A theory of thin lamellar eutectic growth with anisotropic interphase boundaries

Akamatsu, Silvère; Bottin-Rousseau, Sabine; Şerefoğlu, Melis; Faivre, G

doi:10.1016/j.actamat.2012.02.031

Cited by 52 publications

(63 citation statements)

References 20 publications

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“…In a steady-state condition, the (lam ellar) tilt angle 0, is defined by tan 9, = Vd/ V . On the basis o f in situ directional solidification observations using thin sam ples o f m etallic and transparent organic eutectic alloys, a conjecture was form ulated recently that relates the value o f 6, to the anisotropy o f the free energy o f the interphase boundaries (interfacial anisotropy) [20,21]. The m ain underlying hypotheses are that (i) only the solid-solid interfaces are anisotropic (i.e., in a nonfaceted alloy, the anisotropy o f the solid-liquid interfaces has a negligible effect on the lam ellar grow th dynam ics) and (ii) the solid-liquid interface keeps virtually the same shapew ith m irror sym m etry about the m idplane o f a lam ella-as for standard (nontilted) lam ellae.…”

Section: Introductionmentioning

confidence: 99%

Interphase anisotropy effects on lamellar eutectics: A numerical study

et al. 2015

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In directional solidification of binary eutectics, it is often observed that two-phase lamellar growth patterns grow tilted with respect to the direction z of the imposed temperature gradient. This crystallographic effect depends on the orientation of the two crystal phases α and β with respect to z. Recently, an approximate theory was formulated that predicts the lamellar tilt angle as a function of the anisotropy of the free energy of the solid(α)-solid(β) interphase boundary. We use two different numerical methods-phase field (PF) and dynamic boundary integral (BI)-to simulate the growth of steady periodic patterns in two dimensions as a function of the angle θ(R) between z and a reference crystallographic axis for a fixed relative orientation of α and β crystals, that is, for a given anisotropy function (Wulff plot) of the interphase boundary. For Wulff plots without unstable interphase-boundary orientations, the two simulation methods are in excellent agreement with each other and confirm the general validity of the previously proposed theory. In addition, a crystallographic "locking" of the lamellae onto a facet plane is well reproduced in the simulations. When unstable orientations are present in the Wulff plot, it is expected that two distinct values of the tilt angle can appear for the same crystal orientation over a finite θ(R) range. This bistable behavior, which has been observed experimentally, is well reproduced by BI simulations but not by the PF model. Possible reasons for this discrepancy are discussed.

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Section: Introductionmentioning

confidence: 99%

Interphase anisotropy effects on lamellar eutectics: A numerical study

et al. 2015

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“…As reported in Refs. [22][23][24], the tilting angle of the phase boundary may considerably differ from the actual tilting angle. This is demonstrated for different anisotropy strengths in Fig.…”

Section: Anisotropy Of C 2 In Two Dimensionsmentioning

confidence: 99%

“…6, where for comparison, results for ideal locking (realization of the actual tilting angle), and predictions of an analytical formulation based on the assumption of a symmetric-pattern (SP) described in Refs. [22,24] are also displayed. For small anisotropies (so  0.1), the present simulations are in an excellent agreement with the analytical SP model, and thus with the results from the boundary integral method [24] and from quantitative phase-field modelling based on the multi-phase concept [24].…”

Section: Anisotropy Of C 2 In Two Dimensionsmentioning

confidence: 99%

“…A broad variety of the eutectic systems show interfaces with anisotropic interfaces. Recent papers [22][23][24][25][26] address the effect of anisotropy of the solid-solid and solid-liquid interfaces on the eutectic pattern; reporting e.g., the existence of locked and unlocked relative orientations in the case of supercritical anisotropy [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Phase-field modeling of eutectic structures on the nanoscale: the effect of anisotropy

et al. 2017

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Eutectic solidification front formed in the presence of a highly anisotropic solid-liquid interfacial free energy. It has been demonstrated that the eutectic pattern is sensitive to the morphology of the solid-liquid interface. ABSTRACTA simple phase-field model is used to address anisotropic eutectic freezing on the nanoscale in two (2D) and three dimensions (3D). Comparing parameter-free simulations with experiments, it is demonstrated that the employed model can be made quantitative for Ag-Cu. Next, we explore the effect of material properties, and the conditions of freezing on the eutectic pattern. We find that the anisotropies of kinetic coefficient and the interfacial free energies (solid-liquid and solid-solid), the crystal misorientation relative to pulling, the lateral temperature gradient, play essential roles in determining the eutectic pattern. Finally, we explore eutectic morphologies, which form when one of the solid phases are faceted, and investigate cases, in which the kinetic anisotropy for the two solid phases are drastically different.

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“…To explain the origin for this requirement, we must recall the following facts [14,15]: (i) a (eutectic) grain is a portion of the solid, inside which the crystal-lattice orientation of each of the eutectic phases is uniform; (ii) eutectic growth patterns are sensitive to the degree of anisotropy of the surface energies of the various interfaces present, especially, AB interphase boundaries; this degree of anisotropy depends on the orientation of the di↵erent phases with respect to one another and the sample, and therefore varies from grain to grain; (iii) eutectic grains can be classified into two broad categories called "floating" and "locked". The floating grains are those in which anisotropy e↵ects are su ciently weak for the dynamical features of the eutectic patterns to be those that are reviewed in the Introduction (including, in particular, uniformisation over time by -di↵usion).…”

Section: Extended Abac Lamellar Patternsmentioning

confidence: 99%

Stability of three-phase ternary-eutectic growth patterns in thin sample

et al. 2016

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To cite this version:S Bottin-Rousseau, M S erefoglu, Sinan Yücetürk, Gabriel Faivre, Silvère Akamatsu. Stability of three-phase ternary-eutectic growth patterns in thin sample. Acta Materialia, Elsevier, 2016, 109, pp.259 -266. <10.1016/j.actamat.2016 Abstract Near-eutectic ternary alloys subjected to thin-sample directional solidification can exhibit stationary periodic growth patterns with an ABAC repeat unit, where A, B and C are the three solid phases in equilibrium with the liquid at the eutectic point. We present an in-situ experimental study of the dynamical features of such patterns in a near-eutectic In-In 2 Bi-Sn alloy. We demonstrate that ABAC patterns have a wide stability range of spacing at given growth rate. We study quantitatively the -di↵usion process that is responsible for the spacing uniformity of steady-state patterns inside the stability interval. The instability processes that determine the limits of this interval are examined. Qualitatively, we show that ternary-eutectic ABAC patterns essentially have the same dynamical features as two-phase binary-eutectic patterns. However, lamella elimination (low-stability limit) occurs before any Eckhaus instability manifests itself. We also report observations of stationary patterns with an [AB] m [AC] n superstructure, where m and n are integers larger than unity.Keywords: Eutectic solidification, directional solidification, solidification microstructures, ternary eutectics, three phase microstructures. IntroductionThe solidification microstructures of ternary eutectic alloys take many di↵er-ent forms depending on the composition and grain structure of the alloy, the geometrical and thermal features of the solidification device, and the solidification history. The most important of these factors are the number of growing phases and the dimensionality of the samples. We are concerned here with two-dimensional three-phase microstructures. These are typically observed in near-eutectic ternary alloys subjected to thin-sample directional solidification (thin-DS). Solidification microstructures are, we recall, nothing else than the trace left behind in the solid by out-of-equilibrium self-organized patterns formed during solidification. At constant solidification rate V and applied thermal gradient G, these patterns generally reach, or, at least, asymptotically tend towards a steady-state. The most wellknown example of a steady-state eutectic growth pattern is the periodic (lamellar) two-phase solidification pattern of near-eutectic binary alloys analyzed by Jackson and Hunt (JH) a long time ago [1]. The repeat unit of such a pattern is an AB pair of lamellae, where A and B are the two solid phases in equilibrium with the liquid at the eutectic point. These AB patterns have mirror symmetry with respect to the mid-plane of the lamellae, which is actually a condition for their steadiness. Regarding ternary eutectic alloys, the basic repeat unit of stationary thin-DS patterns is ABAC, where A, B and C are the three eutectic solid phases. It has mirror sy...

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A theory of thin lamellar eutectic growth with anisotropic interphase boundaries

Cited by 52 publications

References 20 publications

Interphase anisotropy effects on lamellar eutectics: A numerical study

Interphase anisotropy effects on lamellar eutectics: A numerical study

Phase-field modeling of eutectic structures on the nanoscale: the effect of anisotropy

Stability of three-phase ternary-eutectic growth patterns in thin sample

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