Predicting Room-Temperature Conductivity of Na-Ion Super Ionic Conductors with the Minimal Number of Easily-Accessible Descriptors

Abstract

Given the vast compositional possibilities ${\text{Na}}_n{M}_m{M}_{m^{\prime }}^{\prime }{\text{Si}}_{3-p-a}{P}_p{\text{As}}_a{O}_{12}$, Na-ion superionic conductors are attractive but complicated for designing materials with enhanced room-temperature Na-ion conductivity ${\sigma }_{\text{Na},300\hspace{0.17em}K}$. An explicit regression model for ${\sigma }_{\text{Na},300\hspace{0.17em}K}$ with easily-accessible descriptors is proposed by exploiting density functional theory molecular dynamics (DFT-MD). Initially, it is demonstrated that two primary descriptors, the bottleneck width along Na-ion diffusion paths $d_1$ and the average Na–Na distance $⟨d_{\text{Na}-\text{Na}}⟩$, modulate room-temperature Na-ion self-diffusion coefficient $D_{\text{Na},300\hspace{0.17em}K}$. Then, two secondary easily-accessible descriptors are introduced: Na-ion content n, which influences $d_1$, $⟨d_{\text{Na}-\text{Na}}⟩$, and Na-ion density ${\rho }_{\text{Na}}$; and the average ionic radius $⟨r_M⟩$ of metal ions, which impacts $d_1$ and $⟨d_{\text{Na}-\text{Na}}⟩$. These secondary descriptors enable the development of a regression model for ${\sigma }_{\text{Na},300\hspace{0.17em}K}$ with n and $⟨r_M⟩$ only. Subsequently, this model identifies a promising yet unexplored stable composition, ${\text{Na}}_{2.75}{\text{Zr}}_{1.75}{\text{Nb}}_{0.25}{\text{Si}}_2{\text{PO}}_{12}$, which, upon DFT-MD calculations, indeed exhibits ${\sigma }_{\text{Na},300\hspace{0.17em}K}>{10}^{-3}$ S cm⁻¹. Furthermore, the adjusted version effectively fits $140$ experimental values with $R^2=0.718$.