From Hamiltonians to Phase Diagrams pp 169-206 | Cite as

# Solid Substitutional Alloys

Chapter

## Abstract

For a disordered substitutional alloy, the structure-dependent contributions to the total energy are most conveniently written in the form [see (2.52-54)]
and analogously for the electrostatic energy. For primitive lattices and for
non-primitive lattices in which all sites are equivalent the product of the
average structure factor
and
(for partially ordered alloys,

$$
E2 = \Sigma \{ |S(q)|2F_{NN} (q) + [S(q)D*(q) + S*(q)D(q)F_{Nc} (q) + |D(q)|^2 F_{cc} (q)
$$

*S*(q) and the difference structure factor*D*(q) vanishes, i.e.$$
D*(q)s(q){\text{ }} = {\text{ }}S*(q)D(q){\text{ }} = {\text{ }}0
$$

(7.1)

*D*(0) = 0 (the proof is given by*Inglesfield*[7.1], see also [7.2]). For a*completely*random alloy we find easily that$$
D*(q)S(q){\text{ }} = {\text{ }}c(1 - c)
$$

(7.1)

*D*(q) may be expressed in terms of the order parameter, see below).## Keywords

Reciprocal Lattice Vector Substitutional Alloy Einstein Model Random Alloy Valence Electron Concentration
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1987