New aspects of some small-signal ac frequency response functions

• Published in: Solid state ionics 1985-01, Vol.15 (2), p.159-161
• Main Author: Macdonald, J.Ross
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Diffusion in solids; Exact sciences and technology; Physics; Self-diffusion and ionic conduction in nonmetals; Transport properties of condensed matter (nonelectronic)
• ISSN: 0167-2738; 1872-7689
• DOI: 10.1016/0167-2738(85)90095-5

First, it is shown how an expression for the ac conductivity of an ionically conducting material derived by Almond and West and co-workers from an earlier “universal dielectric response” equation of Jonscher may be related to and subsumed under a response function proposed much earlier. Doubt is cast on the identification of a parameter in the Almond-West analysis as the ionic hopping frequency. The earlier function, first proposed by Ravaine and Souquet, is widely used to describe the depressed arcs often obtained when experimental impedance data are plotted in the complex plane. A general relation which yields either this response or that of Cole and Cole for the complex dielectric constant is discussed and shown to involve inadequate high and low frequency limits. Finally, a new distribution-of-activation-energies model which can fit both unsymmetric and symmetric arcs in either the impedance or complex dielectric constant plane is briefly discussed. This model does yield physically realistic high and low frequency limiting response as well as predictions of the temperature dependence of power-law frequency response exponents.