Possible universalities in the ac frequency response of dispersed, disordered materials

The plausibility of recent suggestions that the electrical conductivity of crystalline and glassy disordered materials may often arise from two separate physical processes, each involving dispersed response, is examined by means of a detailed, complex-non-linear-least-squares analysis of small-signal frequency-response data on CaTiO3:30%Al3+ over a temperature range from 51 to 626 K. Earlier preliminary analysis on a few of the available 16 data sets, which showed that they could indeed be described by a combination of conductive-system dispersion and dielectric-system dispersion, is confirmed and extended. Complex non-linear least squares analysis provides a high-resolution method of isolating, identifying, and examining these separate response contributions. It was found that the conductive-system part of the full response could be well represented over a wide temperature range by a power-law model with an exponent close to 0.5, presence of diffusion. A new analysis procedure showed that the relaxation time and de conductivity exhibited the same thermally activated temperature response with no pre-exponential T dependence. The dielectric system dispersion was well described by a thermally activated exponential-distribution-of-activation-energies model, whose effective power-law exponent exhibited [1-(T/T-0)] temperature dependence from 51 to 296 K. Thus, when the present analysis methods were applied to these data, the constant-loss 'second universality', found earlier for this and other materials, one which involves a power-law exponent of unity, did not appear in the 64 to 224 K region where it was previously identified for the present material.