Phase field investigation on sidebranching dynamics in transient growth

A computationally efficient quantitative phase field formulation is used to investigate the sidebranching dynamics under different transient conditions in directional solidification for realistic parameters of a dilute alloy. The sidebranch growths where the pulling speed or temperature gradient increases with constant increasing rates are simulated and discussed by using the noise amplification theory. The results show that in transient growth, the tip shape can rapidly adjust with the instantaneous conditions, and the tip velocity changes continuously due to the change of tip undercooling. Therefore, under our given transient conditions, the sidebranch spacing or sidebranching frequency depends strongly on the transient conditions and transient history, which is different with that in steady-state conditions where the sidebranching frequency is found to be independent of the temperature gradient and primary spacing, but varies as a power law of pulling speed.