Particle size effects on the energies of bulk and surface F-centres

Abstract

Calculations, using the point-ion lattice approximation, of the energies of F-centres in NaF and NaCl have been performed for small particles approximately 15–50 Å in edge length. Three-dimensional harmonic oscillator functions, which allow calculation of both bulk and surface centres, were used as the basis functions in a variational solution of the Schrödinger equation. Symmetry reduction leads directly to selection rules for the transitions in bulk and surface F-centres. The use of a screened potential for the nearest Na⁺ ions has negligible effect on the energies. The possible existence of surface F-centres is demonstrated and reasonable agreement of the transition energies with available spectral data is found. The effect of increasing particle size on the energies of the bulk and surface F-centres is negligible for particles larger than 25 Å.