Abstract
A method of characterizing electrically heterogeneous electroceramics for a full three‐dimensional collection of randomly shaped grains is presented. Finite element modeling, solving Maxwell's equations in space and time is used to simulate impedance spectroscopy (IS) data. This technique overcomes several deficiencies associated with previous methods used to simulate IS data and allows comprehensive treatment of a full three‐dimensional granular representation of ceramic microstructure without the requirement for equivalent circuits based on the Brickwork layer model (BLM) or the introduction of constant phase elements to describe any nonideality of the IS response. This is applied to a full three‐dimensional ceramic microstructure with varying grain size and electrical properties to generate IS plots that highlight limitations of the BLM in data analysis.
Highlights
Introduction and BackgroundI MPEDANCE spectroscopy (IS) is widely employed to deconvolute the intrinsic and/or extrinsic contributions to the electrical properties of electroceramics by measuring the impedance response over a frequency spectrum,[1,2] commonly from mHz to MHz
This combination results in an ideal arc in the complex impedance and electric modulus plane plots, Z* and M*, respectively, and an ideal Debye peak in spectroscopic plots of the imaginary components of impedance, Z′′, and electric modulus, M′′, with a full-width half maximum (FWHM) of 1.14 decades on a logarithmic frequency scale.[5]
The trend continues for Vgc:gb = 100 where the Z* arc associated with the grain-boundary response remains lower for the encased model, Fig. 2(e), the grain-core M′′ spectroscopic response shown in Fig. 2(f) is comparable for both models and is that of a near-ideal Debye-like response
Summary
I MPEDANCE spectroscopy (IS) is widely employed to deconvolute the intrinsic (bulk) and/or extrinsic (grain boundary, electrode effects, etc.) contributions to the electrical properties of electroceramics by measuring the impedance response over a frequency spectrum,[1,2] commonly from mHz to MHz. To a first approximation, the grain-core (bulk) response is described in an equivalent circuit by a parallel combination of a resistor and a capacitor (RC) This combination results in an ideal arc in the complex impedance and electric modulus plane plots, Z* and M*, respectively, and an ideal Debye peak in spectroscopic plots of the imaginary components of impedance, Z′′, and electric modulus, M′′, with a full-width half maximum (FWHM) of 1.14 decades on a logarithmic frequency scale.[5] Due to heterogeneities associated with defects, impurities, and complex conduction processes, such an ideal response for the grain core is seldom obtained.
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