Numerical simulation of rapid and directional solidification of Al-Pb alloys

A model has been developed to describe the rapid and directional solidification of immiscible Al-Pb alloys by taking into account the common actions of nucleation, diffusion growth and migration of the minority phase droplets. Numerical solutions have been performed for Al-Pb bearing alloys solidified under vertical Bridgeman directional solidification conditions. It is shown that at a high solidification velocity a constitutional supercooling region where the liquid-liquid decomposition takes place appears in front of the solid/liquid interface. For a given temperature gradient, a higher solidification velocity leads to a higher nucleation rate and, therefore, a higher density of the minority phase droplets. The average radius of droplets (R¯) in the melt at the solid/liquid interface can be related to the solidification velocity (v) by R¯(z=0)=C2v-0.39±0.01 in which the value of C2 is a constant.