On unconstrained solidification of spherical metallic drops

The solidification of metallic droplets into powder particles involves a complex interplay between heat diffusion, surface tension, and geometric constraints. In confined, curved systems -- such as those encountered in atomisation, abrasion, and micrometeorite formation -- positive curvature and finite boundaries significantly modify classical solidification dynamics. In this study, we systematically investigate the solidification of metallic spheres, focusing on how curvature and confinement influence nucleation pathways, growth kinetics, and interfacial stability. Two competing growth modes -- radial outward and circumferential -- are analysed using Stefan-type models under a quasi-steady approximation. A generalisation of Mullins--Sekerka stability theory is developed to account for finite spherical domains, revealing that particle size and curvature introduce new destabilising parameters that govern microstructural length scales. Experimental observations of dendritic and cellular morphologies are interpreted through this framework, demonstrating that the interaction between growth fronts, undercooling, and curvature collectively determines the final particle structure. These findings underscore the need to re-evaluate classical solidification theories in the context of curved geometries, with implications for both engineered and naturally occurring metal powders.