Phase-field simulations and geometrical characterization of
cellular solidification fronts
The structure and dynamics of cellular solidification fronts produced during
the directional solidification of dilute binary alloys are studied by
phase-field simulations. A quantitative phase-field model in conjunction
with a multi-scale simulation algorithm allows us to simulate arrays with
ten to forty cells in three dimensions on time scales that are long enough
to allow for a significant reorganization of the array. We analyze
the geometry of the complex two-phase structure (mushy zone) and
extract the fraction of solid and the connectivity of the two phases
as a function of depth. We find a transition from stable arrays
at high values of the crystalline anisotropy to unsteady arrays
at low anisotropy that continuously exhibit tip splitting and cell
elimination events.