Site-by-site Madelung energies in semi-infinitive NaCl

Abstract

Superposition can be used to determine electrostatic energies of ions at arbitrary sites on a semi-infinite NaCl lattice. In this way, Madelung energies are found for ions at locations near a surface, an edge, or a corner of a macroscopic crystal. Proceeding sequentially into the crystal from a site on a surface or an edge, the electrostatic energies tend rapidly to the bulk value. Sequences of ions originating at a corner, however, have energies that approach a limiting value only slowly. The method is a rather direct application of Coulomb’s law that should be understandable to interested students in elementary physics courses. It provides an extraordinary exercise in the use of superposition.