Simulation of impedance spectra for core-shell grain structures using finite element modeling

The volume fraction of core- and shell-regions is an important parameter in the control of temperature-dependent electrical properties of core–shell-microstructured electroceramics such as BaTiO3. Here, we highlight the potential unreliability of using capacitance ratios, obtained by simulating impedance spectra, to extract accurate volume fractions of the two regions. Two microstructures were simulated using a finite element approach: an approximation to a core–shell structure (the encased model) and a series-layer model (SLM). The impedance response of the microstructures was simulated for a range of input volume fractions. The volume fractions obtained from the simulation agreed with the input values for the SLM microstructure but differed for the encased model. Current density and electric field plots revealed that this discrepancy was caused by differences between the physical and electrical microstructures of the encased model. A stream trace analysis of current density demonstrated that the current follows the path of least resistance through the core, leaving regions of shell with lower current density. These differences are important when attempting to extract volume fractions from encased microstructures with small cores. In the present case, core volume fractions less than 0.7 produce differences in excess of 25%.