Continuous displacement formulation of alloys

Journal Article · Tue Jun 01 04:00:00 EDT 1999 · Journal of Statistical Physics

DOI:https://doi.org/10.1023/A:1004531307259· OSTI ID:687502

Kikuchi, Ryoichi ^[1]

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1. Univ. of California, Berkeley, CA (United States). Dept. of Materials Science and Mineral Engineering

The conventional permutational statistics of cooperative phenomena is extended to include displacement of atoms from their reference lattice points. The formulation is done in the cluster variation method (CVM) framework, by changing summations in energy and entropy to integrals. It is demonstrated for the pair approximation of CVM on phase-separating fcc binary alloys. The treatment can take into account local lattice distortion due to atomic size difference, the elastic effects, and the pressure effects. To compare stability of states under pressure, the grand potential {Omega}(T, V, {l_brace}{mu}{sub i}{r_brace}) is extended to Z(T, p, {l_brace}{mu}{sub i}{r_brace}) by a Legendre transform. Although the new function Z(T, p, {l_brace}{mu}{sub i}{r_brace}) vanishes in equilibrium, and is called the ZERO-potential in the paper, it remains nonzero and is used to determine the coexisting phases when the chemical potentials are modified. Numerical calculations are done using the natural iteration technique on model inter-atomic potentials of the Lennard-Jones type. The numerical results of using {Omega}(T, V, {l_brace}{mu}{sub i}{r_brace}) and Z(T, p, {l_brace}{mu}{sub i}{r_brace}) potentials for phase-separating diagrams, for composition and pressure dependence of the lattice constant, and for the bulk modulus are reported and discussed.

• OSTI ID: 687502
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 5-6 Vol. 95; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
BINARY ALLOY SYSTEMS
ELASTICITY
FCC LATTICES
FUNCTIONS
ITERATIVE METHODS
LATTICE PARAMETERS
NUMERICAL ANALYSIS
PRESSURE DEPENDENCE
STATISTICAL MECHANICS
VARIATIONAL METHODS