https://doi.org/10.1140/epjst/e2019-900103-0
Regular Article
Theoretical modeling of crystalline symmetry order with dendritic morphology
1
Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia
2
Friedrich-Schiller-Universität-Jena, Physikalisch-Astronomische Fakultät, 07743 Jena, Germany
3
GPM, CNRS-UMR 6634, University of Rouen Normandy, 76801 Saint Étienne Du Rouvray, France
4
Centre for Numerical Modelling and Process Analysis, University of Greenwich, Old Royal Naval College, Park Row, London SE10 9LS, UK
a e-mail: l.v.toropova@urfu.ru
Received:
13
June
2019
Received in final form:
15
July
2019
Published online:
11
February
2020
Stable growth of a crystal with dendritic morphology with n-fold symmetry is modeled. Using the linear stability analysis and solvability theory, a selection criterion for thermally and solutally controlled growth of the dendrite is derived. A complete set of non-linear equations consisting of the selection criterion and an undercooling balance (which determines the implicit dependencies of the dendrite tip velocity and tip diameter on the total undercooling) is formulated. The growth kinetics of crystals having different lattice symmetry is analyzed. The model predictions are compared with phase field modeling data on ice dendrites grown from pure undercooled water.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020
