Comparison of Some Random-Barrier, Continuous-Time Random-Walk, and Other Models for the Analysis of Wide-Range Frequency Response of Ion-Conducting Materials

Several theoretical models are fitted to an exact wide-frequency-range data set representing a new random-free-energy, effective-medium expression for mobile-ion response at low temperatures. A continuous-time, random-walk K1 model, indirectly involving a stretched-exponential temporal correlation function, led to the best fit, much superior to those of two dielectric-dispersion models as well. Two types of approaches are compared for analyzing 0.4Ca(NO3)2 ·0.6KNO3 (CKN) experimental data covering a very wide frequency range: a simplified conventional approach, usually involving only some or all of the real part of conductivity, denoted type 1, and an approach involving nonlinear least-squares fitting of full complex data over its entire range, denoted type 2. The type-2 analysis uses a composite fitting model involving the K1 and involves 10 free parameters needed to well represent electrode polarization, conductive-system dispersion, nearly constant loss, and limiting far-infrared vibrational effects. It confirmed that the latter were purely dielectric and led to σ′ ′ and ε′ ′ boson peaks; included a mobile-charge explanation of the nearly constant loss region; and yielded reasonable values of the K1-model fractional exponent, 1, and plausible values of a completely blocking double-layer capacitance. The good type-2 fit parameter estimates were used to generate extrapolated model response over a 20-decade range at complex conductivity and complex relative permittivity levels, as well as their accurate slopes over that range. The maximum slope of the log-log σ ′ curve failed to approximate wel