First principles evaluation of phase stability in the In-Sn binary system

The In-Sn binary alloy system exhibits several unusual features that challenge crystallographic and thermodynamic expectations. We combine first principles total energy calculation with simple thermodynamic modeling to address two key points. First, we evaluate energies along the Bain path to interpret the discontinuous transition between the phases $\alpha$-In (Pearson type tI2) and $\beta$--In$_3$Sn (also Pearson type tI2) that are identical in symmetry. Second, we demonstrate that the solid solution phases $\beta$-In$_3$Sn and $\gamma$-InSn$_4$ (Pearson type hP1) exist at high temperatures only, and they exhibit eutectoid decompositions at low temperatures.