Statistical analysis of the disorder of two-dimensional cellular arrays in directional solidification

Abstract

By introducing a weighted Wigner-Seitz construction and, for the first time in directional solidification, using the minimal spanning tree (MST) approach and the (m,σ)-diagram, the statistical analysis of the topological defects and disorder of two-dimensional (2-D) cellular arrays has been carried out. For “standard” growth of massive Pb-30 wt pct Tl alloys, the underlying honeycomb has been brought out, which was rather unexpected, as the percentage of defects is so high that the cellular arrays are “melted” by the defects, with a structure close to that of a 2-D liquid. Furthermore, disorder can be described by a Gaussian noise applied on an array of hexagonal cells, Lewis's law is satisfied, and for a sufficiently large number of cells, a peak is evidenced in the primary spacing distribution, which indicates that, in some way, the cell size is selected. Nevertheless, the associated standard deviation is rather large. It is conceivable that the defects can have a leading role in the selection of the primary spacing.