Uniquely selected primary dendrite arm spacing during competitive growth of columnar grains in Al-Cu alloy

The steady-state value of primary dendrite arm spacing (PDAS) in the columnar dendrites growing between the converging and diverging grain boundaries is investigated by means of quantitative phase-field simulations. The simulations show that there is a unique value of PDAS under a given solidification condition in the system with grain boundaries. This is in contrast to existence of allowable range of PDAS under a given solidification in a system without the grain boundaries, i.e., an infinitely large columnar grain investigated in many early works. Such a unique value of PDAS depends on the pulling speed and inclination angle of the crystal, but not on the initial condition; that is, it is independent of the history of solidification condition. The dependences of the unique value on the pulling speed and inclination angle qualitatively agree with the theoretical models.