The shape of dendritic tips for rapid non-equilibrium solidification

Abstract The shape of dendritic tips for rapid nonequilibrium solidification is studied based on the Geometrically Morphological Theory (Toropova et al. in Acta Mater 296:121232, 2025; Alexandrov et al. in Phys Lett A 501:129375, 2024) and numerical simulations. The shape function for dendritic tips that takes into account Lorentz-type coordinate transformations is checked against the crystal shapes simulated numerically. This study shows that the dendrite tip, primary stem and external envelope are well-described by Geometrically Morphological Theory with compression-stretching coordinate transformations in the diffusion-limited solidification regime and without these transformations in the kinetic regime.