Primary dendrite distribution and disorder during directional solidification of Pb-Sb alloys

Pb-2.2 wt pct Sb and Pb-5.8 wt pct Sb alloys have been directionally solidified from a single-crystal seed with its [100] orientation parallel to the growth direction, to examine the primary dendrite distribution and disorder of the dendrite arrays. The dendrite distribution and ordering have been investigated using analysis techniques such as the Gauss-amplitude fit to the frequency distribution of nearest and higher-order spacings, minimum spanning tree (MST), Voronoi polygon, and Fourier transform (FT) of the dendrite centers. Since the arrangement of dendrites is driven by the requirement to accommodate side-branch growth along the 〈100〉 directions, the FT images of the fully developed dendrite centers contain spots which indicate this preferred alignment. A directional solidification distance of about three mushy-zone lengths is sufficient to ensure a steady-state dendritic array, in terms of reaching a constant mean primary spacing. However, local dendrite ordering continues throughout the directional solidification process. The interdendritic convection not only decreases the mean primary spacing, it also makes the dendrite array more disordered and reduces the ratio of the upper and lower spacing limits, as defined by the largest 5 pct and the smallest 5 pct of the population.