Modes of vibrations due to single ion substitutional impurities in alkali halides

Modes of vibrations due to single ion impurities in alkali halides are studied by Green's function technique. The Green functions computed on the basis of shell model parameters fitted to the neutron data are used in the computation. The modes of vibrations are computed by considering the vibrations of the defect and its six nearest neighbour ions, having O h symmetry. Using group theory symmetry coordinates are constructed for the seven‐atom defect space and analytical expressions are derived for various modes of vibrations, in terms of Green's functions of the perfect lattice and the perturbation matrix as a result of the defect. Mass changes at the defect site as well as the changes in the short‐range interaction due to the presence of the defect are taken into account. The change Δ A in the short range interaction parameter A is fitted to the observed single ion frequencies in various alkali halides. A considerable softening of the nearest neighbour short‐range interaction varying from 8% in KBr:Cl to 64% in KI:Na is found.