Grain-boundary energies in metals from local-electron-density distributions.

Abstract

The energy contributions of the inhomogeneous electron gas in the vicinity of grain boundaries in s-p metals are investigated theoretically. Because there are typically of the order of ${10}^{2}$ to ${10}^{4}$ atoms per unit cell in grain-boundary problems, the method of choice typically involves the use of pair potentials, which derive from perturbation theory on a homogeneous electron gas. Since grain boundaries in metals are localized electronic defects, we formulated the problem in terms of perturbation theory on an inhomogeneous electron gas. In that case, we found that the zeroth- and first-order perturbation terms are significant and depend on the local geometric structure of the bound- ary, unlike the pair-potential approach. Reasonable results were obtained for energies computed to second order for model boundaries in aluminum. A simple, accurate approximation was found for the zeroth- and first-order terms. The sum of the second-order and Ewald-like terms can also be approximated in a pair-potential-like form which depends on the average of the electron densities seen by the atoms in the pair. This suggests a viable approach for computing the grain-boundary structure and energy which is presumably more accurate than the usual pair-potential method.