Coherent and incoherent phase stabilities of thermoelectric rocksalt IV-VI semiconductor alloys

Nanostructures formed by phase separation improve the thermoelectric figure of merit in lead chalcogenide semiconductor alloys, with coherent nanostructures giving larger improvements than incoherent nanostructures. However, large coherency strains in these alloys drastically alter the thermodynamics of phase stability. Incoherent phase stability can be easily inferred from an equilibrium phase diagram, but coherent phase stability is more difficult to assess experimentally. Therefore, we use density functional theory calculations to investigate the coherent and incoherent phase stability of the IV-VI rocksalt semiconductor alloy systems Pb(S,Te), Pb(Te,Se), Pb(Se,S), (Pb,Sn)Te, (Sn,Ge)Te, and (Ge,Pb)Te. Here we use the term coherent to indicate that there is a common and unbroken lattice between the phases under consideration, and we use the term incoherent to indicate that the lattices of coexisting phases are unconstrained and allowed to take on equilibrium volumes. We find that the thermodynamic ground state of all of the IV-VI pseudobinary systems studied is incoherent phase separation. We also find that the coherency strain energy, previously neglected in studies of these IV-VI alloys, is lowest along [111] (in contrast to most fcc metals) and is a large fraction of the thermodynamic driving force for incoherent phase separation in all systems. The driving force for coherent phase separation is significantly reduced, and we find that coherent nanostructures can only form at low temperatures where kinetics may prohibit their precipitation. Furthermore, by calculating the energies of ordered structures for these systems we find that the coherent phase stability of most IV-VI systems favors ordering over spinodal decomposition. Our results suggest that experimental reports of spinodal decomposition in the IV-VI rocksalt alloys should be re-examined.