Crossover Scaling of Wavelength Selection in Directional Solidification of Binary Alloys

We simulate cellular and dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with adaptive-mesh refinement. The spacing of primary branches is examined for a wide range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a nontrivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers. This result is further validated using published experimental data, which obeys the same scaling function.