Statistical Properties of Polycrystalline Dielectrics

Abstract

In this paper we consider the determination of the two‐point electric field correlation tensor in a random polycrystalline medium subjected to a constant average electric field. The medium is supposed to be statistically homogeneous and isotropic and to be composed of crystals all of the same kind. For media whose principal permittivities do not differ greatly from one another, we employ perturbation techniques to linearize the governing equations and derive explicit expressions for both the correlation function and the cross correlation of the electric field and permittivity tensor. We also determine the effective permittivity in this limit. For media with arbitrary principal permittivities, we derive bounds on the effective permittivity which depend on certain two point correlation functions and which reduce to our perturbation solution in the limit of small differences in principal permittivities.