https://doi.org/10.1140/epjst/e2019-900057-9
Regular Article
Phase field model derivation for rapid crystal growth in polycrystalline alloys
1
Ural Federal University, Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, 620000 Ekaterinburg, Russia
2
Friedrich-Schiller-Universität Jena, Otto Schott Institute of Materials Research, 07743 Jena, Germany
3
KU Leuven, Department of Materials Engineering (MTM) 3001 Leuven Belgium
a e-mail: nizovtseva.irina@gmail.com
Received:
18
March
2019
Received in final form:
12
July
2019
Published online:
11
February
2020
A phase field model of rapid multi–grain growth is developed. Using a multi–phase model for polycrystalline growth in multi–component alloying systems and the model of fast phase transformations, the Gibbs free energy change on crystallization is formulated as a driving force for polycrystalline growth. The model of fast phase transitions, which introduces not only classical slow variables (concentration, chemical potential and phase field), but also the fast ones (diffusion flux and gradient flow), was used to capture short periods of times usually occurring in the rapid solidification and in the fast solid-state transformations. The evolution equations for the fast crystallization are written using multi–phase interpolation functions among growing polycrystallites.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020
