Concept 06 / 07Solid State
Imperfections in Solids: Schottky, Frenkel, Non-Stoichiometric and Impurity Defects
Point and line defects, stoichiometric defects (vacancy, interstitial, Schottky and Frenkel) with their effect on density, impurity defects created by aliovalent doping, and non-stoichiometric defects: metal excess by anion vacancies (F-centres) and by interstitial cations, and metal deficiency.
Real crystals are never perfect. Defects are irregularities in the arrangement of particles. Point defects involve a single site; line defects involve rows of sites. Point defects form more readily at higher temperatures and on rapid crystallisation, and they strongly affect properties.
Stoichiometric defects (composition unchanged).
Vacancy defect (non-ionic solids): some lattice sites are empty; density decreases. Produced on heating.
Interstitial defect (non-ionic): extra particles occupy interstitial sites; density increases.
Schottky defect (ionic): equal numbers of cations and anions are missing, keeping the crystal neutral (see figure). Density decreases. Found in highly ionic compounds with cations and anions of similar size: NaCl, KCl, CsCl, AgBr. At room temperature, NaCl has about Schottky pairs per .
Frenkel (dislocation) defect (ionic): the smaller ion (usually the cation) leaves its site and occupies an interstitial site, creating a vacancy there. Density is unchanged. Found where the ions differ greatly in size: ZnS, AgCl, AgBr, AgI. AgBr shows both Schottky and Frenkel defects.
Impurity defects. Adding an ion of different charge creates vacancies to maintain neutrality. If NaCl is crystallised with a little , each replaces two , occupying one site and leaving the other vacant. So the number of cation vacancies equals the number of ions. Similarly in AgCl.
Non-stoichiometric defects (composition changes).
Metal excess due to anionic vacancies (F-centres): when NaCl crystals are heated in sodium vapour, Na atoms deposit on the surface, ions diffuse out to combine with them, and the Na atoms ionise, releasing electrons that diffuse in and occupy the anion vacancies. These trapped electrons are F-centres (Farbenzentren, colour centres); they absorb visible light, making NaCl yellow, KCl violet and LiCl pink. Such crystals are also paramagnetic.
Metal excess due to extra cations at interstitial sites: ZnO is white when cold and yellow when hot, as it loses oxygen, ; the excess ions sit in interstitial sites with electrons nearby, giving colour and conductivity.
Metal deficiency: some cations are missing, and neighbouring cations take a higher charge to compensate. FeO is really (range to ), with some ions; similarly FeS and NiO.
Key Takeaways:
- Schottky: cation and anion vacancies in pairs, density falls (similar-size ions).
- Frenkel: cation to interstitial site, density unchanged (very different sizes).
- in NaCl creates one cation vacancy per .
- F-centres: electrons in anion vacancies; colour and paramagnetism.
- Metal deficiency: with some .
- Pitfall: Frenkel defects do not change density because no ion leaves the crystal.
Brain-Teaser 1: NaCl is doped with mol percent of . How many cation vacancies are there per mole of NaCl?
Solution: mol means per mole of NaCl. Each creates one vacancy: cation vacancies.
Brain-Teaser 2: Analysis shows a nickel oxide sample to be . What fraction of the nickel is present as ?
Solution: Let be the number of per formula unit. Charge balance: , so and . Fraction .
Brain-Teaser 3: Why does ZnO turn yellow on heating and white again on cooling?
Solution: On heating, ZnO loses a little oxygen: . The extra ions move to interstitial sites and the electrons occupy neighbouring interstitial sites (metal excess defect); these electrons absorb blue light, so the solid looks yellow. On cooling, oxygen is taken up again and the defect disappears.
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