The thermodynamic stability of germanium tin $\mathrm{Ge_{1-x}Sn_x}$ alloys is investigated across the composition range $0 \le x \le 1$ by applying density functional theory (DFT) together with the cluster expansion formalism (CE). It is known that GeSn alloys are immiscible and that non-equilibrium growth techniques are required to produce metastable films and nanostructures. Insight into the driving forces behind component segregation is gained by investigating the equilibrium thermodynamics of GeSn systems. The alloy free energy of mixing is computed by combining enthalpies from CE with entropy terms for configurational and vibrational degrees of freedom. Volume deformations due to the large mismatch in ionic radii are readily found to be the key driving force for immiscibility at all temperatures of relevance. This leads to a study of epitaxial stabilisation by employing latticed matched substrates to favour growth of alloys with fractional compositions of $\mathrm{x=0}$, approximately $\mathrm{x=0.5}$ and $\mathrm{x=1}$. Reduction of the free energy of mixing due to epitaxial strain in thin films is quantified for each substrate leading to indicators for growth of kinetically stable films.
