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Evaluation of Lattice Sums in Disordered Ionic Systems

  • Edgar R. Smith
  • John W. Perram
Part of the NATO Advanced Science Institutes Series book series (volume 92)

Abstract

The potential energy of a crystal of point ions in an external field or the field set up by an impurity is written down and from it a set of equations for the distortion of the lattice caused by the field are derived. Since the distortions may often be small, it is clear that solutions of the linearized equations will be very useful. The linearized equations may be studied by Fourier transform techniques. These techniques require that lattice sums for ion-ion and ion-defect potentials be analysed with some care. The relevant sums are analysed in this paper, in a form which allows their use in some lattice distortion problems.

Keywords

Lattice Vector Singular Term Reciprocal Lattice Ionic Crystal Electrostatic Energy 
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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References

  1. 1.
    De Leeuw, S.W., Perram, J.W. and Smith, E.R., Proc. Roy. Soc. (Lond.) A. In press.Google Scholar
  2. 2.
    Whittaker, E.T. and Watson, G.N., “Modern Analysis”, (1958) ch. 12. Cambridge University Press.Google Scholar
  3. 3.
    Gradshteyn, I-S. and Ryzhik, I.M., “Table of Integrals, Series and Products”, (1965) p. 480. Academic Press.Google Scholar
  4. 4.
    See ref. 2, ch. 10.Google Scholar
  5. 5.
    Smith, E.R., Proc. Roy. Soc. (Lond.) A. In press.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Edgar R. Smith
    • 1
  • John W. Perram
    • 2
  1. 1.Department of MathematicsUniversity of MelbourneParkvilleAustralia
  2. 2.Matematisk InstitutOdense UniversitetOdense MDenmark

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