Evaluation of Lattice Sums in Disordered Ionic Systems
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.
KeywordsLattice Vector Singular Term Reciprocal Lattice Ionic Crystal Electrostatic Energy
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