Development of new energy becomes popular due to the energy shortages and environmental pollution. The existing commercial secondary batteries are primarily lithium-ion batteries, which use organic solvents and lithium salts as electrolytes. These batteries have two significant drawbacks, i.e., global lithium resources are insufficient and unevenly distributed, and organic solvents are flammable, having safety risks. These drawbacks severely affect the further development of lithium-ion batteries. Sodium solid-state electrolytes (SSEs) are emerged as an ideal material for future battery electrolytes due to the high energy density, good thermal stability, strong mechanical rigidity, low cost and improved safety. This paper was to explore a potential sodium SSEs by a high-throughput screening method based on machine learning (ML) and first-principles calculations. The potential sodium SSEs were predicted by machine learning models and were validated through Ab initio molecular dynamics (AIMD) simulations. In addition, the conduction mechanism of sodium ions was also analyzed based on the results of the first-principles calculations.

The dataset of inorganic sodium-containing compounds was established before building ML models. All the data in this dataset were from the Materials Project database. Solid-state electrolytes have good thermodynamic stability and insulation. The materials with a band gap less than 1.5 eV or energy above hull greater than 0.03 eV/atom were excluded, resulting in a final dataset of 3631 sodium-containing inorganic compounds.

To achieve the optimal performance of the regression model, we tried four ML algorithms, i.e., Random Forest (RF), eXtreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and K-Nearest Neighbors (KNN). Magpie (Materials Agnostic Platform for Informatics and Exploration) was used to obtain the crystal structure information into 145 attributes as the input of ML models. To validate the performance of the screened sodium solid-state electrolytes and further analyze the migration mechanism of sodium ions, AIMD simulations and CI-NEB (Climbing Image Nudged Elastic Band) calculations were conducted to calculate their ionic conductivity, activation energy, probability density distribution, van Hove correlation functions and energy barriers along specific diffusion paths.

In the four machine learning regression models, XGBoost has the optimum performance on both training and testing sets with R² = 0.999 and 0.994, respectively, indicating its high accuracy and strong generalization ability. The XGBoost model is used to predict 3631 of sodium-containing inorganic compounds, discovering that 126 of them have a potential to be superior SSEs. We further screen these and select 14 compounds for AIMD simulations, among which four materials (i.e., Na₃HfTiSi₂PO₁₂, Na₃Bi(BO₃)₂, Na₂LuPCO₇ and Na₂LuPWO₈) show a high ionic conductivity and a low activation energy. Since the difference between the machine learning prediction and AIMD calculated value is within an order of magnitude, the high-throughput screening method used is reliable. Among the four candidate SSE materials, Na₃HfTiSi₂PO₁₂ belongs to the NASICON family. A previous study indicates that Na₃HfZrSi₂PO₁₂ is a promising sodium SSE material, which is similar to Na₃HfTiSi₂PO₁₂, except that Ti is replaced by Zr, indirectly proving the reliability of the machine learning model prediction.

To clarify the sodium ion migration mechanism, the motion trajectories of various particles in each compound are investigated. The results show that at all simulation temperatures, the diffusion of sodium ions is evident, while other ions remain relatively stable, forming reliable channels for sodium ion migration. From the distinct parts, the four materials exhibit migration correlation, indicating that sodium ions do not move independently but rather diffuse cooperatively, which contributes significantly to the ionic conductivity. The migration pathways of Na₃Bi(BO₃)₂, Na₂LuPCO₇ and Na₂LuPWO₈ are discussed according to the probability density distributions. Moreover, the energy barrier of migration in Na₂LuPCO₇ shows that the maximum obstacle is to bypass the triangular plane formed by CO₃ within the diffusion channel.

We used the best-performing XGBoost model to search the established dataset of 3631 inorganic sodium-containing compounds, identifying 126 compounds with a high ionic conductivity. Also, we selected 14 of the 126 compounds for AIMD simulations to calculate their ionic conductivity and activation energy, ultimately identifying four inorganic sodium-containing compounds (i.e., Na₃HfTiSi₂PO₁₂, Na₃Bi(BO₃)₂, Na₂LuPCO₇ and Na₂LuPWO₈) with a high ionic conductivity. We derived the van Hove correlation functions and probability density distributions based on the AIMD simulation results. It was indicated that the common characteristic of the four high ionic conductivity materials could be the presence of stable sodium ion diffusion channels with sodium ions migrating in a coordinated manner. Finally, the migration mechanism of sodium ions was analyzed based on the results of AIMD and CI-NEB.