A new understanding of the dielectric relaxation of solids

Abstract

The frequency dependence of the dielectric response of solids shows an apparently bewildering variety of patterns, virtually none of which corresponds to the classical Debye behaviour. However, a wide ranging critical analysis of the existing wealth of data shows that the dielectric loss obeys power-law dependences on frequencies, both below and above any loss peaks that may be present. This corresponds to power-law dependences on time under step-function excitation and it applies completely generally regardless of the detailed physical and chemical nature of the materials in question and also applies equally to dipoles, ions and hopping electrons as the polarizing species. Moreover, the power-law responses persist down to the lowest temperatures in the milliKelvin range, thus proving the importance of non-thermal transitions. The power laws are characterized by exponents in the range ± 1 and they cover as special cases the complete range of the observed types of response, from virtually frequency-independent “flat” losses often seen in low-loss materials, through various forms of asymmetric loss peaks to strongly dispersive behaviour in which both the real and the imaginary components of the susceptibility vary almost inversely with frequency. The “universality” of the power law strongly suggests the dominance in all materials of a common mechanism of dielectric relaxation and this is found in many-body interactions which provide a model capable of explaining the totality of the observed responses of solids, including both the frequency- and the temperature-dependence. In this interpretation, the classical one-particle Debye law represents but a singularity in a more general behaviour and is usually overshadowed by the new many-body mechanisms.