Primary arm array during directional solidification of a single-crystal binary alloy: Large-scale phase-field study

Primary arm arrays formed during the directional solidification of a single-crystal binary alloy were investigated by performing large-scale phase-field simulations using the GPU supercomputer TSUBAME2.5 at Tokyo Institute of Technology. The primary arm array and spacing were investigated by Voronoi decomposition and Delaunay triangulation, respectively. It was concluded that a hexagonal array was dominant for both the dendrite and cell structures and that penta–hepta defects, which are typical defects in hexagonal patterns, were formed. The primary arms continuously moved such that the number of hexagons increased, and the distribution of primary arm spacing became uniform over time even after the number of primary arms was constant. The order of array was highest in the growth condition of the dendrite close to the cell-to-dendrite transition region. In addition, we proposed a realistic and accurate evaluation method of primary arm array by removing small sides from the Voronoi polygons.