Soft-phonon anharmonicity, floppy modes, and Na diffusion in Na3FY (Y=S,Se,Te) : Ab initio and machine-learned molecular dynamics simulations

Abstract

A class of Na-based antiperovskites ${\mathrm{Na}}_{3}XY$ $(X=\mathrm{F},\mathrm{H};Y=\mathrm{S},\mathrm{Se},\mathrm{Te})$ was recently reported with a remarkably high ionic conductivity \ensuremath{\sim}0.1 mS/cm near room temperature. Herein, we report comprehensive atomic dynamics investigations using ab initio and large-scale machine-learned molecular dynamics (MLMD) simulation on these sodium superionic conductors. Previous studies identified the role of soft phonons involving rotations of ${\mathrm{FNa}}_{6}$ octahedral units in Na diffusion. In contrast, our MLMD simulations show that the Na diffusion pathways are essentially uncorrelated and do not involve the collective dynamics of octahedral rotations or reorientations. Moreover, while the soft phonons do not involve any $Y$ atomic dynamics, the diffusion pathways are sterically hindered unless facilitated by $Y$ displacements and Na vacancies. However, we do find that the anharmonic low-energy phonon modes of wave vectors along the $M\text{\ensuremath{-}}R$ line at the Brillouin zone (BZ) boundary are important precursors of Na diffusion. These modes involve vibrations perpendicular to the F-Na ionic bond, along $\ensuremath{\langle}100\ensuremath{\rangle}$ directions, which provide the initial pathways for the Na diffusion. We have calculated the branch-resolved phonon spectral energy density (SED) in the entire BZ using the MLMD simulations. The SED results as a function of temperature reveal the large anharmonicity of the soft phonon modes, which leads to floppy dynamics of Na atoms. The volume of cubic-${\mathrm{Na}}_{3}\mathrm{FS}$ is the smallest among the three antiperovskites and has the largest mean-phonon energy. Our calculated Na diffusion coefficient at 700 K in ${\mathrm{Na}}_{3}\mathrm{FS}$ of $\ensuremath{\sim}0.63\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$ is significantly larger than $\ensuremath{\sim}0.16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{s}$ in ${\mathrm{Na}}_{3}\mathrm{FTe}$, which clearly shows contrast with the hypothesis of a softer lattice leading to faster diffusion. The estimated diffusion barrier energy for ${\mathrm{Na}}_{3}\mathrm{FS}$ with 2% Na vacancy is \ensuremath{\sim}0.44 eV, which is in fair agreement with the reported value of 0.44 eV estimated from the total conductivity measurement with Na-vacant iodine-doped ${\mathrm{Na}}_{3}\mathrm{FS}$. Similarly, for ${\mathrm{Na}}_{3}\mathrm{FSe}$ and ${\mathrm{Na}}_{3}\mathrm{FTe}$, the barrier energies have been estimated to be 0.50 and 0.55 eV, respectively. Our large-scale MLMD-based theoretical study provides a comprehensive understanding of the role of soft phonons, host dynamics, and vacancies in Na diffusion in ${\mathrm{Na}}_{3}\mathrm{F}Y$ $(Y=\mathrm{S},\mathrm{Se},\mathrm{Te})$ and other materials of this class, which will be helpful in designing materials for application in solid-state batteries.