Finite-cluster description of electromigration

The problem of vacancy migration in a metal under the influence of an electric current is studied in several model situations. The wind force is calculated as a function of the position of the atom which moves towards the vacancy. A currently used model in pseudopotential calculations implies that plane waves are scattered by a potential which is found by subtracting the unperturbed lattice potential from the potential of the system with the vacancy. As soon as the atom has started to move the scattering potential in this "subtracted" model (SM) consists practically of two vacancies with the atom somewhere in between, which forms a cluster of three scatterers. Owing to neglect of the background lattice, the SM is bound to fail for strong scatterers. A new model is called finite cluster model (FCM). It allows for the treatment of stronger scatterers and the background lattice is accounted for depending on the size of the cluster. In this FCM the system is modeled by a finite cluster of atoms surrounding the vacancy. Results are obtained and discussed for the SM treated exactly which means that all multiple scattering effects are accounted for, and in the Born approximation. The FCM is treated exactly, for clusters containing 1, 3, 5, 7, 11, 15, and 19 atoms. The system treated has the fcc structure, the atomic potentials are represented by spherical wells, and in the results presented only $s$ scattering is accounted for. The force in the region of interest appears to be largely reduced by the presence of an environment, particularly for stronger scatterers.