Evaluating dielectric impedance spectra using effective media theories

The immittance spectra (i.e., impedance and modulus representations) are calculated for various effective medium theories, i.e., the Maxwell-Wagner (MW), Hashin-Shtrikman (HS), Bruggeman Asymmetric (BA) and Bruggeman Symmetric (BS) models, with emphasis on their individual microstructures. In addition the brick-layer (BL) model is also considered. The BL and MW-HS models yield similar single impedance arcs for a relatively low volume fraction conductive matrix (coating on the low conductivity phase). The BA model yields single impedance arcs different from the MW-HS models. The BL and MW-HS models yield virtually identical dual impedance arc behavior for a low volume fraction insulating matrix (coating on the high conductivity phase). At low volume fractions of insulating matrix, the low frequency arc due to the insulating material for the BA model is much smaller than for the MW-HS model. The BS model exhibits single impedance arc behavior when the volume fraction of conductor is above or near the percolation threshold and dual arc behavior somewhat below the percolation threshold. Equivalent circuits for these model materials are discussed, and application is made to experimental data for various electroceramic systems.