Resistivity and magnetoresistivity measurements near the metal-insulator and superconductor-insulator transition in granular Al-Ge

Evaluating the Microstructure of Conductor-Insulator Composites using Effective Media and Percolation Theories

The widely used Bruggeman symmetric and asymmetric media equations and the Clausius-Mossetti approximation are presented, and the idealized microstructures characterizing these media are examined.

The percolation equations for the conductivity (σm) and complex dielectric constant (ɛm = ɛrm + iɛim) for ideal perfect conductor–conductor and conductor–perfect insulator continuum media (and lattices) are then introduced. The parameters characterizing the microstructure in the percolation equations are a critical volume fraction or percolation threshold (φc) and two exponents (t&s). The equations characterizing the crossover region, which occurs whenever the ratio of the conductivities of the two components is finite, or dielectric measurements are made, are also introduced. A general effective media equation, which has the same parameters as the percolation equations is noted, and its success in obtaining φc, when the ratio of the conductivities is finite, examined.

The microstructures that allow φc to have values between a few percent and over 60%, as well as the occurrence of non–universal values of t, will also be discussed.