a Frenkel defect
/ FRENK-ell /
A Frenkel defect is a single ion that has jumped off its proper seat into a nearby empty gap, leaving its old seat vacant. Nothing is added or removed from the crystal — one ion has simply relocated from a lattice site to an interstitial site — so charge and mass are automatically conserved. Picture one person in a packed theatre standing up and squeezing into the aisle: their seat is now empty (a vacancy) and there is an extra body in the aisle (an interstitial), but the total headcount is unchanged.
Because it is one ion split into a vacancy-plus-interstitial pair, a Frenkel defect needs a structure with room for the interstitial. It is therefore favoured in OPEN structures and for the SMALLER ion of the pair — usually the cation. In silver halides (AgCl, AgBr) cation Frenkel disorder dominates: Ag_Ag^x ⇌ Ag_i• + V_Ag', a silver ion hops to a gap leaving a silver vacancy. In fluorite oxides (ZrO2, CaF2, UO2) the roomy anion sublattice makes ANION Frenkel (also called anti-Frenkel) disorder easy: O_O^x ⇌ O_i'' + V_O••. The equilibrium count again follows a Boltzmann law, n proportional to exp(-E_F/2kT), with the Frenkel formation energy E_F.
Which intrinsic disorder a crystal chooses — Schottky or Frenkel — is decided by which costs less energy, and that is set by structure and ion sizes: close-packed rock-salt oxides pick Schottky (no room for interstitials), open fluorite and silver-halide structures pick Frenkel. This choice governs the intrinsic diffusion and ionic conductivity of the pure material, and easy anion Frenkel disorder is part of why fluorite-type oxides are the backbone of oxygen-ion solid electrolytes.
In calcium fluoride (CaF2) the fluorine ions are the mobile species: a fluoride hops into an interstitial hole, F_F^x ⇌ F_i' + V_F•, and the resulting vacancies and interstitials let the crystal conduct fluoride ions — the same anti-Frenkel trick that makes fluorite oxides oxygen conductors.
Frenkel means one ion becomes a vacancy AND an interstitial; the total number of ions never changes.
Schottky versus Frenkel is not a matter of taste: a given crystal is dominated by whichever has the lower formation energy. Both types coexist in every real crystal; we speak of the one that is far more numerous.