Evolution of Dendritic Patterns During Directional Solidification of Ni-Base Alloys: Towards Hexagonally Ordered, Close-Packed Dendrite Arrays

Abstract Dendrites are the predominant microstructural feature formed during the solidification of metallic alloys. In directionally solidified alloys, the length scale and regularity of dendritic patterns strongly influence final properties. We introduce a supervised machine learning approach, shape-limited primary spacing (SLPS), that automatically and rapidly quantifies local primary dendrite arm spacing (PDAS) and packing order from microstructural images. SLPS provides a general, image-driven framework for quantifying directionally solidified dendrite structures. By applying SLPS to directionally solidified microstructures and to complementary simulations using a solutal dendrite model, we investigate how hexagonally ordered dendrite arrays correspond to near steady-state tip growth under homogeneous liquid composition. The admissible range of local PDAS is determined by local growth-rate variations and the degree of lateral adjustment to thermal–solutal gradients. Simulations comparing packing geometries (square vs. hexagonal in two-dimensional cross sections) reveal that hexagonal arrays adapt local PDAS more readily than square arrays, owing to enhanced secondary-arm development and tertiary-to-primary branching. Consequently, hexagonally packed dendrite arrays yield finer PDAS than square-packed ones. These findings provide a mechanistic basis for process design: seeding or processing routes that promote hexagonally ordered, close-packed dendrite arrays can achieve finer PDAS, thereby reducing microsegregation, lowering the propensity for defect-grain formation, and shortening solution heat treatment times. Graphical Abstract