Monte Carlo computer simulation was used to test the extended Maxwell-Garnett expression for the effective diffusivity in a simple model of a two phase material. The effective diffusivity was determined in fcc, bcc and sc arrangements of dispersed spheres at variable densities, for cases where the diffusivity in the dispersed phase was less than, or greater than, the diffusivity in the matrix phase. It was shown that the above equation agrees very well with the simulation data for all densities up to where the spheres of the dispersed phase touch and over six orders of magnitude in the ratio of the diffusivity of the dispersed phase to the diffusivity of the matrix phase.

The Effective Diffusivity in Two-Phase Material. I.V.Belova, G.E.Murch: Defect and Diffusion Forum, 2003, 218-220, 79-86