Solid State Ionics, Vol.150, No.3-4, 263-279, 2002
Resolution of conflicting views concerning frequency-response models for conducting materials with dispersive relaxation, and isomorphism of macroscopic and microscopic models
Possible errors in the widely used 1972-1973 macroscopic original-electric-modulus formalism are identified, corrected, and their consequences considered. These errors include misidentification of the high-frequency-limiting dielectric constant arising entirely from mobile charges, epsilon(Cl infinity), and the failure to treat properly the high-frequency-limiting dielectric constant associated with bulk dipolar and vibrionic effects, epsilon(Dinfinity). It is shown that the corrected modulus formalism, which describes dispersed mobile-charge effects, is isomorphic in form with the 1973 microscopic continuous-time random-walk hopping model of Scher and Lax after a minor but significant correction is made to the latter's response function. This firmly established correction, which nevertheless could not be determined by Kronig-Kramers transformation, involved inversion of synthetic frequency-response data to determine a distribution of relaxation times and led to extension of the real part of the Scher-Lax dielectric response to higher frequencies by the inclusion of a nonzero limiting value. This isomorphism, along with excellent data fitting using the corrected modulus formalism, suggests that since the Scher-Lax stochastic model involves no explicit Coulomb interactions, cation motion in glasses is dominated by short-range interactions. Finally, two very-high-frequency processes, which each lead to a limiting plateau value of the real part of the conductivity at sufficiently high frequencies, are discussed in detail.
Keywords:conductivity relaxation;electric modulus formalism;Kohlrausch-Williams-Watts;stretched-exponential;immittance-spectroscopy data fitting;disordered materials;ionic glasses