Onset of sidebranching in directional solidification

Georgelin, Marc; Pocheau, Alain

doi:10.1103/physreve.57.3189

Cited by 63 publications

(86 citation statements)

References 44 publications

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“…, where the power exponent agrees well with that in previous investigations [6][7][8]11]. Figure 2 also shows that the location of first sidebranch approaches to the dendritic tip as the pulling velocity increases.…”

Section: The Model and Resultssupporting

confidence: 89%

“…Therefore, the asymptotic analysis on the initial sidebranch spacing may be invalid for large primary spacing in the trapped wave instability sidebranching mechanism. in directional solidification [6][7][8]11]. Figure 2 presents the steady dendritic morphologies with different pulling velocities but the same primary spacing.…”

Section: The Model and Resultsmentioning

confidence: 99%

“…The trapped wave instability mechanism [10], based on the asymptotically analysis, demonstrated that the initial sidebranch spacing is related to the eigen-frequency of neutral mode. Experiments and numerical simulations confirmed that the initial sidebranch spacing is almost independent of the thermal gradient but has a scaling law relationship with pulling velocity like 2 V α λ − ∝ [6][7][8]11]. Although previous investigations provided plenty of information about initial sidebranch spacing, two important factors were usually overlooked: interdendritic interaction and surface tension anisotropy.…”

Section: Introductionmentioning

confidence: 83%

“…As a typical self-organised dissipative system, dendritic growth is one of the most investigated phenomena [3]. In free dendritic growth, the selection of tip radius and tip velocity has been discussed for almost half century [6,7]. However, in directional solidification, things become more complicated because of the interdendritic interaction.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Phase field investigation on the selection of initial sidebranch spacing in directional solidification

Wang

et al. 2012

IOP Conf. Ser.: Mater. Sci. Eng.

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Section: The Model and Resultssupporting

confidence: 89%

Section: The Model and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phase field investigation on the selection of initial sidebranch spacing in directional solidification

Wang

et al. 2012

IOP Conf. Ser.: Mater. Sci. Eng.

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“…(68) and (69) for parameters corresponding to the impure succinonitrile (SCN) alloy of Ref. [27]. The alloy parameters together with the values of the pulling speed and the temperature gradient are listed in Table I.…”

Section: Numerical Testsmentioning

confidence: 99%

Quantitative phase-field model of alloy solidification

et al. 2004

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We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [ R. F. Almgren, SIAM J. Appl. Math 59, 2086 (1999)], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)].The performance of the model is demonstrated by calculating accurately for the first time within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions. 2

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Phase field investigation on sidebranching dynamics in transient growth

Zheng

Dong

Wei

et al. 2014

Crystal Research and Technology

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A computationally efficient quantitative phase field formulation is used to investigate the sidebranching dynamics under different transient conditions in directional solidification for realistic parameters of a dilute alloy. The sidebranch growths where the pulling speed or temperature gradient increases with constant increasing rates are simulated and discussed by using the noise amplification theory. The results show that in transient growth, the tip shape can rapidly adjust with the instantaneous conditions, and the tip velocity changes continuously due to the change of tip undercooling. Therefore, under our given transient conditions, the sidebranch spacing or sidebranching frequency depends strongly on the transient conditions and transient history, which is different with that in steady‐state conditions where the sidebranching frequency is found to be independent of the temperature gradient and primary spacing, but varies as a power law of pulling speed.

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Onset of sidebranching in directional solidification

Cited by 63 publications

References 44 publications

Phase field investigation on the selection of initial sidebranch spacing in directional solidification

Phase field investigation on the selection of initial sidebranch spacing in directional solidification

Quantitative phase-field model of alloy solidification

Phase field investigation on sidebranching dynamics in transient growth

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