Determination of sendust intrinsic permeability from microwave constitutive parameters of composites with sendust spheres and flakes

Abstract

Intrinsic permeability of sendust alloys is determined from the measured microwave permittivity and permeability of composites filled with either spherical or flaky sendust powders. The permittivity and permeability measurements are performed applying the coaxial reflection-transmission technique in the 0.05 to 18 GHz frequency range. The effects of the filling factor, inclusion shape, and size on composite constitutive parameters are discussed. The permeability of metal inclusion is retrieved from the measured permeability of composites using a generalized Maxwell Garnett equation that accounts for the percolation threshold. The equation parameters are found by fitting the measured dependence of composite permittivity and permeability on frequency and filling. The inclusion dimensions calculated from the found parameters agree with the results of grain-size analyses. The alloy intrinsic permeability is retrieved from inclusion permeability with the account for skinning. The fitted frequency and damping factor of ferromagnetic resonance depend on the inclusion shape. The calculated reflectivity map of the flake-filled composite shows that sendust powders are promising fillers for interference suppressors and microwave absorbers at frequencies close to 1 GHz.

A Technique to Retrieve High-Frequency Permeability of Metals From Constitutive Parameters of Composites With Metal Inclusions of Arbitrary Shape, Estimate of the Microwave Permeability of Nickel

“…may be treated [3,4] together with permeability. The measurement of several transport properties of composite samples is necessary because realistic mixing models (the general models that account for inclusion shape and interaction) have several unknown parameters that cannot be determined accurately treating the measured permeability only [5][6][7].…”

“…Despite the fact that particle thickness d and resistivity ρ are rarely known precisely, the value of d/ρ ratio may be determined with reasonable accuracy. This ratio is related to magnetic loss (i.e., to the imaginary part of permeability μ ), so the d/ρ-value may be readily fitted to obtain zero loss at the frequency much lower than the ferromagnetic resonance (FMR) frequency (μ = 0 at f → 0 [5,6]), see Section 3.…”

“…The proposed technique is based on the application of a mixing rule to describe the permittivity and permeability dependence for a composite on volume fraction (on filling factor) p of a metal [1,2,5,6,16,17].…”

“…The permittivity measurements with Ni are more complicated than measurements of composites with iron or sendust powders [5][6][7], as Ni powders are electrically conductive because of oxide-free particle surface. A thin (less than 2% of inclusion diameter) oxide layer inherent to iron-based alloys suppresses the electric contact between the neighboring particles and decreases the effective permittivity of inclusion down to ∼ 10 3 [18]; the inclusion in a shell is conventionally considered as a homogeneous substance.…”

“…A thin (less than 2% of inclusion diameter) oxide layer inherent to iron-based alloys suppresses the electric contact between the neighboring particles and decreases the effective permittivity of inclusion down to ∼ 10 3 [18]; the inclusion in a shell is conventionally considered as a homogeneous substance. The estimates of inclusion permeability based on the comparison of composite permittivity and permeability [5,6] are valid for metal powders in an oxide shell as the effective permittivity of inclusion (∼ 10 3 ) is still much higher than its permeability.…”