Calculations of Alloy Phases with a Direct Monte-Carlo Method

ABSTRACTA method for calculating the boundaries that describe solid-solid phase transformations in the phase diagrams of alloys is described. The method is first-principles in the sense that the only input is the atomic numbers of the constituents. It proceeds from the observation that the crux of the Monte-Carlo method for obtaining the equilibrium distribution of atoms in an alloy is a calculation of the energy required to replace an A atom on site i with a B atom when the configuration of the atoms on the neighboring sites, κ is specified, δHκ(A→B) = EB(κ)−EA(κ).Normally, this energy difference is obtained by introducing interatomic potentials, vij ,into an Ising Hamiltonian, but we calculate it using the embedded cluster method (ECM). In the ECM an A or B atom is placed at the center of a cluster of atoms with the specified configuration κ ,and the atoms on all the other sites in the alloy are simulated by the effective scattering matrix obtained from the coherent potential approximation. The interchange energy is calculated directly from the electronic structure of the cluster. The table of δHκ(A→B)'s for all configurations κ and several alloy concentrations is used in a Monte Carlo calculation that predicts the phase of the alloy at any temperature and concentration. The detailed shape of the miscibility gaps in the palladium-rhodium and copper-nickel alloy systems are shown.