ACCURATE FITTING OF IMMITTANCE SPECTROSCOPY FREQUENCY-RESPONSE DATA USING THE STRETCHED EXPONENTIAL MODEL

A new method of accurately calculating two stretched-exponential (Kohl rausch-Williams-Watts (KWW)) models and fitting them by complex non-li near least squares (CNLS) to small-signal frequency-domain data is des cribed and used for the detailed analysis of data for the disordered m aterials Li2O-Al2O3-2SiO(2) glass at 24 degrees C and Na2O . 3Si0(2) f rom 303 K to 398.5 K. Fitting was carried out with two different KWW m odels, KWW0 and KWW1, and with others, and included possible electrode polarization effects and epsilon(D infinity), the high-frequency-limi ting dielectric constant, taken as a free parameter. For conductive-sy stem dispersion, epsilon(D infinity), and E-infinity are usually unequ al. The present most-physically-appropriate KWW model, the KWW1, was m uch superior for the present data to all other models investigated. In particular, the power-law or 'Jonscher' model was found to be inferio r for fitting the trisilicate data, contrary to earlier conclusions of Nowick and Lim, based on their comparison of the fitting utility of t he power-law model and the Moynihan KWW modulus formalism. In addition , serious limitations of the modulus formalism were found and are illu strated; indicating that it should not be considered for future fittin g. For the Na2O . 3SiO(2) data, very-high-accuracy CNLS KWW1 fitting d isclosed a small change in activation energy near 341 K and somewhat i rregular, but well-determined, temperature dependence of the beta expo nent of the KWW1 model. Although the differences between fit predictio ns and the trisilicate data are too small to distinguish on ordinary M ''(omega) or -rho ''(omega) plots, the very small relative residuals of the fit nevertheless show appreciable serial correlation, rather th an random behavior, indicating that some systematic errors still remai n.