“Constant-loss” relaxation response in crystals and glasses

Abstract

Nowick and his associates have stated that many ionic crystals and glasses exhibit a loss per cycle which is independent of frequency over an appreciable range and have suggested that such behavior constitutes a “new universality”. Furthermore, much such data seem to approach an asymptotic, nearly temperature-independent ac loss at sufficiently low temperatures. In order to further evaluate these conclusions, small-signal ac relaxation data for a CaTiO₃:30% Al³⁺ ceramic material are analyzed in detail and the results compared to those published by Nowick and associates for the same material. It is found that a plausible conducting-system dispersion model based on the effective-medium approximation for hopping charges yields results globally similar to, but somewhat different in detail from, those of Nowick et al. But a response model which includes both such conducting-system response and dielectric-system dispersion well fits the data over a wide temperature range. To do so, it requires the presence of a non-zero high-frequency-limiting resistivity probably arising from localized charge motion. No constant-loss individual dispersions appear in the model, but it nevertheless yields approximately constant loss over a limited frequency range at low temperatures. It suggests that asymptotic behavior is associated with the nearly temperature-independent dielectric-dispersion contribution to the response at low temperatures, and it does not verify the Nowick conclusion that the slope of the ac conductivity approaches a constant value near 0.6 at high temperatures.