Predicting ionic conductivity in solids from the machine-learned potential energy landscape

TL;DR

This work addresses the challenge of rapidly identifying solid-state electrolytes with high ionic conductivity by leveraging a universal machine-learned interatomic potential to derive PES-based descriptors. It introduces a frozen-framework PES scan with minimum-percolation energy (MPE), level map (LM), and free-volume (FV) descriptors, which are combined into the SSE-ranking descriptor $\Xi$ to screen Li-containing materials from the Materials Project. Validation against AIMD and ML-driven MD shows significant enrichment for high-conductivity candidates, with eight of the top ten $\Xi$-ranked structures predicted to be superionic at room temperature and several standout materials (e.g., LiB$_3$H$_8$) exhibiting high conductivities, demonstrating practical potential for accelerating SSE discovery. The approach offers substantial speed-ups over conventional first-principles MD and traditional ML MD, and lays groundwork for extensions to other ions and differentiable, generative material design pipelines.

Abstract

Discovering new superionic materials is essential for advancing solid-state batteries, which offer improved energy density and safety compared to the traditional lithium-ion batteries with liquid electrolytes. Conventional computational methods for identifying such materials are resource-intensive and not easily scalable. Recently, universal interatomic potential models have been developed using equivariant graph neural networks. These models are trained on extensive datasets of first-principles force and energy calculations. One can achieve significant computational advantages by leveraging them as the foundation for traditional methods of assessing the ionic conductivity, such as molecular dynamics or nudged elastic band techniques. However, the generalization error from model inference on diverse atomic structures arising in such calculations can compromise the reliability of the results. In this work, we propose an approach for the quick and reliable screening of ionic conductors through the analysis of a universal interatomic potential. Our method incorporates a set of heuristic structure descriptors that effectively employ the rich knowledge of the underlying model while requiring minimal generalization capabilities. Using our descriptors, we rank lithium-containing materials in the Materials Project database according to their expected ionic conductivity. Eight out of the ten highest-ranked materials are confirmed to be superionic at room temperature in first-principles calculations. Notably, our method achieves a speed-up factor of approximately 50 compared to molecular dynamics driven by a machine-learning potential, and is at least 3,000 times faster compared to first-principles molecular dynamics.

Figures (10)

• Figure 1: Flowchart of the logical steps performed in our study
• Figure 2: Level map isosurfaces at the threshold of 0.5 eV. The corresponding structure compositions, Materials Project identifiers and values of the combined $\Xi$ descriptor defined in \ref{['l_met_val']} (rounded to two digits) are: \ref{['fig:vesta:mp-1211296']} Li(BH)$_6$ -- mp-1211296 -- 0.99, \ref{['fig:vesta:mp-2530']} Li$_2$Te -- mp-2530 -- 0.97, \ref{['fig:vesta:mp-1191476']} Li$_2$In$_2$GeS$_6$ -- mp-1191476 -- 0.35, and \ref{['fig:vesta:mp-768738']} Li$_3$Bi(BO$_3$)$_2$ -- mp-768738 -- 0.00. The isosurfaces are shown in red everywhere except \ref{['fig:vesta:mp-768738']}, where yellow color is used for the isosurface and red is reserved to denote the oxygen atoms. The structures and isosurfaces are visualized using the VESTA software Momma:db5098.
• Figure 3: Descriptor evaluation scores. The top panel shows the scores obtained with $T = 1000$ K labels from the Kahle2020 dataset. Scores obtained from that dataset with the alternative procedure, when positive classes are defined by the room-temperature-extrapolated conductivity values, are shown in the middle panel. The bottom panel contains the scores resulting from the experimentally measured conductivity labels reported at room temperature in the Laskowski2023 dataset. The top-performing FV descriptors, based on all three evaluation scores, are combined into the SSE-ranking descriptor $\Xi$ (see text) with its performance indicated by the dashed red line. For the reference, a random guess classifier performance is also shown (dashed purple line). The uncertainties are estimated with bootstrapping.
• Figure 4: AIMD conductivity values against $1 / T$ for the top-$\Xi$ structures. Vertical axis is clipped at minimal conductivity value of $10^{-2}$ S / cm with values below that threshold being indicated as triangles. While the target temperatures in our simulations are exactly 500, 667 and 1000 K (with the additional simulations at 417 and 363 K for some materials), small shifts are added to the horizontal axis values to improve marker visibility. The five LGPS-like structures from the top-$\Xi$ list are omitted from our AIMD studies and therefore not shown in this plot.
• Figure 5: Distributions of conductivities estimated with MD driven by SevenNet. A random sample of size 30 is compared with 100 structures from the top of the $\Xi$-ordered list. In each panel, both histograms are normalized to have the same total weight. The top left (right) panel shows the distributions of values extracted from the $T = 1000$ K ($T = 500$ K) runs. The bottom panel shows the distributions obtained by extrapolating to the room temperature.