Defects in crystals Nonstoichiometry Point defects Vacancy Point

Other defects Line defects • Edge dislocation • Screw dislocation Plane defects • Stacking

Non-stoichiometry Example: Fe. O Stoichiometric case: Fe 2+ : O 2 - = 1:

Effect of defects on properties Frenkel defects • Ag. Br, Ag. Cl • ionic

Relevance of non-stoichiometry • • electrical conductivity corrosion electrode surface activity catalysis Examples of

Problem Set 1. The average energy required to create a vacancy in a monatomic

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Defects in crystals, Non-stoichiometry

Point defects Vacancy

Point defects Interstitial

Point defects Substitutional impurity

Point defects Schottky pair

Point defects Frenkel defect

Other defects Line defects • Edge dislocation • Screw dislocation Plane defects • Stacking fault • Small angle grain boundaries

Non-stoichiometry Example: Fe. O Stoichiometric case: Fe 2+ : O 2 - = 1: 1 Usually: partial oxidation of Fe 2+ occurs non-stoichiometric composition: Fe 1 -x. O Say for example: Fe 3+/Fe 2+ = 0. 05 Let: [Fe 2+] = b [Fe 3+] = a ; a/b = 0. 05 charge balance : 3 a + 2 b = 2 Solving : a = 0. 05; b = 0. 93 Therefore the non-stoichiometric composition = Fe 0. 98 O

Effect of defects on properties Frenkel defects • Ag. Br, Ag. Cl • ionic conduction, photography Substitutional impurities • Extrinsic semiconductors • n-type: P doped Si • p-type: B doped Si

Relevance of non-stoichiometry • • electrical conductivity corrosion electrode surface activity catalysis Examples of non-stoichiometric materials • Tungsten bronzes: Nax. WO 3 colored materials • 123 oxides: YBa 2 Cu 3 O 7 -x high Tc superconductors

Problem Set 1. The average energy required to create a vacancy in a monatomic solid is 1. 1515 e. V/mol. Compute the ratio of vacancies at 1000 K and 500 K. 2. How are the density of crystals affected by the presence of Schottky and Frenkel defects ? 3. Addition of Ca 2+ increases the conductivity of KCl crystal. However, it is found that the conductivity is still due to the motion of K+ ions rather than the doped Ca 2+ ions. Discuss the mechanism for the enhanced conductivity. 4. If the ratio of A 3+ to A 2+ in a nonstoichiometric sample of an ionic crystal AO is 0. 15, what is the nature of the defect ? Derive the correct formula for AO. 5. Discuss the nature of nonstoichiometry in (a) copper sulfide, (b) zinc oxide, (c) praseodymium oxide. What are the different structures in the case of (c). 6. Ni. Te exhibits nonstoichiometry. Draw schematic diagrams to illustrate the crystal structures of the two extreme formulations.