Theory of Dielectric Relaxation for a Single-Axis Rotator in a Crystalline Field

Abstract

The dielectric relaxation times associated with a single‐axis polar rotator which may occupy several sites as it turns about its axis are calculated in terms of the probabilities of transition from one site to another. Two special cases are considered in detail: (a) that in which all of the sites are equivalent, and (b) that in which one site is stable with respect to the others. It is assumed that the only important elementary process is a rotational jump to an adjacent site (single‐jump hypothesis). Fluctuations of barrier height are ignored. If the dipole has three or more accessible sites, and one is more stable than the others, a distribution of relaxation times develops naturally. The corresponding dielectric loss peak will be somewhat asymmetric. If the sites are all equivalent, only a single dielectric relaxation time is found, and the corresponding dielectric loss peak will be of the simple Debye type. The theory predicts that the dielectric loss peaks in certain polar crystals will become narrower and more symmetrical as the temperature is raised.