The problem of calculating the effective diffusivity in nanocrystalline materials is addressed. Two simple two-dimensional grain patterns are constructed and several equations are derived from the Hart–Mortlock and Maxwell–Garnett equations. Monte Carlo computer simulation is used to test the validity of the various equations. It is shown that one of the derived equations provides an excellent description of the effective diffusivities up to a volume fraction of atoms in grain boundaries of 40%.
Journal of Physics and Chemistry of Solids Vol. 64, Issue 5, p. 873-878