Direct calculation of force constant changes around impurities in crystals

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Abstract
Calculations of the changes in energy associated with symmetry-adapted displacements of a central ion and its nearest neighbours (allowing for polarisation of all other ions) provide values of the corresponding force constants. The changes in these force constants when the central perfect-lattice ion is replaced by a foreign ion have been calculated on the basis of shell model interaction potentials for the defect systems Ni2+:MgO, Mn2+:MgO and Mn4+:MgO. The results show that simple models for force constant changes introduced by defects, as commonly used in Green function analyses of defect problems, are seriously inconsistent. Nevertheless some agreement is demonstrated between the present calculations of force constant changes and values found from fitting experimental results in Green function treatments.

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