Q4(a)(i). Crystal defects; stoichiometric defects

Crystal defects

1. A real crystal is never perfect. Defects are classed by size: point defects (vacancies, interstitials, substituted atoms), line defects (dislocations) and plane defects (grain boundaries, stacking faults).
2. Point defects are of two kinds: stoichiometric (the ratio of ions stays as in the formula) and non-stoichiometric (excess metal or excess non-metal, e.g. Fe_(0.95)O), besides impurity defects (Sr²⁺ in NaCl creates a cation vacancy).
3. Defects form even in a pure crystal because they raise the entropy: above 0 K the Gibbs energy is lowest with a small equilibrium number of defects, which rises steeply with temperature.

Stoichiometric defects

1. Schottky defect: a cation vacancy and an anion vacancy in equal numbers (pairs, for a 1:1 salt), so the crystal stays neutral. The ions are lost to the surface. Mass falls and volume hardly changes, so the density decreases. Found in highly ionic solids with high coordination number and cations and anions of similar size: NaCl, KCl, KBr, CsCl.
2. Frenkel defect: an ion (usually the smaller cation) leaves its site and sits in an interstitial position, creating a vacancy–interstitial pair. No ion is lost, so the density is unchanged. Found where cations are small and anions large or polarisable, with lower coordination: AgCl, AgBr, AgI, ZnS. In CaF₂ the anion moves (anion Frenkel or anti-Frenkel defect).
3. AgBr shows both types (Frenkel predominant).
4. Number of defects: for N sites, n_S≈ Ne^(-Δ H_S/2kT) for Schottky pairs and n_F≈√(NNᵢ) e^(-Δ H_F/2kT) for Frenkel pairs (Nᵢ interstitial sites). They are rare at room temperature and grow rapidly on heating.
5. Effects: both increase ionic conductivity (ions hop into vacancies), and they allow diffusion in solids. They do not give colour or electronic conductivity; these come from non-stoichiometric defects (F-centres).

Application. Frenkel defects in AgBr let interstitial Ag⁺ reach the latent-image sites in photographic film; vacancy conduction in doped ZrO₂ (yttria-stabilised zirconia) is the basis of oxygen sensors in car exhausts and solid-oxide fuel cells.