Modes of vibrations due to (U-center + additive cation impurities) in alkali halides

Abstract

Local and resonant modes due to hydride ions in various alkali halides containing additive cation impurities have been computed by the Green function technique. Local vibrations due to U-centers in alkali halides have O h symmetry. When one of the six nearest neighbour cations is replaced by an additive impurity, the site symmetry of the system is lowered from O h to C 4 v . The phonon Green functions matríx is analysed according to the irreducible representation of the point group symmetry pertaining to the substitutional impurity. We have considered the vibrations of the hydride ion and all its six nearest neighbours. Analytical expressions have been derived for various modes of vibrations. Using group theory the 21 × 21 matrix has been block diagonalized into various irreducible representations. The effect of mass changes and the changes in short-range force constants have been taken into account. The computed results of the localized modes have been compared with the available experimental results. Good agreement has been found. Theoretical results on resonant modes are also displayed, which will be of use in future experiments on these systems.