Phase field modeling the selection mechanism of primary dendritic spacing in directional solidification

Selection mechanisms of primary dendritic spacing in directional solidification are investigated by the phase field method. Results show that the lower and upper limits of primary spacing are determined by the interdendritic solutal interactions and the interdendritic undercooling respectively. The upper limit of primary spacing resulting from overgrowth of the tertiary arm could be about four times as large as the lower limit. The microstructural evolution from the onset of planar instability during directional solidification with a constant pulling velocity can be divided into three stages: an initial competition stage, a submerging stage and a lateral adjustment stage. Simulation results also demonstrate that the final primary spacing with a constant pulling velocity is very close to the lower limit due to the dendrite submerging mechanism.