Molecular Model forUCenters in NaCl and KCl

Abstract

In the harmonic approximation, the molecular model has been used to study the vibrations of $U$ centers in NaCl and KCl where we have considered an impurity ion and its nearest neighbors moving while the rest of the crystal is at rest. For interactions we have used the rigid-ion model with short-range forces limited to nearest neighbors only. The 21×21 matrix obtained in this way has been diagonalized to get the eigenfrequencies and eigenvectors. If the $U$ center is treated as an isotopic impurity, the resulting vibration frequencies are almost the same as those obtained from the Green's-function method using the rigid-ion model. Thus within the framework of the rigid-ion approximation, the molecular model is a good representation of the system. The maximum amplitude of the neighboring ions corresponding to the local-mode frequency is very small compared to that of the impurity. This lends further support to the molecular model. Using the experimental infrared absorption frequency due to $U$ centers in NaCl and KCl, we have estimated the weakening of overlap forces between the impurity and its nearest neighbors.