A complex quantitative model for nearly-constant loss was proposed which was based upon an effective-medium approach. Unlike previous nearly-constant loss response models, it satisfied the Kronig–Kramers transform relationships. Here, the effective-medium dielectric-level model depended directly upon the concentration of mobile

charges, and its complex dielectric response was assumed to arise from electrical interactions between vibrating and/or hopping ions and the bulk matrix material. Combination of the effective-medium response, with dispersive hopping as described by the Kohlrausch K1 model (a version of the corrected-modulus formalism approach), led to a behavior that could well represent predominant nearly-constant loss at low temperatures. At higher temperatures, there was a dispersive response, followed by nearly-constant loss. Complex non-linear least-squares fitting of experimental data sets that exhibited both types of response led to excellent fits. Moreover, the effective-medium nearly-constant loss model, which involved physically possible responses, could analytically represent a wide range of nearly-constant loss behaviors. These ranged from an approximate or exact power-law frequency dependence, for both parts of the complex dielectric constant, or to such a response for its real part and very close to a constant loss over a wide range of frequencies for the associated imaginary part. The latter was sometimes observed.

Effective-Medium Model for Nearly Constant Loss in Ionic Conductors. J.R.Macdonald: Journal of Applied Physics, 2003, 94[1], 558-65