A theoretical study was made of the properties of the Frenkel–Debye boundary layer at the (111) surface of a pure crystal with anti-Frenkel defects (anion vacancies, interstitials). The work was based upon theoretical determinations of the adsorption energies of the F ion at the terrace, step and kink sites of the surface. These, together with assumed experimental step distances and theoretical kink concentrations, essential requirements for a quantitative description of the surface charge which compensated that of the space-charge region. The results showed that, for realistic surface conditions, the surface and space charges (and the potential between surface and bulk) were considerably reduced when compared with those for an unlimited number of accessible surface sites. Upon approaching the surface, a marked increase in the anion vacancy concentration with respect to that of the bulk existed, and was expected to lead to an increased ion conductivity in near-surface regions and thin fluorite layers.

Theory of the Frenkel–Debye Boundary Layer at the (111) Surface of Pure CaF2. H.Dabringhaus, M.F.Butman: Journal of Physics - Condensed Matter, 2003, 15[34], 5801-20