Subcritical-supercritical bifurcation crossover in directional solidification

The Mullins-Sekerka planar-cellular instability in directional solidification should be subcritical when the partition coefficient k<0.45 and latent heat is ignored. However, Merchant and Davis [Phys. Rev. Lett. 63, 573 (1989)] predicted that as the solute concentration is reduced, the increasingly important thermal diffusion field would lead to a crossover from a subcritical to a supercritical bifurcation. We have performed directional solidification experiments on a series of succinonitrile samples containing different concentrations of Coumarin 152, and have found preliminary evidence for the predicted crossover at a concentration ${\mathit{C}}_{\mathit{t}}$ ∼ 0.1%.