Computational and experimental (re)investigation of the structural and electrolyte properties of Li4P2S6, Na4P2S6 , and Li2Na2P2S6

The ionic materials ${\mathrm{Li}}₄{\mathrm{P}}₂{\mathrm{S}}₆$ and ${\mathrm{Na}}₄{\mathrm{P}}₂{\mathrm{S}}₆$ are both based on the same building blocks of the dimer ions (${\mathrm{P}}₂{\mathrm{S}}₆{)}^{4\ensuremath{-}}$. Motivated by new experimental structural and ion conductivity studies, we computationally examine this family of materials, finding ${\mathrm{Na}}₄{\mathrm{P}}₂{\mathrm{S}}₆$ and its modification ${\mathrm{Li}}₂{\mathrm{Na}}₂{\mathrm{P}}₂{\mathrm{S}}₆$ to be promising Na ion electrolytes. Using first-principles calculations based on density functional theory and density functional perturbation theory within the harmonic phonon approximation, we show that vibrational effects provide nontrivial contributions to the structural stabilization of these materials. Computed nonresonant Raman phonon spectra and temperature-dependent ionic conductivity for ${\mathrm{Na}}₄{\mathrm{P}}₂{\mathrm{S}}₆$ are both found to be in reasonable agreement with experiment. First-principles analysis of ionic conductivity in both ${\mathrm{Na}}₄{\mathrm{P}}₂{\mathrm{S}}₆$ and ${\mathrm{Li}}₂{\mathrm{Na}}₂{\mathrm{P}}₂{\mathrm{S}}₆$ indicates that Na ions move primarily within the interlayer region between the (${\mathrm{P}}₂{\mathrm{S}}₆{)}^{4\ensuremath{-}}$ layers, efficiently proceeding via direct or indirect hops between vacancy sites, with indirect processes involving intermediate interstitial sites.