First-principles study of vibrational entropy effects on the PbTe-SrTe phase diagram

We present first-principles calculations of the solid-state phase diagram of PbTe-SrTe that include both configurational and vibrational contributions to the free energy. These configurational and vibrational free energies were calculated using the cluster expansion (CE) approach and quasiharmonic phonon calculations, respectively. The coupled configurational and vibrational degrees of freedom were taken into account by including temperature-dependent CE interactions with the $T=0\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ values and temperature dependence of the interactions determined from total energies and phonon free energies, both calculated using density functional theory. This Hamiltonian was then employed in Monte Carlo simulations to obtain a quantitative prediction of the PbTe-SrTe phase diagram. The phase diagram consists of a miscibility gap with a maximum temperature of \ensuremath{\sim}500 K, with the inclusion of the vibrational entropy resulting in a more than fourfold increase in the calculated solubility limits of SrTe in PbTe. Our results suggest that the equilibrium solubility of this system is likely much larger than previously thought and deserves further experimental investigation.