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

Abstract

Previous work on the relaxation times associated with a polar single‐axis rotator where the dipole may occupy three or four orientational sites by turning in a lattice point has been extended to include the more general case where the energies of the sites (as well as the intervening barriers) are all different. The results for these more general models tend to confirm the view that the presence of barriers of different magnitudes between the equilibrium orientations of a dipole can be the source of a set of discrete dielectric relaxation times. The dielectric properties of some specialized three‐ and four‐position models are then considered in detail. A very narrow or an extremely wide set of relaxation times can be obtained depending on the nature of the barrier system, and accordingly, a wide range of dielectric behavior can be accommodated. Despite the wide range of behavior, certain qualitative features (noted in Sec. VII in italics) appear to persist in many of the models. These features may be useful in applying the theory in a general way. The equations given will facilitate the calculation of the properties of three‐ and four‐position models not already considered.