Effective-medium model for nearly constant loss in ionic conductors

A complex quantitative model for nearly constant loss (NCL) is proposed based on an effective-medium approach. Unlike previous NCL response models, it satisfies the Kronig–Kramers transform relations. Here the effective-medium dielectric-level model depends directly on the concentration of mobile charge present and its complex dielectric response is identified as arising from electrical interactions between vibrating and/or hopping ions and the bulk matrix material. The parallel combination of the effective-medium response with dispersive hopping described by the Kohlrausch K1 model, a version of the corrected-modulus-formalism approach, leads to behavior that can represent dominant NCL at low temperatures well and, at higher temperatures, dispersive response followed by NCL. Complex nonlinear-least-squares fitting of experimental data sets that exhibit both types of response leads to excellent fits. Further, the effective-medium NCL model, which involves physically realizable response, can represent a wide range of NCL behavior analytically. Such behavior ranges from either approximate or exact power-law frequency dependence for both parts of the complex dielectric constant or to such response for its real part and very close to constant loss over a wide range of frequency for the associated imaginary part, as sometimes observed.