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 10-40 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.