Equilibrium and growth facetted shapes in isothermal solidification of silicon: 3D phase-field simulations

Boukellal, Ahmed Kaci; Elvalli, Ahmed Kerim Sidi

doi:10.1016/j.jcrysgro.2019.06.005

Cited by 18 publications

(27 citation statements)

References 44 publications

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“…Since the interface width W 0 = ξd 0 is adjusted by varying the numerical parameter ξ, this fixes the relaxation time to τ 0 = (47 √ 2/120)(d 2 0 /D)ξ 3 . In the present work, as in [4,19,22,23], the equation for the time evolution of the phase-field is written in terms of the anisotropy vector A. This vector appears when, in the original phase-field equation for solidification of a pure melt [21], one rewrites the following sum of three terms as a vector divergence, η=x,y,z…”

Section: Phase-field Equationsmentioning

confidence: 99%

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Tip dynamics for equiaxed Al-Cu dendrites in thin samples : Phase-field study of thermodynamic effects

Boukellal

Rouby

2021

Computational Materials Science

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Section: Phase-field Equationsmentioning

confidence: 99%

“…It is worth mentioning that this formulation can be easily implemented for most anisotropy functions of the surface energy, a s (see Appendix A). For instance, the case of a surface energy anisotropy that leads to facetted growth shapes was recently considered by using this anisotropy vector formulation [23].…”

Section: Phase-field Equationsmentioning

confidence: 99%

Tip dynamics for equiaxed Al-Cu dendrites in thin samples : Phase-field study of thermodynamic effects

Boukellal

Rouby

2021

Computational Materials Science

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“…In this case, facets only appear for a discrete set of orientations, namely the eight 111 directions in the present case, and these facets are separated by large rough portions of the interface. As shown in [23], it is necessary that both anisotropy functions associated with the surface energy γ and the kinetic attachment coefficient β present singularities in the 111 directions, in order to account for the large facets observed in [10,17]. This is the point of view that we will adopt here, based on the aforementioned experimental, numerical, and analytical results, as well as on our previous phase-field studies of equiaxed faceted solidification in two [24] and in three dimensions [23].…”

Section: Introductionmentioning

confidence: 91%

Quantitativeness of phase-field simulations for directional solidification of faceted silicon monograins in thin samples

2022

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We report the results of a two-dimensional reference model for the formation of facets on the left and the right side of a silicon monograin that is solidified by pulling a thin sample in a constant temperature gradient. Anisotropy functions of both the surface energy and the kinetic attachment coefficient are adapted from a recent model for free growth of silicon micrometer size grains [Boukellal et al., J. Cryst. Growth 522, 37 (2019)]. More precise estimates of the physical parameters entering these functions are obtained by reanalyzing available experimental results. We show that the reference model leads to a differential equation for the shape of the solid-liquid interface. The numerical solutions of this equation give a reference law Λ(V f ) relating the facet length Λ to the facet normal velocity V f . In parallel, phase-field simulations of the reference model are performed for two growth orientations, [001] and [011]. Facet lengths Λ obtained from simulations at different facet velocities are first extrapolated to the limit of vanishing interface width. This extrapolation is made possible by constructing a master curve common to the whole range of V f values considered. The extrapolated Λ values are then compared with the ones predicted by the Λ(V f ) reference law. Both sets give comparable values, with an accuracy of a few percent, which confirms that the phase-field model can give quantitative results for faceted solidification of silicon.

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“…This model was extended later to the case of a dilute binary alloy [26,27]. Since, many examples of 3D simulations of alloy solidification that give quantitative agreement with the experiments were reported [5][6][7][8]15,28,29], following K. Glasner, we replace the usual phase-field ϕ ∈ [−1, 1] by the preconditioned phase-field…”

Section: Phase-fieldmentioning

confidence: 99%

Oscillatory-nonoscillatory transitions for inclined cellular patterns in three-dimensional directional solidification

et al. 2020

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The oscillatory behavior of cellular patterns produced by directional solidification of a transparent alloy under microgravity conditions was recently observed to depend on the misorientation of the main crystal axis with respect to the direction of the imposed thermal gradient [Pereda et al., Phys. Rev. E 95, 012803 (2017)]. To characterize the oscillatory-nonoscillatory transition resulting from the variations of the crystal misorientation, new experiments performed in DECLIC-DSI onboard the International Space Station and phase-field simulations are analyzed and combined in the present study. Experimental results are extracted from movies showing regions that extend on both sides of a boundary between two grains with respective misorientations of roughly 3 and 7 degrees. A set of tools are developed to analyze the experimental data and the same analysis is reproduced for the numerical data. A number of points are addressed in the simulations, like the effects of the system dimensions. The oscillatory state is found to be favored by the increase of the geometrical degrees of freedom. In bulk samples, a good agreement is found between the experimental and the numerical oscillatory-nonoscillatory threshold given by the ratio of the drift time to the oscillation period at the transition. The existence and the origin of bursts of localized groups of oscillating cells within a globally nonoscillatory pattern are characterized. A qualitative description of the physical mechanism that governs the oscillatory-nonoscillatory transition is provided.

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Equilibrium and growth facetted shapes in isothermal solidification of silicon: 3D phase-field simulations

Cited by 18 publications

References 44 publications

Tip dynamics for equiaxed Al-Cu dendrites in thin samples : Phase-field study of thermodynamic effects

Tip dynamics for equiaxed Al-Cu dendrites in thin samples : Phase-field study of thermodynamic effects

Quantitativeness of phase-field simulations for directional solidification of faceted silicon monograins in thin samples

Oscillatory-nonoscillatory transitions for inclined cellular patterns in three-dimensional directional solidification

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