Influence of Force-Constant Changes on the Lattice Dynamics of Cubic Crystals with Point Defects

The crystal-point impurity problem is examined for the case of changes in nearest-neighbor forces around the defect site. Using the recently developed group-theoretical techniques, expressions are found for the frequencies of the perturbed modes due to impurities in face-centered and body-centered cubic crystals, assuming only central forces. By solving coupled equations for double-time Green's functions, expressions are also obtained for the defect mean-square displacement and its amplitude of vibration in each perturbed mode. Applications are then made to recent optical and M\"ossbauer measurements.