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We employ THz-range temperature-dependent Raman spectroscopy andfirst-principles lattice-dynamical calculations to show that the undoped sodiumion conductors Na$_3$PS$_4$ and isostructural Na$_3$PSe$_4$ both exhibitanharmonic lattice dynamics. The anharmonic effects in the compounds involvecoupled host lattice -- Na$^+$ ion dynamics that drive the tetragonal-to-cubicphase transition in both cases, but with a qualitative difference in theanharmonic character of the transition. Na$_3$PSe$_4$ shows almost purelydisplacive character with the soft modes disappearing in the cubic phase as thechange of symmetry shifts these modes to the Raman-inactive Brillouin zoneboundary. Na$_3$PS$_4$ instead shows order-disorder character in the cubicphase, with the soft modes persisting through the phase transition andremaining active in Raman in the cubic phase, violating Raman selection rulesfor that phase. Our findings highlight the important role of coupled hostlattice -- mobile ion dynamics in vibrational instabilities that are coincidentwith the exceptional conductivity in these Na$^+$ ion conductors.

Anharmonic Lattice Dynamics in Sodium Ion Conductors