Applicability Study of Classical and Contemporary Models for Effective Complex Permittivity of Metal Powders

Abstract

Microwave thermal processing of metal powders has recently been a topic of a substantial interest; however, experimental data on the physical properties of mixtures involving metal particles are often unavailable. In this paper, we perform a systematic analysis of classical and contemporary models of complex permittivity of mixtures and discuss the use of these models for determining effective permittivity of dielectric matrices with metal inclusions. Results from various mixture and core-shell mixture models are compared to experimental data for a titanium/stearic acid mixture and a boron nitride/graphite mixture (both obtained through the original measurements), and for a tungsten/Teflon mixture (from literature). We find that for certain experiments, the average error in determining the effective complex permittivity using Lichtenecker's, Maxwell Garnett's, Bruggeman's, Buchelnikov's, and Ignatenko's models is about 10%. This suggests that, for multiphysics computer models describing the processing of metal powder in the full temperature range, input data on effective complex permittivity obtained from direct measurement has, up to now, no substitute.

Studies of permittivity and permeability of dielectric matrix with cuboid metallic inclusions in different orientations

“…Polarization P and magnetization M are the key physical quantities to understand the eff and eff inside the system. In macroscopic view, the polarization P measures how a dielectric responds to the E field [17][18][19]25,[31][32][33] (Fig. 3).…”

Candidate for Tissue Mimicking Material Made of an Epoxy Matrix Loaded With Alginate Microspheres

“…Thus, mixing formulas are developed to quantitatively predict the effective complex permittivity of the composite materials by knowing the dielectric properties of its constituents. Different mixing formulas are discussed and examined in [26][27][28][29]. Looyenga (Eq.…”

“…There is a very good agreement between the parameters extracted from the samples made of the two different epoxies and containing different volume fractions of inclusions. According to [26], the Lichtenecker formula (Eq. (5)) is more accurate in predicting the real part of the effective complex permittivity, while the imaginary part (conductivity) can be predicted with a lower error by using the Maxwell Garnett model (Eq.…”

A Unit Cell Approach to Model and Characterize the Metal Powders and Metal-Dielectric Composites at Microwave Frequencies

“…However, apart from the core-shell model, the classical mixing formulas such as the Mean-field approach by MaxwellGarnett [12], the Litchenker's Logarithmic mixture formula [13,14], the Bruggeman mixing formula [15], the analytical approaches using the diagrammatic expansions [16] and Fourier series [17] have also the potential to be used for the metal powder composites in a way similar to the dielectric mixtures for which these formulas were originally proposed. A detailed study about the use of various classical and coreshell mixing formulas for the computation of effective permittivity of various metal composites has recently been presented in [18], where it is concluded that most of these formulas provide an error of the order of 10% when compared with some experimental data. However, the experimental data of the complex permittivity of the metal powders employed for comparison in [18] have mainly been obtained using the cavity perturbation technique [7], which is usually valid for low loss samples [19] as it is based on the assumption that the test specimen does not change the field configuration significantly inside the cavity.…”

“…A detailed study about the use of various classical and coreshell mixing formulas for the computation of effective permittivity of various metal composites has recently been presented in [18], where it is concluded that most of these formulas provide an error of the order of 10% when compared with some experimental data. However, the experimental data of the complex permittivity of the metal powders employed for comparison in [18] have mainly been obtained using the cavity perturbation technique [7], which is usually valid for low loss samples [19] as it is based on the assumption that the test specimen does not change the field configuration significantly inside the cavity. It looks rather more appropriate to make use of the reflection-transmission approach [20,21] instead of the cavity resonant technique to estimate the effective dielectric and magnetic properties of metal powders.…”