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Solid Substitutional Alloys

  • Jürgen Hafner
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 70)

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)]
$$ E2 = \Sigma \{ |S(q)|2F_{NN} (q) + [S(q)D*(q) + S*(q)D(q)F_{Nc} (q) + |D(q)|^2 F_{cc} (q) $$
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 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)
and 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)
(for partially ordered alloys, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Jürgen Hafner
    • 1
  1. 1.Institut für Theoretische PhysikTechn. Universität WienWienAustria

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