PHASE-DIAGRAM AND CRITICAL-BEHAVIOR OF THE SI-GE UNMIXING TRANSITION - A MONTE-CARLO STUDY OF A MODEL WITH ELASTIC DEGREES OF FREEDOM

A statistical-mechanical model of binary semiconductor alloys, consist ing of a distortable diamond lattice whose sites may be occupied by A atoms, B atoms, or vacancies, is studied by Monte Carlo computer simul ations. By extending a grand-canonical lattice gas, the model allows f or atomic displacements governed by the Keating valence force field. U nphysical boundary conditions are avoided by keeping the pressure cons tant. This model is similar to a compressible Ising model, but differs from it by the occurrence of a bilinear coupling between spin field a nd displacement field. The interplay between the chemical and translat ional degrees of freedom shows up in the form of the unmixing phase di agram of a system whose parameters were chosen in an attempt to mimic a Si-Ge alloy. Methods of thermodynamic integration to obtain the free energies of different phases are discussed. The critical behavior of the unmixing transition is studied by a multihistogram data analysis. The finite-size scaling of the data is in better agreement with mean-f ield-like critical behavior than with an Ising transition or Fisher-re normalized exponents. Vegard's law is verified, and it is shown that t he Keating potential leads to a negative coefficient of thermal expans ion.