Quantitative phase field simulation of deep cells in directional solidification of an alloy

The formation of deep cells after the onset of Mullins-Sekerka instability during the thin-film directional solidification of a succinonitrile/acetone alloy has been simulated quantitatively by phase field modeling. The solute trapping introduced by the diffusive interface is corrected by a simple interface model, so that at the interface the equilibrium segregation is restored and the Gibbs-Thompson relation is satisfied. With the increasing pulling speed, the transitions from planar to λ_c/2 shallow cells, smaller wavelength finite-depth cells, and deep cells are clearly illustrated. The formation of deep cells with change of overall morphologies is performed, and its wavelength transition is consistent with the reported experiments. Furthermore, during the development of a cellular pattern starting from a planar interface, the crossover wavelength under different solidification speeds, where the deformation is comparable to the wavelength, agrees reasonably well with the Warren-Langer theory.