https://doi.org/10.1140/epjs/s11734-025-02113-w
Regular Article
Dendritic shapes for various crystalline symmetries: theory, modeling and experiment
1
Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität-Jena, 07743, Jena, Germany
2
Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
a
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Received:
10
October
2025
Accepted:
15
December
2025
Published online:
9
January
2026
This study develops the Geometrically Morphological Theory (Toropova et al. in Acta Mater 296:121232, 2025) to describe the shapes of dendritic tips, stems, and envelopes for various tip functions. Analytical expressions derived from the theory demonstrate strong agreement with the experimental data for dendrites exhibiting four- and six-fold crystalline symmetries. The analysis highlights the distinct asymptotic behaviors of two shape functions, 
and 
, characterizing the tip region.
© The Author(s) 2026
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