Solid Substitutional Alloys

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


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.
$$ D*(q)s(q){\text{ }} = {\text{ }}S*(q)D(q){\text{ }} = {\text{ }}0 $$
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
$$ D*(q)S(q){\text{ }} = {\text{ }}c(1 - c) $$
(for partially ordered alloys, D(q) may be expressed in terms of the order parameter, see below).


Reciprocal Lattice Vector Substitutional Alloy Einstein Model Random Alloy Valence Electron Concentration 
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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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