Generalised Maxwell-Garnett equation: Application to electrical and chemical transport

In this paper we discuss the implementation of different equilibrium concentrations in each of the phases into the Maxwell-Garnett effective medium formula for diffusion in heterogeneous media. We put the derivation given by Kalnin et al., J. Phys. Chem. Solids, 2002, 63, 449, on safer grounds and extend it to non-dilute carrier concentrations. The relation to Maxwell's mixing rule is also elaborated. It is shown that the formula can not only successfully be applied to conductivity problems but also to describe steady state chemical diffusion in heterogeneous media such as polycrystalline samples. The comparison with the brick layer model corroborates these points but also shows that - in the case of heterogeneous media - one has to be cautious in applying steady state results to transient kinetics.