Computational impedance spectra of arbitrary 3D microstructures of dielectrics

We report an efficient computational method for computing impedance spectra of arbitrary three-dimensional (3D) microstructures. It is based on the phase-field description of multiphase microstructures and the Fourier spectral iterative perturbation method (SPM) for solving Maxwell’s equations. The only inputs are the spatially varying local dielectric constants, electrical conductivity, and electric polarization. It allows for general crystalline anisotropy and large inhomogeneity in dielectric and electrical properties. We apply it to three representative heterogeneous microstructures: (1) polycrystalline electroceramics with different grain sizes, (2) ceramic/polymer composites with varying volume fractions of ceramic fillers, and (3) ferroelectric thin films with different domain configurations. The computed frequency-dependent electrical responses, including complex impedance and electrical modulus, are shown to be in general agreement with existing experimental measurements of similar microstructures. The method is computationally efficient and can be used to compute the impedance spectra of large sets of experimentally digitized microstructures to generate microstructure-impedance databases. It can also be integrated with the phase-field method of microstructure evolution to model the temporal evolution of impedance spectra.