Phase field investigation on cellular tip splitting during directional solidification

Cellular growth during directional solidification with different cellular spacings is investigated by using the quantitative phase field model. Simulation results reveal that the cellular tip splitting is not noise-induced but deterministic. The non-monotonic curvature distribution from cellular tip to grooves reveals the tip splitting instability. The monotonicity of curvature distribution is determined by the ratio of the cellular tip radius to the cellular width.