Estimation of the Phenomenological Effective Diffusivity in Nanocrystalline Materials

In this study we construct two new equations to describe the effective diffusivity in nanomaterials where diffusionproceeds via both the grains and the grain boundaries in comparable amounts. We analyze two very simple 2D grain configurations by Monte Carlo methods to test the validity of the equations. In addition, we also test the Hart and the recently extended Maxwell-Garnett equations. It is shown that one of the two new equationsprovides a very good description of diffusion in the grain modelspostulated.