On the length-scale and location of channel nucleation in directional solidification

This work provides evidence that channels in directionally solidified hypoeutectic Pb-Sn alloys nucleate at the dendrite tips. Using a finite-element simulator, distinctive ‘convective signatures’ are shown to exist for convectively unstable cases, where the instability of a system is shown to be largely a function of the thickness of an inverted density layer that exists ahead of the moving solidification front. With D the diffusion coefficient in the melt and V the solidification rate, the thickness of this layer, and therefore the stability of the systems studied, is shown to be a function of the length scale D/ V, where it is shown that channeling can be turned on or off simply by changing this length scale. This work also validates a finite element model of dendritic solidification by comparing predicted results to data resulting from eleven directionally solidified hypoeutectic Pb-Sn samples, which were produced under various thermal gradients and solidification rates. For all but one of the cases, which was thought to be borderline between channeling and not channeling, predictions of whether channel defects formed were supported by experiments. Finally, it was determined that, while the strength of the convection in the overlying liquid depends on the square root of its height, one need not model the entire domain to predict channel defects.