Extension of van der Pauw's theorem for measuring specific resistivity in discs of arbitrary shape to anisotropic media

Van der Pauw (1958) has described a method of measuring electrical resistivity in discs of arbitrary shape based on a theorem which is applicable to samples of isotropic material. In this paper the theorem has been shown to be applicable also to samples of anisotropic material, and it is shown that it measures the geometric mean of the principal components of the resistivity tensor in the plane of the sample. An isotropic body may be regarded as the special case of an anisotropic one in which the principal components of the resistivity tensor are all equal. It follows that van der Pauw's method may be applied to any material, and that it always measures (ρ 1 ρ 2 ) ½ , where ρ 1 and ρ 2 are the principal components of the resistivity tensor in the plane of the sample.