Generalized effective-medium approach to the conductivity of an inhomogeneous material. Stroud, D. *Physical Review B*, 12(8):3368--3373, October, 1975. Paper doi abstract bibtex 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-t-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.

@article{stroud_generalized_1975,
title = {Generalized effective-medium approach to the conductivity of an inhomogeneous material},
volume = {12},
url = {http://link.aps.org/doi/10.1103/PhysRevB.12.3368},
doi = {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-t-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.},
number = {8},
urldate = {2016-06-03TZ},
journal = {Physical Review B},
author = {Stroud, D.},
month = oct,
year = {1975},
pages = {3368--3373}
}

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