Atomistic Insight into Ion Transport and Conductivity in Ga/Al-Substituted Li$_7$La$_3$Zr$_2$O$_{12}$ Solid Electrolytes

Abstract

Garnet-structured Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ is a promising solid electrolyte for next-generation solid-state Li batteries. However, sufficiently fast Li-ion mobility required for battery applications only emerges at high temperatures, upon a phase transition to cubic structure. A well-known strategy to stabilize the cubic phase at room temperature relies on aliovalent substitution; in particular, the substitution of Li$^{+}$ by Al$^{3+}$ and Ga$^{3+}$ ions. Yet, despite having the same formal charge, Ga$^{3+}$ substitution yields higher conductivities ($10^{-3}$~S/cm) than Al$^{3+}$ ($10^{-4}$~S/cm). The reason of such difference in ionic conductivity remains a mystery. Here we use molecular dynamic simulations and advanced sampling techniques to precisely unveil the atomistic origin of this phenomenon. Our results show that Li$^{+}$ vacancies generated by Al$^{3+}$ and Ga$^{3+}$ substitution remain adjacent to Ga$^{3+}$ and Al$^{3+}$ ions, without contributing to the promotion of Li$^{+}$ mobility. However, while Ga$^{3+}$ ions tend to allow limited Li$^{+}$ diffusion within their immediate surroundings, the less repulsive interactions associated with Al$^{3+}$ ions lead to a complete blockage of neighboring Li$^{+}$ diffusion paths. This effect is magnified at lower temperatures, and explains the higher conductivities observed for Ga-substituted systems. Overall this study provides a valuable insight into the fundamental ion transport mechanism in the bulk of Ga/Al-substituted Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ and paves the way for rationalizing aliovalent substitution design strategies for enhancing ionic transport in these materials.