Electrical conductivity in inhomogeneous media

The history of this field is reviewed, with emphasis on the relationship to the development of molecular field concepts in dielectric theory, in the last century, and with emphasis on the relationship to the study of disordered structures, in recent decades. A few of the many methods for calculating effective conductivities will be presented and discussed. One of these is based on the direct macroscopic application of the Clausius‐Mossotti relationship. In that connection we emphasize the shortcomings of the commonly accepted Lorentz derivation for the internal field and restate a less well known existing alternative derivation. The symmetrical and unsymmetrical effective medium theories of Bruggeman are presented. Connection is made to transport in randomly chosen resistor networks, to percolation threshold problems, and to transport in magnetic fields in the presence of inhomogeneities. Two more specialized topics are also discussed. One of these is the variability in field effect transistor thresholds arising from the limited size of the samples in which threshold is determined by the onset of percolation. The other specialized topic: The occurrence of strong spatial inhomogeneities in fields and currents in metals, in the presence of lattice defects, even though the mean free path is large compared to the extent of the defect.