Conductivity of inhomogeneous materials: Effective-medium theory with dipole-dipole interaction

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Abstract
We extend the old effective-medium theory, originally due to Bruggeman, by incorporating dipole-dipole interactions to account for local-field effects. The interactions are represented approximately by use of effective depolarization factors. For close-packed clusters of conducting regions, a description which is appropriate at the percolation threshold, we predict an onset of percolation processes when 15.6 vol% is conducting. This is in very good agreement with numerical simulations as well as with experimental data for the metal-insulator transitions in metal-ammonia solutions and in alkali-tungsten bronzes.