First-principles study of superionic Na9+xSnxM3−xS12 (M = P, Sb)†
Inspired by the fast lithium superionic conductor Li10GeP2S12, a new class of quaternary fast sodium-ion conductors, Na9+xSnxP3−xS12, has recently been identified. Among these, Na11Sn2PS12 was the fastest sodium ion-conducting sulphide in spite of its moderately low migration barriers. The isostructural Na+-ion electrolytes Na9+xSnxSb3−xS12 found soon thereafter combined only slightly lower ionic conductivity with excellent air stability and processability in aqueous solutions. Here we apply density functional theory to comprehensively study the stability and homogeneity range of these disordered Na+ ion conductors: For Na9+xSnxP3−xS12 we explored the composition range 1.75 ≤ x ≤ 2.25 as well as x = 1 (Na10SnP2S12), x = 0 (Na3PS4) and x = 3 (Na4SnS4). For Na9+xSnxSb3−xS12 we extended the range of calculations to x = 0, 1, 3, and 1.625 ≤ x ≤ 2.375. In both cases we find that the lowest energy composition is the stoichiometric phase with x = 2 and clarify that these compositions are also stable against decomposition into Na4SnS4 and Na3PS4 (or Na3SbS4). Our ab initio molecular dynamics (AIMD) simulations show that despite the exceptionally high local mobility of Na on Na6 sites, the negligible Na6 concentration in the stable lowest energy structure rules out a previously supposed key role of Na6 in ionic conductivity at room temperature. On the other hand, an onset of PS4 (but not SnS4) orientational disorder is observed above 500 K in our high temperature AIMD studies and characterised by analysing van Hove correlation functions. This orientational disorder affects the relative Na site energies enabling Na6 site occupancy and lowers the barriers for Na+ migration and. As soon as the orientational disorder allows for a significant Na6 occupancy, it also significantly contributes to the Na+ ion transport.