Adatom mobility on the surface planes of a simple metal

An approach using the Density Functional Approximation, which had in an earlier paper been applied to the binding of an adatom to a jellium metal (r_s = 4a₀), has been extended to a partially structured metal surface by introducing a layer of surface atoms to replace an equivalent layer of jellium. The model has been used to estimate the adatom motion energies over several quite close packed planes for a simple surface. An important preliminary step was to determine the general electron density contours for each surface by a simple variational method. The ensuing shielding charge distributions have an important bearing on the adatom motion energy. Adatom energies were calculated at three positions: (1) A above a surface atom, (2) B above a bridge position between two surface atoms and (3) C above a central position between three or four neighboring atoms. The motion energy was taken to be E_B ? E_C. As might have been expected this quantity was larger for the less closely packed planes, although it was always quite small due to the nature of the metal — large r_S, small ion core and typical s-p binding. To a rather surprising degree the strength of the shielding charge, the energies and the positions of the adatoms proved to be quite smooth functions of a parameter chosen to measure the close packing of the surface, namely the square of the interplanar distance divided by the surface area per atom.