Numerical investigation of electrostatic force density in ionic crystals such as NaCl

Abstract

We investigate the density of electrostatic force in a continuous medium modeled as an ionic crystal similar to that of NaCl. The theoretical model is three-dimensional and consists of a lattice of ions of alternating signs. The ions can interact with each other and the externally applied electric field and pressure via elastic springs, which model short-range chemical bonds, and long-range Coulomb interactions. The condition of equilibrium can be solved numerically to yield the basic physical parameters of the structure including Young's modulus, the dielectric permittivity, and the electrically induced strain. We then compare these results to the theoretical predictions obtained according to various formulas for the electrostatic force density that can be found in the literature. It is shown that Helmholtz force density predicts the numerically computed strain almost perfectly while other expressions result in large errors. The numerical simulations are limited to statics.