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Quasielastic neutron scattering (QENS) measurements combined with firstprinciples based moleculardynamics calculations were conducted to study thedynamics of Li$^+$ ions in a solid-state electrolyteLa$_{2/3-x}$Li$_{3x}$TiO$_{3}$ (LLTO) with $x=0.13$. By using a large$^7$Li-enriched single crystal sample, a QENS signal was clearly observed alongthe three principal axes [110], [111], and [001] at a temperature ($T$) of 600K. Wave vector dependence of the linewidth of the QENS signal along eachdirection was explained well using the Chudley-Elliot model for jumps betweenthe A sites of the perovskite lattice through the bottleneck square, which wasalso supported by molecular dynamics calculations. At $T=600$ K, the estimatedself-diffusion coefficient of Li$^+$ ($D_{Li}$) in the $ab$ plane[$D^{ab}_{Li}=(6.8\pm0.5)\times 10^{-6}$ cm$^2$/s] was slightly larger thanthat along the $c$ axis [$D^{c}_{Li}=(4.4\pm0.3)\times 10^{-6}$ cm$^2$/s],suggesting quasi-isotropic diffusion, that is, the three-dimensional diffusionof Li$^+$ ions. The decrease in $D_{Li}$ with decreasing $T$ was reasonablyexplained by a thermal activation process with the activation energy determinedfrom ionic-conductivity measurements. Furthermore, the estimated values of theself-diffusion coefficient of Li$^+$ ions are comparable to those in thesulfide-based Li$^+$ ion conductor, Li$_{7}$P$_{3}$S$_{11}$, although its ionicconductivity is 10 times larger than that for LLTO. The obtained microscopicinformation on Li$^+$ diffusion in LLTO clarifies how to understand the Liconduction mechanism in LLTO and Li$_{7}$P$_{3}$S$_{11}$ in a unified mannerand can provide a way to increase the Li$^+$ ionic conductivity in oxide-basedsolid electrolytes.

physical review. b./physical review. b

Microscopic dynamics of lithium diffusion in single crystal of the  solid-state electrolyte La$_{2/3-x}$Li$_{3x}$TiO$_{3}$ ($x=0.13$) studied by  quasielastic neutron scattering