The displacements and polarization caused by point defects in ionic crystals

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Abstract
The lattice statics method for the calculation of point defect properties, first proposed by Kanzaki, is here extended to discuss the polarization and displacements caused by charged point defects in ionic crystals. The method allows the determination of the exact displacement and polarization fields for a defect in a given crystal model. Detailed discussion is given for the NaCl structure using the deformation dipole model. It is shown that the long-range displacement field can be rigorously separated into pure strain and pure polarization components, the last being strictly isotropic. For a model without deformation dipoles (Szigeti effective charge e∗=e) the polarization components are exactly as assumed in the method of Mott and Littleton. Different expressions however apply when e∗≠e, as is generally the case. The elastic strengths of the cation vacancies are calculated to be much larger than those of the anion vacancies; this is also an effect of the deformation dipoles, especially of their localization on the anions.