Finite Elements Approach to Predicting Impedance Response of Geometrically Convoluted Samples

Abstract

Capacitance and resistance are extensive variables that depend on the geometry of a sample. Therefore, to obtained a normalized value, attributable to the material and not the sample shape and dimension, the geometry has to be taken into account. While with certain geometric forms simple division of multiplication, based on length and cross-section can be applied, with more convoluted forms this is not as straightforward. Ideal measurement will be done on samples geometrically simple. However, with awkward shapes or irregular electrode placements, measurements are still done and the geometry effect can be corrected after the fact. As an example is a ceramic disc with grain and boundary resistance and capacitance, that could be encountered in studies of advanced high temperature materials, e.g., for sensors of high-temperature fuel cells. The disks prepared by various methods of synthesis are contacted on their flat sides to the impedance analyzer circuitry. Our study correlates the (simulated) measured data to data that would be expected if perfectly symmetrical all-covering contacts were used.