This title appears in the Scientific Report :
2020
Please use the identifier:
http://dx.doi.org/10.1103/PhysRevMaterials.4.033802 in citations.
Please use the identifier: http://hdl.handle.net/2128/26450 in citations.
Modeling of dendritic growth using a quantitative nondiagonal phase field model
Modeling of dendritic growth using a quantitative nondiagonal phase field model
The phase field method has emerged as the tool of choice to simulate complex pattern formation processes in various domains of materials sciences. For the phase field model to faithfully reproduce the dynamics of a prescribed free-boundary problem with transport equations in the bulk and boundary co...
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Personal Name(s): | Wang, Kai |
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Boussinot, Guillaume / Hüter, Claas / Brener, Efim A. (Corresponding author) / Spatschek, Robert | |
Contributing Institute: |
Theoretische Nanoelektronik; PGI-2 Werkstoffstruktur und -eigenschaften; IEK-2 |
Published in: | Physical review materials, 4 (2020) 3, S. 033802 |
Imprint: |
College Park, MD
APS
2020
|
DOI: |
10.1103/PhysRevMaterials.4.033802 |
Document Type: |
Journal Article |
Research Program: |
Controlling Collective States |
Link: |
OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://hdl.handle.net/2128/26450 in citations.
The phase field method has emerged as the tool of choice to simulate complex pattern formation processes in various domains of materials sciences. For the phase field model to faithfully reproduce the dynamics of a prescribed free-boundary problem with transport equations in the bulk and boundary conditions at the interfaces, the so-called thin-interface limit should be performed. For a phase transformation driven by diffusion, the kinetic cross-coupling between the phase field and the diffusion field has recently been introduced, allowing a control on interface boundary conditions in the general case where the diffusivity in the growing phase DS neither vanishes (one-sided model) nor equals the one of the disappearing phase DL (symmetric model). Here, we investigate the capabilities of this nondiagonal phase field model in the case of two-dimensional dendritic growth. We benchmark our model with Green's function calculations (sharp-interface model) for the symmetric and one-sided cases, and our results for arbitrary DS/DL allow us to propose a generalization of the theory by Barbieri and Langer [Phys. Rev. A 39, 5314 (1989)] for finite anisotropy of interface energy. We also perform simulations that evidence the necessity of introducing the kinetic cross-coupling and of eliminating surface diffusion. Our work opens up the way for quantitative phase field simulations of phase transformations with diffusion in the growing phases playing an important role in the pattern and velocity selections. |