Predicting Reactivity and Passivation of Solid-State Battery Interfaces

Abstract

In this work, we build a computationally inexpensive, data-driven model that utilizes atomistic structure information to predict the reactivity of interfaces between any candidate solid-state electrolyte material and a Li metal anode. This model is trained on data from ab initio molecular dynamics (AIMD) simulations of the time evolution of the solid electrolyte–Li metal interfaces for 67 different materials. Predicting the reactivity of solid-state interfaces with ab initio techniques remains an elusive challenge in materials discovery and informatics, and previous work on predicting interfacial compatibility of solid-state Li-ion electrolytes and Li metal anodes has focused mainly on thermodynamic convex hull calculations. Our framework involves training machine learning models on AIMD data, thereby capturing information on both kinetics and thermodynamics, and then leveraging these models to predict the reactivity of thousands of new candidates in the span of seconds, avoiding the need for additional weeks-long AIMD simulations. We identify over 300 new chemically stable and over 780 passivating solid electrolytes that are predicted to be thermodynamically unfavored. Our results indicate many potential solid-state electrolyte candidates have been incorrectly labeled unstable via purely thermodynamic approaches using density functional theory (DFT) energetics, and that the pool of promising, Li-stable solid-state electrolyte materials may be much larger than previously thought from screening efforts. To showcase the value of our approach, we highlight two borate materials that were identified by our model and confirmed by further AIMD calculations to likely be highly conductive and chemically stable with Li: LiB₁₃C₂ and LiB₁₂PC.

Introduction

Solid-state batteries (SSBs) offer an alternative energy storage solution with increased energy density and safety¹⁻³ for addressing anthropogenic climate change by electrifying transportation and enabling storage of intermittent renewable energy sources.⁴⁻⁶ The defining feature of SSBs is the solid-state electrolyte (SSE), which replaces the traditional liquid electrolyte found in today’s commercial Li-ion and Li metal batteries. A leading strategy for designing SSEs is to use ceramic crystalline solids as they are generally nonflammable and mechanically rigid. Furthermore, ceramic SSEs may enable the use of Li metal anodes since an SSE with the appropriate mechanical properties has the potential to mitigate dendrite growth.^7,8 If SSEs more readily enable the use of Li anodes, SSBs will provide a significant increase in overall energy density due to Li metal’s significantly higher capacity and voltage than traditional graphitic anodes. With these promising characteristics, major efforts are underway to identify solid materials that can achieve the required performance necessary for commercial applications. The main challenge lies in identifying materials with comparable ionic conductivity to that of commercialized liquid electrolytes. However, high ionic conductivity is not the sole criteria for SSB performance; additional critical requirements for candidate SSEs are chemical and electrochemical stability at the interface with a Li metal anode, as an unstable interface can result in capacity degradation through the loss of Li active material.

With over 20,000 Li-containing inorganic solids in the Materials Project (MP) database,⁹ the number of potential crystalline SSE candidates is too large to explore through purely experimental means. A common high-throughput computational technique to assess the chemical stability of candidate materials and their compatibility with battery electrodes consists of using density functional theory (DFT) to compute the distance above the convex hull of the pure phase or its chemical mixing energy (ΔE_rxn) with other battery components. A global kinetic stabilization barrier, of, for example, 100 meV/atom or 4 times room temperature k_BT, is often used for distance from the hull or ΔE_rxn to assume when a phase will not decompose or when two phases will not react. This strategy is used widely in the computational materials search field vis-à-vis solid-state batteries, from finding electrode coating materials to SSEs with high ionic conductivity to materials promising for dendrite suppression.¹⁰⁻¹⁵

Using a single value of kinetic stabilization for all crystal structures, neglecting mechanistic considerations specifically for each material, risks oversimplification. By ignoring the specific structure or chemical barriers for reactivity found in each material, the possibility of false labels arises. DFT energetics-based approaches also require assumptions to be made about reaction products, as the distance above the convex hull depends on which (mixed) phases are considered to be lowest in energy.

In this work, we leverage ab initio molecular dynamics (AIMD) to create a data set of Li|SSE metal interfaces which we label as either stable, passivating, or reactive. Through our ab initio approach, we aim to capture the chemical reactivity of a diverse set of Li|SSE interfaces and probe whether the thermodynamic driving force is enough to overcome kinetic barriers for interfacial reactivity. Our aim is to go beyond the purely thermodynamic picture for chemical mixing. From this labeled data set, we then train and develop logistic regression models capable of assessing the stability of any number of candidate interfaces. To our knowledge, this is the first model that (1) considers the kinetic barrier for reactivity in each material captured from structurally dependent AIMD calculations and (2) is computationally inexpensive enough to screen large numbers of candidate interfaces.

From the generated data set, we observe several materials previously predicted to be reactive (|ΔE_rxn| > 100 eV/atom) actually maintain a stable interface with Li at high temperatures, indicating that the thermodynamic driving force for mixing alone may be an incomplete method of classification. Furthermore, the classifier trained from this data set identifies over 300 new stable interfaces and 780 potentially passivating interfaces that are predicted to be unstable using the ΔE_rxn metric with 100 meV/atom cutoff. Finally, we validate our predictions by testing the model on a hold-out set of materials. We find a 64.7% classification accuracy for our predictions outside the training set, an improvement of 2 times over random guesswork. The model features a 76.9% precision and recall within the test set.

We hope this effort highlights the need for more rigorous criteria for determining interfacial stability while also identifying several new potential candidates for future experimental studies. From the new data set of stable materials predicted in this work, we highlight LiB₁₃C₂ and LiB₁₂PC, unexplored SSE candidates which likely feature strong interfacial stability and high Li-ion conductivity, based in our calculations. Additionally, we note that our framework can be applied to any interfaces and thus may be of interest for other applications with solid-state interfaces.

Results and Discussion

Generating the Data Set of Li|SSE

We perform AIMD simulations using the Vienna ab initio simulation package (VASP) from a set of SSE candidates compiled from the Materials Project (MP) and the inorganic crystal structures database (ICSD). We consider as SSE candidates those materials that are predicted to be structurally stable, i.e. phases are within 50 meV/atom from the convex hull of their DFT generated phase diagram from the MP, and also have a computed bandgap energy E_G > 0.8 eV. Bandgaps for materials in the MP were pulled directly from the database, while for materials in the ICSD we took the computed bandgap from their relaxed crystal structure (see the Methods section). This way, we ensure any instability seen in MD is due to the presence of Li. We also limit our screening to electronic insulators, which is a requirement for any electrolyte in an electrochemical device. These materials are listed in Table 1.

Table 1. Training Set of SSE Candidate Materials^a.

composition	ref	ΔErxn (eV/atom)	label
Li6NBr3	ICSD-84090	0.000	stable
Li2S	mp-1153	0.000	stable
Li7PN4	mp-14712	0.000	stable
Li3N	mp-2251	0.000	stable
LiMgN	mp-37906	0.000	stable
Li3P	mp-736	0.000	stable
Sr2LiCBr3N2	mp-569782	–0.005	stable
Li7La3Zr2O12	mp-942733	–0.006	stable
Li2SiN2	mp-684024	–0.014	stable
Li2TiO3	mp-2931	–0.056	stable
KLiS	mp-8430	–0.086	stable
Li4SiO4	ICSD-35169	–0.094	stable
RbLiS	mp-8751	–0.119	stable
Li(BH)6	mp-1198726	–0.130	stable
LiSmS2	mp-34477	–0.175	stable
LiTaO3	mp-3666	–0.236	stable
Li2PNO2	mp-1020019	–0.332	stable
Li3VO4	mp-19219	–0.363	stable
Li7VGeO8	mp-769539	–0.391	stable
Li6WN4	mp-3503	0.000	passivating
NaLiSe	mp-28603	–0.068	passivating
LiErSe2	mp-15797	–0.077	passivating
LiErS2	mp-15791	–0.097	passivating
LiHoS2	mp-15790	–0.110	passivating
LiDyS2	mp-15789	–0.120	passivating
Li2TiSiO5	mp-6332	–0.251	passivating
LiAlSiO4	mp-6326	–0.220	passivating
Li6FeCl8	mp-28828	–0.332	passivating
Li3Sc2(PO4)3	mp-6565	–0.501	passivating
Li3ErCl6	mp-676361	–0.162	reactive
LiLaTi2O6	mp-767402	–0.210	reactive
CsLi2BS3	mp-559238	–0.409	reactive
LiScTl2Cl6	mp-1205649	–0.417	reactive
Li6ZnGe2O8	ICSD-100167	–0.431	reactive
Li3BS3	mp-5614	–0.491	reactive
Li3InCl6	mp-676109	–0.506	reactive
LiSnPO4	mp-27017	–0.524	reactive
BaLiBS3	mp-554076	–0.529	reactive
LiMnPO4	mp-18997	–0.546	reactive
LiGaCl3	mp-29344	–0.607	reactive
Li6TeO6	mp-7941	–0.616	reactive
Li3Fe2(PO4)3	ICSD-98361	–0.669	reactive
Li10GeP2S12	mp-696138	–0.680	reactive
Li2GePbS4	mp-19896	–0.682	reactive
Li3PS4	ICSD-180318	–0.708	reactive
LiGa(PO3)4	mp-1211020	–0.759	reactive
Li2B2S5	mp-29410	–0.799	reactive
Li7P3S11	mp-641703	–0.805	reactive
LiBiF4	mp-28567	–0.860	reactive
LiSO3F	mp-7744	–1.110	reactive

^aThe table includes elemental formula, reference ID from the MP or ICSD database, and ΔE_rxn with Li metal for each SSE in our training set. The final column shows the AIMD determined label for reactivity with Li metal based on the simulations from this work. Materials are ordered by their ΔE_rxn with Li metal within each labeled group.

Computational cells were constructed by creating an orthorhombic representation of the SSE unit cell paired with the (100) Li metal surface without straining the SSE original cell more than 5% and keeping the total number of atoms below 150 (see the Methods section). The particular surface used for the SSE was chosen as to minimize strain, and we expect the reactivity of different SSEs surfaces to differ as seen in previous Li insertion studies in other systems.¹⁶ Our study assumes that the overall reactivity seen from our limited AIMD calculations of the chosen surface is representative of bulk reactivity. Note that the computational cell includes two interfaces, due to repeating boundary conditions, and the reactivity at both interfaces is considered in this study.

Each computational cell is simulated at 550 K for 40 ps. Although we are primarily interested in room temperature stability, we choose to simulate the interfaces at high temperature in order to accelerate the kinetics in the simulation to a computationally tractable time scale under ab initio constraints. Previous AIMD work on the Li|SSE in sulfide electrolytes showed enough dynamics to capture the reactivity of those materials in a 10 ps time window at 300 K, and showed no noticeable difference for calculations up to 50 ps.¹⁷ Therefore, we expect stability at 550 K is likely to be a stricter lower bound for stability at room temperature. If melting of the SSE is observed at 550 K during the simulation, a calculation at 400 K is done instead. At these high simulated temperatures, we expect even the slow kinetics of the least reactive surface, which even if we assume we selected in our case for a particular SSE while constructing the computational cell, would show enough reactivity in our simulations to depict a Li|SSE pair as reactive. Li metal exhibits a melting temperature of 453.65 K under standard conditions and therefore melts during our high temperature calculations. We assume molten Li to be more reactive than solid Li due to its higher Li mobility, and thus we consider the reactivity of the SSE against liquid Li to be a much stricter metric for stability with solid Li.

In Figure 1 we show visual snapshots of the computational cell at the beginning (t = 0 ps) and end (t = 40 ps) of the simulation for three representative cases of Li|SSE interfaces. Based on the results of these simulations, we label each SSE candidate in the following manner: stable, passivating, or reactive. Stable SSEs have nearly zero crossing of non-Li (“sublattice”) atoms over the original interfaces within the computational cell. Those that are passivating exhibit limited reactivity, or change in position of SSE sublattice atoms, only near the original interfaces of our computational cell. Reactive interfacial cells exhibit transport of SSE sublattice atoms far from the original interfaces, and also exhibit Li metal atoms flowing into the SSE section of the computational cell, substantially changing the coordination environment of what used to be the SSE material. Note that results from AIMD simulations remain only a prediction, just like ΔE_rxn, and are limited due to their computational cell size and time-scale. For example, Li₂PNO₂, which is shown as stable from our AIMD calculations and calculation setup, has shown passivating properties experimentally.¹⁸ The purpose of our study we present here is to develop a high-throughput ab initio technique different from what is currently used, and is by no means perfect and fully representative of experiment.

Figure 1.

Labeling of training set interfaces. Here we visualize the time evolution of three interfaces in the training set Li₂PNO₂ (stable), LiDyS₂ (passivating), and Li₃InCl₆ (reactive) from a 40 ps DFT-MD calculation at 550 K. In the bottom we plot the normalized MSD for reactive atoms which cross the original Li|SSE, with colored labels assigned by inspection of the simulation cells.

We formalize these three class labels by establishing a reactivity metric for each computational cell based on the displacement of the atoms over the simulation. For each atom we calculate the mean-squared displacement (MSD) along the axis perpendicular to the interfacial plane. The location of the original interfaces (i.e., the one in the middle of the computational cell and the one at the edge) is defined as a plane halfway between the edge-most SSE atoms and Li metal atoms. Any atoms that cross either of the original interfacial planes are considered “reactive” atoms. For each simulation, the average MSD is calculated for all sublattice atoms in the SSE meeting the “reactive” criterion. Atomic displacements due to thermal vibrations are on the order of 0.1 Ų in their MSD for ceramic crystals,¹⁹ and we use a higher threshold of 0.5 Ų after crossing the original interfaces to consider the SSE as having reacted with Li. Note that all Li|SSE cells considered stable saw no major change in the SSE structure from Li insertion, and any material that did see reactivity from Li insertion also showed SSE atoms moving slightly into the original Li metal phase to meet the criteria above. Any SSE with a sublattice MSD of “reactive” atoms above this threshold is considered unstable. For those unstable Li|SSE, we also include Li that crossed the original interfaces for the average MSD calculation, accounting for cases where Li enters the SSE to react within the original SSE boundary. Finally, this number is normalized by the original SSE length along the axis perpendicular to the interfaces, giving one normalized MSD metric for each Li|SEE computational cell. A bar plot of this reactivity metric for each Li|SSE can be found in Figure 1, where the colors of the bars depict the supervised labels for each Li|SSE determined by inspection of the simulation cell. Stable Li|SSE exhibits a normalized MSD below 0.05. Passivating materials maintain their SSE sublattice structure—no Li enters to completely react the material—while showing some reactivity at the interfaces, placing their normalized MSD values between the stable and reactive Li|SSEs. Reactive materials show reactivity at the interface and Li enters the SSE to change its sublattice structure, yielding the higher portion of MSD values. For additional clarity on the classification of the training set, Figure S1 in the Supporting Information presents the two materials (LiDyS₂ and Li₆ZnGe₂O₈) at the passivating/reactive boundary of normalized MSD values, depicting this distinction despite how close they are in terms of the reactivity metric. To compare the normalized MSD vs ΔE_rxn, we also plot the training set along axes of the two variables in Figure S2. While SSEs with higher normalized MSDs feature higher ΔE_rxn, inconsistencies in each grouping indicate the need to account for structural features specific to each SSE when classifying a particular Li|SSE pairing with ΔE_rxn.

Previous experimental and computation work has shown Li|SSE interfaces can be effectively stable by forming passivating products that are electronically insulating.²⁰⁻²² Following this line of thinking, we include results of projected density of state (pDOS) calculations for passivating and reactive Li|SSE computational cells after 40 ps of simulation in the Supporting Information. Note that all calculations depict an electronically conductive system, arising from amorphous Li in the high temperature computational cell. Contributions to the pDOS from individual elements allow for analysis as to how the insulating SSE is changing upon reaction with Li. From the materials predicted to be passivating (Figure S3), only Li₆FeCl₈ shows significant Fe states contribution at the Fermi energy. These arise from Fe atoms in the surface of SSE melting into the liquid Li part of the cell while the rest of the SSE cell remains unchanged and hence retains a moderate normalized MSD value and passivating prediction for the material. For interfaces predicted to be reactive via AIMD (Figure S4), a few materials show clear signs of being an insulator. For these cases, all of the original SSE cell reacts during the calculation, and hence there is no passivating prediction. The resulting atomic configuration features insulating behavior, but due to our limited computational cell size from the computational cost of AIMD, we do not capture a passivating behavior that may be present at larger computational cell sizes. Hence, we decide to predict these materials as reactive out of caution. Only materials that have very limited reactivity (minimal mixing) are considered passivating, as we wish to maintain the strictest criteria to consider a candidate material stable/passivating.

Creating an Interfacial Reactivity Classifier

In order to train models for predicting the Li|SSE reactivity, we extract a set of descriptors for each SSE. We use the structural features of Sendek et al.²³ (used in an ionic conductivity screening model, summarized in Table S1), the DFT formation energy (E_form), and ΔE_rxn with Li metal.

With our training data points labeled as stable (19 examples), passivating (10 examples), and reactive (21 examples), we train two models as described in the Methods section of this work: one for differentiating between stable and unstable Li|SSE, and one for differentiating between reactive and unreactive Li|SSE. Here, “unstable” includes those labeled either passivating or reactive. Similarly, “unreactive” includes interfaces labeled either stable or passivating. This presents two data splits: one conservatively stable and the other conservatively reactive. We train a binary classification logistic regression model on each data set split by minimizing the 5-fold cross-validation error over the feature set by testing all N feature models for N = [1, 10].

For the “stable model” (SM), which uses the stable vs passivating/reactive data split for training, we find that an 8-feature logistic regression model with a 8% cross-validation misclassification rate performs the best (Figure 2a). For the “reactive model” (RM), which uses the stable/passivating vs reactive data split for training, a 7-feature logistic regression model is sufficient to achieve a 6% cross-validation misclassification (Figure 2b). Note that due to the computational cost of AIMD the data set here only includes 50 interfaces.

Figure 2.

Feature search for linear models. The misclassification rates are shown here with increasing number of features for our SM (a) and RM (b) models. Both binary models use the same data for training but partitioned differently. The SM model splits the data set into stable vs passivating/reactive, while the RM model splits the data as stable/passivating vs reactive. The best feature combination is used for each number of features. As a benchmark we also show the misclassification of the current thermodynamic only ΔE_rxn metric, random guessing, and baseline misclassification.

In order to put these misclassification rates into context, we attempt to classify these same materials using only the thermodynamic metric of ΔE_rxn with the typical 100 meV/atom cutoff. This results in a 22% misclassification using the SM data split, and a 26% misclassification error using the RM data split. This suggests that a multifeature model with structural features can predict interfacial reactivity with approximately 3–4 times lower error than just the thermodynamic stability alone.

For further analysis of our training set, in Figure S5 we visualize the full data set in reduced dimensions of the full feature space, along with all the SSE candidates that are found in the Materials Project database, to assess whether the training distribution is broadly representative of the full SSE chemical space. In this simplified representation, our training set appears to be noticeably spread out over our feature space, suggesting it is approximately representative of the broader materials search space of Li|SSE.

Unlike deep learning models which suffer from a lack of interpretability,²⁴ the simple linear models trained in this work can be physically interpreted for the trends behind their predictions. Figure 3 presents our data set in 2-feature space between ΔE_rxn and two separate structural features: (a) the average atomic volume (AAV) and (b) the packing fraction of the SSE (PF). These represent two of the most important features of the best performing 7 and 8 feature models. In both plots a decision boundary for the SM and RM binary predictors is included, which separates future prediction between stable and passivating/reactive interfaces and stable/passivating and reactive interfaces, respectively. The decision boundary is determined by optimizing a 2-feature model with each data split, using each structural feature separately with ΔE_rxn. While the current use of the ΔE_rxn metric assumes a universal kinetic barrier of 100 meV/atom, depicted in purple, our linear model informs a kinetic barrier prediction for reactivity based on the unique structural characteristics of each SSE, such as the AAV and PF. In higher dimensions, as in the 8- and 7-feature models for the SM and RM, respectively, the kinetic stabilization barrier can be represented as an 8- or 7-dimensional plane informed by additional structural features of the SSE. For a closer look at the composition of these models, Table S2 includes the coefficients for each input in the final SM and RM linear predictors, showing the relative contribution of each feature toward the final prediction. The importance of atomic density to SSE interfacial stability suggests that dense materials are more stable against the driving force to mix with Li metal. This may be due to the lower mobility of species, and hence limited reaction pathways, in tightly packed lattices. For the SM, the sublattice bond ionicity of the SSE is inversely correlated with reactivity, having a negative linear coefficient and contributing to a stable prediction the higher the feature value of a potential candidate. Together, two factors–a higher density and higher sublattice bond ionicity–imply that short and ionic bonding in the SSE may be key to stabilizing the crystal when interfaced with Li metal. Since a high packing fraction could lead to smaller and less accessible Li diffusion pathways in the SSE, thus inhibiting Li ion conductivity, optimizing for both stability and conductivity will be key for enabling a functional SSB device.

Figure 3.

Decision boundary for the 2-feature reactivity predictors and resulting expansion of the material search space. Top two panels show the spread of the training data in 2-feature space. In purple we show the decision boundary of the current thermodynamic model −100 meV/atom. Additionally we show the decision boundaries of the 2-feature SM and RM type binary predictors, based on different splits of the training data, which represent the kinetic stabilization barrier dependence on the average atomic volume (a) and packing fraction (b). The lower two panels depict 3535 SSE candidates in the t-SNE representation of our full feature space. Panel (c) shows the labeling using the current method of interfacial reactivity prediction, where all interfaces with |ΔE_rxn| < 100 meV/atom are considered stable, totaling 229 candidates. In panel (d) we present the predictions for the combined SM and RM framework, with 533 predicted stable interfaces and 788 predicted passivating interfaces.

Validating the New Reactivity Predictor and Expanding the Material Search Space

The two models (SM and RM) discussed above were applied to all 3,535 SSE candidate materials in the MP database (i.e., all Li containing compounds within 100 meV/atom of the convex hull and with a E_G > 1.5 eV). Note this is higher than the E_G > 0.8 eV used to select materials for the training set, as we wish to have a stricter criteria for low conductivity (necessary for SSE materials) when predicting new SSE candidates.

Using the thermodynamic metric ΔE_rxn > 100 meV/atom by itself identifies 229 stable interfaces, while the models trained in this work achieves markedly different predictions. The SM predicts 599 stable interfaces, much higher than the currently used metric. Note there are 32 materials newly considered reactive that exhibit a |ΔE_rxn| < 100 meV/atom, and hence previously labeled stable. Additionally, for the RM, the number of predicted interfaces to be stable/passivating is 1321. It is worth noting that 59 interfaces predicted to be reactive by the RM are labeled stable by the SM, seemingly contradicting each other. Figure 3c visualizes all candidate Li SSEs in the MP database, classified on their stability with Li metal based on 100 meV/atom thermodynamic stability only. This is generated by reducing the dimensions of the feature set for all SSE candidates using the t-distributed stochastic neighbor embedding (t-SNE) scheme under the scikit-learn python package. Since both stable and passivating predictors have some disagreement on the reactivity labels, the following criteria determine the final label using predictions from both models:

• 1.Stable interfaces: those considered stable by both the SM and RM. Final count: 533 out of 3535 candidates.
• 2.Passivating interfaces: those considered reactive by the SM and stable by RM. Final count: 788 out of 3535 candidates.
• 3.Reactive interfaces: those considered reactive by the RM model. Final count: 2214 out of 3535 candidates.

By utilizing the stricter criteria of being labeled stable by both models, we can minimize false positive labels and have more confidence in stable predictions outside the training set. Figure 3d illustrates the predictions of our combined kinetic reactivity classifier framework in the t-SNE representation, showing the expansion of the material search space available for materials development compared to the ΔE_rxn-only approach.

For further analysis, Figure S6 includes the distributions in |ΔE_rxn| for the predictions of each label group. The stable and passivating materials have essentially the same ranges in |ΔE_rxn|, though the peak in the passivating materials’ distribution is about 300 meV/atom higher than for stable materials and for reactive interfaces it sits at around 750 meV/atom. Despite the similar ranges and distributions in ΔE_rxn, it is the interfaces’ structural information (such as the packing fraction and the ionicity of the bonds of the SSE sublattice) that ultimately determines whether there is enough driving force for that particular interface to chemically mix. This is especially important for cases of materials with little driving force (as little as 0 meV/atom) that are still labeled as passivating/reactive, and materials with high ΔE_rxn (as high as 796 meV/atom) labeled as stable.

In some cases, materials with little to no thermodynamic driving force to react are predicted to be reactive by our model. Note that Li₆WN₂ has the lowest MSD metric from all the passivating materials (Figure 1) and sits at the boundary between stable and passivating labels. This material is calculated to have no thermodynamic driving force for mixing, but ab initio MD recovers some mixing at the interface resulting in LiN-type species, which are very thermodynamically stable as well. There are other cases of nitrides with a low ΔE_rxn that exhibit reactivity: Mg₃N₂ (ΔE_rxn with Li = 24 meV/atom), which has been used to stabilize a polymer interface with Li metal, and BN (ΔE_rxn with Li = 34 meV/atom), used to improve contact at the Li|SSE interface. Both exhibit reactivity in experiments, producing the very stable Li₃N, confirmed by X-ray photoelectron spectroscopy (XPS) measurements.^25,26 Similarly, C₃N₄ partly reacts when in a composite with Li metal to also form Li₃N, despite featuring a much larger |ΔE_rxn| with Li of 763 meV/atom, exhibiting a similar passivating behavior as the previous two nitrides with lower driving force for chemical mixing with Li.²⁷ In the end, the ΔE_rxn is just one more metric, taking into account the thermodynamics of the 0 K phase diagram composed of the phases known in the Materials Project. With ab initio MD, we can bring finite temperature dynamics and improve the ab initio prediction of reactivity. ΔE_rxn certainly has predictive power by itself in guessing the SSE reactivity with Li at higher temperatures, but the performance improves, and predictions can significantly change, when informed by the structural composition of the SSE. The stability predictions from this model can be used to find new stable solid-ion conductors using established or new material screening frameworks for Li solid electrolyte applications. Table 2 shows materials predicted to have a high ionic conductivity by the model in Sendek et al.,²³ and were previously considered reactive but found to be kinetically stabilized/passivating by the model developed in this work. From the positive predictions, we highlight LiSiB₆, which has been found in previous SSE computational screening work to have favorable mechanical properties for Li dendrite suppression,²⁸ and it has also been reported to be a decomposition product at low voltages of the super ionic conductor Li₅SiBS₆.²⁹

Table 2. Validation Set and Model Predictions^a.

^aThe table includes materials kept out of the training set and labeled by the reactivity classifier trained in this work, together with their actual labels from AIMD calculations. The validation misclassification rate of 6/17 (35.3%) results from wrong outcomes from passivating predictions. Note that the training set and test set include only 50 and 17 materials, respectively, due to the computational cost of AIMD. Materials marked with ∗ are also predicted to be high ionic conductors (σ_Li > 10^–4 mS/cm) by Sendek et al.²³ These materials have an |ΔE_rxn| > 100 meV/atom with Li metal and hence were missed by the previous conductivity screening. See the data availability section for all stable and passivating predictions.

To test the validity of our model beyond the 50 materials in the training data, we simulate via AIMD the 17 additional materials included in Table 2. The resulting test set includes seven stable, three passivating, and seven reactive Li|SSE. Using the models trained previously yields an overall test set misclassification rate of 35.3% for these materials. This is around half the random guessing misclassification rate of 63.7% or the baseline misclassification rate of 58.2%. The precision and recall are 76.9% (see the Methods section for calculation of these). Note that passivating predictions are the only ones that result in false labels (2 materials are in fact reactive, 3 are stable). However, a stable interface falsely labeled passivating can still be considered useful, as this prediction would yield an appropriate candidate to be used in an interface with Li metal. Hence we color these predictions yellow in the table. Reactive materials falsely predicted passivating or stable are unequivocal model failures and are colored red. These fully negative outcomes account for only a 17.6% misclassification error. There is only 1 false stable prediction and no false reactive predictions, though due to the small size of our validation set and the small number of stable and reactive predictions there is less certainty that this small error or no error is representative of all our predictions as a whole.

While determining which materials to select for our test set, we chose materials predicted to be good Li ion conductors as these would exhibit high promise for SSB applications. From these we highlight the highly stable LiB₁₂PC and LiB₁₃C₂, which both feature a boron lattice held together by borate icosahedrons with 1D Li channels (Figure 4a). Our calculations have shown this dense boron lattice remains stable over the simulation time despite its predicted thermodynamic instability (ΔE_rxn = 152 meV/atom), and hence has gone unnoticed from previous screening work (Figure 4b). The lithium diffusion channels have a large width of 3.5–3.9 Å, indicating a lightly bonded and very mobile Li ion. We model the vacancy hopping rate at high temperatures to estimate the 1D diffusion coefficient of vacancies in these diffusion channels, resulting in predicted diffusivities of 2.69 × 10^–5 and 8.19 × 10^–5 cm²/s for LiB₁₂PC and LiB₁₃C₂, respectively (Figure 4c). Vacancy concentrations for these materials would be dependent on synthesis procedures and material processing, but assuming a vacancy concentration of 0.05% of Li sites yields bulk ionic conductivities of 4.43 × 10^–4 and 1.30 × 10^–3 S/cm, for LiB₁₂PC and LiB₁₃C₂, respectively. These values are comparable to the best performing oxide ionic conductors, such as Li₇La₃Zr₂O₁₂,³⁰ and hence we report these as a minimum target for vacancy concentrations in these materials. Higher vacancy content could enable orders of magnitude higher ionic conductivity. These materials balance the atomic density requirements to be stable with Li metal with a dense B lattice and immobile B, C, and P populating half of the channels, while keeping large and highly mobile Li diffusion channels for good Li-ion conduction. Both borate compounds have previously been reported and synthesized as large single crystals (on the order of a few hundred microns).^31,32 Boron carbide materials are known for their hardness and high tensile strength and are of great interest for military and aerospace applications, which may be relevant properties for dendrite suppression in batteries with Li metal anodes.³³⁻³⁵ The lithiated versions, such as LiB₁₃C₂ reported here, have shown improved mechanical performance in this regard.³⁶ To the best of our knowledge, no ionic conduction measurement or calculation and no Li vacancy estimate has been shown for these materials, and neither has their stability with Li metal or their performance in the solid-state battery device been tested.

Figure 4.

LiB₁₃C₂ and LiB₁₂PC: new stable SSEs with high ionic conductivity. (a) The crystal structures of LiB₁₃C₂ and LiB₁₂PC are shown, which exhibit 1D lithium diffusion channels held together by a lattice of boron icosahedron. (b) To confirm the stability prediction from the classifier trained in this work, we perform interfacial AIMD for 40 ps for both materials and see no reactivity of the boron lattice with Li metal. (c) Width of the diffusion channels in the borate materials, and their modeled Li vacancy diffusivity and conductivity using AIMD. The large diffusion channels, with a shortest width of 3.52 or 3.75 Å, lead to a high vacancy diffusivity which, if we assume a vacancy concentration of only 0.05% of Li sites, results in a high ionic conductivity σ_Li of 4.43 × 10^–4 and 1.30 × 10^–3 S/cm for LiB₁₂PC and LiB₁₃C₂, respectively.

Conclusion

In this work, high-temperature AIMD is used to document the reactivity of a representative sample of 50 Li-containing crystals that could serve as SSE materials for all solid-state batteries. With this training set, two logistic regression models were built to classify the reactivity of SSE candidates with Li metal: a “reactive model” (SM) to differentiate between stable and reactive/passivating materials, and an “unreactive model” (RM) to differentiate between stable/passivating and reactive materials. A framework with both models was used to find over 300 additional stable interfaces with Li metal, compared to the predictions of the thermodynamic only ΔE_rxn metric commonly used in computational materials discovery work. The logistic regression models are informed by easily calculable structural features. The atomic density in the SSE material and the ionicity of its sublattice, among other features, were found to influence the reactivity beyond simple thermodynamics. We validate our model with an additional 17 materials, resulting in test set accuracy of 64.7% which is nearly two times better than the random guessing accuracy of 36.3% or baseline accuracy of 41.8%. The 533 stable materials and 788 passivating materials predicted in this work may be used in future materials discovery and screening work for solid-state battery applications, such as materials with high ion conductivity, materials with appropriate mechanical properties to suppress dendrite growth, materials for coatings, etc. To validate the utility of our approach, we applied an ionic conductivity predictor from the literature to the new stable materials and found LiB₁₃C₂ and LiB₁₂CP. These materials maintain a stable interface with Li metal and feature highly diffusive Li channels, as shown from our AIMD calculations.

This work is the first to attempt to classify interfacial reactivity across chemical spaces for SSBs, and the workflow can be easily adapted to assess reactivity in other solid-state systems, such as SSE|cathode interfaces. Future studies should not only focus on new systems, but also on utilizing higher level computation to label the reactivity, such as larger computational cells enabled by machine learned interatomic potentials, or more complex exchange correlation functional and more complete energetic phase diagrams to compute the energetics of chemical mixing. Additionally, future efforts should focus on the challenge of accounting for different surface terminations, and the different levels of reactivity that may be found in each.

Methods

Materials Selection and Preparation

For the overall data set used in this work, we collected 67 Li-containing SSE candidates materials, 62 from Materials Project (MP) and 5 from the Inorganic Crystal Structure Database (ICSD), that meet a low electronic conductivity criteria (E_G > 0.8 eV) and are thermodynamically stable phases on their own. For thermodynamic stability, we use the MP convex hull calculations from DFT-formation energies and chose those with a value of E_hull < 0.1 eV/atom. ICSD compounds are considered stable due to an experimental reference associated with each compound, and their bandgap and ΔE_rxn values were determined from our own calculations (see DFT Methods section). The selected compounds (see Table 1) present a chemically diverse group of SSE candidates by anionic atoms (oxide, halide, nitrides, polyanionic groups) and cationic atoms (transition metals, borates, carbon, silicon, alkali and alkaline earth metals). SSE compounds were further restricted to those with a crystal structure that can be represented with an orthorhombic cell. To construct the orthorhombic representation, we convert our initial SSE lattice vectors (a₁, a₂, a₃) to the final lattice vectors (a^′₁, a^′₂, a^′₃). Without loss of generality, we choose a₃ to be the along the longest lattice vector as to maximize the amount of SSE phase along the longest axis of the final Li|SSE structure, as this would include sufficient extent of SSE material to see any passivating behavior and this way better assess the extent of reactivity. We then cut along the a₃ direction. This allows to break translational periodicity along the cut direction, without changing the structure. Then the remaining two lattice vectors can be transformed by finding an appropriate supercell lattice vector a^′₂ = na₁ + ma₂, m, n ∈ Z. We find an m, n such that a^′₂·a₁ ≈ 0, within a 5% tolerance. These constraints allow for the creation of rectangular computational cells for moderately expensive AIMD simulations (1–6 weeks of total simulation time). Li|SSE structure files were built along the axis and a (100) surface that minimizes lattice strain when placing the SSE and Li cell in the same computational cell, using the structure files for Li (mp-135) and SSE found in material databases. Note we optimize for computational cost and the SSE surface that yields the smallest cell. Variations of reactivity in some SSEs may exist based on surface terminations, but there are also reported anisotropies for the reactive dynamics in Li and SiO₂ interfaces from similar AIMD calculations.³⁷ An average of the Li and SSE lattice parameters were used to determine the interfacial computational cell parameters that make up the interfacial plane. Spacing between materials of 1.8–3.0 Å was used throughout the simulations, depending on the element found on the SSE surface, as halides, for example, tend to have larger bond lengths with Li.

Ab Initio Molecular Dynamics (AIMD) and Density Functional Theory (DFT) Calculations

The stability of interfaces in the training set was determined via AIMD using the DFT Vienna ab initio Simulation Package (VASP)³⁸ within the projector augmented wave (PAW) formalism.³⁹ For the exchange-correlational functional, we employ the mixed scheme of the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE),⁴⁰ including the rotationally invariant Hubbard (+U)^41,42 correction for transition metal compounds based on the PYMATGEN RelaxSet for DFT ionic relaxations from the Materials Project.⁹ All calculations used a 500 eV energy cutoff, with a Gaussian smearing with a width of 0.05 eV and a 1 × 1 × 1 Gamma-centered K grid to improve run time and computational cost, though note that with the large computational cells (∼8 × 8 × 40 ų) the gamma point will likely be enough for convergence. An NVT ensemble with a Nose-Hoover thermostat is used to model the time evolution of the interfaces, as implemented in VASP, which is set to maintain a temperature of 550 K. Atomic evolution in these simulations occurs in time-steps of 2 fs and run for 40–60 ps. Structure relaxation calculations were similarly done on materials from the ICSD, using a convergence criterion of a maximum force on each ion of 0.02 eV/Å and a self-consistent field convergence of 0.001 eV in energy difference between electronic steps. These results were used to compute their E_form and ΔE_rxn feature values. A 550 K simulation temperature is used to speed up reaction kinetics. Li (T_M = 453.5 K) is liquid at this temperature, but we assume reactivity with liquid Li at 550 K is an overestimate on the reactivity with Li metal an room temperature. Since we wish to develop a reactivity classifier that can find stable materials, an overestimate on the reactivity allows for a stricter criteria for stability and added confidence on the stability predictions. For SSEs that melted during our 550 K simulations, 400 K simulations were performed instead.

Building a Machine Learning-Based Reactivity Classifier

With the data collected from the MD simulations, we aim to find interpretable connections between SSE thermodynamic and structural descriptors and the kinetic reactivity with Li metal. Features used are shown in Table S1, taken from previous work on an ionic conductivity predictors in SSEs.²³ Other features were also tested, such as compositional (magpie) and structural (DensityFeatures, BondFractions, MinimumRelativeDistances) features from matminer, but there was little difference in the training and CV misclassification rate (see Figure S7).⁴³ We employed the scikit-learn Python package’s logistic regression classifier using the L2 penalty and Limited-memory Boyden–Fletcher–Goldfarb–Shanno (LBFGS) optimization algorithm.⁴⁴ The regularization strength was found to not affect the final model performance or feature composition significantly, and therefore we used the default regularization weight. Additionally, the StratifiedKFold function was utilized to explore all feature combinations using 5-fold cross-validation in a manner that splits our training set and validation set into sections with equal proportions of each label. Two binary models are trained, one grouping passivating materials with reactive materials (a “reactive model”) and one grouping passivating and stable materials (an “unreactive model”). In the end, both models are used for the reactivity predictions with Li metal for all the SSE candidates found in the MP database, as described in the main text.

For the calculation of random guessing misclassification error (E(RG)), the following formula was used:

1

where P and G are the probability to find a particular class and the probability to guess a particular class, respectively. For the calculation of E(RG), we assume P = G for all classes. They were determined by the fraction of each class over the test set. For the baseline misclassification error, we take the error from guessing the majority class only, which results in a lower error than random guessing. Precision and missclassification errors for the test set were calculated considering the items highlighted red in Table 2, as false positive, and those highlighted yellow as false negatives.

Ionic Conductivity Validation

After finding the LiB₁₃C₂ and LiB₁₂PC by running the reactivity screening from this work and the ionic conductivity screening from our group’s previous work,²³ we estimated the ionic conductivity of the observed 1D diffusion channels (see Figure 4). AIMD calculations were performed at 500, 700, and 900 K for the LiB₁₃C₂ and LiB₁₂CP with a Li vacancy in each of the two channels in the computational cell running along the [100] crystallographic direction. Extrapolating the diffusivity from the slope of the mean squared displacement of the Brownian motion will not capture the ionic transport, as lacking an applied potential for directed diffusion will result in a net zero motion random walk in one dimension. Instead, diffusivity is estimated by 1D Fick’s first law using the hopping rate of the vacancy from a 380–400 ps calculation at each temperature. To estimate the ionic conductivities, the Nernst–Einstein relation is used, and a vacancy concentration of 0.05% of all Li sites is assumed in order to use the vacancy diffusivity for an ionic conductivity estimate. However, we note that the actual vacancy concentration in these materials will be dependent on the synthesis procedure and material processing, but we present this value as a target to reach ionic conductivities greater than 10^–4 S/cm, as this is often considered the minimum requirement for practical solid electrolyte materials.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsami.4c06095.

• Tables of selected features and their weights for the classifier trained in this work; additional figures and DFT calculations on the interfaces used for the training set; additional feature searches and performance metric concerning the logistic regression model construction (PDF)

• Stable, passivating, and reactive predictions of the SSE materials screened in this work (XLSX)

Author Contributions

E.G.L., B.R., and E.J.R. conceived and conceptualized the idea. E.G.L. conducted the calculations, curated the data, developed code, and wrote the manuscript. A.R. and B.R. developed code. T.P.D., A.D.S., and E.J.R. supervised the project. B.M., D.J., A.D.S., and T.P.D. reviewed and edited the manuscript. All authors contributed to the final version of the manuscript.

The authors declare no competing financial interest.