Jr. Macdonald, ACCURATE FITTING OF IMMITTANCE SPECTROSCOPY FREQUENCY-RESPONSE DATA USING THE STRETCHED EXPONENTIAL MODEL, Journal of non-crystalline solids, 212(2-3), 1997, pp. 95-116
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.