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An interpretation of the Cowley and Christy-Hall theories for binary alloy short-range order parameters

Authors
Journal
Journal of Physics and Chemistry of Solids
0022-3697
Publisher
Elsevier
Publication Date
Volume
27
Issue
2
Identifiers
DOI: 10.1016/0022-3697(66)90046-1
Disciplines
  • Physics

Abstract

Abstract It is shown that the statistical mechanics employed by Cowley in deriving his equations for the Warren short-range order parameters (α ij ) of a binary alloy implies a different definition for α ij at each stage of the derivation. These definitions are made explicit here and provide an answer to the major criticisms of Cowley's theory made by Hall and others. It is also shown that Cowley's theory does include contributions to α ij from all sites in the alloy which affect α ij in an approximately correct way, whereas the theory of Christy-Hall includes only the direct i, j interaction. It is concluded that Cowley's theory is an approximate solution of an N-body problem and the Christy-Hall theory is the solution of a simple two-body problem which has none of the important cooperative effects of an N-body problem.

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