https://doi.org/10.1140/epjs/s11734-025-02072-2
Regular Article
The shape of dendritic tips for rapid non-equilibrium solidification
1
Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
2
Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
3
Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität-Jena, 07743, Jena, Germany
Received:
13
September
2025
Accepted:
13
November
2025
Published online:
21
November
2025
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.
© The Author(s) 2025
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