Morphological and topological characterization of coarsened dendritic microstructures

Qualitative and quantitative characterization of the coarsening dendritic samples has been achieved. Five directionally solidified Al-15wt.%Cu samples were isothermally coarsened for 10, 90, 255, 536, and 964 minutes. Quantitative characterization included the analysis of interface shape distributions and the measurement of topological properties. Qualitatively, the interfacial normal distributions described the degree of directionality found in the microstructure. These results were then supplemented with phase-field calculations that used the experimental reconstructions as an initial condition.; Measuring the principal curvatures scaled by the length scale, the inverse of the surface area per unit volume ( S-1v ), allowed for the creation of interface shape distributions (ISD) which provided the probability of having an interfacial patch of a given curvature range in the microstructure. The ISD of all coarsened samples indicated that cylindrical interfaces appeared in the 90-minute sample and remained for the later coarsened samples and that most of the interfacial patches were saddle-shaped. The appearance of a peak in the ISD indicated that the microstructure was not evolving in a self-similar manner, despite the linear relationship between S-1v and the cube root of coarsening time. The interfacial normals indicated that the microstructure of the earliest coarsened sample had a four-fold symmetry that disappeared for the later coarsened samples and that the majority of interfaces were parallel with the solidification direction. Topological characterization included the measurement of the scaled genus, number of handles, and the number of liquid particles as a function of coarsening time. The scaled genus decreased with coarsening time due to the simplification of the microstructure and the increased number of liquid droplets with coarsening time. Further characterization was achieved by using the three-dimensional reconstructions of the 10- and 90-minute coarsened samples as an initial condition to phase-field calculations. It was shown that the average flux in curvature space provided by the phase-field calculations can be used to describe qualitatively the evolution of the interface shape distributions during non-self-similar coarsening. Interfacial velocity calculated by the phase-field simulation aided in the discovery that liquid tubes are being created through topological singularities.