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Solid State Ionics, Vol.124, No.1-2, 1-19, 1999
Critical examination of the mismatch-and-relaxation frequency-response model for dispersive materials
Accurate calculations of the frequency and time responses of the hew dynamic-mismatch conductive-system frequency-response model of Funke, designated by CMR, indicate that its predictions are inconsistent with some of the physically based assumptions used in deriving the model. Although it does not lead to good quantitative agreement with real-part conductivity data for 0.4Ca(NO3)(2).0.6KNO(3) [CKN] for several temperatures, it may be useful for fitting other disordered or crystalline materials showing frequency dispersion. Calculation of the full complex-conductivity frequency response, not well fitted by the KWW response model, and of its unique underlying distribution of relaxation times, leads to specification of the conditions necessary for the appearance of two peaks in the frequency response of the imaginary part of the complex modulus. Important conclusions about modulus plotting and the modulus formalism fitting approach are presented, and the normalization expression used in the CMR is corrected. The appropriate expression found for the tau(0), normalization quantity, which is relevant for scaling, cannot be fully evaluated independently of experimental results. It involves a conductive-system-effective dielectric constant whose zero-frequency values, epsilon(C0) were found from the CKN fitting to be of the order of 10 and showed small temperature dependence. On the other hand, based on limited data, tau(0), itself showed approximate Arrhenius behavior. CMR macroscopic transient response is shown to be fitted exceptionally well by the combination of an ordinary exponential and a stretched exponential, both applying over the full time range, a type of parallel response quite different from the serial responses of the Ngai coupling model and of the closely related but more plausible distribution-of-relaxation-times cutoff model.
Keywords:IONICALLY CONDUCTING GLASSES;NON-ARRHENIUS CONDUCTIVITY;ELECTRICAL RELAXATION;SCALING PROPERTIES;DISORDERED SOLIDS;AC CONDUCTIVITY;DECAY FUNCTION;MOBILE IONS;MELTS;BEHAVIOR