Impedance spectroscopy on solids: The limits of serial equivalent circuit models

Impedance spectroscopic data obtained on solids are often interpreted in terms of serial equivalent circuit models. In these models each relaxation process in a spectrum is usually related to exactly one transport or reaction process, i.e. to one sample region (e.g. bulk, grain boundary, electrode) or reaction step. These quasi-one-dimensional, serial models implicitly assume frequency-independent current lines. In this contribution it is shown by finite element calculations that in real systems current lines are often frequency-dependent and that the current passes different sample regions at different frequencies. Several effects such as additional semicircles in the complex impedance plane or non-ideal impedance arcs result from frequency-dependent current lines and cannot be understood in terms of serial (quasi-one-dimensional) equivalent circuit models. In particular, it is discussed that (a) one and the same transport process can be reflected in two or even more impedance arcs and (b) that an arc in the impedance plane can depend on more than one transport process (e.g. charge transport in the bulk and across grain boundaries) even if the dielectric relaxation times of the corresponding sample regions (e.g. bulk and grain boundary) are distinctly different.