  Many frequency-response analyses of experimental data for homogeneous glasses
and single-crystals involving mobile ions of a single type indicate that
estimates of the stretched-exponential beta1 shape parameter of the Kohlrausch
K1 fitting model are close to 1/3 and are virtually independent of both
temperature and ionic concentration. This model, which usually yields better
fits than others, is indirectly associated with temporal-domain
stretched-exponential response having the same beta1 parameter value. Here it
is shown that for the above conditions several different analyses yield the
important and unique value of exactly 1/3 for the beta1 of the K1 model. It is
therefore appropriate to fix the beta1 parameter of this model at the constant
value of 1/3, then defined as the U model. It fits data sets exhibiting
conductive-system dispersion that vary with both temperature and concentration
just as well as those with beta1 free to vary, and it leads to a
correspondingly universal value of the Barton-Nakajima-Namikawa (BNN) parameter
p of 1.65. Composite-model complex-nonlinear-least-squares fitting, including
the dispersive U-model,the effects of the bulk dipolar-electronic dielectric
constant, and of electrode polarization when significant, also leads to
estimates of two hopping parameters that yield optimum scaling of experimental
data that involve temperature and concentration variation.
