1.58E−7	0.55					280
0.515Li2O—0.015Al2O3—0.07TiO2—0.4P2O5	1.25E−7	0.56					280
0.525Li2O—0.025Al2O3—0.05TiO2—0.4P2O5	2.17E−7	0.56					280
0.53Li2O—0.03Al2O3—0.04TiO2—0.4P2O5	2.72E−7	0.54					280
0.54Li2O—0.04Al2O3—0.02TiO2—0.4P2O5	1.97E−7	0.55					280
0.545Li2O—0.045Al2O3—0.01TiO2—0.4P2O5	7.14E−8	0.56					280
0.95(0.6Li2S—0.4SiS2)—0.05Li4SiO4	1.51E−3	0.34					281
0.90(0.6Li2S—0.4SiS2)—0.1Li4SiO4	4.34E−4	0.37					281
0.8(0.6Li2S—0.4SiS2)—0.2Li4SiO4	1.63E−4	0.43					281
0.95(0.6Li2S—0.4SiS2)—0.05Li3PO4	9.32E−4	0.35					281
0.9(0.6Li2S—0.4SiS2)—0.1Li3PO4	4.55E−4	0.37					281
0.7(0.6Li2S—0.4SiS2)—0.3Li3PO4	2.08E−5	0.46					281
0.6(0.6Li2S—0.4SiS2)—0.4Li3PO4	5.33E−6	0.51					281
0.95(0.6Li2S—0.4SiS2)—0.05Li4GeO4	1.21E−3	0.28					281
0.9(0.6Li2S—0.4SiS2)—0.1Li4GeO4	3.18E−4	0.34					281
0.85(0.6Li2S—0.4SiS2)—0.15Li4GeO4	1.14E−4	0.41					281
Li7PS6	8.0E−5						282
0.7Li2S—0.3P2S5	3.2E−3	0.12					283
0.95(0.6Li2S—0.4SiS2)—0.05Li3BO3	1.40E−3						284
0.93(0.6Li2S—0.4SiS2)—0.07Li3BO3	3.71E−4						284
0.85(0.6Li2S—0.4SiS2)—0.15Li3BO3	3.39E−4						284
0.75(0.6Li2S—0.4SiS2)—0.25Li3BO3	7.15E−5						284
0.95(0.6Li2S—0.4SiS2)—0.05Li3AlO3	1.22E−3						284
0.94(0.6Li2S—0.4SiS2)—0.06Li3AlO3	6.67E−4						284
0.92(0.6Li2S—0.4SiS2)—0.08Li3AlO3	3.94E−4						284
0.825(0.6Li2S—0.4SiS2)—0.175Li3AlO3	1.25E−4						284
0.975(0.6Li2S—0.4SiS2)—0.025Li3GaO3	7.05E−4						284
0.95(0.6Li2S—0.4SiS2)—0.05Li3GaO3	3.36E−4						284
0.92(0.6Li2S—0.4SiS2)—0.08Li3GaO3	3.06E−4						284
0.89(0.6Li2S—0.4SiS2)—0.11Li3GaO3	1.20E−4						284
0.97(0.6Li2S—0.4SiS2)—0.03Li3InO3	3.11E−4						284
0.95(0.6Li2S—0.4SiS2)—0.05Li3InO3	2.99E−4						284
0.90(0.6Li2S—0.4SiS2)—0.10Li3InO3	6.81E−5						284
(0.67Li2S—0.33SiS2)—(0.75Li2S—0.25P2S5)	1.2E−3	0.28					285
0.2Li3N—0.8SiS2	1.46E−6	0.45					286
0.3Li3N—0.7SiS2	2.97E−5	0.36					286
0.4Li3N—0.6SiS2	2.74E−4	0.30					286
0.5Li3N—0.5SiS2	4.47E−5	0.34					286
0.6Li3N—0.4SiS2	2.25E−8	0.63					286
0.6Li2S—0.4P2S3	5.70E−6						287
0.63Li2S—0.37P2S3	2.55E−5						287
0.667Li2S—0.333P2S3	1.1E−4	0.40					287
0.7Li2S—0.3P2S3	7.90E−5						287
0.75Li2S—0.25P2S3	5.08E−5						287
0.6Li2S—0.4SiS2	5.1E−4	0.33					288
0.555Li2S—0.4SiS2—0.045Li3N	1.5E−3	0.28					288
0.525Li2S—0.4SiS2—0.075Li3N	9.6E−4	0.29					288
0.1Li2O—0.1LiCl—0.65B2O3—0.1SiO2—0.05Al2O3	1.9E−4	0.427					289
0.75Li2O—0.25P2S5	1.80E−5	0.48					290
0.75(0.7Li2O—0.3Li2S)—0.25P2S5	2.42E−5	0.48					290
0.75(0.5Li2O—0.5Li2S)—0.25P2S5	2.83E−5	0.46					290
0.75(0.4Li2O—0.6Li2S)—0.25P2S5	4.99E−5	0.44					290
0.75(0.3Li2O—0.7Li2S)—0.25P2S5	8.89E−5	0.40					290
0.75(0.2Li2O—0.8Li2S)—0.25P2S5	1.63E−4	0.38					290
0.75(0.1Li2O—0.9Li2S)—0.25P2S5	2.27E−4	0.36					290
0.75Li2S—0.25P2S5	1.80E−4	0.41					290
0.45Li2—0.55SiS2	1.08E−4	0.40					291
0.5Li2—0.5SiS2	3.36E−4	0.32					291
0.55Li2—0.45SiS2	6.53E−4	0.30					291
0.60Li2—0.4SiS2	1.19E−3	0.29					291
0.63Li2—0.37SiS2	1.05E−3	0.30					291
0.65Li2—0.35SiS2	7.41E−4	0.33					291
0.95(0.5Li2—0.5SiS2)—0.05(0.5Li2O—0.5P2O5)	4.27E−4	0.38					291
0.95(0.53Li2—0.47SiS2)—0.05(0.53Li2O—0.47P2O5)	5.91E−4	0.33					291
0.95(0.55Li2—0.45SiS2)—0.05(0.55Li2O—0.45P2O5)	1.01E−3	0.34					291
0.95(0.58Li2—0.42SiS2)—0.05(0.58Li2O—0.42P2O5)	1.06E−3	0.34					291
0.95(0.6Li2—0.4SiS2)—0.05(0.6Li2O—0.4P2O5)	1.01E−3	0.27					291
0.95(0.63Li2—0.37SiS2)—0.05(0.63Li2O—0.37P2O5)	8.71E−4	0.33					291
0.95(0.65Li2—0.35SiS2)—0.05(0.65Li2O—0.35P2O5)	5.34E−4	0.32					291
0.95(0.67Li2—0.33SiS2)—0.05(0.67Li2O—0.33P2O5)	1.99E−4	0.37					291
0.8(0.55Li2—0.45SiS2)—0.2(0.55Li2O—0.45P2O5)	7.88E−5	0.41					291
0.8(0.6Li2—0.4SiS2)—0.2(0.6Li2O—0.4P2O5)	7.69E−5	0.41					291
0.8(0.65Li2—0.35SiS2)—0.2(0.65Li2O—0.35P2O5)	5.21E−5	0.42					291
0.65Li2S—0.35P2S5	4.14E−5						292
0.675Li2S—0.325P2S5	7.84E−5						292
0.7Li2S—0.3P2S5	1.58E−3	0.39					292
0.725Li2S—0.275P2S5	4.51E−4						292
0.75Li2S—0.25P2S5	3.67E−4						292
0.6Li2S—0.4SiS2	1.69E−4						293
0.1LiI—0.9(0.6Li2S—0.4SiS2)	2.35E−4						293
0.2LiI—0.8(0.6Li2S—0.4SiS2)	3.52E−4						293
0.3LiI—0.7(0.6Li2S—0.4SiS2)	7.42E−4						293
0.5Li2S—0.5SiS2	1.58E−6						293
0.1LiI—0.9(0.5Li2S—0.5SiS2)	3.99E−5						293
0.2LiI—0.8(0.6Li2S—0.4SiS2)	1.23E−4						293
0.3LiI—0.7(0.6Li2S—0.4SiS2)	3.62E−4						293
Li6Si2S7	4.11E−4	0.37					294
0.95Li6Si2S7—0.05Li6B4O9	4.11E−4	0.35					294
0.9Li6Si2S7—0.1Li6B4O9	3.76E−4	0.39					294
0.875Li6Si2S7—0.125Li6B4O9	2.77E−4	0.39					294
0.75Li6Si2S7—0.25Li6B4O9	1.42E−4	0.40					294
0.95Li6Si2S7—0.05Li6B4S9	4.90E−4	0.37					294
0.925Li6Si2S7—0.075Li6B4S9	3.65E−4	0.38					294
0.9Li6Si2S7—0.1Li6B4S9	4.73E−4	0.38					294
0.875Li6Si2S7—0.125Li6B4S9	4.40E−4	0.37					294
0.75Li6Si2S7—0.25Li6B4S9	5.02E−4	0.36					294
0.63Li6Si2S7—0.37Li6B4S9	4.39E−4	0.39					294
(Li2S)60(SiS2)28(P2S5)12	1.23E−3	0.34					295
Li7La3Zr2O12-5 wt % LiPO3	2.5E−6	0.51					120
Li7La3Zr2O12-3 wt %	1.5E−5	0.44					120
65Li2O•27B2O3•8SiO2
Li7La3Zr2O12-5 wt %	2.5E−5	0.39					120
40.2Li2O•5.7Y2O3•54.1SiO2
0.6Li2S—0.4P2S5	3.32E−6	0.52					296
0.667Li2S—0.333P2S5	3.836E−5	0.44					296
0.7Li2S—0.3P2S5	3.77E−5	0.45					296
0.75Li2S—0.25P2S5	2.79E−4	0.40					296
0.8Li2S—0.2P2S5	1.32E−4	0.44					296
(0.75Li2S—0.25P2S5)	2.68E−4	0.26					297
0.95(0.75Li2S—0.25P2S5)—0.05LiBH4	3.98E−4	0.25					297
0.89(0.75Li2S—0.25P2S5)—0.11LiBH4	6.18E−4	0.26					297
0.67(0.75Li2S—0.25P2S5)—0.33LiBH4	1.13E−3	0.21					297
Li7P2.9S10.85Mo0.01	4.8E−3	0.24					298
Li7P3S11	2.6E−3	0.29					298
Li7P2.9Mn0.1S10.7I0.3	5.6E−3	0.22					299
Li11AlP2S12	8.02E−4	0.26					300
Li3PS4	1.78E−4	0.33					301
Li3PS4 - 2 wt % Al2O3	2.27E−4	0.35					301
Li3PS4 - 5 wt % Al2O3	1.96E−4	0.35					301
Li3PS4 - 8 wt % Al2O3	1.60E−4	0.36					301
Li3PS4 - 10 wt % Al2O3	1.50E−4	0.36					301
Li3PS4 - 30 wt % Al2O3	9.96E−5	0.36					301
Li3PS4 - 50 wt % Al2O3	9.38E−7	0.44					301
Li3PS4 - 70 wt % Al2O3	3.92E−8	0.60					301
Li3PS4 - 90 wt % Al2O3	1.54E−9	0.79					301
Li3PS4 - 2 wt % SiO2	2.28E−4	0.32					301
Li3PS4 - 5 wt % SiO2	1.96E−4	0.33					301
Li3PS4 - 8 wt % SiO2	1.60E−4	0.33					301
Li3PS4 - 10 wt % SiO2	1.50E−4	0.33					301
Li3PS4 - 30 wt % SiO2	1.00E−4	0.35					301
Li3PS4 - 50 wt % SiO2	3.80E−5	0.36					301
Li3PS4 - 70 wt % SiO2	5.92E−6	0.38					301
Li3PS4 - 90 wt % SiO2	8.53E−9	0.41					301
Li3PS4 - 5 wt % Li6ZnNb4O14	2.28E−4	0.29					301
Li3PS4 - 10 wt % Li6ZnNb4O14	2.43E−4	0.31					301
Li3PS4 - 15 wt % Li6ZnNb4O14	2.41E−4	0.32					301
Li3PS4 - 20 wt % Li6ZnNb4O14	2.22E−4	0.33					301
Li3PS4 - 30 wt % Li6ZnNb4O14	1.87E−4	0.34					301
Li3PS4 - 50 wt % Li6ZnNb4O14	1.42E−4	0.36					301
Li3PS4 - 70 wt % Li6ZnNb4O14	7.23E−5	0.38					301
Li3PS4 - 90 wt % Li6ZnNb4O14	2.99E−7	0.40					301
Li3PS4	1.46E−4	0.38					302
Li3PS4 - 10 wt % Li7La3Zr2O12	2.96E−4	0.36					302
Li3PS4 - 20 wt % Li7La3Zr2O12	3.70E−4	0.35					302
Li3PS4 - 25 wt % Li7La3Zr2O12	4.10E−4	0.35					302
Li3PS4 - 30 wt % Li7La3Zr2O12	5.38E−4	0.36					302
Li3PS4 - 35 wt % Li7La3Zr2O12	4.00E−4	0.36					302
Li3PS4 - 40 wt % Li7La3Zr2O12	3.33E−4	0.36					302
Li3PS4 - 60 wt % Li7La3Zr2O12	2.19E−4	0.40					302
Li3PS4 - 70 wt % Li7La3Zr2O12	1.26E−5	0.43					302
Li3PS4 - 90 wt % Li7La3Zr2O12	6.04E−6	0.44					302
Li7La3Zr2O12	5.20E−8	0.47					302
Li3.45Ge0.45P0.55S3.1Se0.9	9.8E−4						303
Li3.4Ge0.4P0.6S3.2Se0.8	1.17E−3						303
Li3.35Ge0.35P0.65S3.3Se0.7	1.20E−3						303
Li3.3Ge0.3P0.7S3.4Se0.6	1.33E−3						303
Li3.25Ge0.25P0.75S3.5Se0.5	5.03E−4						303
Li3.20Ge0.20P0.8S3.6Se0.4	1.08E−3						303
Li3.15Ge0.15P0.85S3.7Se0.3	8.16E−4						303
Li3.1Ge0.1P0.9S3.8Se0.2	1.13E−3						303
Li3.05Ge0.05P0.95S3.9Se0.1	1.41E−3						303
Li3PS4	9.35E−4						303
0.8Li20—0.2P2S5	1.54E−5						304
0.05Li2S—0.75Li2O—0.2P2S5	1.39E−5						304
0.1Li2S—0.7Li2O—0.2P2S5	1.59E−5						304
0.15Li2S—0.65Li2O—0.2P2S5	2.32E−5						304
0.2Li2S—0.6Li2O—0.2P2S5	2.89E−5						304
0.25Li2S—0.55Li2O—0.2P2S5	3.80E−5						304
0.3Li2S—0.5Li2O—0.2P2S5	4.35E−5						304
0.35Li2S—0.45Li2O—0.2P2S5	5.26E−5						304
0.4Li2S—0.4Li2O—0.2P2S5	4.45E−5						304
0.45Li2S—0.35Li2O—0.2P2S5	6.35E−5						304
0.5Li2S—0.3Li2O—0.2P2S5	8.11E−5						304
0.55Li2S—0.25Li2O—0.2P2S5	1.12E−4						304
0.6Li2S—0.2Li2O—0.2P2S5	1.12E−4						304
0.65Li2S—0.15Li2O—0.2P2S5	1.13E−4						304
0.7Li2S—0.1Li2O—0.2P2S5	1.09E−4						304
0.75Li2S—0.05Li2O—0.2P2S5	1.43E−4						304
0.8Li2S—0.2P2S5	2.99E−4						304
0.75Li2O—0.25P2S5	1.55E−5						304
0.05Li2S—0.7Li2O—0.25P2S5	1.42E−5						304
0.1Li2S—0.65Li2O—0.25P2S5	2.52E−5						304
0.15Li2S—0.6Li2O—0.25P2S5	2.67E−5						304
0.2Li2S—0.55Li2O—0.25P2S5	2.74E−5						304
0.25Li2S—0.5Li2O—0.25P2S5	3.80E−5						304
0.3Li2S—0.45Li2O—0.25P2S5	5.88E−5						304
0.35Li2S—0.4Li2O—0.25P2S5	1.33E−5						304
0.4Li2S—0.35Li2O—0.25P2S5	2.44E−5						304
0.45Li2S—0.3Li2O—0.25P2S5	2.30E−5						304
0.5Li2S—0.25Li2O—0.25P2S5	9.56E−6						304
0.55Li2S—0.2Li2O—0.25P2S5	7.06E−5						304
0.6Li2S—0.15Li2O—0.25P2S5	9.27E−5						304
0.65Li2S—0.1Li2O—0.25P2S5	1.15E−4						304
0.7Li2S—0.05Li2O—0.25P2S5	9.76E−5						304
0.75Li2S—0.25P2S5	1.60E−4						304
0.7Li20—0.3P2S5	5.78E−11						304
0.05Li2S—0.65Li2O—0.3P2S5	1.51E−8						304
0.1Li2S—0.6Li2O—0.3P2S5	7.78E−8						304
0.15Li2S—0.55Li2O—0.3P2S5	2.90E−7						304
0.2Li2S—0.5Li2O—0.3P2S5	1.67E−5						304
0.25Li2S—0.45Li2O—0.3P2S5	8.64E−7						304
0.3Li2S—0.4Li2O—0.3P2S5	1.62E−6						304
0.35Li2S—0.35Li2O—0.3P2S5	3.68E−6						304
0.4Li2S—0.3Li2O—0.3P2S5	5.86E−6						304
0.45Li2S—0.25Li2O—0.3P2S5	5.10E−6						304
0.5Li2S—0.2Li2O—0.3P2S5	8.33E−6						304
0.55Li2S—0.15Li2O—0.3P2S5	1.01E−5						304
0.6Li2S—0.1Li2O—0.3P2S5	2.29E−5						304
0.65Li2S—0.05Li2O—0.3P2S5	2.48E−5						304
0.7Li2S—0.3P2S5	5.34E−5						304
0.9Li3PS4•10ZnO	2.9E−4						305
0.7Li2S—0.3P2S5	7.10E−4	0.23					306
0.7Li2S—0.29P2S5—0.01Li3PO4	1.83E−3	0.19					306
0.7Li2S—0.28P2S5—0.02Li3PO4	9.89E−4	0.21					306
0.7Li2S—0.27P2S5—0.03Li3PO4	4.40E−4	0.25					306
0.7Li2S—0.25P2S5—0.05Li3PO4	2.67E−4	0.29					306
0.7Li2S—0.3P2S5	1.67E−3	0.23					307
0.99(0.7Li2S—0.3P2S5)—0.01Li2ZrO3	2.86E−3	0.18					307
0.98(0.7Li2S—0.3P2S5)—0.02Li2ZrO3	1.22E−3	0.25					307
0.95(0.7Li2S—0.3P2S5)—0.05Li2ZrO3	7.42E−4	0.29					307
Li2.7PO3.9	7E−8	0.68					308
Li3.6(Si0.19P0.82)O4.2	2.0E−7	0.57					308
Li3.1PO3.8N0.16	2.00E−6	0.57					308
Li3.3PO3.8N0.22	2.40E−6	0.56					308
Li2.9PO3.3N0.46	3.30E−6	0.54					308
Li4.4PO4.3	9.39E−7	0.64					309
Li4.0PO3.9N0.4	1.70E−6	0.62					309
Li3.7PO3.4N0.7	2.36E−6	0.60					309
Li3.5PO3.2N0.8	2.59E−6	0.59					309
Li3.4PO3.1N0.9	2.81E−6	0.58					309
Li3.2PO3.0N	2.99E−6	0.57					309
Li2.9PO2.6N0.91	2.1E−6	0.52					310
Li1.8PO1.2N1.5	1.7E−6	0.49					310
Li3.3PO2.9N0.83	3.1E−6	0.47					310
0.45B2S3—0.55Li2S	8.19E−5	0.23					311
0.815(0.45B2S3—0.55Li2S)—0.185LiI	3.08E−4	0.20					311
0.69(0.45B2S3—0.55Li2S)—0.31LiI	7.58E−4	0.23					311
0.33B2S3—0.67Li2S	2.26E−4	0.31					311
0.95(0.33B2S3—0.67Li2S)—0.05LiI	4.37E−4	0.29					311
0.9(0.33B2S3—0.67Li2S)—0.1LiI	4.81E−4	0.28					311
0.85(0.33B2S3—0.67Li2S)—0.15LiI	4.92E−4	0.28					311
0.75(0.33B2S3—0.67Li2S)—0.25LiI	6.10E−4	0.27					311
0.66(0.33B2S3—0.67Li2S)—0.34LiI	5.22E−4	0.32					311
0.6(0.33B2S3—0.67Li2S)—0.4LiI	4.89E−4	0.35					311
0.29B2S3—0.71Li2S	2.71E−4	0.32					311
0.95(0.29B2S3—0.71Li2S)—0.05LiI	3.72E−4	0.31					311
0.875(0.29B2S3—0.71Li2S)—0.125LiI	6.27E−4	0.29					311
0.78(0.29B2S3—0.71Li2S)—0.22LiI	6.56E−4	0.29					311
0.64(0.29B2S3—0.71Li2S)—0.36LiI	8.10E−4	0.36					311
	3.03E−4	0.36					311
0.92(0.25B2S3—0.75Li2S)—0.08LiI	3.83E−4	0.30					311
0.89(0.25B2S3—0.75Li2S)—0.11LiI	3.48E−4	0.33					311
0.5Li2S—0.5SiS2	4.80E−5						312
0.985(0.5Li2S—0.5SiS2)—0.015Li3PO4	6.28E−5						312
0.975(0.5Li2S—0.5SiS2)—0.025Li3PO4	8.76E−5						312
0.95(0.5Li2S—0.5SiS2)—0.05Li3PO4	8.68E−5						312
0.9(0.5Li2S—0.5SiS2)—0.1Li3PO4	6.76E−5						312
	1.85E−4						312
0.99(0.6Li2S—0.4SiS2)—0.01Li3PO4	2.53E−4						312
0.97(0.6Li2S—0.4SiS2)—0.03Li3PO4	3.97E−4						312
0.95(0.6Li2S—0.4SiS2)—0.05Li3PO4	2.03E−4						312
0.9(0.6Li2S—0.4SiS2)—0.1Li3PO4	5.20E−5						312
0.61Li2S—0.39SiS2	5.24E−4						312
0.99(0.61Li2S—0.39SiS2)—0.01Li3PO4	5.05E−4						312
0.985(0.61Li2S—0.39SiS2)—0.015Li3PO4	5.96E−4						312
0.98(0.61Li2S—0.39SiS2)—0.02Li3PO4	7.69E−4						312
0.975(0.61Li2S—0.39SiS2)—0.025Li3PO4	6.36E−4						312
0.97(0.61Li2S—0.39SiS2)—0.03Li3PO4	5.83E−4						312
0.95(0.61Li2S—0.39SiS2)—0.05Li3PO4	4.68E−4						312
0.9(0.61Li2S—0.39SiS2)—0.1Li3PO4	1.28E−4						312
0.99(0.65Li2S—0.35SiS2)—0.01Li3PO4	3.60E−4						312
0.97(0.65Li2S—0.35SiS2)—0.03Li3PO4	2.62E−4						312
0.95(0.65Li2S—0.35SiS2)—0.05Li3PO4	1.81E−4						312
0.9(0.65Li2S—0.35SiS2)—0.1Li3PO4	7.13E−5						312
0.7Li2S—0.3P2S5	5.2E−3						313
LiI	3.07E−7						314
0.998LiI—0.002CaI2	9.80E−7						314
0.99LiI—0.01CaI2	5.54E−6	0.43					314
LiI	2.74E−8	0.43					315
0.8LiI—0.2Al2O3	6.84E−6	0.35					315
0.7LiI—0.3Al2O3	2.07E−5	0.33					315
0.6LiI—0.4Al2O3	3.94E−5	0.33					315
0.5LiI—0.5Al2O3	2.58E−5	0.33					315
0.4LiI—0.6Al2O3	6.76E−6	0.37					315
Li3.5P0.5Si0.5O4	4.27E−7	0.57					19
Li3.5P0.5Ge0.5O4	7.89E−6	0.56					19
Li3.5As0.5Si0.5O4	4.05E−6	0.55					19
Li3.5V0.5Si0.5O4	1.20E−5	0.53					19
Li3.5As0.5Ge0.5O4	2.83E−5	0.51					19
Li3.5V0.5Ge0.5O4	3.00E−5						19
Li3.5As0.5Ti0.5O4	3.22E−5	0.52					19
Li3.5As0.5V0.5O4	4.01E−5	0.49					19
LiHf2(PO4)3—0.1Li2O	1.12E−4						19
LiHf2(PO4)3—0.2Li2O	2.78E−5						19
LiHf2(PO4)3—0.3Li2O	2.58E−5						19
LiHf2(PO4)3—0.4Li2O	3.40E−5						19
LiTi2(PO4)3	1.69E−6	0.30					316
0.95LiTi2(PO4)3—0.05Li3PO4	5.52E−5	0.29					316
0.9LiTi2(PO4)3—0.1Li3PO4	1.38E−4	0.28					316
0.8LiTi2(PO4)3—0.2Li3PO4	1.93E−4	0.31					316
0.7LiTi2(PO4)3—0.3Li3PO4	2.45E−4	0.30					316
0.95LiTi2(PO4)3—0.05Li3BO3	3.59E−5	0.30					316
0.9LiTi2(PO4)3—0.1Li3BO3	2.54E−4	0.30					316
0.8LiTi2(PO4)3—0.2Li3BO3	2.97E−4	0.30					316
0.7LiTi2(PO4)3—0.3Li3BO3	2.45E−4	0.29					316
0.5LiTi2(PO4)3—0.5Li3BO3	2.73E−5	0.31					316
LiTi2(PO4)3	1.00E−4						317
LiTi2(PO4)3—0.15LiPO4	6.00E−4						317
LiTi2(PO4)3—0.3LiPO4	9.92E−4						317
LiTi2(PO4)3—0.6LiPO4	1.23E−3						317
LiTi2(PO4)3—0.9LiPO4	1.10E−3						317
LiTi2(PO4)3—0.15LiBO3	4.80E−4						317
LiTi2(PO4)3—0.3LiBO3	1.66E−3						317
LiTi2(PO4)3—0.6LiBO3	1.12E−3						317
LiTi2(PO4)3—0.9LiBO3	8.91E−4						317
LiTi2(PO4)3—1.5LiBO3	6.48E−4						317
LiTi2(PO4)3—0.2Li2SO4	8.35E−4						317
LiTi2(PO4)3—0.4Li2SO4	1.66E−3						317
LiTi2(PO4)3—0.6Li2SO4	5.67E−4						317
LiTi2(PO4)3—0.4LiCl	6.45E−4						317
LiTi2(PO4)3—0.8LiCl	1.28E−3						317
LiTi2(PO4)3—1.2LiCl	1.02E−3						317
LiTi2(PO4)3—0.4LiNO3	1.18E−3						317
LiTi2(PO4)3—0.8LiNO3	1.49E−3						317
LiTi2(PO4)3—1.2LiNO3	9.95E−4						317
Li0.39La0.54TiO3	1.08E−3	0.316					318
(Li0.39La0.54)1.006Al0.006Ti0.994O3	1.13E−3	0.308					318
(Li0.39La0.54)1.01Al0.02Ti0.98O3	1.58E−3	0.278					318
(Li0.39La0.54)1.03Al0.06Ti0.94O3	1.39E−3	0.290					318
(Li0.39La0.54)1.005Cr0.01Ti0.99O3	9.52E−4	0.300					318
	1.01E−3	0.315					318
(Li0.39La0.54)1.025Cr0.05Ti0.95O3	1.04E−3	0.298					318
La0.51Li0.34TiO2.94	1E−3	0.38					319
La0.57Li0.26TiO2.99	1E−3	0.34					319
La0.6Li0.16TiO3.01	6.3E−4	0.33					319
La0.64Li0.067TiO3	7.9E−5	0.36					319
(La0.5Li0.5)0.95Sr0.05TiO3	1.49E−3						319
(La0.5Li0.5)0.9Sr0.1TiO3	1.30E−3						319
(La0.5Li0.5)0.75Sr0.25TiO3	8.99E−5						319
(La0.5Li0.5)0.95Ba0.05TiO3	7.61E−4						319
La0.63Li0.1Mg0.5W0.5O3	1.69E−6	0.39					319
Li0.5La0.5TiO3	8.67E−4	0.28					320
Li0.5La0.5Ti0.98Sn0.02O3	4.86E−4						320
Li0.5La0.5Ti0.96Sn0.04O3	3.89E−4						320
Li0.5La0.5Ti0.94Sn0.06O3	3.52E−4	0.294					320
Li0.5La0.5Ti0.9Sn0.1O3	2.60E−4						320
Li0.5La0.5Ti0.98Zr0.02O3	4.16E−4						320
Li0.5La0.5Ti0.96Zr0.04O3	2.86E−4						320
Li0.5La0.5Ti0.94Zr0.06O3	2.23E−4						320
Li0.5La0.5Ti0.9Zr0.1O3	7.05E−5						320
Li0.5La0.5Ti0.998Mn0.002O3	9.12E−4						320
Li0.5La0.5Ti0.996Mn0.004O3	9.64E−4						320
Li0.5La0.5Ti0.994Mn0.006O3	1.08E−3						320
Li0.5La0.5Ti0.992Mn0.008O3	1.13E−3						320
Li0.5La0.5Ti0.99Mn0.01O3	1.13E−3						320
Li0.5La0.5Ti0.998Ge0.002O3	9.12E−4						320
Li0.5La0.5Ti0.996Ge0.004O3	9.64E−4						320
Li0.5La0.5Ti0.994Ge0.006O3	1.08E−3						320
Li0.5La0.5Ti0.992Ge0.008O3	1.13E−3	0.265					320
Li0.5La0.5Ti0.99Ge0.01O3	1.13E−3						320
La0.58Li0.36Ti0.95Mg0.05O3	2.1E−4	0.29					321
La0.56Li0.36Ti0.95Al0.05O3	6.4E−4	0.26					321
La0.55Li0.36Ti0.95Mn0.05O3	1.9E−4	0.29					321
La0.55Li0.36Ti0.95Ge0.05O3	3.6E−4	0.29					321
La0.55Li0.36Ti0.95Ru0.05O3	5.2E−5	0.28					321
La0.51Li0.36Ti0.95W0.05O3	7.3E−4	0.27					321
La0.55Li0.36Ti0.9W0.1O3	4.4E−4	0.27					321
La0.55Li0.36Ti0.995Al0.005O3	1.1E−3	0.28					321
La0.55Li0.36Ti0.992Al0.008O3	6.5E−4	0.29					321
La0.54Li0.36Ti0.995W0.005O3	2.6E−4	0.30					321
La0.54Li0.36TiO3	8.9E−4	0.29					321
La0.606Li0.06Ti0.94Al0.06O3	1.68E−6	0.36					322
La0.566Li0.1Ti0.9Al0.1O3	7.34E−6	0.35					322
La0.516Li0.15Ti0.85Al0.15O3	9.66E−6	0.36					322
La0.466Li0.2Ti0.8Al0.2O3	4.28E−5	0.33					322
La0.416Li0.25Ti0.75Al0.25O3	7.66E−5	0.35					322
La0.366Li0.3Ti0.7Al0.3O3	1.72E−5	0.33					322
Li0.12La0.63TiO3	2.00E−4						323
Li0.18La0.61TiO3	4.43E−4						323
Li0.24La0.59TiO3	9.93E−4						323
Li0.3La0.57TiO3	1.10E−3						323
Li0.39La0.54TiO3	1.02E−3						323
Li0.45La0.52TiO3	9.05E−4						323
LiZr2(PO4)3	4.77E−7						324
Li1.05Al0.05Zr1.9(PO4)3	5.79E−7						324
Li1.1Al0.1Zr1.8(PO4)3	6.35E−7						324
Li1.2Al0.2Zr1.6(PO4)3	1.90E−6	0.48					324
Li1.225Al0.225Zr1.55(PO4)3	2.13E−6	0.48					324
Li1.25Al0.25Zr1.5(PO4)3	2.06E−6	0.48					324
Li1.275Al0.275Zr1.45(PO4)3	3.05E−6	0.48					324
Li1.3Al0.3Zr1.4(PO4)3	1.91E−6	0.48					324
LiHf2(PO4)3	3.42E−6						325
LiHfTi(PO4)3	5.63E−7						325
Li0.1Zr1.1Nb0.9P3O12	6E−6						325
LiTi2(PO4)3	1.04E−7						326
Li1.1Sc0.1Ti1.9(PO4)3	1.75E−5						326
Li1.2Sc0.2Ti1.8(PO4)3	4.11E−5	0.34					326
Li1.3Sc0.3Ti1.7(PO4)3	4.06E−5						326
Li1.4Sc0.4Ti1.6(PO4)3	9.43E−6						326
Li1.5Sc0.5Ti1.5(PO4)3	5.42E−7						326
Li1.1Y0.1Ti1.9(PO4)3	2.94E−7						326
Li1.2Y0.2Ti1.8(PO4)3	7.95E−7						326
Li1.3Y0.3Ti1.7(PO4)3	1.01E−6	0.40					326
Li1.4Y0.4Ti1.6(PO4)3	2.97E−7						326
LiTi2(PO4)3—0.5LiF	2.318E−4	0.28					327
LiTi2(PO4)3	7.181E−6	0.48					327
14Li2O—9Al2O3—38TiO2—39P2O5	1.3E−3	0.33					328
Li6.6La3Zr1.6Ta0.4O12	3.13E−4	0.38					329
Li6.6La2.875Y0.125Zr1.6Ta0.4O12	3.17E−4	0.35					329
Li6.6La2.75Y0.25Zr1.6Ta0.4O12	4.36E−4	0.34					329
Li6.6La2.5Y0.5Zr1.6Ta0.4O12	2.26E−4	0.39					329
Li2ZrS3	7.3E−6						330
Li2.2Zn0.1Zr0.9S3	1.2E−4						330
0.7Li2S—0.3P2S5	8.1E−5	0.425					12
Li7PS6	1.61E−6	0.16					176

Section II. Labels for Comparing all Descriptors-Simplification Combinations

A subset of the digitized labels was used for comparing between the different semi-supervised learning models. In total, the label subset is comprised of 155 structures. The subset is required because not all structures are compatible with all the descriptor transformations. Some descriptor-structure combinations produce coding errors, imaginary values, or infinite values. To directly compare all the descriptors, its necessary to have a common set of labels. The 155 labels that worked for all descriptors is listed in the subsequent table:

	σ25° C.	Ea	Space	Space	Other
Compound	(S cm−1)	(eV)	Group	Group #	names	ICSD	Citation
Li4P2O7	<1E−10	1.617	P1	2		248414	8
Li7P3S11	3.2E−3	0.124	P1	2		157654	5
Li7BiO6	8.80E−07	0.58	P1	2		155950	3
Li7SbO6	6.70E−08	0.7	P1	2		413370	3
Li6CuB4O10	1.00E−13	0.92	P1	2	β-Li6CuB4O10	4819	10
LiAlSi3O8	1.30E−10		C1	2		81980	1
Li3BP2O8	9.60E−12	0.62	P1	2		248343	7
LiSn2(PO4)3	2.04E−9		P1	2		83832	2
LiV(PO4)F	8.1E−7	0.23	P1	2		183876	6
Li2NaBP2O8	4.40E−18	1.21	P1	2		291512	7
LiMgSO4F	5.40E−08	0.54	P1	2		281119	9
Li2ZnGeO4	1.00E−07	0.4	Pc	7		34362	13
Li4SiO4	5.00E−10	0.55	P21/m	11		238603	17
Li3.7P0.3Si0.7O4	3.84E−7		P21/m	11		35168	19
Li7.22Si1.5P0.5O8	1.64E−7	0.48	P21/m	11		238602	16
Li3InCl6	2.04E−3	0.35	C2/m	12		89617	20
Li2P2S6	7.80E−11	0.48	C2/m	12		253894	21
LiPO3	1.00E−09		P2/c	13		51630	28
LiAlSi4O10	1.01E−10		P2/c	13		194284	1
LaLiO2	<1E−10	0.92	P21/C	14		239278	36
LiBO2	1.00E−08	0.71	P21/C	14		200891	34
LiSbO2	<1E−10	0.88	P21/C	14		262075	39
LiYO2	1.80E−08	0.72	P21/C	14		45511	33
LiAlCl4	1.00E−06	0.47	P21/C	14		35275	32
Li3BO3	7.40E−11	0.63	P21/C	14		9105	30
Li2SO4	1.40E−14	1.1	P21/C	14		2512	29
Li6Ge2O7	8.50E−07	0.43	P21/C	14		31050	31
LiGaBr4	7.00E−6	0.54	P21/C	14		61337	25
Li4Zn(PO4)2	<1E−10	1.3	P21/C	14	α-Li4Zn(PO4)2	255464	38
La(Li0.76Mg0.08)O2	7.27E−10	0.66	P21/C	14		239280	36
(La0.9Sr0.1)LiO2	6.29E−10	0.62	P21/C	14		239279	36
Li2Sr2Al(PO4)3	<1E−10	1.02	P21/C	14		431319	40
Li2.5V2(PO4)3	1.9E−7		P21/C	14		240269	37
Li2SnS3	1.50E−05	0.59	C2/c	15		251656	43
LiVO3	2.048E−9		C2/c	15		51443	48
Li6Zr2O7	5.20E−10	0.68	C2/c	15		73835	41
Li3AlF6	5.00E−07	0.54	C2/c	15		85171	42
LiTa2PO8	1.6E−3	0.32	C2/c	15		267438	44
LiBaP2O7	1.00E−10		C2/c	15		280927	45
Li3Na5(TiS4)2	8.80E−06	0.4	C2/c	15		391258	46
LiGd(PO3)4	<1E−10	1.7	C2/c	15		416442	47
Li3.7Zn0.7Ga0.3(PO4)2	<1E−10	0.91	P212121	19	β′-	255466	38
					Li3.7Zn0.7Ga0.3(PO4)2
Li3SbS4	1.5E−6	0.518	Pmn21	31		8407	51
Li3PS4	2.60E−07	0.49	Pmn21	31	γ-Li3PS4	180318	52
Li3SbS3	1.00E−07	0.4	Pna21	33		424834	55
LiGaO2	2.40E−14	0.86	Pna21	33		18152	53
LiB6OgF	5.40E−24	1.38	Pna21	33		420286	54
LiSi2N3	6.17E−08	0.64	Cmc21	36		34118	56
Li2(PO2N)	<1E−10	0.57	Cmc21	36		188493	57
LiGa2GeS6	3.80E−08	0.47	Fdd2	43		254406	58
Li3AlO4	5.00E−10	0.99	Pmmn	59		16229	64
Li14Nd5(Si11N19O5)O2F2	1.7E−10	0.69	Pmmn	59		262923	65
Li2SiN2	1.60E−07		Pbca	61		420126	66
Li5GaO4	5.00E−09	0.71	Pbca	61	α-Li5GaO4	9082	64
Li3PS4	1.60E−04	0.36	Pnma	62	β-Li3PS4	180319	52
Li3PO4	4.2E−18	1.24	Pnma	62	γ-Li3PO4	79427	70
Li3PO4	<1E−10	1.14	Pnma	62	γ-Li3PO4	20208	68
Li4SnS4	7.0E−5	0.29	Pnma	62		290832	80
Li4SnSe4	2E−5	0.45	Pnma	62		193768	76
Li4GeS4	2.00E−07	0.53	Pnma	62		290831	79
Li4GeS4	2E−7	0.53	Pnma	62		92200	71
Li2ZnI4	4.00E−08	0.58	Pnma	62		402062	81
Li3.5Ge0.5V0.5O4	1.77E−5		Pnma	62		66576	84
Li6.6SiPO8	1.48E−7	0.49	Pnma	62		238601	16
Li3.75Ge0.75V0.25O4	5.66E−6		Pnma	62		150918	73
Li4Zn(PO4)2	<1E−10	1.1	Pnma	62	β-	255465	38
					Li4Zn(PO4)2
Li2.88PO3.73N0.14	1.4E−13	0.97	Pnma	62		79426	70
Li2Mg2(MoO4)3	<1E−10	0.71	Pnma	62		170956	75
Li3.70Ge0.85W0.15O4	3.80E−5		Pnma	62		150920	73
Li14Zn(GeO4)4	1.00E−06	0.24	Pnma	62		100169	72
Nd0.54Li0.36TiO3	3.42E−8	0.50	Pnma	62		81047	86
Li6.5O8P1.5Si0.5	4.49E−07	0.44	Pnma	62		238600	16
Pr0.51Li0.39TiO2.96	5.34E−7	0.44	Pnma	62		81048	86
LiZnSO4F	2.80E−05	0.2455	Pnma	62		261343	78
Li3.5Zn0.5Ga0.5(PO4)2	<1E−10	1.02	Pnma	62	β-	255468	38
					Li3.5Zn0.5Ga0.5(PO4)2
Li4H8C14O4	1E−8	0.777	Cmcm	63	LiCl*H2O	281198	88
Li2MgBr4	7.80E−10	0.77	Cmmm	65		73276	89
Li0.18La0.61TiO3	2.0E−4	0.432	Cmmm	65		99398	90
LiBiO2	3.80E−08	0.1	Ibam	72		46022	30
LiZnPS4	5.4E−8		I4	82		95785	69
(Li1.19Zn0.9)PS4	0.65E−5	0.25	I4	82		264463	69
(Li1.69Zn0.66)PS4	1.30E−4	0.181	I4	82		264462	69
(Li0.5Ce0.5)(MoO4)	1.3E−8	0.4	I41/a	88		186450	91
(Li0.5Ce0.25Sm0.25)(MoO4)	1.8E−10	0.5	I41/a	88		186452	91
(Li0.5Ce0.25Pr0.25)(MoO4)	1E−9	0.5	I41/a	88		186451	91
Li2TeO4	<1E−10	1.129	P4122	91		1485	92
Li3BN2	1.60E−10	0.67	P42212	94	α-Li3BN2	655673	93
Li2B4O7	1.00E−10		I41cd	110		65930	94
La0.52Li0.45TiO3	5.01E−4		P4/mmm	123		50434	97
Li(NdTiO4)	<1E−10	0.87	P4/nmmZ	129		91844	99
Li4PS4I	1.2E−4	0.37	P4/nmmZ	129		432169	101
Li(LaTiO4)	<1E−10	0.83	P4/nmmZ	129		91843	99
La0.62Li0.14(Mg0.5W0.5)O3	1.2E−5	0.37	P4/nmm	129		151902	100
Li6ZnO4	9.40E−09	0.61	P42/nmc	137		62137	64
Li10SnP2S12	7E−3	0.27	P42/nmc C	137		193755	107
Li10SnP2S12	3.98E−3	0.305	P42/nmc	137		255750	108
Li10GePS12	1.21E−2		P42/nmc	137		188887	104
Li10GeP2S12	2.46E−2	0.274	P42/nmc	137		241439	108
Li10GeP2S12	1.20E−02	0.25	P42/nmc	137		255749	110
Li10.35Ge1.35P1.65S12	1.44E−2	0.269	P42/nmc S	137		193947	104
Li10.35Si1.35P1.65S12	6.5E−3		P42/nmcS	137		252037	109
Li9.81Sn0.81P2.19S12	5.5E−3		P42/nmc	137		252040	109
Li10.2(Sn0.2Si0.8)1.2P1.8S12	7.82E−3		P42/nmcS	137		5667	111
Li10.2(Sn0.2Si0.8)1.2P1.8S12	2.69E−3		P42/nmcS	137		257948	111
Li10.5(Sn0.2Si0.8)1.5P1.5S12	8.79E−3		P42/nmcS	137		5668	111
Li10(Ge0.776Sn0.224)P2S12	1.41E−2	0.276	P42/nmc	137		255748	108
LiLaNb2O7	<1E−8		I4/mmm	139		72566	114
Li4Sr3Nb6O20	<1E−10		I4/mmm	139		87824	115
Li4Sr3.056Nb6O20	<1E−10	0.74	I4/mmm	139		109168	115
Li4Sr3Nb5.77Fe0.23O19.77	<1E−10		I4/mmm	139		87823	115
Li4SrN2	2.30E−13	0.9	I41/amd	141		87413	116
LiAlO2	1.10E−12	0.97	I41/amd	141	r-LiAlO2	99517	33
LiSCO2	<1E−10	1.047	I41/amd	141		257819	117
LiSCO2	1.00E−12	0.87	I41/amd	141		36124	33
Li0.9Sc0.9Zr0.1O2	<1E−10	0.912	I41/amd	141		257820	117
Li7La3Zr2O12	1.63E−6	0.54	I41/acdZ	142	“tetraganol-LLZO”	183684	119
LiAlGeO4	<1E−10	0.97	R3H	146		257741	123
LiGaSiO4	3.00E−16	0.9	R3H	146		65125	122
LiGa0.5Al0.5GeO4	<1E−10	1.06	R3H	146		257740	123
LiNaSO4	8.80E−10		P31c	159		14364	125
Li5NCl2	1.20E−06	0.5	R3m	166		84763	131
LiGe2(PO4)3	4.83E−9	0.654	R3cH	167		69763	133
LiZr2(PO4)3	2.96E−10		R3cH	167		201935	2
LiTi2(PO4)3	7.61E−6	0.38	R3cH	167		95979	132
LiGe2(PO4)3	3.33E−7		R3cH	167		263767	2
Li1.3(Al0.23Y0.07Ti1.7)(PO4)3	3.84E−8		R3cH	167		253243	138
Li9Mg3(PO4)4F3	<1E−10	0.835	P63	173		426103	148
LiLa9Si6O26	<1E−10		P63/m	176		291218	150
Li0.284Sm4.512Si3O12.91	<1E−10		P63/m	176		83279	150
Pb6.12Ca1.9Li1.96(PO4)6	<1E−10	1.05	P63/m	176		59615	149
Li5La3Nb2O12	8E−6	0.43	I213	199		54865	159
(K0.1Li0.9)(SbO3)	1.36E−8		Pn3Z	201		200984	160
Li2CoTi3O8	<1E−10	1.33	P4332	212		86166	163
Li2ZnGe3O8	<1E−10	2.14	P4332	212		86169	163
Li2MgTi3O8	<1E−10	0.71	P4332	212		86165	163
(Li0.55Mg0.45)(Li0.445Mg0.055)Ti1.504	1.53E−11	0.786	P4332	212		168145	164
(Li0.61Mg0.39)(Li0.46Mg0.005Ti0.035)Ti1.504	6.56E−10	0.685	P4332	212		168144	164
Li2VCl4	6.95E−6		F43m	216		74959	166
Li5NI2	4.00E−6		F43m	216		16800	165
Li6PO5Cl	5.54E−10	0.66	F43m	216		421479	173
Li7PN4	1.60E−07	0.4	P43n	218		69017	95
Li9NS3	8.30E−07	0.52	Pm3m	221		240749	185
Li3OBr	1.10E−06	0.74	Pm3m	221		67265	194,195
Li2(OH)Br	1.20E−6	0.75	Pm3m	221		200874	184
LiI	1E−7		Fm3m	225		414244	197
Li7.2N1.6Cl2.4	8.4E−7	0.49	Fm3m	225		49646	131
Li0.19La0.67(Ti0.9Co0.1)O3	1.08E−4		Fm3m	225		151535	182
LiCdCl4	5.80E−07	0.44	Fd3m	227		74958	199
Li2MnCl4	4.79E−6		Fd3m	227		69678	166
Li2MgCl4	6.24E−7		Fd3m	227		74957	166
LiSrTa2O6F	<1E−10	0.604	Fd3m	227		236010	200
Li1.9Mn0.9Ga0.1Cl4	2.37E−7		Fd3m	227		50305	198
Li(Li0.34Ti1.66)O4	6.03E−8	0.506	Fd3m	227		168137	164
(Li0.74Mg0.26)(Li0.40Mg0.04Ti1.56)O4	1.51E−9	0.639	Fd3m	227		168142	164
(Li0.826Mg0.174)(Li0.374Mg0.026Ti1.60)O4	4.24E−9	0.615	Fd3m	227		168141	164

Section III. Labels Used for the Final SOAP Model

Once the best-performing descriptor-simplification is identified, an expanded set of labels can be employed. The mathematical transformation for the SOAP descriptor is compatible with most of the ˜26,000 structures. In addition to the 155 labels used for descriptor comparisons, 64 labels were added. The full list of labels is included in the table below:

	σ25° C.	Ea	Space	Space	Other
Compound	(S cm−1)	(eV)	Group	Group #	names	ICSD	Citation
Li4P2O71	<1E−10	1.617	P1	2		248414	8
Li7P3S11	3.2E−3	0.124	P1	2		157654	5
Li7BiO6	8.80E−07	0.58	P1	2		155950	3
Li7SbO6	6.70E−08	0.7	P1	2		413370	3
Li6CuB4O10	1.00E−13	0.92	P1	2	β-Li6CuB4O10	4819	10
LiAlSi3O8	1.30E−10		C1	2		81980	1
Li3BP2O8	9.60E−12	0.62	P1	2		248343	7
LiSn2(PO4)3	2.04E−9		P1	2		83832	2
LiV(PO4)F	8.1E−7	0.23	P1	2		183876	6
LiMgSO4F	5.40E−08	0.54	P1	2		281119	9
Li2NaBP2O8	4.40E−18	1.21	P1	2		291512	7
Li2ZnGeO4	1.00E−07	0.4	Pc	7		34362	13
Li4SiO4	5.00E−10	0.55	P21/m	11		238603	17
Li4SiS4	5.00E−08	0.56	P21/m	11		59708	15
Li3.7P0.3Si0.7O4	3.84E−7		P21/m	11		35168	19
Li7.22Si1.5P0.5O8	1.64E−7	0.48	P21/m	11		238602	16
Li2P2S6	7.80E−11	0.48	C2/m	12		253894	21
Li3InCl6	2.04E−3	0.35	C2/m	12		89617	20
Li17Sb13S28	1.05E−9	0.4	C2/m	12		429902	24
LiPO3	1.00E−09		P2/c	13		51630	28
LiAlSi4O10	1.01E−10		P2/c	13		194284	1
LaLiO2	<1E−10	0.92	P21/c	14		239278	36
LiBO2	1.00E−08	0.71	P21/c	14		200891	34
LiSbO2	<1E−10	0.88	P21/c	14		262075	39
LiYO2	1.80E−08	0.72	P21/c	14		45511	33
Li3BO3	7.40E−11	0.63	P21/c	14		9105	30
Li2SO4	1.40E−14	1.1	P21/c	14		2512	29
LiGaBr4	7.00E−6	0.54	P21/c	14		61337	25
LiAlCl4	1.00E−06	0.47	P21/c	14		35275	32
Li6Ge2O7	8.50E−07	0.43	P21/c	14		31050	31
Li4Zn(PO4)2	<1E−10	1.3	P21/c	14	α-Li4Zn(PO4)2	255464	38
Li2.5V2(PO4)3	1.9E−7		P21/c	14		240269	37
La(Li0.76Mg0.08)O2	7.27E−10	0.66	P21/c	14		239280	36
(La0.9Sr0.1)LiO2	6.29E−10	0.62	P21/c	14		239279	36
Li2Sr2Al(PO4)3	<1E−10	1.02	P21/c	14		431319	40
LiClC3H7NO	1.6E−4	0.881	P21/c	14		238683	35
Li2CrCl4	<1E−10	1.22	C2/c	15		202627	49
Li2ZrO3	6.10E−10	0.78	C2/c	15		94894	33
Li6Zr2O7	5.20E−10	0.68	C2/c	15		73835	41
Li3AlF6	5.00E−07	0.54	C2/c	15		85171	42
Li2SnS3	1.50E−05	0.59	C2/c	15		251656	43
LiVO3	2.048E−9		C2/c	15		51443	48
LiTa2PO8	1.6E−3	0.32	C2/c	15		267438	44
LiBaP2O7	1.00E−10		C2/c	15		280927	45
LiGd(PO3)4	<1E−10	1.7	C2/c	15		416442	47
Li3Na5(TiS4)2	8.80E−06	0.4	C2/c	15		391258	46
Li3.7Zn0.7Ga0.3(PO4)2	<1E−10	0.91	P212121	19	β′-Li3.7Zn0.7Ga0.3(PO4)2	255466	38
Li3SbS4	1.5E−6	0.518	Pmn21	31		8407	51
Li3PS4	2.60E−07	0.49	Pmn21	31	γ-Li3PS4	180318	52
Li3SbS3	1.00E−07	0.4	Pna21	33		424834	55
LiGaO2	2.40E−14	0.86	Pna21	33		18152	53
LiB6O9F	5.40E−24	1.38	Pna21	33		420286	54
LiSi2N3	6.17E−08	0.64	Cmc21	36		34118	56
Li2(PO2N)	<1E−10	0.57	Cmc21	36		188493	57
LiGa2GeS6	3.80E−08	0.47	Fdd2	43		254406	58
La0.595Li0.215TiO3	8.53E−4		Pmmm	47		92234	59
La0.62Li0.14TiO3	4.42E−4		Pmmm	47		92231	59
La0.64Li0.08TiO3	3.35E−4		Pmmm	47		92228	59
Li0.02Na0.48La0.5Nb2O6	3.99E−6		Pmmm	47		180635	60
Li0.04Na0.46La0.5Nb2O6	5.91E−6		Pmmm	47		180634	60
Li0.07Na0.43La0.5Nb2O6	1.23E−5		Pmmm	47		180633	60
Li0.1Na0.4La0.5Nb2O6	1.21E−5		Pmmm	47		180632	60
Li0.2Na0.3La0.5Nb2O6	1.18E−5		Pmmm	47		180631	60
Li0.3Na0.2La0.5Nb2O6	1.11E−5		Pmmm	47		180630	60
Li0.4Na0.1La0.5Nb2O6	9.92E−6		Pmmm	47		180629	60
Li5AlO4	5.00E−10	0.99	Pmmn	59		16229	64
Li14Nd5(Si11N19O5)O2F2	1.7E−10	0.69	Pmmn	59		262923	65
Li2SiN2	1.60E−07		Pbca	61		420126	66
Li5GaO4	5.00E−09	0.71	Pbca	61	α-Li5GaO4	9082	64
Li3PO4	4.2E−18	1.24	Pnma	62	γ-Li3PO4	79427	70
Li3PO4	<1E−10	1.14	Pnma	62	γ-Li3PO4	20208	68
Li3PS4	1.60E−04	0.36	Pnma	62	β-Li3PS4	180319	52
Li4SnS4	7.0E−5	0.29	Pnma	62		290832	80
Li4SnSe4	2E−5	0.45	Pnma	62		193768	76
Li4GeS4	2.00E−07	0.53	Pnma	62		290831	79
Li4GeS4	2E−7	0.53	Pnma	62		92200	71
Li(BH4)	1E−8		Pnma	62		239763	77
Li2ZnI4	4.00E−08	0.58	Pnma	62		402062	81
Li4Zn(PO4)2	<1E−10	1.1	Pnma	62	β-Li4Zn(PO4)2	255465	38
Li2Mg2(MoO4)3	<1E−10	0.71	Pnma	62		170956	75
Li0.2Ca0.4TaO3	3.53E−9	0.54	Pnma	62		151936	74
Li3.5Ge0.5V0.5O4	1.77E−5		Pnma	62		66576	84
Li3.75Ge0.75 V0.25O4	5.66E−6		Pnma	62		150918	73
Li14Zn(GeO4)4	1.00E−06	0.24	Pnma	62		100169	72
Li3.70Ge0.85W0.15O4	3.80E−5		Pnma	62		150920	73
Li6.6SiPO8	1.48E−7	0.49	Pnma	62		238601	16
Li2.88PO3.73N0.14	1.4E−13	0.97	Pnma	62		79426	70
Li6.5O8P1.5Si0.5	4.49E−07	0.44	Pnma	62		238600	16
Nd0.54Li0.36TiO3	3.42E−8	0.50	Pnma	62		81047	86
Pr0.51Li0.39TiO2.96	5.34E−7	0.44	Pnma	62		81048	86
LiZnSO4F	2.80E−05	0.2455	Pnma	62		261343	78
Li3.5Zn0.5Ga0.5(PO4)2	<1E−10	1.02	Pnma	62	β-Li3.5Zn0.5Ga0.5(PO4)2	255468	38
Li0.2(Ca0.36Sr0.04)TaO3	9.2E−9		Pnma	62		151937	74
Li4GeO4	2.80E−10	0.73	Cmcm	63		18096	87
Li4H8Cl4O4	1E−8	0.777	Cmcm	63	LiCl*H2O	281198	88
Li2MgBr4	7.80E−10	0.77	Cmmm	65		73276	89
Li0.18La0.61TiO3	2.0E−4	0.432	Cmmm	65		99398	90
LiBiO2	3.80E−08	0.1	Ibam	72		46022	30
LiZnPS4	5.4E−8		I4	82		95785	69
(Li1.19Zn0.9)PS4	0.65E−5	0.25	I4	82		264463	69
(Li1.69Zn0.66)PS4	1.30E−4	0.181	I4	82		264462	69
(Li0.5Ce0.5)(MoO4)	1.3E−8	0.4	I41/a	88		186450	91
(Li0.5Ce0.25Sm0.25)(MoO4)	1.8E−10	0.5	I41/a	88		186452	91
(Li0.5Ce0.25Pr0.25)(MoO4)	1E−9	0.5	I41/a	88		186451	91
Li2TeO4	<1E−10	1.129	P4122	91		1485	92
Li3BN2	1.60E−10	0.67	P42212	94	α-Li3BN2	655673	93
Li2B4O7	1.00E−10		I41cd	110		65930	94
LiY(BH4)4	1.26E−6		P42c	112		239762	77
LiPN2	1.6E−7	0.40	I42d	122		66007	95
Li0.33La0.5TiO3	1E−3	0.15	P4/mmm	123		82671	96
La0.5Li0.5TiO3	9.25E−4	0.39	P4/mmm	123		92236	59
La0.52Li0.45TiO3	5.01E−4		P4/mmm	123		50434	97
La0.565Li0.305TiO3	9.57E−4		P4/mmm	123		92235	59
La0.58Li0.27TIO3	5.99E−4		P4/mmm	123		82672	97
Li4PS4I	1.2E−4	0.37	P4/nmmZ	129		432169	101
Li(LaTiO4)	<1E−10	0.83	P4/nmmZ	129		91843	99
Li(NdTiO4)	<1E−10	0.87	P4/nmmZ	129		91844	99
La0.62Li0.14(Mg0.5W0.5)O3	1.2E−5	0.37	P4/nmm	129		151902	100
La0.63Li0.11(Mg0.5W0.5)O3	6.8E−6	0.38	P4/nmm	129		151901	100
La0.65Li0.05(Mg0.5W0.5)O3	1.8E−7	0.46	P4/nmm	129		151900	100
Li6ZnO4	9.40E−09	0.61	P42/nmc	137		62137	64
Li10SnP2S12	3.98E−3	0.305	P42/nmc	137		255750	108
Li10SnP2S12	7E−3	0.27	P42/nmc C	137		193755	107
Li10GePS12	1.21E−2		P42/nmc	137		188887	104
Li10GeP2S12	1.20E−02	0.25	P42/nmc	137		255749	110
Li10GeP2S12	2.46E−2	0.274	P42/nmc	137		241439	108
Li10.35Ge1.35P1.65S12	1.44E−2	0.269	P42/nmc S	137		193947	104
Li10.35Si1.35P1.65S12	6.5E−3		P42/nmcS	137		252037	109
Li9.81Sn0.81P2.19S12	5.5E−3		P42/nmc	137		252040	109
Li10(Ge0.776Sn0.224)P2S12	1.41E−2	0.276	P42/nmc	137		255748	108
Li10.2(Sn0.2Si0.8)1.2P1.8S12	7.82E−3		P42/nmcS	137		5667	111
Li10.2(Sn0.2Si0.8)1.2P1.8S12	2.69E−3		P42/nmcS	137		257948	111
Li10.5(Sn0.2Si0.8)1.5P1.5S12	8.79E−3		P42/nmcS	137		5668	111
LiLaNb2O7	<1E−8		I4/mmm	139		72566	114
Li4Sr3Nb6O20	<1E−10		I4/mmm	139		87824	115
Li4Sr3.056Nb6O20	<1E−10	0.74	I4/mmm	139		109168	115
Li4Sr3Nb5.77Fe0.23O19.77	<1E−10		I4/mmm	139		87823	115
Li3BN2	8.70E−08	0.55	I41/amd	141	β-Li3BN2	155126	93
LiScO2	<1E−10	1.047	I41/amd	141		257819	117
LiScO2	1.00E−12	0.87	I41/amd	141		36124	33
Li4SrN2	2.30E−13	0.9	I41/amd	141		87413	116
LiAlO2	1.10E−12	0.97	I41/amd	141	r-LiAlO2	99517	33
Li0.9Sc0.9Zr0.1O2	<1E−10	0.912	I41/amd	141		257820	117
Li7La3Zr2O12	1.63E−6	0.54	I41/acdZ	142	“tetraganol-LLZO”	183684	119
Li7La3Zr2O12	9.9E−6	0.43	I41/acdZ	142		238687	121
Li7La3HfO12	9.85E−7	0.53	I41/acdZ	142	“tetragonal-LLHO”	174202	118
LiAlGeO4	<1E−10	0.97	R3H	146		257741	123
LiGaSiO4	3.00E−16	0.9	R3H	146		65125	122
LiGa0.5Al0.5GeO4	<1E−10	1.06	R3H	146		257740	123
LiGaGeO4	<1E−10	1.12	R3	148		257739	123
LiNaSO4	8.80E−10		P31c	159		14364	125
Li4P2S6	2.38E−07	0.29	P31m	162		242170	127
Li2.667Mg0.667P2S6	4.00E−06	0.46	P31m	162		95607	126
Li3.333Mg0.333P2S6	8.20E−8	0.517	P31m	162		95606	126
Li3ErCl6	3.3E−4	0.41	P3m1	164		50151	129
Li5NCl2	1.20E−06	0.5	R3m	166		84763	131
LiGe2(PO4)3	3.33E−7		R3cH	167		263767	2
LiGe2(PO4)3	4.83E−9	0.654	R3cH	167		69763	133
LiZr2(PO4)3	2.96E−10		R3cH	167		201935	2
LiTi2(PO4)3	7.61E−6	0.38	R3cH	167		95979	132
Li(Ti0.4Sn1.6)(PO4)3	3.15E−6		R3cH	167		183677	135
Li(Ti0.6Sn1.4)(PO4)3	9.42E−6		R3cH	167		183676	135
Li(Ti1.4Sn0.6)(PO4)3	2.28E−5	0.32	R3cH	167		183672	135
Li1.3Al0.3Ti1.7(PO4)3	7E−4		R3cH	167		257190	139
Li1.3(Al0.3Ti1.7)(PO4)3	8.02E−7		R3cH	167		253240	138
Li1.2Al0.2Ge1.8(PO4)3	4.83E−5	0.387	R3cH	167		263760	133
Li1.3(Al0.23Y0.07Ti1.7)(PO4)3	3.84E−8		R3cH	167		253243	138
Li1.3(Al0.23Sc0.07Ti1.7)(PO4)3	1.94E−7		R3cH	167		253242	138
Li1.3(Al0.23Ga0.07Ti1.7)(PO4)3	4.46E−6		R3cH	167		253241	138
LiIO3	1.90E−07		P63	173		35473	147
Li9Mg3(PO4)4F3	<1E−10	0.835	P63	173		426103	148
LiEu9Si6O26	<1E−10		P63/m	176		291220	150
LiLa9Si6O26	<1E−10		P63/m	176		291218	150
Li0.284Sm4.512Si3O12.91	<1E−10		P63/m	176		83279	150
Pb6.12Ca1.9Li1.96(PO4)6	<1E−10	1.05	P63/m	176		59615	149
Li3(NH2)2I	1E−5	0.58	P63mc	186		167528	152
Ba3LiTa5ZrSi4O26	<1E−10	0.79	P62m	189		239277	153
Li3N	1.2E−3	0.25	P6/mmm	191		26540	154
Li3N	3.00E−04	0.26	P6/mmm	191		156894	155
Fe2Na2K(Li3Si12O30)	<1E−10	1.22	P6/mcc	192		235750	156
Li3P	7.03E−4	0.18	P63/mmc	194		642223	157
Li5La3Nb2O12	8E−6	0.43	I213	199		54865	159
(K0.1Li0.9)(SbO3)	1.36E−8		Pn3Z	201		200984	160
Li8SiP4	4.5E−5	0.404	Pa3	205		235186	161
Li8GeP4	1.8E−5	0.435	Pa3	205	α-Li8GeP4	235184	161
Li3AlN2	5.00E−08	0.45	Ia3	206		257464	162
Li2ZnGe3O8	<1E−10	2.14	P4332	212		86169	163
Li2MgTi3O8	<1E−10	0.71	P4332	212		86165	163
Li2CoTi3O8	<1E−10	1.33	P4332	212		86166	163
(Li0.55Mg0.45)(Li0.445Mg0.055)Ti1.504	1.53E−11	0.786	P4332	212		168145	164
(Li0.61Mg0.39)(Li0.46Mg0.005Ti0.035)Ti1.504	6.56E−10	0.685	P4332	212		168144	164
Li2VCl4	6.95E−6		F43m	216		74959	166
Li5NI2	4.00E−6		F43m	216		16800	165
Li6PO5Cl	5.54E−10	0.66	F43m	216		421479	173
LiCe(BH4)3Cl	1.03E−4		I43m	217		185218	178
Li7PN4	1.60E−07	0.4	P43n	218		69017	95
Li4B7O12Cl	2.4E−5		F43c	219		1125	179
Li9NS3	8.30E−07	0.52	Pm3m	221		240749	185
Li3OBr	1.10E−06	0.74	Pm3m	221		67265	194, 195
Li2(OH)Br	1.20E−6	0.75	Pm3m	221		200874	184
(La0.55Li0.45)(Ti0.9Al0.1)O3	1.51E−3		Pm3m	221		254045	186
(La0.6Li0.4)(Ti0.8Al0.2)O3	5.68E−4		Pm3m	221		254046	186
(La0.65Li0.35)(Ti0.7Al0.3)O3	1.61E−4		Pm3m	221		254047	186
(La0.402Li0.368Sr0.230)(TiO3)	2.87E−5	0.36	Pm3m	221		190827	183
(La0.46Li0.429Sr0.111)(TiO3)	1.97E−4	0.33	Pm3m	221		190826	183
(La0.49Li0.461Sr0.049)(TiO3)	7.09E−4	0.33	Pm3m	221		190825	183
(Li0.16Sr0.69)(Ga0.25Ta0.75)O3	3.69E−6	0.359	Pm3m	221		291520	187
Li0.31La0.63((Ti0.9Co0.1)O3	2.60E−4		Pm3m	221		151533	182
LiI	1E−7		Fm3m	225		414244	197
Li7.2N1.6Cl2.4	8.4E−7	0.49	Fm3m	225		49646	131
Li0.19La0.67(Ti0.9Co0.1)O3	1.08E−4		Fm3m	225		151535	182
LiCdCl4	5.80E−07	0.44	Fd3m	227		74958	199
Li2MgCl4	6.24E−7		Fd3m	227		74957	166
Li2MnCl4	4.79E−6		Fd3m	227		69678	166
Li(Li0.34Ti1.66)O4	6.03E−8	0.506	Fd3m	227		168137	164
Li1.9Mn0.9Ga0.1Cl4	2.37E−7		Fd3m	227		50305	198
(Li0.74Mg0.26)(Li0.40Mg0.04Ti1.56)O4	1.51E−9	0.639	Fd3m	227		168142	164
(Li0.826Mg0.174)(Li0.374Mg0.026Ti1.60)O4	4.24E−9	0.615	Fd3m	227		168141	164
LiSrTa2O6F	<1E−10	0.604	Fd3m	227		236010	200

Section IV. W_σ Optimization

Ward's minimum variance method applied to the conductivity labels (Wσ) is used to assess the utility of each descriptor-simplification combination. The Wσ is calculated after agglomerative clustering, for each clustering set:

W _σ=Σ_k=1^nCΣ_i∈Ck[log(σ_RT)_i−log(σ_RT)_k]²

where n_C is the number of clusters in a set, C_k is cluster k, and where log(σ_RT)_k denotes the mean for all labels in cluster k. Lower Wσ values indicate that the descriptor-simplification combination results in clustering where structures with similar conductivity are grouped together. Whereas a large Wσ indicates that the clusters have little correlation to the conductivity labels.

A frozen-state strategy is employed to prevent any label from dropping out of the Wσ calculation. The frozen-state strategy operates by calculating the partial variance (PV) for each label at each clustering depth:

PV _{x,C k} =[log(σ_RT)_x−log(σ_RT)_k]²

where PV_x,Ck is the partial variance for label x, when label x is assigned to cluster k. The PV for each label is saved before summing all the partial variances to yield the Wσ. At each subsequent clustering depth, all new clusters are checked to determine whether any cluster contains a single label. If a label is the only label in a cluster, then that label's partial variance is frozen: its PV_x,Ck becomes equal to the saved state from the previous cluster depth:

PV _{x,C j} =PV _{x,C k}

where Cj denotes the cluster with only one label and Ck denotes the cluster that label x previously resided in. Without the frozen state strategy, poor models will reach desirable Wσ values at sufficient depths of clustering. The artificial depression of the Wσ value occurs because clusters that contain a single label evaluate to 0 (the label mean and cluster mean are the same). Whereas the frozen state strategy effectively “remembers” how well (or poorly) the label was clustered before it drops out.

Hyperparameter tuning was employed for some of the descriptors. At least one W_σ representation exists for each unique combination of structure simplification and descriptor. However, some of the descriptors can be altered by tuning associated hyperparameters, resulting in more W_σ representations. The descriptors with hyperparameter tuning are the global instability index, radial distribution function, smooth overlap of atomic positions (SOAP), and mXRD. A grid search was done over the hyperparameters, for each descriptor, with parameters shown in Table 3.

TABLE 3
	Hyper-		Values attempted in
Descriptor	parameter	Description	grid search
Global	r_cut	The distance, in angstroms, to search	[1.0, 1.1, . . . , 5.9, 6.0]
instability		for neighbors when calculating bond
index		valences.
Radial	cutoff	The distance, in angstroms, over which	[1, 2, . . . , 29, 30]
distribution		the radial distribution function should
function		be calculated.
	bin_size	The radial distance, in angstroms, for	[0.01, 0.02, . . . , 0.09,
		each bin.	0.1, 0.2, . . . , 0.9, 1.0]
Smooth	rcut	The radial cutoff for the local region in	[1, 2, . . . , 29, 30]
overlap of		angstroms.
atomic	nmax	The number of radial basis functions	[2, 3, . . . , 8, 9]
positions		used.
(SOAP)	lmax	The maximum degree of spherical	[1, 2, . . . , 8, 9]
		harmonics used.
	average	The averaging mode.	[‘outer’, ‘inner’]
mXRD	pattern_length	The number of 2θ values that will be	[101, 201, . . . , 901,
		calculated between 0° and 90°.	1001]

Ultimately, the SOAP-CAN descriptor-simplification outperforms all other descriptor-simplifications when the averaging hyperparameter is set to ‘outer’. Setting the ‘outer’ hyperparameter results in averaging over the power spectrum of different sites. Whereas the ‘inner’ setting averages over the sites first, before summing up the magnetic quantum numbers. The other three hyperparameters (rcut, nmax, and Imax) are less consequential, with most combinations tested outperforming all other non-SOAP descriptors. To illustrate the point, three different SOAP-CAN outcomes are depicted in FIG. 4, plotted against the best-performing outcomes from density-CAN, mXRD-A40, orbital field matrix, and structure heterogeneity-A40. The three SOAP-CAN outcomes are those with the lowest W_σ mean for the depth of clustering ranges: 2-100, 101-200, and 201-300. The respective hyperparameters for the three SOAP-CAN descriptors are [rcut=2, nmax=4, Imax=2], [rcut=4, nmax=2, Imax=2], and [rcut=3, nmax=5, Imax=3].

Section V. W_Ea Optimization

Each clustering outcome is also assessed by labeling with approximate activation energies for ion hopping. The activation energies are calculated using a bond valence site energy (BVSE) method developed by Adams and Rao^331,332. The strategy approximates the E_a as the sum of an attractive Morse-type potential term and a repulsive Coulombic interaction term. The Morse-type potential term represents mobile ion interactions with lattice anions. While the Coulombic interaction term represents mobile ion interactions with lattice cations. Relative to DFT-based methods, the BVSE method is a computationally lean approach that can be used to readily assess thousands of structures. However, the BVSE method tends to overestimate activation energies because it (1) does not allow for structural relaxation as the mobile ion moves and (2) does not consider repulsive interactions between mobile ions^331,332. The BVSE method has been implemented by He et al. and is available for use through their python API³³³. Using the BVSE method, we label 6845 structures with activation energies (6845 is the number of structures successfully solved given a computing time cutoff of 20-minutes for each structure). Ward's minimum variance method applied to the activation energy labels (W_Ea) is calculated in a similar manner to the Wu:

$W_{\mathrm{Ea}}=\sum _{k=1}^{n_c}\sum _{i\in C_k}{\left[{\left(E_{a,\mathrm{BVSE}}\right)}_i-{\left(\stackrel{\_}{E_{a,\mathrm{BVSE}}}\right)}_k\right]}^2$

where n_C is the number of clusters in a set, C_k is cluster k, and where (E_a,B_VSE)_k denotes the mean for all labels in cluster k. Each descriptor's W_Ea results are shown in FIG. 5 for the first 50 clustering sets. For simplicity, only the best-performing simplification-descriptor combination is shown for each descriptor.

For E_a labels, all descriptor-simplification pairings result in better semi-supervised ML performance than randomized clustering. The SOAP descriptor performs well relative to most, but five other descriptors outperform it: CAVD, orbital field matrix-CAN, density, mXRD-CAMN, and the packing efficiency descriptors. The favorable performance of CAVD is anticipated because the BVSE calculation directly uses the CAVD descriptor as a parameter. The favorable performance of the density and packing efficiency descriptors may be explained by their similarity to CAVD: the Voronoi decomposition to encode void space is dependent on the density and packing efficiency of the structure. Similarly, the orbital field matrix descriptor relies on calculation of Voronoi polyhedra to understand the coordination environment for each atom. A mXRD-CAMN descriptor-simplification performs well on the BVSE label set; however, the mXRD representation used by Toyota (mXRD—A40) drops from to 14^th best on the E_a label set. The result may suggest that the mXRD—A40 pairing does not generalize well. When comparing the top 10 descriptors for each label set, 6 descriptors are common to both approaches: SOAP, density, mXRD, structure heterogeneity, orbital field matrix, and bond fraction.

Section VI. Second-Order SOAP Descriptor

Semi-supervised ML models may be further improved by merging descriptors and clustering on the union representation. Second order descriptor unions are examined by combining the best-performing descriptors with all other descriptors. The two input descriptor vectors (d_A and d_B) were combined with a mixing ratio (a) to yield the union representation (d_AB):

d _AB =d _A ∪αd _B

The ideal mixing ratio is unknown for each union and we find that incremental changes to the mixing ratio do not result in continuous changes to the W_σ. Thus, outcomes are manually screened for mixing ratios from 10⁻⁶ to 10⁶ (see supplemental information—section VI). Most descriptor unions result in no improvement to the W_Q, across all mixing ratios. However, the W_σ for SOAP when mixing with the non-simplified sine Coulomb matrix descriptor (for α=2·10⁻⁶-4·10⁻⁶) is lowered by 2-3%, with the exact percentage depending on the depth of clustering.

Almost no descriptor combinations are successful in reducing the W_σ. Excluding combinations that include the SOAP-CAN descriptor, no combinations outperform the 1^st order SOAP-CAN representation. For combinations that include SOAP-CAN, some mixing ratios with the sine Coulomb matrix and the Ewald energy descriptors resulted in modest improvements in the W_σ. The best improvement is found when mixing SOAP-CAN with the sine Coulomb descriptor for α=2·10⁻⁶, 3·10⁻⁶, and 4·10⁻⁶. All three combinations result in the same improved curve, plotted below in FIG. 6.

The agglomerative dendrogram in the main text shows that the 2^nd-order SOAP-CAN descriptor facilitates aggregation of high-conductivity labels. In the simplified 9-cluster representation, most of the high-conductivity (σ_RT>10⁻⁵ S cm⁻¹) labels are contained within the 2^nd “mega cluster”. The 2^nd mega cluster accounts for only 15% of the input structure. By clustering further, increasingly dense representations are found. For example, at the 241^st clustering depth, the 21 high-conductivity labels have been sorted into five subclusters (FIG. 7). Taken together, the five subclusters account for 52.5% of the high conductivity labels while containing only 2.2% of the input structures. We note that the control (random clustering) exhibits a Ward Variance 214% greater than the 2^nd-order SOAP-CAN model at the 241^st clustering depth. The difference in Ward Variance illustrates that the 2^nd-order SOAP-CAN model is much better at identifying high-conductivity structures, relative to random selection.

Section VII. Climbing Image—Nudged Elastic Band

Migration barriers for Li ion hopping are evaluated with the Climbing Image—Nudged Elastic Band (CI-NEB) method as implemented in the QuantumESPRESSO PWneb software package^334-337. Density-functional theory (DFT) calculations are performed using the Perdew-Burke-Ernzerfof (PBE) generalized gradient approximation functional and projector-augmented wave (PAW) sets^338,339. Convergence testing for the kinetic-energy cutoff of the plane-wave basis and the k-point sampling is performed for each structure to ensure an accuracy of 1 meV per atom. The lattice parameters and atomic positions of the as-retrieved structure are optimized. Supercells are created for each structure that are a minimum of 10 Å in each lattice direction to minimize interactions between periodic images of the mobile ion. To study the migration barrier in the dilute limit, a single Li vacancy is created in the boundary endpoint structures of each studied pathway. A uniform background charge is used to balance excess charge. Each boundary configuration is relaxed until the force on each atom is less than 3×10⁻⁴ eV/Å. Images are created by linearly interpolating framework atomic positions between the initial and final boundary configurations. The initial pathway for the mobile ion is generated from the BVSE output minimum energy pathway to promote faster convergence of the NEB calculation. An NEB force convergence threshold of 0.05 eV/Å is used. The calculation is first converged using the default NEB algorithm and then restarted with the CI scheme to allow for the maximum energy of the pathway to be determined.

Section VIII. a-Li_2.95B_0.95Si_0.05S₃ Impedance

Electrochemical impedance data for the amorphized Si-substituted Li₃BS₃ (a-Li_2.95B_0.95Si_0.05S₃) suggests the presence of two RC features. The VSP-300 potentiostat can supply a maximum sinusoidal frequency of 3 MHz, sufficient to resolve a partial semicircle in the Nyquist impedance plot (FIG. 17). Attempted fits to the partial semicircle reveal that it would not intersect the origin at higher frequencies, suggesting the presence of an additional RC feature. It is plausible that two RC features exist, describing the bulk and grain-boundary transport of Li⁺. A more conservative estimate of the conductivity (σ_tot) can be derived by extrapolating a linear of the Warburg tail to the x intercept. While the more conservative estimate is used in the main manuscript, we note here that the actual bulk conductivity is likely higher.

Section IX. Full List of Promising Structures

Excluding the labeled dataset, there are 50 compounds that are predicted to be stable and to exhibit a Li-hopping activation energy below 600 meV. Ten of the predicted compounds have already been experimentally examined and are hereafter excluded: Li₂O, Li₂S, LiCl, LiI, LiBr, Li₆AsS₅I, Li₄Ti₅O₁₂, Li₂InCl₃, LiInI₄, Li₆NiCl₈. Another nine are excluded because they are used in cathodes, anodes, or glassy electrolyte formulations: LiFeCl₄, Li₂CO₃, Li₂PtO₃, Li₂NiGe₃O₈, Li₂CrO₄, Li₂SeO₄, LiAlS, Li₂Mn₃NiO₈, LiInSe₂. The remaining 31 promising structures are discussed below and plotted by ascending activation energy in FIG. 18.

a. Stable Compounds

Each structure is examined in order of ascending activation energy in FIGS. 20A-20AE.

b. Quasi-Stable Compounds (E_hull below 15 meV)

Excluding the labeled dataset, there are 34 compounds that are predicted to be within 15 meV of the convex hull (E_hull) and to exhibit a Li-hopping activation energy below 600 meV. Ten of the predicted compounds have already been experimentally examined and are hereafter excluded: Li₃SbS₄, Li₆AsS₅I, Li₆PS₅₁, Li₃ScCl₆, Li₂MnBr₄, Li₃N, LiTi₂P₃O₁₂, Li₁₀SiP₂S₁₂, Li₂ZnCl₄, Li₃InO₃. Another three are currently being excluded because they are used in cathodes: Li₃NbS₄, Li₃CuS₂, Li₆VCl₈. The remaining 21 promising structures are discussed below and plotted by ascending activation energy in FIG. 19.

See FIGS. 22A-22U.

c. Unknown-Stability Compounds (Sans Materials Project Entry)

There are 18 predictions that have no associated Material's Project entry. These structures lack stability data. Seven of the predicted compounds have already been experimentally examined and are hereafter excluded: Li₂O, Li₂S, Li₇Y₇Zr₉S₃₂, Li₄SnSe₄O₁₃, Li₂MnBr₄, Li₅AlS₄, Li₃Fe₂P₃O₁₂. Another five are currently being excluded because they are used in cathodes: Li₂Mn₃NiO₈, Li₂Mn₃CoO₈, Li₅Mn₁₆O₃₂, Li₂Mn₁₅AlO₃₂, Li₃V₂P₃O₁₂. The remaining 6 promising structures are discussed below and plotted in order of ascending activation energy in FIG. 21.

See FIGS. 24A-24F.

Example 2: Experimental Validation of the Semi-Supervised Learning Model: Li₃BS₃

From the ten most promising candidates, Li₃BS₃ was selected for synthesis and characterization. Li₃BS₃ stands out because it has been explored experimentally and computationally before. Experimentally, Vinatier et al. previously determined that Li₃BS₃ has a total DC conductivity of 2.5·10⁻⁷ S cm⁻¹ with an activation energy of 700 meV⁶². The DC measurement was not included in our label set because DC measurements cannot differentiate between ionic and electronic conductivity, so they were categorically discounted from the label set (see supplemental information I for more details on label selection). Although the conductivity and activation energy reported by Vinatier et al. are underwhelming, there are promising theoretical reports. Density functional theory molecular dynamics (DFT-MD) simulations from Sendek et al.⁶³ suggest that Li₃BS₃ should have a room temperature conductivity between 3.1·10⁻⁶ and 9.7·10⁻³ S cm⁻¹. Our NEB-calculated activation energy for Li₃BS₃ is 260 meV, corroborating a previous NEB result from Bianchini et al.⁶⁴. Additionally, Li₃BS₃ is practically attractive because: (1) Li₃BS₃ contains no redox-active metals, (2) band edge calculations have suggested stability against metallic Li⁶⁵, (3) DFT-MD calculations have suggested a kinetic barrier for decomposition against metallic Li⁶³, and (4) the synthesis is reported⁶⁶. It is simpler to avoid redox active metals in the SSE as they may be reduced and oxidized at electrode interfaces. However, we note that Li_0.5La_0.5TiO₃ is a widely studied SSE that contains redox active Ti^67,68 so the compounds we report here that contain Mn, V, and Cu should not be categorically discounted. It is important to note that while studying Li₃BS₃ as a candidate Li-ion conductor for model validation, Kimura et al. reported that a so-called “Li₃BS₃ glass” exhibits an ionic conductivity of 3.6·10⁻⁴ S/cm⁻¹ at 25° C.⁶⁹.

Li₃BS₃ is prepared using solid-state synthesis from Li₂S, B, and S precursors. The diffraction and quantitative Rietveld refinement are shown in FIG. 26A, suggesting a phase pure material. Electrochemical impedance spectroscopy (EIS) is employed at various temperatures and the resultant conductivity is plotted according to the Arrhenius-like relationship (FIG. 26B):

$\sigma =\frac{{\sigma }_0}{T}{e}^{-\frac{E_a}{k_{B}T}}$

where T is the temperature, k_B is the Boltzmann's constant, σ₀ is the conductivity prefactor and E_a is the activation energy for ionic conductivity. The room temperature ionic conductivity (σ_{25° C.}) is 7.16(±0.21)·10⁻⁷ S cm⁻¹ and the activation energy is 400±47 meV. The low conductivity and high activation energy may be due to lack of charge-carrying defects in the Li₃BS₃ lattice^70,71. Although a sufficient carrier concentration is necessary for facile ionic conduction in most materials, the descriptors in the semi-supervised model do not explicitly encode for charge-carrying defects. In the label set, conductivity is likely influenced by the defect concentration but defects are typically not reported. Still, the semi-supervised model may infer a structure's capacity to support conductive defects via correlation with the descriptors.

Li₃BS₃ Synthesis:

Li₃BS₃ is synthesized by reaction of Li₂S (Alfa Aesar, 99.9%), S₈ (Acros Organics, >99.5%), and elemental B (SkySpring Nanomaterials, Inc. 99.99%). The reactants are first mixed stoichiometrically (300 rpm for 1 h) using a planetary ball mill (MSE PMV1-0.4L) in 50 mL ZrO₂ jars with ZrO₂ balls. Two grams of reactants are always combined with 2 large balls (10 mm diameter), 34 medium balls (5 mm diameter), and 8 grams of small balls (3 mm diameter). Loading of ball mill jars occurs in an Ar-filled glovebox (Mbraun) and the jars are sealed before removal. After the 1 h of milling, the precursor mixture is pumped back into the glovebox and 330-340 mg of the powder is loaded into carbon coated vitreous silica ampoules (10 mm ID×12 mm OD). The ampoules are evacuated (<10 mtorr) prior to sealing. Pure Li₃BS₃ is obtained via a four-step heating protocol in a Lindberg/Blue furnace: (1) ramp to 500° C. at 5° C. min-1, (2) hold at 500° C. for 12 h, (3) ramp to 800° C. at 5° C. min-¹, and (4) hold at 800° C. for 6 h. The hot melt is then quenched from 800° C. into room temperature water. Recovered ingots are typically covered in a C shell. The C shell is either sanded off or the ingot is ground into smaller pieces and the C is manually removed.

Example 3: Defect Engineering of Lithium Solid State Electrolyte Material

To test the hypothesis, we use two strategies to engineer vacancies: aliovalent substitution and amorphization via extended ball milling. Aliovalent substitution has been shown to improve conductivity in Li-argyrodites, -sulfides, and -garnets by introducing vacancies^70,71. Similarly, amorphization can introduce defects and vacancies that enable Li⁺ hopping^69,71-73.

Aliovalent substitution of Li₃BS₃ is achieved by substituting Si for B. The XRD patterns and quantitative Rietveld refinements of Li_2.975B_0.975Si_0.025S₃ and Li_2.95B_0.95Si_0.05S₃ are shown in FIG. 26A. The lattice parameters from the refinements are plotted vs. stoichiometry with the Li₃BS₃ end-member in FIG. 26E. The linear trend shows that the materials obey Vegard's law and confirms that Si incorporates into the lattice as a solid-solution. Substitution to 7.5% Si continues the Vegard trend but unidentified impurities are present. With 5% Si substitution, the ionic conductivity is improved to 1.82(±0.21)·10⁻⁵ S cm⁻¹ and the activation energy is decreased to 333±47 meV (FIG. 26D). All error bars reported for electrochemical measurements represent the standard deviation of three replicate cells. Kimura et al. demonstrated that extended ball milling of Li₃BS₃ causes amorphization and improves ionic conductivity, likely due to introduction of defects^62,69. Extended ball milling is attempted on the 5%-substituted Li₃BS₃ to assess whether both defect engineering strategies are compatible. Planetary ball milling of the 5%-substituted Li₃BS₃ for 100 h achieves amorphization (a-Li_2.95B_0.95Si_0.05S₃), as verified by the lack of distinct peaks in the XRD pattern shown in FIG. 26A.

We find that amorphization significantly improves Li-ion conductivity. EIS measurements of a-Li_2.95B_0.95Si_0.05S₃ are shown in FIG. 26E. A high-frequency semicircle is partially resolved which may represent grain boundary or bulk ionic transport. A Warburg tail is evident at lower frequencies, indicating that electronic charge transfer is blocked. Although multiple high-frequency semicircles may exist (see Example 1B: section VII), a conservative estimate of the ionic conductivity is determined by linear fit of the Warburg tail and extrapolation to the x-intercept. The ˜σ_{25° C.} of a-Li_2.95B_0.95Si_0.05S₃ is 1.07(±0.08)·10⁻³ S cm⁻¹ with an activation energy of 345±2 meV (FIG. 26D). The electronic conductivity as measured by DC polarization is less than 4·10⁻¹⁰ S cm⁻¹.

To determine if the local structure in the crystalline material is maintained after amorphization, we turn to ⁷Li and ¹¹B NMR. If the local structure is not altered by amorphization, then it is likely that the ion diffusion pathways are similar. Comparing the ion diffusion pathways is important because the machine learning points to the structure of the crystalline Li₃BS₃ phase. The ⁷Li NMR spectra of Li₃BS₃, Li_2.95B_0.95Si_0.05S₃, and a-Li_2.95B_0.95Si_0.05S₃ are shown in FIG. 26D. All materials show a single resonance at the same chemical shift, suggesting the Li local environment remains unchanged. The resonance width narrows significantly in the amorphous material due to the higher mobility. The ¹¹B NMR measurements are shown in FIG. 26G. The ¹¹B NMR for Li₃BS₃ and Li_2.95B_0.95Si_0.05S₃ show a single, quadrupolar environment that can be assigned to the [BS₃]³⁻ moieties^69,74. The signal from the a-Li_2.95B_0.95Si_0.05S₃ shows a similar signal to that of the crystalline phases but the shape changes, similarly to the previous measurement for amorphous Li₃BS₃⁶⁹. Li₃BS₃, Li_2.95B_0.95Si_0.05S₃, and a-Li_2.95B_0.95Si_0.05S₃ all exhibit a major peak at ˜60 ppm and a relatively minor peak ˜0 ppm. The major peak is assigned to trigonal planar [BS₃]³⁻ while the minor peak likely indicates a minor impurity with tetrahedrally coordinated B^75-77. The change in shape of the ¹¹B spectrum upon amorphization is likely due an averaging of the quadrupolar couplings due to the fast Li dynamics. Thus, Li₃BS₃ and a-Li_2.95B_0.95Si_0.05S₃ have similar local structures and we can attribute the faster Li dynamics to the introduction of charge-carrying defects.

Although investigation of interfacial stability is beyond the scope of the model, we note that the Si-substituted Li₃BS₃ is a promising candidate for future investigations into interfacial stability. Work by Park et al. demonstrated that the (010) facet for Li₃BS₃ has a conduction band minimum 0.5 eV above the Li/Li⁺ couple⁶⁵. Since decomposition of Li₃BS₃ is likely to be mediated by electron injection from Li, their results suggest that thermodynamic stability can be engineered via orientation. From a kinetic perspective, high-temperature DFT-MD simulations show no mobility for B and S, suggesting large kinetic diffusion barriers⁶³. Since decomposition of Li₃BS₃ would entail the diffusion of these species, the reaction may be sluggish or wholly precluded. Interfacial stability has been previously demonstrated for a glassy electrode in the Li—B—S—Si—O phase space⁷⁸. The result may indicate that stability can be engineered into Si-substituted Li₃BS₃ by partial isovalent substitution of 0 for S. Finally, recently-synthesized Li—B—S—X (X═Cl, Br, I) quaternaries have exhibited promising conductivities⁷⁹. With similar elemental composition, the Si-substituted Li₃BS₃ may be a good candidate for a multi-electrolyte architecture with the halide-containing quaternaries¹³

In addition to our experimental model validation, another of the predicted materials, KLi₆TaO₆, was recently synthesized with aliovalent Sn-substitution by Suzuki et al⁸⁰. With a reported ionic conductivity near 10⁻⁵ S cm⁻¹, KLi₆TaO₆ is better than 70% of the SSEs in the semi-supervised labels. Further improvement may be possible via extended amorphization to introduce structural defects, as is observed for Li₃BS₃.

Substituted Li₃BS₃:

Aliovalent substitution is accomplished by adding elemental Si (Acros, 99+%) into the precursor mixture prior to the 1 h mix. Si-substitution stoichiometry assumed that each Si atom replaces one Li and B: Li_3−xB_1−xSi_xS₃. Aside from the addition of Si, all steps are the same as for the synthesis of Li₃BS₃. Amorphization is accomplished via extended planetary ball milling in Ar of the 5% Si-substituted Li₃BS₃ (Li_2.95B_0.95Si_0.05S₃). Approximately 1 g of Li_2.95B_0.95Si_0.05S₃ is combined in a ZrO₂ ball mill jar with 3 large balls (10 mm diameter), 51 medium balls (5 mm diameter), and 12 g of small balls (3 mm diameter). The powder is ground in a planetary ball mill (MSE PMV1-0.4L), under Ar atmosphere, for 100 h.

Material Characterization:

Li₃BS₃ materials are characterized using powder X-ray diffraction (XRD) and electrochemical impedance spectroscopy (EIS). XRD patterns are attained on a Rigaku Smartlab by scanning from 10° to 70° 2θ at 2 degrees per minute. The Smartlab employs a Cu-Kα source with a 20 kV accelerating voltage. For EIS measurements, 50-100 mg of powder is first hot-pressed (100° C., 5 min) into a ¼″ diameter pellet. The pellet faces are polished using diamond lapping powder (Allied High Tech Products Inc.) in sequentially finer grits: 60, 30, 6, 0.5, and 0.1 micron. Au contacts are sputtered (90 s at 40 mA) onto the polished surfaces using a 108 Auto Sputter Coater (Cressington). Pellets are then assembled into a Swagelok ¼″ cell with stainless steel current collectors. After applying pressure with a hand vise (˜100 MPa), EIS data is collected on a VSP-300 with a Biologic low-current channel. All EIS data is collected to an upper frequency of 3 MHz. The lower frequency is case dependent, with a frequency cutoff selected such that the Warburg polarization feature is visible. ⁷Li and ¹¹B MAS MAS NMR spectra were acquired using a Bruker DSX-500 spectrometer with a 4 mm ZrO₂ rotor. The operating frequencies for ⁷Li and ¹¹B are 190.5 and 160.5 MHz, respectively. The ⁷Li and ¹¹B spectra were referenced to a 1 M LiCl aq. solution and BF₃-OEt₂, respectively. A spinning speed of 12 kHz was used, and the spectra were gathered after applying a single 0.5 μs to 15° pulse for both ⁷Li and ¹¹B.

Further Discussion for Examples 1-3

Identification of functional materials is critical for improving technologies. Here, we show the utility of using semi-supervised learning as a method for guiding next-generation materials discovery in emerging fields. The method's focus on identifying the relationships between descriptors, prior to labeling, enables understanding of compositional spaces where most inputs are unlabeled. We demonstrate how semi-supervised learning can be used to identify descriptors correlated with superionic conductivity in Li SSEs. By analyzing all Li-containing structures from the ICSD and MP database, we identify 212 materials that show promise as SSEs. All 212 structures exhibit a BVSE-predicted E_a below 0.6 eV.

The results illustrate why careful screening of descriptors is useful when identifying new materials. While chemical intuition can be useful for descriptor selection, chemical intuition is often biased to favor previously investigated compositional spaces. For material discovery in emerging fields, use of handpicked descriptors may miss complex phenomena that more generally describe the dataset. Descriptor screening reveals which material properties are correlated to a property of interest to help enhance chemical intuition. In the case of Li SSEs, spatial descriptors excel over compositional, bonding, and electronic descriptors: the Smooth Overlap of Atomic Positions (SOAP), modified X-ray diffraction (mXRD), and general density descriptors are within the top four models. For spatial descriptors, simplification of the input structure tends to improve clustering outcomes. Removing the mobile ions from the structure and simplifying the remaining atoms, i.e. the “CAN” simplification, is most effective. Thus, the placement of framework atoms, but not their precise identity, is most correlated with ionic conductivity. Specifying the mobile ion positions hurts the model performance, suggesting a low correlation of mobile ion positions with ionic conductivity.

Predictions from the semi-supervised method are promising starting points for experimental identification of new superionic conductors but defects must be considered. The proposed materials are diverse, with the top thirty including halides, sulfides, tellurides, nitrides, oxides, and oxyhalides (see Example 1B: section IX). As a structure that falls outside of the eight routinely studied SSE classes, we demonstrate experimental characterization of Li₃BS₃ to confirm the utility of the approach. However, pure Li₃BS₃ exhibits poor ionic conductivity. Defects must be introduced into the material to achieve a superionic conductivity above 10⁻³ S cm⁻¹, a value that surpasses most reported SSEs. We note that the defects are introduced while maintaining the local structure of the crystalline material and thus the ionic conduction pathways are likely similar. The need to introduce defects highlights the paramount importance that defects play when measuring real materials. Many of the highest performing SSEs contain charge-carrying defects that are not explicitly encoded in their structure files. It is likely that some of the descriptors indirectly encode information about defects. By using experimental conductivity values as the evaluation metric, we may be prioritizing descriptors that encode information about a structures ability to support charge-carrying defects. Although Li₃BS₃ is a poor conductor, it is clearly able to support charge-carrying defects. The large conductivity difference between pristine Li₃BS₃ and a-Li_2.95B_0.95Si_0.05S₃ highlights the importance of these defects. To improve predictive models and enhance chemical intuition, descriptors that explicitly encode defects are needed.

Now developed, the semi-supervised learning approach can serve as a template for material discovery beyond Li SSEs. The code is thoroughly documented following pythonic coding standards and made freely available on Github. Although the present effort focuses on Li SSEs, the approach is applicable to any material discovery space where labels are sparse. Discovery of new Li cathodes could be accomplished by using Li diffusivity, cathode capacity, and metal redox couple voltages as labels. Discovery of divalent SSEs (e.g. Mg²⁺, Ca²⁺, Zn²⁺) could foreseeably be accomplished in a similar manner. The semi-supervised learning strategy may accelerate identification of fast ionic conductors for ion exchange membranes, solid oxide fuel cells, and various sensor applications.

Example 4: Optional Aspects with Respect to Substitution for B in Lithium Thioborate

In some aspects, the “first dopant” Q in FX1 (Li_3−z[B+Q]₁[S+G]₃) optionally comprises one or more transition metal elements. On the other hand, in some aspects, the “first dopant” Q in FX1 is free of transitional metal elements due to the propensity of transition metal elements to participate in redox reactions occurring in a solid state battery. Selection of the first dopant element (the one or more dopant element corresponding to first dopant Q) is generally dependent on application-specific particular chemistry, redox reactions, voltages, and other conditions.

Example 5: Particularly Useful Aspects

In an aspect, a particularly useful material disclosed herein has a composition characterized by formula FX15A: Li_3−xB_1−xSi_xS₃ (FX15A); wherein x is greater than 0 and less than or approximately equal to 0.05. For example, in an aspect, a furthermore particularly useful material disclosed herein has a composition characterized by formula FX15B: Li_aB_bSi_xS_c (FX15B); wherein a is approximately 2.95, b is approximately 0.95, x is approximately 0.05, and c is approximately 3.0. For example, in an aspect, a yet furthermore particularly useful material disclosed herein has a composition characterized by formula FX15C: Li_2.95B_0.95Si_0.05S₃ (FX15C). It is found that the compositions of FX15A, FX15B, and FX15C may correspond to an optimum or near-optimum doped composition of lithium thioborate with respect to ionic conductivity, optionally with respect to other additional features, where the undoped composition and low-doped composition (e.g., x being less than 0.025) have lower ionic conductivity and higher dopant amounts (e.g., x being greater than or equal to 0.075) cause formation of unfavorable impurities and/or other unfavorable features (e.g., too much disruption of crystallographic structure with respect to that of Li₃BS₃). It is found that compositions of FX15A, FX15B, and FX15C have high ionic conductivity and low electronic conductivity, especially if the material is amorphized. For example, as also discussed in Examples 1A-3, whereas a room temperature (e.g., 25° C.) ionic conductivity of undoped Li₃BS₃ without substitution may be approximately 7.2·10⁻⁷ S/cm substitution/doping of the composition thereby making Li_2.95B_0.95Si_0.05S₃ (FX15C) may result in an increase of ionic conductivity (relative to that of the undoped Li₃BS₃) by a factor of approximately 25 such as to an ionic conductivity of approximately 1.82(±0.21)·10⁻⁵ S cm⁻¹ at room temperature (e.g., 25° C.). Amorphization of the composition Li_2.95B_0.95Si_0.05S₃ (FX15C) may further increase the ionic conductivity (relative to that of the undoped Li₃BS₃) by a factor of at least 1375 such as to an ionic conductivity of approximately 1.07(±0.08)·10⁻³ S cm⁻¹ at room temperature (e.g., 25° C.) or even about 3·10⁻³ S cm⁻¹ according to some aspects. In contrast, the electronic conductivity of these doped compositions of FX15A, FX15B, and FX15C have low electronic conductivity, such as, for example, in aspects, less than or equal to about 4·10⁻¹⁰ S/cm as measured by DC polarization at room temperature (e.g., 25° C.).

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STATEMENTS REGARDING INCORPORATION BY REFERENCE AND VARIATIONS

All references throughout this application, for example patent documents including issued or granted patents or equivalents; patent application publications; and non-patent literature documents or other source material; are hereby incorporated by reference herein in their entireties, as though individually incorporated by reference, to the extent each reference is at least partially not inconsistent with the disclosure in this application (for example, a reference that is partially inconsistent is incorporated by reference except for the partially inconsistent portion of the reference).

The terms and expressions which have been employed herein are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments, exemplary embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims. The specific embodiments provided herein are examples of useful embodiments of the present invention and it will be apparent to one skilled in the art that the present invention may be carried out using a large number of variations of the devices, device components, methods steps set forth in the present description. As will be obvious to one of skill in the art, methods and devices useful for the present methods can include a large number of optional composition and processing elements and steps.

As used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural reference unless the context clearly dictates otherwise. Thus, for example, reference to “a cell” includes a plurality of such cells and equivalents thereof known to those skilled in the art. As well, the terms “a” (or “an”), “one or more” and “at least one” can be used interchangeably herein. It is also to be noted that the terms “comprising”, “including”, and “having” can be used interchangeably. The expression “of any of claims XX-YY” (wherein XX and YY refer to claim numbers) is intended to provide a multiple dependent claim in the alternative form, and in some embodiments is interchangeable with the expression “as in any one of claims XX-YY.”

When a group of substituents is disclosed herein, it is understood that all individual members of that group and all subgroups, including any isomers, enantiomers, and diastereomers of the group members, are disclosed separately. When a Markush group or other grouping is used herein, all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure. When a compound is described herein such that a particular isomer, enantiomer or diastereomer of the compound is not specified, for example, in a formula or in a chemical name, that description is intended to include each isomers and enantiomer of the compound described individual or in any combination. Additionally, unless otherwise specified, all isotopic variants of compounds disclosed herein are intended to be encompassed by the disclosure. For example, it will be understood that any one or more hydrogens in a molecule disclosed can be replaced with deuterium or tritium. Isotopic variants of a molecule are generally useful as standards in assays for the molecule and in chemical and biological research related to the molecule or its use. Methods for making such isotopic variants are known in the art. Specific names of compounds are intended to be exemplary, as it is known that one of ordinary skill in the art can name the same compounds differently.

Certain molecules disclosed herein may contain one or more ionizable groups [groups from which a proton can be removed (e.g., —COOH) or added (e.g., amines) or which can be quaternized (e.g., amines)]. All possible ionic forms of such molecules and salts thereof are intended to be included individually in the disclosure herein. With regard to salts of the compounds herein, one of ordinary skill in the art can select from among a wide variety of available counterions those that are appropriate for preparation of salts of this invention for a given application. In specific applications, the selection of a given anion or cation for preparation of a salt may result in increased or decreased solubility of that salt.

Every device, cell, electrolyte, material, composition, and method described or exemplified herein can be used to practice the invention, unless otherwise stated.

Whenever a range is given in the specification, for example, a temperature range, a time range, or a composition or concentration range, all intermediate ranges and subranges, as well as all individual values included in the ranges given are intended to be included in the disclosure. It will be understood that any subranges or individual values in a range or subrange that are included in the description herein can be excluded from the claims herein.

All patents and publications mentioned in the specification are indicative of the levels of skill of those skilled in the art to which the invention pertains. References cited herein are incorporated by reference herein in their entirety to indicate the state of the art as of their publication or filing date and it is intended that this information can be employed herein, if needed, to exclude specific embodiments that are in the prior art.

As used herein, “comprising” is synonymous with “including,” “containing,” or “characterized by,” and is inclusive or open-ended and does not exclude additional, unrecited elements or method steps. As used herein, “consisting of” excludes any element, step, or ingredient not specified in the claim element. As used herein, “consisting essentially of” does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim. In each instance herein any of the terms “comprising”, “consisting essentially of” and “consisting of” may be replaced with either of the other two terms. The invention illustratively described herein suitably may be practiced in the absence of any element or elements, limitation or limitations which is not specifically disclosed herein.

One of ordinary skill in the art will appreciate that starting materials, biological materials, reagents, synthetic methods, purification methods, analytical methods, assay methods, and biological methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation. All art-known functional equivalents, of any such materials and methods are intended to be included in this invention. The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention that in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims.

Claims

1. A material comprising: a lithium thioborate composition characterized by formula FX1: Li3−z[B+Q]1[S+G]3  (FX1);wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;wherein z is a number greater than 0 and less than or equal to 0.40; andwherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.

2. The material of claim 1 having a greater ionic conductivity than that of an undoped stoichiometric Li3BS3 material by a factor of at least 10 at 25° C., wherein the undoped stoichiometric Li3BS3 material is free of Q and G.

3. The material of claim 1 being characterized by an ionic conductivity greater than 9·10−6 S/cm at 25° C.

4. The material of claim 1, wherein the composition is characterized by the ratio Q/(B+Q) being greater than 0.001 and less than 0.20.

5. (canceled)

6. The material of claim 1, wherein Q is one or more Group 14 elements and/or one or more metal elements.

7. The material of claim 1, wherein Q is Si and/or Ge.

8. The material of claim 1, wherein the composition is characterized by the ratio G/(S+G) being greater than 0.001 and less than 0.20.

9. (canceled)

10. The material of claim 1, wherein G is one or more Group 17 (halogen) elements.

11. The material of claim 1, wherein G is Cl and/or Br.

12. The material of claim 1, wherein the composition is characterized by formula FX2, FX3, or FX4: Li3−x−yB1−x[Q]xS3−y[G]y  (FX2);Li3−xB1−x[Q]xS3  (FX3);Li3−yB1S3−y[G]y  (FX4); wherein:x is selected from the range of 0.005 to 0.20; andy is selected from the range of 0.005 to 0.20.

13. The material of claim 1, wherein the composition is characterized by formula FX3: Li3−xB1−x[Q]xS3  (FX3); wherein:x is greater than 0.25 and less than or equal to 0.05.

14. The material of claim 1 having a total crystallinity less than or equal to 20 wt. %.

15. (canceled)

16. The material of claim 1 being characterized by an ionic conductivity greater than or equal to 1·10−3 S/cm at 25° C.

17. (canceled)

18. The material of claim 3 being characterized by an electronic conductivity less than 4·10−10 S/cm at 25° C.

19. The material of claim 3 being characterized by an activation energy (Ea) for an ionic conductivity of less than 400 meV when its temperature-dependent ionic conductivity is fit to equation EQ1:

20. (canceled)

21. (canceled)

22. (canceled)

23. (canceled)

24. (canceled)

25. A device comprising: a material, the material comprising:a lithium thioborate composition characterized by formula FX1: Li3−z[B+Q]1[S+G]3  (FX1);wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;wherein z is a number greater than 0 and less than or equal to 0.40; andwherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.

26. The device of claim 25 being an electrochemical cell.

27. (canceled)

28. (canceled)

29. A solid state electrolyte comprising: a lithium thioborate composition characterized by formula FX1: Li3−z[B+Q]1[S+G]3  (FX1);wherein Q is a first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;wherein G is a second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;wherein z is a number greater than 0 and less than or equal to 0.40; andwherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.

30. A method of making a material, the method comprising: combining a plurality of precursors comprising lithium, boron, sulfur, and at least one of a first dopant and a second dopant; andheating the combined plurality of precursors to form the material having a lithium thioborate composition;wherein the lithium thioborate composition is characterized by formula FX1: Li3−z[B+Q]1[S+G]3  (FX1);wherein Q is the first dopant being a substitute for B in the composition and being one or more elements each aliovalent with respect to B;wherein G is the second dopant being a substitute for S in the composition and being one or more elements each aliovalent with respect to S;wherein z is a number greater than 0 and less than or equal to 0.40; andwherein the composition comprises only the first dopant, only the second dopant, or both the first dopant and the second dopant.

31. (canceled)

32. (canceled)

33. (canceled)

34. (canceled)

35. (canceled)

36. (canceled)

37. (canceled)

38. (canceled)

39. (canceled)

40. (canceled)

41. (canceled)

42. (canceled)

43. (canceled)

44. (canceled)

45. A method for increasing an ionic conductivity of a reference lithium solid state electrolyte, the method comprising: forming a doped lithium solid state electrolyte having a doped composition;wherein the reference lithium solid state electrolyte has a reference composition, and wherein the doped composition has up to 20 at. % of one or more principal elements substituted with at least one dopant relative to the reference composition;wherein each element of the at least one dopant is aliovalent with respect to the respective substituted principal element; andwherein the doped lithium solid state electrolyte has a greater ionic conductivity than the reference lithium solid state electrolyte by a factor of at least 10.

46. (canceled)

47. (canceled)

48. (canceled)

49. (canceled)

50. (canceled)

51. The material of claim 1 wherein the material is part of a glass electrolyte.

52. The material of claim 1 being amorphous.

53. The material of claim 1 having a total crystallinity less than or equal to 50 wt. %.

54. The material of claim 1 having a total crystallinity less than or equal to 10 wt. %.

55. The material of claim 1 having a total crystallinity less than or equal to 5 wt. %.

56. The material of claim 1, wherein the material has been amorphized to increase its ionic conductivity.

57. The material of claim 56, wherein the amorphized material has an increased amorphous content of the lithium thioborate composition, a decreased total crystallinity of the lithium thioborate composition, and/or an increased concentration of defects in the lithium thioborate composition compared to an equivalent material not having been amorphized.