Paper detail

Lattice dynamics of $\textit{Pnma}$ Sn(S$_{1-x}$Se$_{x}$) solid solutions: energetics, phonon spectra and thermal transport

Alloying is widely used as a means to fine-tune the properties of thermoelectric materials by reducing the lattice thermal conductivity. However, the effects of compositional variation on the lattice dynamics of alloy systems are not well understood, due in part to the difficulty of building realistic first-principles models of structurally-complex solid solutions. This work builds on our previous study of Sn$_{n}$(S$_{1-x}$Se$_{x}$)$_{m}$ solid solutions [Gunn $\textit{et al.}$, $\textit{Chem. Mater.}$ $\textbf{31}$, $\textit{10}$, 3672, $\textbf{2019}$] to explore the lattice dynamics of the $\textit{Pnma}$ Sn(S$_{1-x}$Se$_{x}$) system, which has been widely studied for potential thermoelectric applications. We find that the vibrational internal energy and entropy have a large quantitative impact on the mixing free energy and are likely to be particularly important in alloy systems with competing phases. The thermodynamically-averaged phonon dispersions and density of states curves show that alloying preserves the structure of the low-frequency bands of modes associated with the Sn sublattice but broadens the high-frequency chalcogen bands into a near-continuous spectrum at the 50/50 mixed composition. This results in a general reduction in the phonon mode group velocities and an increase in the number of energy-conserving scattering channels for heat-carrying low-frequency modes, which is consistent with the decrease in thermal conductivity observed in experimental measurements. Finally, we discuss some of the limitations of our first-principles modelling approach and propose methods to address these in future studies.