Growth competition of columnar dendritic grains: A phase-field study

Abstract

We report the results of an extensive phase-field study of the growth competition of columnar dendritic grains in two dimensions. We investigate the influence of the temperature gradient and grain bicrystallography on the selection of both grain and microstructure, focusing on a geometry with two grains with principal crystal axes oriented parallel and at a finite misorientation angle with respect to the axis of the temperature gradient. Our first main finding is that, for well-developed dendritic structures forming at a low-temperature gradient, the rate of elimination of the misoriented grain is a non-monotonic function of the difference in undercooling between the dendrite tips of the two grains. Hence this rate cannot be predicted even qualitatively by the common assumption that the elimination rate increases with this undercooling difference. The breakdown of this assumption is particularly striking for highly misoriented dendritic and degenerate structures that persist for very long times despite growing at a substantially larger undercooling than the well-oriented neighboring grains. Our second main finding is that microscopic thermal fluctuations at the origin of sidebranching can induce significant variations in the macroscopic trajectories of grain boundaries (GBs), thereby making grain selection a stochastic process, while yielding limited variations in the selected primary spacings. In contrast, in the absence of fluctuations, GB motion becomes essentially deterministic and grain elimination is suppressed. In addition, our simulations reproduce quantitatively scaling laws deduced from experiments for both the primary dendritic spacing and the dendrite growth direction of misoriented grains. They further reveal that the “intergrain” primary spacing selected by tertiary branching events at GBs is systematically larger than the “intragrain” primary spacing selected by the transient growth competition between primary branches within a single grain, while obeying the same scaling laws. Finally, the fact that the rate of grain elimination is slower in our 2-D simulations than in experiments suggests that the 3-D grain bicrystallography plays a key role in grain selection. This role is interpreted in the light of 2-D simulations that hinder sidebranching on the misoriented grain.