Primary dendrite spacing: History dependence and influence of interdendritic convection

Lead-antimony alloys (Pb-2.2 wt pct Sb and Pb-5.8 wt pct Sb) and Aluminum-copper alloy (Al-4.1 wt pct Cu) have been directionally solidified from single crystal seeds with their [100] orientation parallel to the growth direction to examine the primary dendrite distribution, its history dependence and the influence of convection. The Pb-Sb alloys are thermally stable and solutally unstable leading to interdendritic convection. The extent of convection is expected to be less in Pb-2.2 wt pct Sb as compared with Pb-5.8 wt pct Sb. The Al-Cu alloy is thermally and solutally stable and therefore convection can occur only due to transverse thermal gradients. This alloy is expected to have the least convection. The dendrite distribution and ordering have been investigated using analysis techniques, such as, Gauss amplitude fit to the frequency distribution of nearest and higher order spacing, Minimum Spanning Tree (MST), Voronoi Polygon, and Fast Fourier transformation (FFT) of the dendrite centers. A directional solidification distance of about three mushy zone length is found to be 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 calculated by the largest 5% and the smallest 5% of the primary spacing population.; History dependence of primary spacings has been studied by examining the spacing distributions after step-increase and step-decrease in the growth speed. The "side-branching instability" process that determines the upper limit of the primary spacings is found to be less sluggish as compared with the "submerging process" that determines the lower spacing limit. In the absence of convection the minimum, the median and the maximum spacings show identical growth speed dependence, A ( V)-0.22. Interdendritic convection causes more reduction in the upper primary spacing limit as compared with the lower limit; and it also reduces the extent of the experimentally observed history dependence of primary spacing.; A mushy zone Rayleigh number (RaB) recently proposed by Beckerman et al.[59] has been used to examine the relationship between increasing RaB that indicates increasing mushy-zone convection and decrease in the primary spacing as compared with that predicted by theoretical models based on purely diffusive mass transport. There is a strong correlation between the extent of increase in the RaB and the corresponding decrease in the primary spacing in the Pb-2.2 and 5.8 wt pct Sb alloys. However, the data for the primary dendrite spacing for any one alloy (Pb-2.2 wt pct Sb or Pb-5.8 wt pct Sb) when plotted as a function of RaB get segregated along lines that are of constant thermal gradients. Also the data for the two antimony alloys get segregated into two different RaB regimes. It is suspected that it is due to an inaccurate mushy-zone permeability assumption used by Beckerman et al. in defining their mushy zone Rayleigh number.