Designing layered oxides as cathodes for sodium-ion batteries: Machine learning and density functional theory based modeling

To accelerate the application of Na-ion batteries in electric vehicles, it is necessary to develop new materials with high average voltage (AV). P2 and O3-type sodium layered oxides (Na${}_x$TMO${}_2$) have been identified as cathodes for sodium-ion batteries with faster Na diffusion and high-rate kinetics for the former. However, a low capacity at the initial stage limits their application. To overcome the issue dual doping of 3d transition metals (TMs) with an equal ratio strategy is employed with the help of combined machine learning (ML) with density functional theory (DFT) calculations and AV of candidate compounds are predicted from a smaller dataset of 650 compounds. Both physical and electronic descriptors of elements for each compound are utilized for ML model training. The evaluation coefficient (R${}^2$) and root mean squared error (RMSE) of the XGBoost model were up to 0.85 and 0.41 respectively to predict the AV during testing of the model. Seven novel quaternary (Na${}_{0.67}$TM1${}_{0.5}$TM2${}_{0.5}$O${}_2$ namely Na${}_{0.67}$Ti${}_{0.5}$Fe${}_{0.5}$O${}_2$, Na${}_{0.67}$Ti${}_{0.5}$Cr${}_{0.5}$O${}_2$, Na${}_{0.67}$V${}_{0.5}$Fe${}_{0.5}$O${}_2$) and pentanary compounds (Na${}_{0.67}$TM1${}_{0.5}$TM2${}_{0.5}$O${}_{1.944}$F${}_{0.056}$ namely Na${}_{0.67}$Ti${}_{0.5}$Cr${}_{0.5}$O${}_{1.944}$F${}_{0.056}$, Na${}_{0.67}$Ti${}_{0.5}$Fe${}_{0.5}$O${}_{1.944}$F${}_{0.056}$, Na${}_{0.67}$Ti${}_{0.5}$V${}_{0.5}$O${}_{1.944}$F${}_{0.056}$, Na${}_{0.67}$Ti${}_{0.5}$Ni${}_{0.5}$O${}_{1.944}$F${}_{0.056}$) were identified from the XGBoost model to exhibit AV between 2.8 to 4.4 V. Thereafter, the AV as predicted by ML model was verified by DFT calculations and the maximum and minimum errors are obtained between 15 - 3 % respectively. The phase stability, electronic structures, magnetic properties, dynamic stability and activation energy for diffusion are studied by DFT and AIMD techniques. Nevertheless, our approach could significantly accelerate the discovery of novel cathodes and provide valuable insights for the study of intercalating materials.