Revealing the effect of interaction between inclusions on the effective microwave permeability of composites

Abstract

The paper considers the application of mixing rules to the analysis of the microwave effective material parameters, the permittivity and permeability, of composites. It is suggested to perform the analysis in terms of the normalized inverse susceptibility defined as the volume fraction of inclusions divided by the effective dielectric or magnetic susceptibility of the composite. This allows the volume fraction dependence of the effective material parameters to be represented in a form that is convenient for the analysis, so that distinguishing features of the dependence become more pronounced and helpful for understanding the factors that affect the effective properties of the composite. The proposed approach is illustrated by the analysis of the measured data on the microwave material parameters of composites comprising Sendust powder with either spherical or platelet powder particles, and Permalloy powders with particles of the stone-like shape. The microwave material parameters are measured with paraffin-based composite samples in the 7/3-mm coaxial air-filled waveguide by the Nicolson‒Ross‒Weir technique. It is shown that for Sendust particles, the interaction between inclusions is low. For the composites comprising spherical particles, the Maxwell Garnet mixing rule is a good approximation of the volume fraction dependence of microwave permeability. For the platelet powder particles, the magnetic performance is governed by the Wiener mixing rule. For composites filled with Permalloy powder, the contribution of the interaction between inclusions to the effective permeability is essential. Therefore, the suggested approach allows the type of mixing rule suitable for description of material parameters of a given composite to be determined.