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 ΔH, entropy ΔS, and hence the phase diagram. The method is illustrated for two prototype semiconductor fcc alloys: one with a large size mismatch (${\mathrm{GaAs}}_{\mathrm{x}}$ ${\mathrm{Sb}}_{1\mathrm{-}\mathrm{x}}$) and one with a small size mismatch (${\mathrm{Al}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ga}}_{\mathrm{x}}$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.