Finite Elements Approach to Predicting Impedance Response of Geometrically Convoluted Samples

The geometry of a sample is of utmost importance in interpretation of impedance measurements and correlating them to the properties of the studied material. The first, always considered, issue is inclusion of the geometrical dimensions, so that capacitance and resistance of a sample can be interpreted and reported for proper comparison based on values per unit dimensions.  In ideal measurements the samples prepared are a prioriprepared in simple geometries, allowing proper electric contact connections so that the calculations are simplified and measurements in a single laboratory, even without data interpretation, lend themselves to quick visual side-by-side comparison.

              However, such arrangement is not always possible and therefore we investigated, by method of computer simulation, dependence of impedance results on geometry of a sample and location of electrode connection.  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.    

              While in part the correlation reveals that a simple multiplication factor can be used in some cases to correct for the geometry of the electrode placement, under conditions of more extreme electrode placements the response is such, that equivalent modeling of the obtained impedance data is not adequately described only by RC circuits. Instead, a constant phase element has to be introduced.

              The simulation for this work was done using the ANSYS software package. The figure shows the geometric layout used for simulation. In this case a sample disk of a 30-mm diameter, thickness 7 mm is connected to the measurement circuit by two symmetrical, centrally placed metal circular electrodes of diameter 14 mm. In the process of simulations the size of the electrodes and their placement vs. the centerr of the sample was varied.  For the data fitting to the suitable equivalent circuits was used the ZView package from Scribner Associates.

This work was supported by the project “CEITEC - Central European Institute of Technology” (CZ.1.05/1.1.00/02.0068) from European Regional Development Fund.