On the physical interpretation of constant phase elements

Complex impedance spectra of ion-conducting lithium borate network glasses are used to study the deformed shape of impedance semicircles which are usually described by a parallel circuit of an ohmic resistor and a phenomenological Constant Phase Element (CPE). Based on the Concept of Mismatch and Relaxation (CMR) of Funke et al. which provides a theoretical treatment of the ion dynamics in disordered materials, a quantitative description of the experimental impedance spectra is presented. It takes into account the contribution of the static glass network by introducing an additional capacitor, and provides both, a physical interpretation of the CPE and an easy-to-handle mathematical formula to calculate the ’real’ capacity of a CPE.