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Three-dimensional dendrite-tip morphology at low undercooling

Karma¹, Lee, Plapp

¹Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|November 23, 2000

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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.

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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.