Molecular dynamics simulations with machine learning potential for Nb-doped lithium garnet-type oxide Li7−xLa3(Zr2−x

Lithium garnet-type oxide ${\mathrm{Li}}_{7}{\mathrm{La}}_{3}{\mathrm{Zr}}_{2}{\mathrm{O}}_{12}$ (LLZO) is one of the most promising solid electrolyte materials. In this study, the Li conduction properties of Nb-doped LLZO, ${\mathrm{Li}}_{6.75}{\mathrm{La}}_{3}({\mathrm{Zr}}_{1.75}{\mathrm{Nb}}_{0.25}){\mathrm{O}}_{12}$, have been investigated by molecular dynamics simulations with the machine learning potential. It is shown that Nb-doped LLZO holds a high-conductivity cubic structure at low temperatures. Two kinds of Li occupation sites, $24d$ and $96h$, are correctly predicted, which form the three-dimensional network of the Li migration pathway. The Li conductivity at 298 K and the activation energy are obtained as ${\ensuremath{\sigma}}_{\mathrm{Li}}=5.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{3.33333pt}{0ex}}\mathrm{S}/\mathrm{cm}$ and ${E}_{a}=223\phantom{\rule{3.33333pt}{0ex}}\mathrm{meV}$, respectively, which are in reasonably good agreement with the experimental data. The free energy difference between the $24d$ and $96h$ sites is expected to be negligibly small. This most likely contributes a high Li conductivity in the Nb-doped LLZO. The Nb substitution for Zr is accompanied with the Li vacancy formation due to the charge neutrality condition, which stabilizes the cubic phase and enhance the Li conduction. The Nb substitution, however, also has a negative effect. The supervalency of the ${\mathrm{Nb}}^{5+}$ ion destabilizes the Li atoms at the surrounding $96h$ sites. The Li conductivity in Nb-doped LLZO is determined by trading off between these effects.