Theory of the Frenkel–Debye boundary layer at the (111) surface of pure CaF₂

Abstract

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.

Analyzing the grain‐boundary resistance of oxide‐ion conducting electrolytes: Poisson‐Cahn vs Poisson‐Boltzmann theories

“…The standard treatments of Gouy‐Chapman and Mott‐Schottky space‐charge layers in ionic solids are based on two main assumptions. First, materials' parameters, such as charge‐carrier mobilities or standard chemical potentials, are assumed to exhibit step functions at the core (abrupt core|space‐charge model). That is, the mobilities, for example, exhibit one value in the bulk phase all the way up to the core and a different value in the grain‐boundary core.…”

“…The abrupt core|space‐charge model currently represents the standard treatment of space‐charge layers at grain boundaries in complex oxides. It is essentially a two‐phase model, in which a grain‐boundary core phase is sandwiched between two slabs of bulk material, the grain‐boundary core being the structurally perturbed region between the two grains.…”

Characterization of atomic step structures on CaF2(111) by their electric potential

“…30 For the (111) surface, it has been predicted that fluorine ions located at type I step or kink positions are energetically favored by 1.52 and 2.25 eV compared to fluorine ions on interstitial sites. 31 Therefore, interstitial-vacancy pairs in the near surface region form a Frenkel-Debye boundary layer where fluorine ions are located at step edges and kink sites while positive vacancies remain below the surface. However, the effective polarization is very small as a simulation predicts 31 only about 10 fluorine ions per lm 2 what is in qualitative agreement with our experimental findings where {111} facets hardly show any but a dark contrast.…”

The effect of space-charge formation on the grain-boundary energy of an ionic solid

“…In order to treat the grain boundary and the space-charge layers, we employ the standard two phase model [22][23][24][25][26][27], in which a thin grain-boundary phase of width w c is abutted on each side by a bulk phase, semi-infinite in extent. The thermodynamics and the kinetics of point defects in the core phase ( c ) are different to those in the bulk phase.…”