Anharmonic Effects on the Vibration Spectrum of the U-Centers in Alkali-Halide Crystals

Broadening of infrared absorption lines due to localized modes of lattice vibrations of U-centers in alkali-halide crystals is investigated by taking into account vibration anharmonic terms. A model is assumed such that a vibration spectrum of an ionic crystal is modified by the presence of a U-center, thus giving rise to a few localized modes whose frequencies lie outside the continuous spectrum (about three times as large as the frequency of the optical mode), and general anharmonic parts are expanded in terms of these vibration normal coordinates. It is shown that third-order terms are ineffective because of an energy conservation relation, and that fourth-order terms each involving three optical modes and one localized mode are responsible for the broadening. The absorption line is of a Lorentzian shape. A simple expression for the damping constant is derived which yields a relation between the line-widths and the ratio, \(ωₒₚ*/kT\), where ω op * is the optical-mode frequency for a given lattice, and is compared with the experimental results of Schaefer. A good agreement is obtained concerning both the temperature and the frequency (ω op * ) dependences that confirms the proposed mechanism of the line-broadening, i.e. fourth-order anharmonic broadening considered in the present paper.