Generalized effective-medium approach to the conductivity of an inhomogeneous material
- 15 October 1975
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 12 (8), 3368-3373
- https://doi.org/10.1103/physrevb.12.3368
Abstract
An old effective-medium approximation for the conductivity tensor of a randomly inhomogeneous medium is generalized to treat, in principle, materials consisting of crystallites of arbitrary shape and conductivity tensors of arbitrary symmetry. The effective-medium approximation is roughly analogous to the coherent-potential approximation (CPA) of alloy theory. The analog of the average--matrix approximation (ATA) is also formulated in a general way. The method is fully tractable analytically for ellipsoidal crystallites. Several applications are discussed. The effective conductivity of a polycrystal consisting of randomly oriented uniaxial crystallites is calculated as a function of the anisotropy of the grains. For a model polycrystal in an intense magnetic field, the CPA and ATA are compared, the former giving more accurate results.
Keywords
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