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

Journal Article · Tue Aug 15 00:00:00 EDT 1989 · Physical Review (Section) B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.40.3197· OSTI ID:5465728

Ferreira, L G; Wei, S; Zunger, A ^[1]

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1. Solar Energy Research Institute, Golden, Colorado 80401 (US)

We present a formalism for calculating the temperature-composition phase diagrams of isostructural solid alloys from a microscopic theory of electronic interactions. {ital 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. {ital Second}, distant-neighbor interactions are renormalized into composition- and volume-dependent effective near-neighbor multisite interactions. {ital Finally}, approximate solutions to the general Ising model (using the tetrahedron cluster variation method) underlying these effective interactions provide the excess enthalpy {Delta}{ital H}, entropy {Delta}{ital S}, and hence the phase diagram. The method is illustrated for two prototype semiconductor fcc alloys: one with a large size mismatch (GaAs{sub {ital x}}Sb{sub 1{minus}{ital x}}) and one with a small size mismatch (Al{sub 1{minus}{ital x}}Ga{sub {ital x}}As), producing excellent agreement with the measured miscibility temperature and excess enthalpies. For lattice-mismatched systems, we find 0{lt}{Delta}{ital H}{sup {ital O}}{lt}{Delta}H{sup D}, where {ital O} denotes some ordered Landau-Lifshitz (LL) structures, and {ital 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{lt}{Delta}{ital H}{sup {ital D}}{lt}{Delta}H{sup O} for all LL structures, so that only a phase-separating behavior is predicted.

• DOE Contract Number: AC02-77CH00178
• OSTI ID: 5465728
• Journal Information: Physical Review (Section) B: Condensed Matter; (USA), Journal Name: Physical Review (Section) B: Condensed Matter; (USA) Vol. 40:5; ISSN PRBMD; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALLOYS
ALUMINIUM ARSENIDES
ALUMINIUM COMPOUNDS
ARSENIC COMPOUNDS
ARSENIDES
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
CUBIC LATTICES
DENSITY
DIAGRAMS
ENERGY
FCC LATTICES
FUNCTIONS
GALLIUM ARSENIDES
GALLIUM COMPOUNDS
INTERACTIONS
ISING MODEL
MATERIALS
MATHEMATICAL MODELS
PHASE DIAGRAMS
PHYSICAL PROPERTIES
PNICTIDES
RENORMALIZATION
SELF-CONSISTENT FIELD
SEMICONDUCTOR MATERIALS
SERIES EXPANSION
SOLIDS
VARIATIONAL METHODS