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Calculations of Alloy Phases with a Direct Monte-Carlo Method

Published online by Cambridge University Press:  01 January 1992

J. S. Faulkner ,
Yang Wang ,
Eva A. Horvath  and
G. M. Stocks
J. S. Faulkner
Affiliation:
Alloy Research Center and Department of Physics, Florida Atlantic University, Boca Raton, FL33431
Yang Wang
Affiliation:
Alloy Research Center and Department of Physics, Florida Atlantic University, Boca Raton, FL33431
Eva A. Horvath
Affiliation:
Alloy Research Center and Department of Physics, Florida Atlantic University, Boca Raton, FL33431
G. M. Stocks
Affiliation:
Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
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Abstract

A 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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 291: Symposium O – Materials Theory and Modeling , 1992 , 143
Copyright
Copyright © Materials Research Society 1993

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References

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