https://doi.org/10.1140/epjs/s11734-024-01399-6
Regular Article
How a growing dendritic crystal reaches its stationary crystallization velocity
1
Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000, Ekaterinburg, Russian Federation
2
Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, 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
2024
Accepted:
5
November
2024
Published online:
5
December
2024
Motivated by important applications in materials science, geo- and biophysics, we develop a theory answering the question of how a growing dendritic crystal reaches its stationary crystallization velocity. To do this, we compare existing theoretical approaches, computational simulations and experimental data for crystal growth laws at certain time intervals. Taking these laws into account, we stitch together all known asymptotics and derive two generalized expressions for the crystal growth velocity as a function of time. We analyze a behaviour of these generalized laws and compare them with experiments. Both expressions have similar behaviour and well describe the experimental data. Therefore, the choice between these expressions is more a matter of taste.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.