The limitations of traditional lithium-ion batteries and the increasing demand for higher energy density, driven by electric vehicles and 5G technology, necessitate the development of all-solid-state lithium metal batteries. Li₇La₃Zr₂O₁₂ (LLZO) is a promising solid-state electrolyte due to its thermal stability, high Li⁺ conductivity, and wide electrochemical window. However, challenges remain, including poor interfacial contact, phase transition issues, structural disorder, chemical segregation, and Li dendrite growth. Molecular dynamics (MD) simulations can provide crucial insights into these microscopic mechanisms, but Density Functional Theory (DFT) calculations are computationally expensive for large systems. Deep interatomic potentials (DPs), trained using machine learning, offer a computationally efficient alternative. However, constructing a comprehensive and representative training dataset is challenging, especially for complex multi-component materials like LLZO. This paper addresses this challenge by introducing a novel training strategy that utilizes principal component analysis (PCA) to ensure adequate coverage of the configuration space.

The development of accurate and efficient interatomic potentials using machine learning has become increasingly important in materials simulations. Various approaches have been proposed, including neural network potentials (NNPs), Gaussian approximation potentials (GAPs), moment tensor potentials (MTPs), gradient-domain machine learning (GDML), and deep potential for molecular dynamics (DeePMD). DeePMD, in particular, uses deep neural networks (DNNs) to efficiently reproduce potential energy surfaces. While these methods offer significant computational advantages, the construction of suitable training sets remains a major hurdle, particularly for complex systems with large configuration spaces like LLZO. Existing studies highlight the importance of diverse and converged training sets for accurate DP modeling, but a systematic and efficient approach for constructing such datasets, especially for multi-component materials, is still lacking.

This study developed a deep learning-based interatomic potential for LLZO using the DeePMD-kit. The training set was iteratively constructed and refined using a combination of data from the Materials Project database, first-principles molecular dynamics simulations at various temperatures (including melting and cooling processes to obtain amorphous structures), and a two-body potential to constrain interatomic distances. The key innovation lies in the use of principal component analysis (PCA) to monitor the convergence of the training set. PCA was employed to extract local structural features from both the training and test sets, creating feature matrices. The 'coverage rate,' defined as the percentage of configurations in the test set that have similar representations in the training set, was used as the convergence criterion. The iterative process involved training the DP model, performing molecular dynamics simulations, calculating PCA coverage, and adding structures with significant DFT-DP energy discrepancies (above 1%) to the training set. This iterative refinement continued until the coverage rate reached a satisfactory level (near 100%). The accuracy of the resulting interatomic potential was assessed by comparing its predictions of energy and forces with DFT calculations for various structures (crystalline, amorphous, and slab). Radial distribution functions (RDFs) were also compared to validate the potential's ability to capture dynamic processes. Finally, the potential was used to study the tetragonal-to-cubic phase transition in LLZO using NPT ensemble molecular dynamics simulations.

The iterative training procedure, guided by PCA coverage analysis, resulted in a highly accurate deep learning interatomic potential for LLZO. The final potential showed excellent agreement with DFT calculations, with root-mean-square errors (RMSEs) for energy below 4 meV/atom and for forces below 200 meV/Å across crystalline, amorphous, and slab structures. The PCA-based coverage analysis showed a significant increase in coverage from 75.34% to 99.51% after four iterations, indicating the effectiveness of the iterative refinement process. The potential accurately predicted radial distribution functions for both crystalline and amorphous LLZO at different temperatures, demonstrating its ability to capture dynamic processes. Molecular dynamics simulations using the developed potential accurately captured the tetragonal-to-cubic phase transition in LLZO, predicting a transition temperature consistent with experimental findings (around 900 K versus 923 K). The predicted thermal expansion coefficient also agreed well with experimental values. The study also demonstrated the efficacy of incorporating two-body potentials in the training set to prevent unphysical artifacts during simulations.

This work successfully addressed the challenge of constructing a converged and representative training set for developing accurate deep learning interatomic potentials for complex materials like LLZO. The innovative use of PCA coverage as a convergence criterion provides a systematic and efficient approach for training high-fidelity potentials. The results demonstrate that this approach leads to a potential that accurately captures both static and dynamic properties of LLZO, including its phase transition behavior. This has significant implications for the simulation of complex phenomena in solid-state batteries, which are difficult to observe experimentally. The ability to accurately simulate phase transitions and other dynamic processes using a computationally efficient method allows for the exploration of large system sizes and long timescales, providing atomic-level insights into the performance of LLZO-based solid-state batteries.

This study presents a highly accurate and efficient deep learning-based interatomic potential for LLZO, achieved through an iterative training process guided by PCA coverage analysis. The potential accurately predicts structural, dynamical, and thermodynamic properties, including the tetragonal-to-cubic phase transition. This method offers a promising approach for developing accurate DPs for complex materials, accelerating materials discovery and design in solid-state battery applications. Future work could explore the application of this method to other solid-state electrolytes and the inclusion of interfacial effects in the training data.

The accuracy of the DP model relies heavily on the quality and diversity of the training set. While the iterative PCA-based approach helped ensure a high degree of coverage, there might be unexplored regions of the potential energy surface, especially for rare or highly unusual configurations. The transferability of the potential to systems significantly different from those in the training set may be limited. Future studies should explore expanding the training set to improve the coverage of the potential energy surface and test its transferability to a wider range of LLZO compositions and conditions.