Abstract
The analytical expressions for the phonon frequency shifts and widths due to the presence of many substitutional impurity atoms in a crystal are obtained. A nearest-neighbor perturbation model including the changes in the mass and the changes in the force-constant has been employed. Furthermore, the effect of impurity concentration on the phonon resonance is considered to obtain the shifts and widths of the phonon frequency. It is carried out to investigate quantitatively the dependence of these physical quantities upon force-constant changes and impurity concentrations. The theoretical results are compared with the inelastic neutron-scattering experiments.
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