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Three-dimensional dendrite-tip morphology at low undercooling
1Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA.
Summary
Dendrite tip morphology is largely independent of anisotropy at low undercoolings. A universal shape, deviating slightly near the tip, is described by a specific mathematical form, matching experimental data.
Area of Science:
- Materials Science
- Physics
- Computational Modeling
Background:
- Dendritic growth is crucial in solidification processes.
- Understanding dendrite tip morphology is key to controlling material properties.
- Previous models often simplified dendrite tip geometry.
Purpose of the Study:
- To investigate the 3D morphology of dendrite tips.
- To determine the influence of anisotropy on tip shape.
- To provide a precise mathematical description of dendrite tip morphology.
Main Methods:
- Phase-field method for simulating dendritic growth.
- Mathematical fitting of simulated tip shapes.
- Reanalysis of experimental data for comparison.
Main Results:
- Dendrite tip morphology is mostly independent of anisotropy at low undercoolings.
- A universal tip shape is identified, deviating near the tip.
- The shape is accurately described by z=-r(2)/2+A(4)r(4) cos 4phi.
- Power law z=-a|x|(5/3) fits the fin shape away from the tip.
Conclusions:
- The phase-field method accurately captures dendrite tip morphology.
- The findings provide a refined understanding of dendritic growth.
- Results align well with experimental observations in succinonitrile.