Anisotropic grain boundary diffusion in binary alloys: Phase-field approach

In this study, we generalize the phase-field model of grain boundary diffusion in polycrystalline materials. Solute transport is described by the modified Cahn-Hilliard equation accounting for diffusion anisotropy, different interaction parameters in grain boundary region and grain bulk, as well as concentration-dependant mobility. The numerical results are provided for solute transport in plain parallel grains and pollycrystalline medium with various directions of fastest (slowest) solute diffusion. This model predicts subdiffusive power-law dependence for propagation of the concentration profile with the exponent varying in a wide range (α=0.25−0.37 for B-type, α=0.45 for C-type kinetics of grain boundary diffusion). Within the proposed phase-field approach, we confirm the validity of Levine-MacCallum conclusion on concentration profile dynamics and modify the ratios for estimation of the effective values of grain boundary mobility.