Geometric considerations for diffusion in polycrystalline solids

Mass transport in polycrystals is usually enhanced by short-circuit diffusion along various defect paths, e.g., grain boundaries, dislocation cores, and triple junctions. In the "kinetic-A" regime, diffusion fields associated with the various diffusion paths overlap each other, forming a macroscopically homogeneous diffusion profile that can be described by an effective diffusion coefficient. Here, we develop a composite diffusion model for polycrystals based on realistic arrangements between various microstructural elements, which usually exhibit complex network morphologies. Asymmetric effective medium equations and power-law scaling relationships are used to evaluate the effective diffusivity of a general isotropic polycrystal, and are compared to predictions of the simple arithmetic rule of mixtures used frequently in the literature. We also examine the grain size and temperature dependence of polycrystalline diffusion in terms of the apparent grain size exponent and activation energy, which in turn provide the basis by which we assess dominant diffusion processes and construct generalized diffusion mechanism maps. Implications of geometry on experimental diffusivity measurements are also discussed.