Question

d. The main defect in stoichiometric Csl is the Schottky defect. The fraction of lattice sites that exhibit Schottky defects, as a function of temperature, is as follows: 1.08 x 10-16 at 300 K, 1.06 x 10-12 at 400 K, 2.63 x 10-10 at 500 K, 1.04 x 10-8 at 600 K, 4.76 x 10-6 at 900 K. Show whether the formation of Schottky defects is given by an Arrhenius (or Boltzmann) expression and, if so, evaluate the enthalpy of formation of (i) one Schottky defect, (ii) 1 mol of Schottky defects. e. Describe briefly the formulae and structures of the high-Tc cuprate superconductors. Indicate their relation to the perovskite structure and show how the coordination environment of Cu may be taken as an indication of its oxidation state. f. Compare critically the methods that may be used to determine the oxygen content, 8, in a material such as LaBa2Cu30s.

Answer 1

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4 fraction defects % lattice Sites that enhibit Schotty defecte Temperature (K) 16 1.O6x 10 1.06 x 10 300 400 -12 500 2.63 X10-10 1.04 x 10-8 600 6 4.76 x 10 goo Asthenius expression for Schottky dlegeeto no = N esept-44/2K1) where ng is the number of Schottky defectes per unit volímes at I kg in a crystal with N čations and N amion sizes jeu unit celé volumes and Ahs is the enthalpy required to form are defect ng/N represents the fraction of lattice site exbibitine Schatty deport X = boltzmann constant 1:38X1023 J/K. 1.08 X 10-16 elanle* 1.38x10-23* 300) eliau1.38X1023 * 400) el-AH2 * 1038 x 10-23* 500) e C-AH/2 * 1.88 X10 el-AH/2 * 1138 x 10 goo) Dividing equatione 1 and 2 we get 30 4.42 x 10-21 J Dividing equations 3 and 4 weget AH D 1.06 X10-12 -10 2. 63 X 10 -8 1. 04_XID 2-23 * 600) 4.76 x 10-6 23 AH 304.42 x 100 21 I

Sites present at temperature Iis The fraction of Schottky obeying Arrhenius Expression Enthalpy of formation of ore Schottky defect = AH = 304.42 x 10-21J AHX NA of 1 mol Enthalpy of formation of Schottky defect = 304.42 x 10-21J X 60023 * 10 1833.522 X 102 183.35 KJ j Thank you

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