Measurement of the complex permittivity of dry rocks and minerals: application of polythene dilution method and Lichtenecker's mixture formulae

Abstract

The complex permittivity of dry rocks and minerals varies over a very wide range, even within a sample there are variation at different temperatures and frequencies. Most rocks and minerals are inhomogeneous materials, therefore, most of the present methods of dielectric measurement designed for artificial homogeneous materials are not suitable for rocks and minerals. The resonant cavity perturbation (RCP) method is a reliable and simple technique to determine the complex permittivity of dielectric materials in the GHz range, and this method is also used extensively. However, the traditional RCP method is sensitive to the measurement of low dielectric constant (ε΄) and low loss factor (ε˝ or tanδ materials. The complex permittivity of most dry rocks and minerals exceeds the span vibration of the RCP method, and cannot be measured by the RCP method directly. This paper proposes a new method to measure the complex permittivity of dry rocks and minerals with the RCP method incorporated in the application of polythene (PE) dilution method and Lichtenecker’s mixture formulae. Dry rocks and minerals were ground into fine powder. The powder of rocks and minerals was mixed with polythene powder in a definite volume per cent. The mixture was heated and pressed into a thin circular slice. The slice was processed into a small rectangular strip sample, the size of which was fitted to the demands of the RCP method. The complex permittivity of the strip was obtained by the RCP method. The relationship between the dielectric properties of the two-phase mixture and those of each phase in the mixture can be expressed by Lichtenecker’s mixture formula. Thus the complex permittivity of dry rocks and minerals can be calculated from the complex permittivity of the mixture in case the complex permittivity of polythene is known. The presented method was verified by measurements of reference materials of various known complex permittivity and other reliable dielectric measurement methods. The results of the experiment showed that this new method is of high accuracy, small sample requirement, and convenient application. Moreover, the complex permittivity of rocks and minerals measured by this method is more reliable than the direct dielectric measurement of rocks or minerals without application of the polythene dilution method and Lichtenecker’s mixture formulae.