Power law frequency dependent dielectric function and nonanalyticity properties

Abstract

A computation of the frequency dependent dielectric function for energetic materials AIP Conf.Temperature and frequency dependences of dielectric properties of sodium sulfate single crystal Experiment yields for many materials a dielectric loss function X"(w) having the behavior X"(w)ex:w·-I(n< I) over a substantial range of frequencies. Writing the conductivity <T(w)is the relaxation frequency spectrum, weconsider two examples in detail: (a) a relaxing center, at which relaxation is assisted by arrival of defects by diffusion; (b) hopping electronic conduction, with variable range, and thermal1y assisted. Example (a) is characterized (and dominated) at high frequencies by g(V)ex:V-l/2 , and for V;::V D , a characteristic Debye relaxation frequency, <T(w) ex: W l/2 results. Example (b) is dominated by low frequency modes, andfor v < VD the behavior is like wo. s over a limited frequency range. If one al10ws in more detail for a distribution of activation energies, then it is argued that <T ex: w" where n < 0.8. Some specific experimental results are briefly referred to.