Application of a polarizable point-ion shell model to a two-dimensional periodic structure: The NiO (001) surface.

Abstract

A two-dimensional polarizable point-ion shell model developed from the original model of Dienes et al. was constructed, using the effective plane-wise summation technique for evaluation of two-dimensional Madelung potentials, and then applied to the NiO (001) surface in which a two-dimensional translation operation is possible, in order to assess the validity of the shell model constructed. Displacements of ions around an imperfection such as a surface plane are obtained by solving the equilibrium equations which contain displacements as unknowns, as in the original model. The two-dimensional shell model treats a crystal which contains a small number of displacements because of the two-dimensional periodicity which is invariably preserved even after a relaxation takes place. The experimental results relevant to the NiO (100) surface obtained in low-energy electron-diffraction and electron energy-loss fine-structure measurements, which are indicative of a reduction of ionic spacings normal to the (001) planes very near to the free surface by 1.9--3.8 % of the bulk lattice constant, were interpreted in terms of the calculations with the two-dimensional polarizable point-ion shell model, using the parameters determined in the bulk, although there were some slight deviations from the experiments. The surface effects upon the parameters were investigated and the relaxation in the surface structure was found to be very sensitive to the electronic polarizability of the ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ion at the top layer. A comparison between the theoretical predictions and the experiments indicated some increment to the polarizability of the ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ion on the surface plane from the bulk value.