Relaxation modes of trapped crystal point defects: The three-neighbor shells model in NaCl

The results of a relaxation-mode analysis are presented for two cases of trapped-defect relaxation in the NaCl structure, in which both defects occupy the same type of site (e.g., impurity divalent ion and trapped vacancy), or in which they occupy the two different types of sites (vacancy pair). The relaxation analysis is presented in the form of a set of basis vectors in occupation-probability space and a set of secular equations. Solutions to the equations provide the relaxation rates and also the coefficients in the linear combinations of the basis vectors which constitute the relaxation modes. Calculations of the relaxation rates and contributions to the polarizability of the various modes for a three-shell model with jump frequencies chosen to represent the relaxation of an impurity-ion vacancy pair in NaCl(Mn) have confirmed the results of Lozovskii. Even though the third shell makes a significant and even large contribution to the process, one mode dominates and the relaxation as seen in a-c measurements would take place with essentially a single relaxation time. The d-c techniques of Dreyfus are sensitive enough to detect more than one of these relaxations at low temperatures, but the slowest of these will always be the dominant one. Any relaxation slower than the major one must be ascribed to some other mechanism.