Decomposition of Universal AC Ionic Conductivity Response into Two Ranges with Constant Exponents

Many disordered materials both crystalline and glasses show universal dynamic response [1], which is characterized by appropriate power-laws. The ac-conductivity as a function of frequency, is given by: σ(ω)=σ(0)+ Aωs where σ(0) is the dc-conductivity and the exponent s (≤1) generally decreases with increasing temperature. In previous work on ionically conducting crystals and glasses, we have observed two ranges in which s = constant, independent of temperature: at high temperatures, s=so (a value between 0.5 and 0.6) and, at low temperatures, s = 1. Further for the s = so region, the parameter A is activated with activation energy related to that of σ(0), while for the s = 1 region, A varies only slowly with temperature. For the cases of borate and silicate glasses as well as for crystalline CaTiO3 doped with 30% A13+, careful analysis was carried out over the region in which the effective s falls from 1.0 to so. The results show that this region can be described by the relation: σ(ω)= σ(0) + Aωs0 + A'ωl.0 with parameters A and A’ consistent with those obtained from the high and low- temperature regions, respectively. Thus, we conclude that two separate types of universal behavior are superimposed throughout the entire temperature region; each is described by a constant value of s, and is due to an independent mechanism of non-Debye relaxational behavior.