Modelling frequency-dependent conductivities and permittivities in the framework of the MIGRATION concept

Frequency-dependent conductivities and permittivities of ion-conducting materials reflect the dynamics of the mobile ions. Experimentally, the development of the ion dynamics with time can thus be monitored from less than a picosecond up to minutes and hours. In this paper, we show that the characteristics of frequency-dependent conductivities and permittivities of solid ion conductors are well reproduced within the framework of the MIGRATION concept. The meaning of the acronym is MIsmatch Generated Relaxation for the Accommodation and Transport of IONs. In this model treatment, a simple set of rules is introduced in order to describe the essence of the ion dynamics in terms of a physical picture of the most relevant elementary processes. The rules are expressed in terms of three coupled rate equations, which form the basis for deriving frequency-dependent model conductivities and permittivities as well as mean square displacements.