Kinetic Monte Carlo simulation of the effective diffusivity in grain boundary networks

The effective diffusivity in grain boundary networks of polycrystalline materials is evaluated using a kinetic Monte Carlo model. This model connects the atomic hopping processes with the coarse-grained diffusion so that the macroscopic simulations can be conducted without the need to resolve atomic details. The effects of various properties of the grain boundary network on the effective diffusivity have been examined, including grain size, two- vs. three-dimensional networks, and distribution of grain boundary diffusivities. It is shown that the effective diffusivity does not depend on the grain size when grain boundary diffusion is the dominant diffusion mechanism in a polycrystalline sample. We find that the behavior of the effective diffusivity is qualitatively the same for two- and three-dimensional models, except that the percolation threshold and the critical exponents need to be changed accordingly when using empirical functions to characterize the effective diffusivity. In addition, we find that the effective diffusivity exhibits large fluctuations due to its dependence on the grain boundary distributions, and therefore the details of the materials microstructure can significantly impact the effective diffusivity in a specific finite-size sample. Finally, we check the applicable range of the effective medium theory and discuss the effects of modeling different grain boundary types with varying diffusivities using just two vs. many types. The grain boundary diffusion program (GBDiff) developed in this study is available under open source licensing as part of the MAterials Simulation Toolkit (MAST) and can be obtained from https://pypi.python.org/pypi/MAST/1.1.0. (C) 2014 Elsevier B.V. All rights reserved.