Structural-Stability Study of AntiperovskiteNa3OCl

The structural phase transition of the high-symmetry cubic phase of antiperovskite $\mathrm{Na}$${}_{3}$$\mathrm{O}\mathrm{Cl}$ is investigated by computing the phonon band structures of 14 different polymorphs with distinct types of $\mathrm{O}\mathrm{Na}$${}_{6}$ octahedral tilting. The resulting $P$-$T$ phase diagram shows that, at high temperature and low pressure, the high-symmetry cubic structure with $Pm\overline{3}m$ symmetry is the most stable phase. At low temperature and high pressure, on the other hand, the monoclinic structure with $P{2}_{1}/m$ symmetry becomes the most stable phase. In between those two, there is a region in the phase diagram where the orthorhombic structure with $Bmmb$ symmetry is the most stable phase. To improve upon the quasiharmonic results, we do additional calculations in the framework of the self-consistent phonon (SCP) theory, including lattice anharmonicity by using cubic and quartic interatomic force constants (IFCs). This is particularly important for the high-symmetry cubic phase. We find that by decreasing the temperature, the frequency of the soft phonon at the $M$ and $R$ symmetry points gradually shifts to lower values. From these results, we can infer that a phase transition occurs around 166--195 K upon soft-mode condensation. Due to the proximity of the soft-mode frequencies at both symmetry points $R$ and $M$, we expect a cubic-to-orthorhombic phase transition to be realized via simultaneous condensation of the two octahedral tilting modes.