Local-Mode Frequency Due to Light Substitutional Impurities in Alkali-Halide Crystals: Application to theUCenter

Abstract

The lattice dynamics in harmonic approximation of ionic crystals with very light substitutional impurities is studied in the framework of rigid-ion and shell models. A vibrational model for the lattice defect which takes into account not only the change of mass, but also the changes of the overlap force constant, electronic polarizability and shell charge, is considered and applied for the evaluation of the local-mode frequencies of the $U$ center in NaCl, Kcl, and KI crystals. It is shown that changes of electronic polarizability and shell charge give rise to a further local change of force constant for the core motion in the shell model. A simple local change of mass is found to be quite inadequate for accounting for the influence of the $U$ center on the lattice dynamics. Instead, fairly good agreement with the experimental results on the impurity-induced infrared absorption is found if the hydrogen ion in alkali halides is considered as belonging to the halogen family with regard to the overlap potential and electronic polarizability.