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Research Article| August 02 2012

A numerical coarse-grained description of a binary alloy

J. M. Rickman;

J. M. Rickman

1Department of Materials Science and Engineering and Department of Physics,

Lehigh University

, Bethlehem, Pennsylvania 18015,

USA

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T. J. Delph;

T. J. Delph

2Department of Mechanical Engineering and Mechanics,

Lehigh University

, Bethlehem, Pennsylvania 18015,

USA

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E. B. Webb, III;

E. B. Webb, III

2Department of Mechanical Engineering and Mechanics,

Lehigh University

, Bethlehem, Pennsylvania 18015,

USA

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R. Fagan

R. Fagan

2Department of Mechanical Engineering and Mechanics,

Lehigh University

, Bethlehem, Pennsylvania 18015,

USA

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Author & Article Information

J. M. Rickman ¹

,

T. J. Delph ²

,

E. B. Webb, III ²

,

R. Fagan ²

1Department of Materials Science and Engineering and Department of Physics,

Lehigh University

, Bethlehem, Pennsylvania 18015,

USA

2Department of Mechanical Engineering and Mechanics,

Lehigh University

, Bethlehem, Pennsylvania 18015,

USA

J. Chem. Phys. 137, 054108 (2012)

https://doi.org/10.1063/1.4739742

We employ Monte Carlo simulation in the semi-grand canonical ensemble to obtain the coarse-grained free energy corresponding to an embedded-atom method description of a binary alloy. In particular, the Ginzburg-Landau free energy for a Cu–Ni alloy was determined from a tabulated histogram of the joint probability density of composition, energy, and volume. Using histogram reweighting techniques, the free energy is extrapolated to a range of points in parameter space from a small number of simulations. The results are interpreted by comparing the free energy with that corresponding to a regular solution model of an alloy. In addition, we obtain expressions for thermodynamic quantities in terms of the joint cumulants of the probability density at a given temperature and chemical potential difference. These expressions may then be likewise extrapolated to obtain the dependence of the composition on the temperature and the chemical potential difference over a wide range of parameter space.

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$\Psi \left(T,P,\Delta \mu \right) = \int _{0}^{\infty } dV exp{\left(-\beta P V \right)}\; \Upsilon \left(T,V,\Delta \mu \right)$

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© 2012 American Institute of Physics.

2012

American Institute of Physics

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