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In this theoretical study, the quasichemical approximation for an A₁-ₗBₗ alloy is formulated for an arbitrary lattice and choice of cluster. The statistical problem of the average number of each class of clusters is collapsed into a polynomial equation. An n-atom cluster of type j is characterized by an excess energy ₉, the number of B atoms n₉ (B) and a degeneracy g₉. If ₉ is a linear function of n₉ (B) and g₉ is a binomial coefficient of n and n₉ (B), then the cluster populations are random. Strains due to lattice-size mismatches, chemical (electron-ion interaction) differences, and differences between the electron-electron Coulomb interactions of the alloy constituents drive nonlinear variations of ₉ on n₉ (B). The g₉ is modified by coherent, externally applied stresses and temperature gradients present during crystal growth. We derive the conditions under which compounds are formed or spinodal decomposition occurs. We also discuss the possibility of materials consisting of arrays of two kinds of domains: one a random alloy and the other an ordered compound. The theory is specialized to semiconductor alloys A₁-ₗBₗC in a distorted zinc-blende structure; numerical results are presented for Ga₁-ₗInₗAs and GaAs₁-ₗSbₗ alloys. A major conclusion is that semiconductor alloys are almost never truly random.
Sher et al. (Tue,) studied this question.