First-principles calculation of alloy phase diagrams: The renormalized-interaction approach

Abstract

We present a formalism for calculating the temperature-composition phase diagrams of isostructural solid alloys from a microscopic theory of electronic interactions. First, the internal energy of the alloy is expanded in a series of volume-dependent multiatom interaction energies. These are determined from self-consistent total-energy calculations on periodic compounds described within the local-density formalism. Second, distant-neighbor interactions are renormalized into composition- and volume-dependent effective near-neighbor multisite interactions. Finally, approximate solutions to the general Ising model (using the tetrahedron cluster variation method) underlying these effective interactions provide the excess enthalpy \ensuremath{\Delta}H, entropy \ensuremath{\Delta}S, and hence the phase diagram. The method is illustrated for two prototype semiconductor fcc alloys: one with a large size mismatch (${\mathrm{GaAs}}_{\mathrm{x}}$${\mathrm{Sb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$) and one with a small size mismatch (${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ga}}_{\mathrm{x}}$As), producing excellent agreement with the measured miscibility temperature and excess enthalpies. For lattice-mismatched systems, we find 0${H}^{O}$${H}^{D}$, where O denotes some ordered Landau-Lifshitz (LL) structures, and D denotes the disordered phase. We hence predict that such alloys will disproportionate at low-temperature equilibrium into the binary constituents, but if disproportionation is kinetically inhibited, some special ordered phases (i.e., chalcopyrite) will be thermodynamically stabler below a critical temperature than the disordered phase of the same composition. For the lattice-matched systems, we find 0${H}^{D}$${H}^{O}$ for all LL structures, so that only a phase-separating behavior is predicted. However, in these systems, longer-period ordered superlattices are found to be stabler, at low temperatures, than the disordered alloy.