A Method for Measuring the Specific Electrical Conductivity of an Anisotropically Conductive Medium

Abstract

The paper deals with the ways of finding an electrical conductivity tensor of a plane and anisotropically conductive sample. Application of the Van der Pauw method to investigate the conductivity of anisotropically conductive media makes the basis of research. Several models of distribution of the electric field potential are presented, their merits and demerits are discussed, and the necessary physical measurements are indicated. On the basis of these models, the respective calculation expressions of the specific conductivity tensor are derived and algorithms for their realization and error calculation are developed.

On the Applying of the Van Der Pauw Method to Anisotropic Media

“…First of all we shall review results achieved in [2] and [4]. After a linear transformation (not conformal) of the variables, in case of the rectangular shape sample, the conduction of which is expressed by tensor σ, we may examine a parallelogram shape sample with electric conductivity, which is of isotropic type and which equals to √ det σ. Measurements of such parallelogram are indicated in Fig.…”

“…We shall note that integrals A α,k are hypergeometric functions which are used in majority mathematical software as standard functions (for example Maple environment), therefore calculation of their values causes no problem. When electrodes are short (l ≈ 0), the articles [2] and [4] state that det σ is found by solving Van der Pauw Eq. (3), and…”

“…In order to avoid this problem and calculate all three components of the tensor (1) (irrespective of a manner of cutting the sample), article of the authors [4] provide a system of transcendent equations that are designed for calculating the latter. The parameters of the system are found by using the sample, which already has five electrodes, and performing more measurements.…”