Modulus spectroscopy for the detection of parallel electric responses in electroceramics

Impedance spectroscopy has become one of the most versatile and essential investigation methods concerning electrical properties of materials for electronic and energy applications. Deriving knowledge about physical mechanisms, however, often demands excellent expertise in evaluating the spectra. Investigating different representations of the same data set can help elucidate the underlying physics, but this is rarely applied. In this work, the importance of using the modulus representation to identify parallel electric responses is rationalized. Those responses result from parallel conducting pathways, e.g., at grain boundaries, or from regions with differing permittivity, e.g., in composites. Qualitative and quantitative data can be obtained, as it is illustrated based on experimental data from electroceramics and respective physical simulation results using the finite element method. The findings should help to study intricate electric responses of materials with chemical or structural heterogeneity.