Cohesion of Ionic Solids in the Born Model

TL;DR: The Born model was originally proposed for the purpose of evaluating the lattice energy of crystals, which approach this idealized picture, and because of its success and simplicity it has subsequently been applied to the description of a variety of physical properties of ionic crystals, with varying degrees of success.

Abstract: Publisher Summary In an idealized picture, an ionic crystal is regarded as composed of spherical, nonoverlapping ions, bearing net charges of integral amount. The electrostatic interactions of these pointlike charges give rise to a net binding (Madelung energy), as each ion is preferentially surrounded by ions of opposite charge. In typical ionic crystals, the Madelung energy is in fact quite close to the observed cohesive energy. The Born model was originally proposed for the purpose of evaluating the lattice energy of crystals, which approach this idealized picture, and because of its success and simplicity it has subsequently been applied to the description of a variety of physical properties of ionic crystals, with varying degrees of success. In the framework of the Born model, it is convenient to describe the lattice energy of an ionic crystal as composed of energy terms arising from interactions between the ions. In addition to the net binding provided by the electrostatic interactions of point-like ionic charges, the binding arising from a synchronization of the electronic motions in the ions is considered explicitly in some versions of the model. The contribution of this so-called “van der Waals interaction” to the lattice energy is small, of the order of a few per cent. The ratio between the polarization energy that is connected with the mutually induced electronic dipoles on a pair of ions and the Coulomb interaction energy of the net charges of the ions is definitely less than the ionic polarizability per unit volume. The attractive forces in the crystal are balanced by the so-called overlap repulsive forces, which oppose the interpenetration of the ions.