Effect of Overlap on Electrostatic Lattice Potentials in Ionic Crystals

A calculation has been made of the effect of ionic overlap on electrostatic lattice potentials. The calculation is based on a model which assumes each ion to consist of a core represented by a point charge, and a valence electron density represented by a normalized Gaussian centered at the core site. The contribution of any ion to the potential at a point in the crystal consists of the sum of two terms. One represents the potential due to a neutral configuration (core plus compensating Gaussian); the second the potential due to the unbalanced Gaussian charge of the ion. Upon taking appropriate lattice sums, the lattice potential is obtained in a rapidly convergent form, involving only the usual Ewald sums. The "self-potential" in NaCl and ZnS is evaluated as a function of the half-width $\alpha$ of the assumed Gaussian valence density of the ions. For $\alpha =0\mathrm{}$ the result is the well-known "Madelung Potential." The effect of overlap on the potential at an interstitial site in NaCl and ZnS structures is also examined. From the results of the analysis it can be concluded that lattice potentials are sensitive to ionic overlap, so that the effect of overlap cannot in general be neglected.