Total-energy local-density calculations on approximately 20 periodic crystal structures of a given AB compound are used to define a long-range Ising Hamiltonian which correctly represents atomic relaxations. This allows us to accurately calculate structural energies of relaxed substitutional ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$ systems containing thousands of transition-metal atoms, simply by adding up spin products in the Ising Hamiltonian. The computational cost is thus size independent. We then apply Monte Carlo and simulated-annealing techniques to this Ising Hamiltonian, finding (i) the T=0 ground-state structures, (ii) the order-disorder transition temperatures ${\mathit{T}}_{\mathit{c}}$, and (iii) the T>${\mathit{T}}_{\mathit{c}}$ short-range-order parameters. The method is illustrated for a transition-metal alloy (${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pd}}_{\mathit{x}}$) and a semiconductor alloy (${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{In}}_{\mathit{x}}$P). It extends the applicability of the local-density method to finite temperatures and to huge substitutional supercells. We find for ${\mathrm{Cu}}_{0.75}$${\mathrm{Pd}}_{0.25}$ a characteristic fourfold splitting of the diffuse scattering intensity due to short-range order as observed experimentally.

• Received 3 May 1994

DOI:https://doi.org/10.1103/PhysRevB.50.6642