Alternating Tip Splitting in Directional Solidification

Utter, Brian; Ragnarsson, Rolf; Bodenschatz, Eberhard

doi:10.1103/physrevlett.86.4604

Cited by 66 publications

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“…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 the thermal gradient is reduced, there is a morphological transition from seaweed to directed dendritic structures that lock into the symmetric anisotropy directions. It has been conjectured that this transition is an effect of the finite surface tension anisotropy [15].…”

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“…Of particular importance is the recent experimental observation [15] that when the thermal gradient is reduced, there is a morphological transition from seaweed to directed dendritic structures that lock into the symmetric anisotropy directions. It has been conjectured that this transition is an effect of the finite surface tension anisotropy [15]. The precise mechanism of this morphological transition remains unexplained, however.…”

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“…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.…”

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“…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.…”

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“…[15]. We use a phase-field model solved on an adaptive grid, gaining access to systems with reduced finite size effects, a factor which has traditionally plagued studies where the size of the system is on the order of the diffusion length.…”

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Seaweed to Dendrite Transition in Directional Solidification

et al. 2003

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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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Seaweed to Dendrite Transition in Directional Solidification

et al. 2003

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Phase Field Modeling of Solidification in Binary Alloys

Provatas¹,

Elder

2010

Phase‐Field Methods in Materials Science and Engineering

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This chapter extends the phase field methodology to include alloysa mixture of two or more components. Following a brief review of some nomenclature regarding alloys and phase diagrams, the kinetics describing the sharp interface evolution of solidification or solid-state microstructure formation in an alloy is discussed. This will be used as a backdrop against which to develop a phase field free energy for a class of two-component (binary) alloys. This free energy will be used to derive equations of motion for the evolution of the order parameter (phase field), impurity concentration, and heat during the growth of an alloy phase. The last stage, as in the case of pure materials, is to make a connection between phase field simulationswhich inherently employ a diffuse interfaceand the corresponding alloy sharp interface models. The reader is assumed to have (or advised to acquire) some background knowledge of binary alloys and their basic thermodynamics.

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Phase Field Modeling on Polymer Crystallization and Phase Separation in Crystalline Polymer Blends

Kyu

Tai-ming

et al. 2010

Encyclopedia of Polymer Blends

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The solidification phenomenon of a liquid has been one of the most fascinating firstorder phase transitions, involving a complex interplay of many physical effects. The simplest solidification front is the planar interface. Usually, the solid-liquid interface is an active free boundary from which latent heat is liberated during solid-liquid phase transformation. Preferentially, this latent heat is conducted away from the convex solid-liquid tips, but it may be trapped in the case of concave interface, thereby leading to the directional growth of interfacial morphologies. Consequently, these interfaces are generally rough with convex and concave curvatures. Among them, the basic patterns are dendrites and seaweeds. A structure with pronounced orientational order is termed as dendrite, and without apparent orientational order it is called seaweed. The dendritic shape is a symmetric needle crystal with a parabolic tip, the sides of which are influenced by a secondary branching. The seaweed morphology was originally introduced on the basis of experimental observations under the name of dense-branching morphology, which is characterized by repeating tip splitting at the interface front [1]. The basic element of the seaweed structure is a doublon, which consists of two fingers with a liquid channel running along the axis of the symmetry between them. Experimentally, Akamatsu[2] showed that the seaweed growth involves a continual creation and elimination of doublons. In directional solidification, the solid-liquid interface is subjected to morphological instabilities in an externally imposed directional temperature gradient. Various interface morphologies have been observed [2-4] depending on the physical properties of the materials. Especially, the anisotropic properties of the solid-liquid interface play a particularly important role in deter mining the stability of the dendrites as well as the transformation between seaweed and dendrite patterns. Thus, an in-depth understanding of the interface morphology during solidification is essential to shed light on the pattern formation aspects of crystal solidification.Theoretical investigations of the solid-liquid phase transition have long been the subject of considerable interest. Among these, there are two main streams: one is the Edited by Avraam I. Isayev

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Alternating Tip Splitting in Directional Solidification

Cited by 66 publications

References 16 publications

Seaweed to Dendrite Transition in Directional Solidification

Seaweed to Dendrite Transition in Directional Solidification

Phase Field Modeling of Solidification in Binary Alloys

Phase Field Modeling on Polymer Crystallization and Phase Separation in Crystalline Polymer Blends

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