Morphological instabilities of lamellar eutectics

Karma, Alain; Sarkissian, Armand

doi:10.1007/bf02648952

Cited by 161 publications

(144 citation statements)

References 29 publications

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“…Note that we have not taken into account crystallographic effects, which would appear through anisotropies in the kinetic coefficients and the surface tensions; the latter would also lead to additional "Herring torque" terms in Young's law. It has been shown by boundary integral simulations [16,17] that all the relevant instabilities and morphologies can be reproduced by the above model. Therefore, we have limited ourselves to an isotropic formulation both for the FBP and the phase-field model.…”

Section: Free-boundary Problemmentioning

confidence: 87%

“…We thoroughly test our model in two-dimensional simulations and compare the outcome to results obtained with the boundary integral method [17]. We find that the dynamics of the solid-liquid interfaces are accurately simulated and independent of the interface thickness for sufficiently thin interfaces, as predicted by the asymptotic analysis.…”

Section: Introductionmentioning

confidence: 90%

“…This spacing is not intrinsically selected by the system, but depends on the growth history. Upon a (large enough) change of pulling velocity, the front undergoes various instabilities and exhibits many classical features of nonlinear physics, such as bifurcations to states of lower symmetry, periodic limit cycles, spatiotemporal chaos and soliton-like traveling perturbations [13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Quantitative phase-field modeling of two-phase growth

2005

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A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth freeenergy functional, specifically designed so that the stable solutions that connect any two phases are completely free of the third phase. For the simplest choice for this functional, the equations of motion for each of the two solid-liquid interfaces can be mapped to the standard phase-field model of single-phase solidification with its quartic double-well potential. By applying the thin-interface asymptotics and by extending the antitrapping current previously developed for this model, all spurious thin-interface corrections to the dynamics of the solid-liquid interfaces can be eliminated. This means that simulation results become independent of the thickness W of the diffuse interfaces. As a consequence, accurate results can be obtained using values of W much larger than the physical interface thickness, which yields a tremendous gain in computational power and makes simulations for realistic experimental parameters feasible. Convergence of the simulation outcome with decreasing W is explicitly demonstrated. Furthermore, the results are compared to a boundary-integral formulation of the corresponding free-boundary problem. Excellent agreement is found, except in the immediate vicinity of bifurcation points, a very sensitive situation where noticeable differences arise. These differences reveal that, in contrast to the standard assumptions of the free-boundary problem, out of equilibrium the diffuse trijunction region of the phase-field model can (i) slightly deviate from Young's law for the contact angles, and (ii) advance in a direction that forms a finite angle with the solid-solid interface at each instant. While the deviation (i) extrapolates to zero in the limit of vanishing interface thickness, the small angle in (ii) remains roughly constant, which indicates that it might be a genuine physical effect, present even for an atomic-scale interface thickness.

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Section: Free-boundary Problemmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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Quantitative phase-field modeling of two-phase growth

2005

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“…Within the operation limits of quasi-planar nearisothermal interface propagation, the pattern selection that defines the regular eutectic growth morphologies is fairly well described by the Jackson-Hunt model, [2,3] and more recent extensions to this, e.g., by phase field simulations and experiments with transparent analogues, for growth behavior beyond the basic state interface stability limits. [4][5][6] The growth mechanisms of irregular eutectics are inherently more complex. Generally, the faceted phase has restricted branching ability, and consequently, progression in three dimensions is considerably more cumbersome than for a nonfaceted component.…”

Section: Introductionmentioning

confidence: 99%

“…[11,13] However, there are still unsettled issues concerning how these chemical modifiers actually work in combination with other minor constituents to affect the relevant nucleation and growth mechanisms. [10][11][12][13][14][15][16] The development of theory and models to describe pattern selection in regular eutectics [4][5][6] has heavily relied on in-situ experimental observations with transparent alloys, [5,[17][18][19] which was decisive for identifying and characterizing dynamic instabilities that limit the range of stable growth. Fischer and Kurz [1] also found use of transparent alloys, succinonitrile-borneol and camphor-naphthalene, as model systems for nonfaceted/ faceted growth in their first attempts to adapt the Jackson-Hunt model to irregular eutectics.…”

Section: Introductionmentioning

confidence: 99%

X-Ray Videomicroscopy Studies of Eutectic Al-Si Solidification in Al-Si-Cu

Mathiesen

Arnberg

et al. 2010

Metall Mater Trans A

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Al-Si eutectic growth has been studied in-situ for the first time using X-ray video microscopy during directional solidification (DS) in unmodified and Sr-modified Al-Si-Cu alloys. In the unmodified alloys, Si is found to grow predominantly with needle-like tip morphologies, leading a highly irregular progressing eutectic interface with subsequent nucleation and growth of Al from the Si surfaces. In the Sr-modified alloys, the eutectic reaction is strongly suppressed, occurring with low nucleation frequency at undercoolings in the range 10 K to 18 K. In order to transport Cu rejected at the eutectic front back into the melt, the modified eutectic colonies attain meso-scale interface perturbations that eventually evolve into equiaxed compositestructure cells. The eutectic front also attains short-range microscale interface perturbations consistent with the characteristics of a fibrous Si growth. Evidence was found in support of Si nucleation occurring on potent particles suspended in the melt. Yet, both with Sr-modified and unmodified alloys, Si precipitation alone was not sufficient to facilitate the eutectic reaction, which apparently required additional undercooling for Al to form at the Si-particle interfaces.

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