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Structure and thermodynamics of Si x Ge 1 −</mml:…

1991; American Physical Society; Volume: 66; Issue: 16 Linguagem: Inglês

10.1103/physrevlett.66.2116

1092-0145

Stefano de Gironcoli, Paolo Giannozzi, Stefano Baroni,

Advanced Chemical Physics Studies

${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ alloys are studied with a new method based on density-functional theory and Monte Carlo sampling. Using perturbation theory with respect to the virtual crystal, we are able to map the alloy onto a lattice gas with long-range interactions, which are determined from first principles. Monte Carlo simulations show that ${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ is a model random alloy with a miscibility gap below \ensuremath{\approxeq}170 K. The bond-length distribution displays three well-defined peaks whose positions depend on composition, but not on temperature. The resulting lattice parameter follows Vegard's law very closely.