The morphological evolution of dendritic microstructures during coarsening

The coarsening process of dendritic microstructures is studied in the Pb-Sn system using three-dimensional reconstructions. We analyze the morphology of the microstructure by determining the interfacial shape distribution, the probability of finding a patch of surface with a given pair of principal curvatures and its anisotropy through measurements of the probability of finding an interfacial normal in a certain direction. We find that the cube of the inverse surface area per unit volume increases linearly with time, despite the apparent lack of microstructural self-similarity. Interfacial normal distributions demonstrate a strong preferential directionality, specifically an evolution to twofold symmetry, as coarsening proceeds. During coarsening, the fraction of interface with normals perpendicular to the directional solidification direction increases dramatically. This preferred direction is a result of the existence of interfaces along the directional solidification direction that have a lower absolute value of the mean curvature than the surrounding interfaces.