Resolution of conflicting views concerning frequency-response models for conducting materials with dispersive relaxation, and isomorphism of macroscopic and microscopic models

• Published in: Solid state ionics 2002-10, Vol.150 (3), p.263-279
• Main Author: Macdonald, J.Ross
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Conductivity relaxation; Dielectric properties of solids and liquids; Dielectrics, piezoelectrics, and ferroelectrics and their properties; Disordered materials; Electric modulus formalism; Exact sciences and technology; Immittance-spectroscopy data fitting; Ionic glasses; Kohlrausch–Williams–Watts; Physics; Stretched-exponential
• ISSN: 0167-2738; 1872-7689
• DOI: 10.1016/S0167-2738(02)00525-8

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, ϵ C1∞, and the failure to treat properly the high-frequency-limiting dielectric constant associated with bulk dipolar and vibrionic effects, ϵ D∞. 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.