The use of the diffusive interface in phase field modelling allowed the treatment of a complicated morphology. However, in dealing with grain boundary diffusion, it was difficult to simulate a diffusion process that was independent of the interface thickness. To counteract this, a model was proposed which embedded a grain-boundary diffusion term in the existing adaptive phase-field model. In this new model, the simulated solute transport was independent of the interface thickness, and the simulated grain boundary diffusion was in good agreement with the classic solution. The proposed scheme was examined for four cases: diffusion through the melt/solid interface without the grain boundary; grain-boundary diffusion only without the melt/solid interface for comparison with the classic Fisher model, where an analytical solution was available; with both the melt/solid interface and grain boundary; and with a tilted grain boundary. For the case without a grain boundary, a simple steady-state one-dimensional solute diffusion was first considered in order to examine the effect of weighting schemes for the effective diffusivities; the concentrations of the top and bottom boundaries were fixed. The harmonic mean gave the best result in comparison with the analytical solution. For an in-series medium, the harmonic mean of the diffusivities, which was derived from the flux continuity made the flux across the interface consistent and independent of the interface thickness. The second example was a simple grain-boundary diffusion without the melt/solid interface. Thus, a simple and efficient model was proposed for the grain boundary diffusion, which could be incorporated into the existing phase field model. In this model, the grain boundary was treated as a line for two-dimensional problems, so that the computational cost was greatly reduced. More importantly, the model proposed was independent of the interface thickness, which amends the traditional phase field formulation for grain boundaries. Similarly, gain boundary could be treated as a surface for three-dimensional problems, and the extension could be possible.

Adaptive Phase Field Modeling of Grain Boundary Diffusion. S.Y.Yeh, C.C.Chen, C.W.Lan: Journal of Crystal Growth, 2011, 318[1], 46-50