The Volumes of Formation of Schottky Defects in Ionic Crystals

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Abstract
In this paper we calculate the volumes and energies of formation of Schottky defects in the alkali halides NaCl, NaBr, KCl and KBr. Both the polarisable point-dipole and a simple shell model are evaluated. The calculation uses a generalised and extended Mott-Littleton approach in conjunction with results derived previously by the lattice statics method of Kanzaki. The polarisable point-dipole model, as might be expected, is bad, but the shell model leads to good values for the Schottky formation energies, which not only compare well with experiment but are insensitive to the size of the region (‘region I’) around the defect for which the lattice displacements are computed explicitly (i. e. as distinct from the outer Mott-Littleton region, ‘region II’) . The predicted volumes of formation of Schottky defects are less than the molecular volume, νm, i. e. the volumes of relaxation are negative (NaCl, - 0.69 vm; NaBr, - 0.73 vm; KCl, - 0.52 vm; KBr, -0,51 vm in the static lattice approximation). This is in conflict with the results of experiments on the effect of pressure upon the ionic conductivity of these crystals although some other experimental data are consistent with negative relaxation volumes. The disagreement is briefly discussed and the possibility that temperature effects are greater than is implied by the quasi-harmonic model is noted as a possible explanation

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