Predicting room-temperature conductivity of Na-ion super ionic conductors with the minimal number of easily-accessible descriptors

Abstract

Given the vast compositional possibilities Na${}_n{M}_m{M}_{m^{\prime }}$Si${}_{3-p-a}$P${}_p$As${}_a$O${}_{12}$, Na-ion superionic conductors (NASICON) are attractive but complicate for designing materials with enhanced room-temperature Na-ion conductivity ${\sigma }_{\mathrm{Na},300K}$. We propose an explicit regression model for ${\sigma }_{\mathrm{Na},300K}$ with easily-accessible descriptors, by exploiting density functional theory molecular dynamics (DFT-MD). Initially, we demonstrate that two primary descriptors, the bottleneck width along Na-ion diffusion paths $d_1$ and the average Na-Na distance $⟨d_{\mathrm{Na}-\mathrm{Na}}⟩$, modulate room-temperature Na-ion self-diffusion coefficient $D_{\mathrm{Na},300K}$. Then, we introduce two secondary easily-accessible descriptors: Na-ion content n, which influences $d_1$, $⟨d_{\mathrm{Na}-\mathrm{Na}}⟩$, and Na-ion density ${\rho }_{\mathrm{Na}}$; and the average ionic radius $⟨r_M⟩$ of metal ions, which impacts $d_1$ and $⟨d_{\mathrm{Na}-\mathrm{Na}}⟩$. These secondary descriptors enable the development of a regression model for ${\sigma }_{\mathrm{Na},300K}$ with $n$ and $⟨r_M⟩$ only. Subsequently, this model identifies a promising yet unexplored stable composition, Na${}_{2.75}$Zr${}_{1.75}$Nb${}_{0.25}$Si${}_2$PO${}_{12}$, which, upon DFT-MD calculations, indeed exhibits ${\sigma }_{\mathrm{Na},300K}>10^{{}^3}$ S$\cdot$cm${}^{-1}$. Furthermore, the adjusted version effectively fits $140$ experimental values with $R^2=0.718$.