Elsevier

Advances in Space Research

Volume 59, Issue 1, 1 January 2017, Pages 472-482
Advances in Space Research

Improvements on effective permittivity measurements of powdered alumina: Implications for bulk permittivity properties of asteroid regoliths

https://doi.org/10.1016/j.asr.2016.08.011Get rights and content

Abstract

Accurate measurements of the dielectric properties of materials are essential in constraining interpretations of radar observations of planetary bodies. For bodies whose surfaces are comprised of regolith this requires an understanding of the behaviour of the bulk permittivity of powders. In this research we measure the effective permittivity of powdered aluminium oxide (or alumina, Al2O3) in a 7 mm and 14 mm (diameter) coaxial airline at 7.5 GHz for multiple samples with varying grain size. The dielectric constant of alumina is extracted from these measurements using the Bruggeman (Effective Medium Approximation) mixing equation. We develop a model to account for heterogeneity within the airline, specifically in regards to local variation in porosity. The results of the model show good correlation to experimental data and effectively correct for grain size effects on the measured bulk permittivity. We show that particle shape can have a significant impact on the output of the model and can be accounted for by modelling particles as ellipsoids rather than perfect spheres, where the depolarization factor must be measured and averaged for a specific sample batch.

Introduction

Active remote sensing techniques in the microwave regime are used in observing planetary bodies through terrestrial/orbiting radar and ground penetrating radar (GPR). The reflectivity and penetration depth of a radar signal incident on a non-conducting surface are largely determined by those materials’ dielectric response at a given frequency (Griffiths, 1999, Feynman et al., 1979). For planetary bodies whose surfaces consist of regolith material, such as the Moon and asteroids, properties of that regolith may be extracted from a radar return if the effective permittivity of the regolith is known (Heiken et al., 1991).

Polarimetric radar is used to measure the degrees of circular/linear polarizations received from a surface which are sensitive to a variety of target features including subsurface structure, surface roughness, regolith thickness, bulk density, and composition (Carter et al., 2011). Models that derive these features from radar data intrinsically make assumptions about physical characteristics of the target that greatly affect the returned signal properties, such as the dielectric permittivity, introducing large sources of uncertainty to interpretations. To overcome this, radar images of planetary bodies are often compared with terrestrial analogues (Carter et al., 2011); however, this is not appropriate for bodies for which no adequate terrestrial analogues exist, such as asteroids. A correlation between circular polarization ratio and visible-infrared taxonomic class has been identified in near-Earth asteroids that would be better understood if the bulk (effective) dielectric properties as a function of mineralogical composition were known (Benner et al., 2008). Providing information on the dielectric permittivity of regolith materials is therefore relevant for missions to asteroids such as 101955 Bennu, the target of NASA’s Origins-Spectral Interpretation-Resource Identification-Security-Regolith Explorer (OSIRIS-REx) mission. To constrain the analysis of radar data on planetary bodies, specifically asteroids, laboratory measurements are needed to better understand the dielectric permittivity of regolith materials (Nolan et al., 2013, Carter et al., 2011).

A popular and effective approach for measuring the permittivity of any dielectric material is the transmission line method utilizing a coaxial airline and network analyser (Chen et al., 2004). This technique has the advantage of broadband measurement, being relatively inexpensive, and recently has been shown to have the capability of measuring powdered samples (Grosvenor, 1993, Stillman and Olhoeft, 2008, Sotodeh, 2014). By measuring powdered samples the effects of grain size distribution, grain shape, and porosity on the effective permittivity can be determined. Measurement techniques for powdered samples have been investigated in the literature (Tuhkala et al., 2013, Ebara et al., 2006); however, the aforementioned effects on the effective permittivity are not well understood.

For a powdered sample, the measured value in the transmission line method is the effective permittivity of the sample. The effective permittivity is a combination of each phase within the airline: water adsorbed on grain surfaces, air, and the solid sample. Samples can be oven baked to remove residual moisture, resulting in a two phase mixture of air and solid sample. Electromagnetic mixing theory can be used to extract the permittivity of the solid phase of the mixture (true permittivity of the sample). Mixing theory is based on the assumption of homogeneity within the sample and uniform particle shape (Sihvola, 1999). These assumptions are not valid when considering a powdered sample in a coaxial airline.

In this research a theoretical model is developed to account for heterogeneity at the boundary of the coaxial airline and shows potential to compensate for particle shape effects. The effective complex permittivity of alumina is measured (using the transmission line method) and input to this model to calculate the dielectric constant of alumina. While both the real (dielectric constant) and imaginary (dielectric loss) parts of relative permittivity affect radar scattering, this paper is focused on using the real part of permittivity measurements to test the validity of the model. Given the results of our experiment, future work will be done applying this model to the dielectric loss. Alumina was chosen for this study as it has well known dielectric properties and is readily available in powdered form at a variety of grain sizes, making it a suitable standard to test the model with. The average grain sizes and porosities of samples measured in this research were chosen to correspond to asteroidal surface regolith material (Shepard et al., 2010, Magri et al., 2001, Clark et al., 2002). Section 2 discusses our measurement procedure and presents the raw, unprocessed permittivity data. Section 3 describes the model developed in this research to correct the raw data. Section 4 discusses the results of processing the data presented in Section 2 with the technique shown in Section 3. The corrected dielectric constant values are compared to results from the literature. Improving the accuracy of measurements of the permittivity of powders will tighten constraints on radar/GPR data and allow more accurate interpretations of planetary datasets.

Section snippets

Sample preparation

Seven sample batches of alumina grit with average grain sizes ranging from 76  μm to 940 μm supplied by Kramer Industries, Inc. were used in the experiment. The particle size distribution for each sample conform to ANSI B47-12-2001 grit size grading standards. The samples were oven baked at a constant temperature of 200 °C for 48 h prior to measurement to evaporate residual moisture. The mass of the sample before and after oven baking was measured using a digital scale within ±1 mg (Sotodeh, 2014).

Boundary Conditions

A physical explanation for some of the observed trends in Fig. 1 is that there are conditions at the boundary of the sample holder (interface between sample and conductor) that are different from those within the bulk sample. Particles pack more densely in the bulk of the sample, whereas grains along the conductor interface have more pore space around them (Fig. 2). At microwave frequencies used in radar applications, porosity has a profound effect on the dielectric properties of a powder, as

Application of model to measured data

Substituting Eqs. (8), (9) into (7) allows the effective permittivity of the entire airline, m, to be calculated for the model mixing scenario. The values for D1,D2,D3, and D4 as well as fb and fs can be determined for a sample by applying the constraints discussed in Section 3. Different values of i used in Eqs. (8), (9) result in different values of m calculated in (7). Iterating through possible values of i from 0 to 100 in (8), (9) results in various calculations of m which are

Conclusion

Air gap correction is well characterized for measurements of permittivity for solid samples using the transmission line method. Currently, no such correction exists to address the increased porosity at boundaries of a sample holder when measuring permittivity of granular samples, nor is magnitude of the systematic error possible by these boundary effects understood. Applying constraints on the porosity and extent of this boundary region allows mixing equations to be used to represent the volume

Acknowledgements

This work was funded in part by the Canadian Space Agency (CSA) and the Natural Sciences and Engineering Research Council of Canada (NSERC).

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