Extraction of effective permittivity and permeability of metallic powders in the microwave range

Abstract

In this work, effective electric permittivity and magnetic permeability of metallic-dielectric mixtures are extracted from electromagnetic full 3D simulation data in the microwave range. The numerical method used here is the finite integration technique with periodic boundary conditions. Simulated mixtures have periodic extend in directions perpendicular to the direction of the plane wave. Thus, it is sufficient to analyze a unit element in order to extract the effective electric and magnetic properties. Using this procedure, the behavior of fine copper powders irradiated by microwaves at a frequency of 2.45 GHz is simulated. Then, the relation between particle size and the mixture's effective properties is studied. By introducing a thin copper oxide or conductive layer it is possible to emulate the effective properties of metallic powder compacts in the early stage of sintering. Thus, this work contributes to improving the insight into the mechanisms of microwave absorption in powders of conductive materials in contrast to non-absorption in bulk metals.

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

“…Hence, the presence of significant thickness of native oxide layer between the metal particle looks more appropriate, which actually increases the penetration of these the microwaves inside the sample thereby enhancing the overall microwave heating inside the sample [7,8]. It may be noted here that the value of the effective material properties given in Table 5 is quite large as compared to that reported in [30]. However, the effective constitutive properties data presented here look more sensible as at the 74% of the packing density, the equivalent material is expected to behave much like the bulk metal with the effective value of the loss factor given by (2), which in usual circumstances can not be very small unless a native oxide layer having a significant thickness is present between the metal particles as shown in the later part of this text.…”

“…Hence, in order to make any constitutive propertied reconstruction technique practically viable in the microwave frequency range, the proposed technique should conform to the waveguide method. Another advantage of using the waveguide based technique as compared to the single unit cell based approach being used in the past [30], is that a number of unit cells are required in this case to fill the cross-section of the rectangular waveguide, which basically helps to know whether the unit cell defined under the particular situation is appropriate under the macro approximation simulating the real material. Under the ideal situation, the constitutive effective properties of the material extracted from the single unit cell using the TEM mode illumination should match with the properties obtained from the rectangular waveguide approach having the TE 10 mode illumination.…”

“…The host medium for simulating the Cu metal compact is taken as the Cu oxide rather than air, which provides the numerical stability and is also close to the real situation [7]. The relative permittivity of Cu oxide is taken as r = 9.483 and r = 0.0755 at 30 GHz [30]. The unit cell structure for this case is defined using the particle size of diameter 0.62 mm, and the gap between the particles is taken as 0.01 mm for a faster convergence.…”

“…The unit cell based numerical simulations in the present case are performed using two standard electromagnetic field simulators, the CST Microwave Studio [28], and the Ansys HFSS [29] in order to obtain the scattering coefficients in the required frequency band. The CST Studio is based on the Finite Integration Technique, and was recently used to model the copper powders at 2.45 GHz [30] using the unit cell concept in free space. The value of the dielectric loss reported by them for the copper particles having a packing density of 0.74 is, however, very low indicating a substantially low value of the effective conductivity which does not look appropriate from the practical point of view.…”

Electric and Magnetic Characterization of Materials

“…The most common and widespread one-and two-port techniques are transmission-line techniques (open-ended coaxial probe (Misra et al (1990); Xu et al (1991)), rectangular (Deshpande et al (1997);Faircloth et al (2006);Jarem et al (1995)) or cylindrical (Ligthart (1983)) waveguide, microstrip or stripline (Barry (1986); Queffelec et al (1994))), free-space measurement (Galek et al (2010); Ghodgaonkar et al (1990)) and cavity resonator (Yoshikawa and Nakayama (2008)). These techniques are different for accuracy and frequency bandwidth of measurement; some are nondestructive and noncontacting and may require sample preparation.…”