Heterogeneous diffusion effects in polycrystalline microstructures

Diffusion in polycrystalline microstructures is influenced by two factors that are not considered in a simple continuum material description. These are kinetic effects, where the diffusivities of grain boundaries differ from those of the grains, and free-energy effects, where the driving force for diffusion is dependent on a free energy function that includes the phase of the diffusion medium as well as its composition. Simulation studies of kinetic diffusion effects in two-dimensional polycrystalline microstructures obtained from the Potts model have shown that the compositional gradients resulting from these effects are transitory in nature, and that average diffusivities are dependent on microstructural features such grain size, diffusion bottlenecks in grain boundary paths, and model lattice artifacts. Similar studies of free-energy effects using the phase-field model show that metastable grain boundary segregation of components occurs, and that the rate and nature of grain growth can be influenced by an imposed composition gradient. Collectively, these studies show that the two simulation techniques, finite-difference solutions of fast grain boundary diffusion in the polycrystalline microstructures obtained from the Potts model and phase-field model solutions of diffusion in evolved and evolving microstructures with spatially dependent chemical potentials, are complementary in studying diffusional effects in polycrystalline microstructures.