Abstract
Recent diffraction experiments have revealed the existence of long-range order in the semiconductor III-V ternary alloy ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As at temperatures up to 800 \ifmmode^\circ\else\textdegree\fi{}C. By combining a self-consistent first-principles local-density calculation of the parameters that describe the interatomic interactions with a mean-field analysis of an Ising-type Hamiltonian model, we have analyzed the thermodynamic stability of ordered and disordered structures. Our calculation shows that the ordered configuration is thermodynamically stable, i.e., has a lower free energy, at the experimental conditions. It thus seems that strain effects are not necessary to account for the observed order.
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