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The thermodynamic stability of germanium tin $\mathrm{Ge_{1-x}Sn_x}$ alloysis investigated across the composition range $0 \le x \le 1$ by applyingdensity functional theory (DFT) together with the cluster expansion formalism(CE). It is known that GeSn alloys are immiscible and that non-equilibriumgrowth techniques are required to produce metastable films and nanostructures.Insight into the driving forces behind component segregation is gained byinvestigating the equilibrium thermodynamics of GeSn systems. The alloy freeenergy of mixing is computed by combining enthalpies from CE with entropy termsfor configurational and vibrational degrees of freedom. Volume deformations dueto the large mismatch in ionic radii are readily found to be the key drivingforce for immiscibility at all temperatures of relevance. This leads to a studyof epitaxial stabilisation by employing latticed matched substrates to favourgrowth 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 dueto epitaxial strain in thin films is quantified for each substrate leading toindicators for growth of kinetically stable films.

Epitaxial Stabilisation of ${\bf \mathrm{Ge_{1-x}Sn_x}}$ Alloys