Convection and channel formation in solidifying Pb−Sn alloys

A suite of experiments on the dendritic solidification of Pb–Sn melts has been carried out. The first goal has been to quantify the longitudinal macrosegregation, and hence the convective vigor through the dendritic (“mushy”) zone during solidification, as a function of the mushy zone Rayleigh number. The mushy zone Rayleigh number Ram is a ratio of the driving compositional buoyancy force to the retarding Darcy frictional force. The second goal has been to characterize the formation of convection channels as a function of Ram. In a fixed furnace, the melts were program cooled and solidified from beneath, at various cooling rates. Two different temperature gradients were examined. Each pairing of cooling rate and temperature gradient results in a different Ram. As expected, the measured longitudinal macrose gregation increased with Ram. The vestiges of convection channels on a solidified ingot surface (which we call “freckle trails”) were observed for all conditions except for the most rapid cooling rate with the smaller temperature gradient (i.e., the smallest Ram) and for the slowest cooling rate with the larger temperature gradient (i.e., the largest Ram). Under the latter solidification conditions, the vestiges of convection channels in an ingot interior (which we call “chimneys”) were observed. Chimneys were not observed in other ingots. When present, the number of freckle trails decreased and the width of the trails increased with increasing Ram. The trails became more diffuse as well. It appears that Ram may control channel characteristics as well as convection and the resulting macrosegregation. There appear to be two critical values, a lower one for surface freckle trails and a higher one for interior chimneys. Conditions at the Earth's inner-outer core boundary (ICB) may be those exhibiting high Ram convection, so that convection channels, if they exist, could be as large as several hundred meters in width.