The hump formation, as a critical onset of the morphological instability near the grain boundary, during directional solidification of a binary polycrystalline alloy was simulated using the phase field model for the first time. In the model, the orientation field was used for treating the grain boundary, and the thin-interface model and anti-trapping solute current were further adopted. Due to the solute diffusion into the grain boundary, even at the pulling speed below the critical value, the constitutional supercooling might occur and the interfaces beside the grain boundary groove were slightly deflected toward the melt. This supercooling and the interface deflection trigger the morphological instability as the pulling speed exceeds the critical value, and this led to the hump formation. As the humps develop, the interfaces behind the humps move backward as a result of solute accumulation. The morphological waves were then developed and they propagate away from the humps, as observed in the experiments.

Phase Field Modeling of Morphological Instability Near Grain Boundary During Directional Solidification of a Binary Alloy: the Hump Formation. S.Y.Yeh, C.C.Chen, C.W.Lan: Journal of Crystal Growth, 2011, 324[1], 296-303