Generalized effective-medium approach to the conductivity of an inhomogeneous material. Stroud, D. Physical Review B, 12(8):3368--3373, October, 1975.
Generalized effective-medium approach to the conductivity of an inhomogeneous material [link]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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