What is constitutional super‐cooling? When does this take place? 

During solidification of an alloy solute gets partitioned between liquid and solid. As it  cools the composition of liquid and solid keeps changing. While the composition of  solid can change only by diffusion that of liquid can change due to both diffusion and  convection current (stirring). The latter is much faster. If there is no convection or  stirring concentration of solute builds up in the boundary layer. Its melting point becomes significantly lower than that of the liquid away from the interface. If the  temperature gradient beyond the solid liquid interface is less than a critical value  constitutional super cooling occurs. This promotes solidification. If the gradient is  more than the critical value the solid liquid interface remains planar.