The effect of shape distribution of inclusions on the frequency dependence of permeability in composites

Microwave material parameters of composites filled with Fe powder are measured as a function of frequency and volume fraction of the powder. The powder is prepared by mechanical milling of Fe in argon atmosphere. The host matrix of the composites is paraffin wax. The permittivity and permeability are measured in the frequency range 0.01-3 GHz. The measured frequency dependences of the permeability is considered in terms of the Bergman-Milton theory, with no additional suggestions imposed on the volume fraction dependence of effective material parameters of composites and the frequency dependence of intrinsic permeability of magnetic powders. The Ghosh-Fuchs theory is found to provide an excellent agreement with the measured permittivity and permeability of the composites, in contrast to the theories employing averaged demagnetization factor of inclusions, such as the Maxwell Garnet approximation. Therefore, the effective material parameters of the composites are affected greatly by the shape distribution of the powder particles. From the measured frequency dependence of permittivity and permeability, the intrinsic permeability of the powder is found.