The present paper is concerned with a theoretical study of the properties of the Frenkel-Debye boundary layer at the (111) surface of pure (undoped) CaF 2 , a crystal with anti-Frenkel defects, i.e. with anion vacancies and interstitials. The study is based on theoretical determinations of the adsorption energies of the fluorine ion at the terrace, step and kink sites on the surface, which are, together with the assumption of experimental step distances and theoretical kink concentrations, necessary pre-requisites for a quantitative description of the surface charge compensating that of the space-charge region. The results show that, for realistic surface conditions, the surface and space charges, and with them the potential between surface and bulk, are reduced considerably compared with those for an unlimited number of accessible surface sites. Nevertheless, on approaching the surface a strong increase in the anion vacancy concentration against that of the bulk still exists, which should lead to an increased ion conductivity in near-surface regions and thin fluorite layers.