Accounting for conducting inclusion permeability in the microwave regime in a modified generalized effective medium theory

We standardize the approach to predict composite permeability, μ_eff, to determine the reflection (R), transmission (T), and absorption (A) using the generalized effective medium theory. For stainless steel (SS) spheres and fibers, we calculate the inclusion permeability based on the effective susceptibility generated by eddy currents in a time-varying magnetic field. This gives reasonable agreement with measured μ_eff when used in the Bruggeman theory and agreement with R, T, and A within 10%. For SS flakes, we fit the imaginary component of μ_eff to a single-peak Lorentzian for each loading and use typical fitting parameters to predict μ_eff and, ultimately, R, T, and A within 5%. The fitting exponent t was constant for all frequencies for a given inclusion shape (4.7, 1.6, and 1.7 for spheres, fibers, and flakes, respectively) and Ax typically varied with inverse volume loading rather than percolation threshold. Interestingly, at percolation for the fibers, A_x approached a constant that approximately equaled the observed percolation threshold.