  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.
