Analysis of Impedance and Admittance Data for Solids and Liquids

Abstract

Some problems of analyzing small‐signal impedance data on solids or liquids are discussed. A method of using ordinary nonlinear least squares fitting procedures with minor modification to fit at the same time real and imaginary functions of the same set of unknown parameters to complex data is described in detail. This method of complex least squares fitting, which has several advantages over previous approaches, is illustrated by fitting equivalent circuit impedances to some polycrystalline β‐alumina impedance data and to synthetic impedance and admittance data calculated from a theoretical model of the response of homogeneous material with completely blocking electrodes. When different physical processes yield response in overlapping frequency regions so that the different processes lead to some melding of effects in an impedance plane representation, interpretation of equivalent circuit parameters becomes difficult even when the degree of fit of the model to the data is excellent. In particular, low frequency extrapolation in the impedance plane to obtain an estimate of bulk resistance, , in an overlapping completely blocking situation can yield estimates of with very large errors. A method is described of avoiding such errors for both conventional and complex least squares estimation. In essence, one must find and fit the unique equivalent circuit whose elements remain related by invariant formulas to underlying microscopic parameters of the material/electrode system no matter what the degree of phenomena overlap.