Evaluation of Lattice Interactions in or near a Cubic Crystal

Abstract

Procedures, based on the methods of Madelung, have been developed for the evaluation of lattice sums of inverse-power particle-interactions, λa—n, at any point in or near a cubic crystal. Although not as elegant mathematically as those of Hove and Krumhansl, they are more complete in including the important cases of a point near a plane or line of particles, and are sufficiently simple in principle to be understood and applied by anyone with a background in differential calculus. Applications to a face-centered cubic ionic crystal are discussed and, as an example, the dipole-dipole van der Waals energy of a chloride ion before a NaCl half-crystal is calculated.