Shell-model calculations of interaction energies between point defects and dislocations in ionic crystals

Abstract

A general method for atomistic calculations of interactions between point-defects and dislocations in cubic ionic crystals is presented. Our lattice model has ions of integer charge interacting by Coulomb and short range, central potentials; the electric potential for the dislocated lattice is computed using the original Madelung method of summing contributions from strings of equivalent ions. The simplest calculations with unpolarizable ions have then been extended to include a proper description of ionic polarization using the shell model. We review methods used to compute the lattice distortion about the dislocation and emphasize the advantage of using flexible boundary regions surrounding the dislocation core; the dislocation thus becomes the appropriate reference configuration for the calculation of the additional relaxation when a vacancy, impurity ion, or interstitial is introduced into the core. This substantial calculation is again reduced by using a harmonic boundary region in which the ionic displacements and polarization are determined by assuming that the crystal responds as a dielectric continuum.

We have so far calculated the binding energies of both cation and anion vacancies at various positions in the core of an α/2 [110] edge dislocation in MgO. The interaction may be attractive or repulsive at different points; it is of order ∼ 1 eV at some sites but close to zero at others. The atomistically-determined binding energies are in close agreement with results derived from internal-friction experiments. We have also compared our binding energies with values found using linear isotropic elasticity theory; the limitations of this latter method are considered.