Seaweed to Dendrite Transition in Directional Solidification

Abstract

We simulate directional solidification using a phase-field model solved with adaptive mesh refinement. For small surface tension anisotropy directed at 45 relative to the pulling direction we observe a crossover from a seaweed to a dendritic morphology as the thermal gradient is lowered, consistent with recent experimental findings. We show that the morphology of crystal structures can be unambiguously characterized through the local interface velocity distribution. We derive semiempirically an estimate for the crossover from seaweed to dendrite as a function of thermal gradient and pulling speed. DOI: 10.1103/PhysRevLett.91.155502 PACS numbers: 81.30.Fb, 68.70.+w The study of solidification microstructures is fundamental to many problems of scientific and practical significance. Among these is the optimization of metal alloys, the properties of which depend on their microstructure [1,2]. In traditional casting, microstructure is formed through solidification and thermomechanical processing, which typically destroys the initial as-cast structure. In emerging technologies, such as strip casting, thin alloy strips are rapidly cooled with little thermomechanical treatment. In these materials, the final microstructure is largely governed by the physics of solidification.The fundamental solidification structure is the dendrite. Dendrites can be grown in isolation, where their growth rate is selected by a solvability criterion that is established due to a singular perturbation in the surface tension anisotropy [3,4]. In casting applications solidification occurs as a competitive growth of multiple arrays, often growing as an advancing front, directionally solidified in a thermal gradient established by heat flow out of a cast.A paradigm used to study solidification in a 2D geometry -a phenomenon with many parallels in strip casting -is directional solidification. In this process a material is solidified while being pulled through a unidirectional temperature gradient G at a velocity v. The solidification front becomes unstable by the MullinsSekerka instability [5], leading to a variety of complex cell and dendrite patterns. A long-standing problem has been to elucidate the mechanism of wavelength selection in such cellular or dendritic arrays. This problem has been extensively examined experimentally [6 -15], and theoretically [6,10,16 -20] using boundary integral methods, phase-field models, and semiempirical thermodynamic considerations.Another class of directionally solidified microstructures recently examined experimentally [6,15] and numerically [6,21] is known as seaweed. These structures are formed through successive tip splitting of primary branches of the solidification front. Surviving tips grow and continue to split, while trailing branches become subsumed by neighbor interactions. Seaweed can emerge when the direction of solidification is tilted at an angle with respect to the direction of a small surface tension anisotropy. Of particular importance is the recent experimental observation [15] that when...

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