Universality, the Barton, Namikawa, and Nakajima relation, and scaling   for dispersive ionic materials
  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. 
J. Ross Macdonald