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Alloying is widely used as a means to fine-tune the properties ofthermoelectric materials by reducing the lattice thermal conductivity. However,the effects of compositional variation on the lattice dynamics of alloy systemsare not well understood, due in part to the difficulty of building realisticfirst-principles models of structurally-complex solid solutions. This workbuilds on our previous study of Sn$_{n}$(S$_{1-x}$Se$_{x}$)$_{m}$ solidsolutions [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 forpotential thermoelectric applications. We find that the vibrational internalenergy and entropy have a large quantitative impact on the mixing free energyand are likely to be particularly important in alloy systems with competingphases. The thermodynamically-averaged phonon dispersions and density of statescurves show that alloying preserves the structure of the low-frequency bands ofmodes associated with the Sn sublattice but broadens the high-frequencychalcogen 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 anincrease in the number of energy-conserving scattering channels forheat-carrying low-frequency modes, which is consistent with the decrease inthermal conductivity observed in experimental measurements. Finally, we discusssome of the limitations of our first-principles modelling approach and proposemethods to address these in future studies.

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