Point defects in ionic crystals Solid state ionics

frenkel defect in agcl

in 1926, yakov frenkel suggested in ionic crystal agi, in thermodynamic equilibrium, small fraction of cations, α, displaced regular lattice sites interstitial positions. related α gibbs energy formation of 1 mol of frenkel pairs, Δg, α = exp(-Δg/2rt), t temperature , r gas constant; typical value of Δg = 100 kj/mol, α ~ 1×10 @ 100 °c , ~6×10 @ 400 °c. idea naturally explained presence of appreciable fraction of mobile ions in otherwise defect-free ionic crystals, , ionic conductivity in them.

frenkel’s idea expanded carl wagner , walter schottky in 1929 theory, described equilibrium thermodynamics of point defects in ionic crystals. in particular, wagner , schottky related deviations stoichiometry in crystals chemical potentials of crystal components, , explained phenomenon of mixed electronic , ionic conduction.

wagner , schottky considered 4 extreme cases of point-defect disorder in stoichiometric binary ionic crystal of type ab:

type-3 disorder not occur in practice, , type 2 observed in rare cases when anions smaller cations, while both types 1 , 4 common , show same exp(-Δg/2rt) temperature dependence.

later in 1933, wagner suggested in metal oxides excess of metal result in electrons, while deficit of metal produce electron holes, i.e., atomic non-stoichiometry result in mixed ionic-electronic conduction.