Solving the inverse electrical problem in materials science: generalized Voight model

This work deals with the theoretical foundationsof high-frequency impedance spectroscopy used forthe study of functional polycrystalline materials. Amethod for constructing an electrical model of asample in the form of a classical and generalizedVoight scheme is described. The impedance hodograph of the classical Voight scheme is an overlay ofsemicircles, from which geometric dimensions it ispossible to determine the parameters of the equivalent scheme. It is shown that for inhomogeneousmaterials, the considered semicircles are rotated relative to the origin of the complex plane and shiftedhorizontally. To model such systems, it is necessaryto use a generalized Voight scheme, in which thecapacitors are replaced with elements of a constantphase. The ways of transition from the “inconvenient” parameters of such two-poles to the electricalcharacteristics of the material volume are considered. Three new integral characteristics of an inhomogeneous medium are proposed: the peak parameters on the imaginary impedance frequency characteristic (the frequency of the impedance resonanceand the half-width of the peak). Both values canbe determined without measuring the geometric dimensions of the sample. In addition, the “dielectricloss correction factor” has been introduced, whichaffects the horizontal offset of the impedance frequency response.