A two-constituent composite medium where the constituents have comparable but different resistivity tensors is considered for the case where the microstructure is columnar and the two Hall resistivities are much greater than all the Ohmic resistivities. Exact relations for such microstructures, along with an exact asymptotic expansion for large values of the Hall-to-Ohmic resistivity ratios, are used to get leading-order closed-form expressions for the elements of the macroscopic or bulk effective resistivity tensor ρ of the composite medium. Numerical computations on some periodic microstructures are performed and compared with the asymptotic results. A self-consistent effective-medium approximation is used to obtain results for ρ e in the case of a disordered microstructure. Those results agree with the exact asymptotics in leading order but they also go beyond that leading order. A somewhat surprising result is that the macroscopic transverse Ohmic resistivity in the plane perpendicular to the columnar axis is tremendously sensitive to whether the planar microstructure is ordered or disordered.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|State||Published - 11 Jul 2012|