Anharmonic Lattice Dynamics in Sodium Ion Conductors

Abstract

We employ terahertz-range temperature-dependent Raman spectroscopy and first-principles lattice dynamical calculations to show that the undoped sodium ion conductors Na 3 PS 4 and isostructural Na 3 PSe 4 both exhibit anharmonic lattice dynamics. The anharmonic effects in the compounds involve coupled host lattice–Na + ion dynamics that drive the tetragonal-to-cubic phase transition in both cases, but with a qualitative difference in the anharmonic character of the transition. Na 3 PSe 4 shows an almost purely displacive character with the soft modes disappearing in the cubic phase as the change in symmetry shifts these modes to the Raman-inactive Brillouin zone boundary. Na 3 PS 4 instead shows an order–disorder character in the cubic phase, with the soft modes persisting through the phase transition and remaining Raman active in the cubic phase, violating Raman selection rules for that phase. Our findings highlight the important role of coupled host lattice–mobile ion dynamics in vibrational instabilities that are coincident with the exceptional conductivity of these Na + ion conductors.

Scaling Relations for Ionic and Thermal Transport in the Na+ Ionic Conductor Na3PS4

“…While the effective medium theory explains the observed density dependence of the thermal transport, the fundamental origin of the astonishingly low thermal conductivities remains unknown. Given the reported anharmonic lattice dynamics , and the glass-like thermal conduction behavior, i.e., almost temperature-independent transport throughout the entire temperature range (Figure b), diffuson-like thermal transport may be suspected. ,, To evaluate the possibility of diffuson-like thermal transport (by extended but non-propagating phonons), the analytical diffuson model reported by Agne et al is used and compared to our thermal transport results. In the diffuson model, the thermal conductivity is dependent on the number density of atoms ( n ), the vibrational density of states ( g (ω)), and the heat capacity ( C (ω)), as follows: κ diff false( ω false) = n 1 / 3 k B π ∫ 0 ω C false( ω false) k B ( g ( ω ) 3 n ) ω d ω where the spectral heat capacity is defined as C false( ω false) = k B true( ℏ ω k normalB T true) 2 e ℏ ω / …”

“…While the effective medium theory explains the observed density dependence of the thermal transport, the fundamental origin of the astonishingly low thermal conductivities remains unknown. Given the reported anharmonic lattice dynamics 8,13 and the glass-like thermal conduction behavior, 18 i.e., almost temperature-independent transport throughout the entire temperature range (Figure 2b), diffuson-like thermal transport may be suspected. 32,34,41 To evaluate the possibility of diffuson-like thermal transport (by extended but nonpropagating phonons), the analytical diffuson model reported by Agne et al 34 is used and compared to our thermal transport results.…”

“…As a consequence of its high ionic conductivity, these materials are currently considered as ionic conductors in solid-state battery applications. 10−12 In part, the fast ionic transport has been explained by largely anharmonic phonon dynamics, 8,13,14 and other considerations about atomic vibrations. 15 However, a deeper investigation and understanding of the thermal transport properties, which are fundamentally linked to the lattice dynamics of a material, 16,17 are missing.…”

“…16,40,41 Then, macroscopic thermal transport can be described by an atom-scale random walk of thermal energy, similar to the mass transport of ionic diffusion. 34 Thus, given the anharmonic phonon dynamics and glass-like thermal transport characteristics, 8,13,18 diffuson-like thermal transport might be prevalent in Na 3 PS 4 .…”

“…Solid Na + ion conductors have attracted significant interest in recent years, because of their possible application as electrolytes in Na + solid-state batteries. − One of the most investigated Na + solid-electrolyte classes is the Na 3 PS 4 material family, because of its relatively high ionic conductivity paired with its structural simplicity and compositional variety, making it a suitable model system for sodium-ion conductors. − Upon substitution and doping, room-temperature ionic conductivities ranging from 0.018 mS cm –1 (Na 3 PS 4 ) , to 0.3 mS cm –1 (Na 3 SbSe 4 ) and up to 40 mS cm –1 (W-doped Na 3 SbS 4 ) , have been achieved. As a consequence of its high ionic conductivity, these materials are currently considered as ionic conductors in solid-state battery applications. − In part, the fast ionic transport has been explained by largely anharmonic phonon dynamics, ,, and other considerations about atomic vibrations . However, a deeper investigation and understanding of the thermal transport properties, which are fundamentally linked to the lattice dynamics of a material, , are missing.…”