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Continuous Displacement of “Lattice” Atoms

Published online by Cambridge University Press:  26 February 2011

Ryoichi Kikuchi  and
Arezki Beldjenna
Ryoichi Kikuchi
Affiliation:
Department of Materials Science and Engineering University of California, Los Angeles, CA 90024-1595
Arezki Beldjenna
Affiliation:
Department of Materials Science and Engineering University of California, Los Angeles, CA 90024-1595
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Abstract

In the existing CVM (Cluster Variation Method) formulations, atoms are placed on lattice points. A modification is proposed in which an atom can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r)dr, and the corresponding pair probability is written as g(r1, r2)dr1dr2. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r1, r2) using the CVM formula. The special feature of the present formulation which is different from the prevailing no-displacement cases of the CVM is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r1, r2) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, an example of a single-component system is solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patters in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons. Future directions are discussed.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 278: Symposium W – Computational Methods in Materials Science , 1992 , 351
Copyright
Copyright © Materials Research Society 1992

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References

1. Kikuchi, R., Phys. Rev. 81, 988 (1951).CrossRefGoogle Scholar
2. Kikuchi, R., J. Chem. Phys. 23, 2327 (1955).CrossRefGoogle Scholar
3. Kikuchi, R. and Beldjenna, A., Physica A (1992) in press.Google Scholar
4. Kikuchi, R., J. Chem. Phys. 60, 1071 (1974).Google Scholar
5. Ortega, J. M. and Rheinboldt, W. C., “Iterative Solution of Nonlinear Equations in Several Variables” (Academic Press) Chap. 7.Google Scholar
6. Kikuchi, R., J. Chem. Phys. 66, 3352 (1977).Google Scholar
7. Kikuchi, R., Phys. Rev. B22, 3784 (1980).Google Scholar
8. Aguilera-Granja, F. and Kikuchi, R., Physica A176, 514 (1991).Google Scholar
9. Gehlen, P. C. and Cohen, J. B., Phys. Rev. A139, 844 (1965).Google Scholar