Theoretical modeling of crystalline symmetry order with dendritic morphology

Abstract

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. © 2020, EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.