Abstract
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%.
Highlights
I MPEDANCE spectroscopy (IS) is a well-established technique to probe the electrical properties of a wide range of materials[1] and devices.[2]
Finite element simulations have shown the electrical microstructure of an encased cubic core–shell microstructure can be significantly different from its physical microstructure
The electrical microstructure is defined by both the electrical properties of the core and shell regions and by how the physical microstructure modifies the electrical field and consequent current pathways in space
Summary
I MPEDANCE spectroscopy (IS) is a well-established technique to probe the electrical properties of a wide range of materials[1] and devices.[2] By measuring impedance spectra over a wide-frequency range, it is often possible to identify and characterize electrically distinct regions, for example, bulk and grain-boundary components in electroceramics. To separate different components or processes requires differences in their characteristic relaxation times (or time constants) of at least two orders of magnitude within the measured frequency range. The core regions are undoped-BaTiO3 (Curie temperature ~125°C), whereas the shell (outer) regions contain a distribution of dopants that alter electrical properties (electrical conductivity, r, and relative permittivity, er) and lower the Curie temperature. Jeon et al[5] showed that a shell thickness of about a third of the core
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