Cellular Array Morphology during Directional Solidification

摘要

Cellular array morphology has been examined in the shallow cell, deep cell and cell to dcndrite transition regime in the Pb-2.2 wt. pct. Sb and Al-4.1 wt. pct. Cu alloy single crystal samples which were directionally solidified along [100]. Statistical analysis of the cellular spacing distribution on the transverse sections has been carried out using minimum spanning tree (MST), Voronoi polygons, radial distribution factor and fast Fourier transformation techniques. Frequency distribution of the number of nearest neighbors and the MST parameters suggest that the arrangement of cells may be visualized as a hexagonal tessellation with superimposed 50% random noise. However, the power spectrum of the Fourier transform of the cell centers shows a diffused single ring pattern that does not agree with the power spectrum from the hexagonal tessellation having a 50% superimposed random noise. The radial distribution factor obtained from the cells is similar to that of the liquids. An overall steady-state distribution in terms of the mean primary spacing is achieved after a directional solidification of about three mushy zone lengths. However, the process of nearest neighbor interaction continues throughout directional solidification, as indicated by about 14% of the cells undergoing submerging in the shallow cell regime, or by an increasing first and second nearest neighbor ordering for the growth condition which corresponds to the cell to dendrite transition. The ratio between the upper and lower limits of the primary spacing, as defined by the largest and the smallest 10% of the population, respectively, is quite unique: 1.43 +-0.11. The nature of cell distribution in the Al-Cu alloy appears to be the same as that in the Pb-Sb.