Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling

Virozub, A.; Rasin, Igal G.; Brandon, Simon

doi:10.1016/j.jcrysgro.2008.09.004

Cited by 47 publications

(27 citation statements)

References 18 publications

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“…For Ge, α = 14.3° [6] and θ = 172° [17]. However, the results shown here for this case are qualitatively the same for any combination of material and crucible for which the condition θ + α > 180°is met.…”

Section: Integration Of Eq (8) Results Insupporting

confidence: 60%

“…They found that α is a material property of the system and can be considered a constant independent of growth rate. Virozub et al [6] revisited the assumption of a constant growth angle and compared a heat transfer and solidification model to directionally solidified drops. The model, which assumed a constant growth angle, was in excellent agreement with experimental results for both silicon and germanium.…”

Section: Introductionmentioning

confidence: 99%

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Shape evolution of detached Bridgman crystals grown in microgravity

Volz

Mazuruk

2014

Crystal Research and Technology

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Detached (or dewetted) Bridgman crystal growth defines that process in which a gap exists between a growing crystal and the crucible wall. In microgravity, the parameters that influence the existence of a stable gap are the growth angle of the solidifying crystal, the contact angle between the melt and the crucible wall, and the pressure difference across the meniscus. During actual crystal growth, the initial crystal radius will not have the precise value required for stable detached growth. Beginning with a crystal diameter that differs from stable conditions, numerical calculations are used to analyze the transient crystal growth process. Depending on the initial conditions and growth parameters, the crystal shape will either evolve towards attachment at the crucible wall, towards a stable gap width, or inwards towards eventual collapse of the meniscus. Dynamic growth stability is observed only when the sum of the growth and contact angles exceeds 180°.

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Section: Integration Of Eq (8) Results Insupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Shape evolution of detached Bridgman crystals grown in microgravity

Volz

Mazuruk

2014

Crystal Research and Technology

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“…The solidification front propagates with the normal velocity V n , V n =q f /(ρ s L h ) while the liquid-gas front is advected by the velocity interpolated from the fixed grid velocities. At the triple point, we correct the position of this point by applying a constant growth angle (Virozub et al, 2008). We do this by introducing an extended element at the end of each interface.…”

Section: Mathematical Formulation and Numerical Methodsmentioning

confidence: 99%

“…A similar method with fixed contact angles has been used by Ajaev and Davis (2004) to consider the effect of the density difference and contact angles on the shape of the solidified drop under zero gravity. Virozub et al (2008) included the gravity and surface tension effects to the problem. The Young-Laplace equation in conjunction with a constant growth angle was numerically solved to find the position of the liquid-gas front.…”

Section: Introductionmentioning

confidence: 99%

A Front-Tracking Method for Three-Phase Computations of Solidification with Volume Change

Tryggvason

Homma

et al. 2013

J. Chem. Eng. Japan

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We use a front-tracking method to simulate solidi cation with volume change of a droplet on a xed cooling plate. The problem includes temporal evolution of three interfaces, i.e., solid-liquid, solid-air, and liquid-air, that are explicitly tracked under the assumption of axisymmetry. The solid-liquid interface is propagated with a normal velocity that is calculated from the normal temperature gradient across the front and the latent heat. The liquid-air front is advected by the velocity interpolated from nearest bulk uid ow velocities. Accordingly, the evolution of the solid-air front is simply the temporal imprint of the triple point at which simple and straightforward conditions are imposed. The governing Navier-Stokes equations are solved for the whole domain, setting the velocities in the solid phase to zero and with the non-slip condition on the solid-liquid interface. Computational results are compared with exact solutions for twodimensional Stefan problems and with corresponding experimental results, and show good agreement.

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“…A few numerical simulations can be found in Schultz et al [15] for water, Virozub et al [16] for water and some semiconductor materials, and Chaudhary and Li [17] for water. More comprehensive works can be found in our previous studies [18,19] in which various parameters have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Direct Numerical Study of a Molten Metal Drop Solidifying on a Cold Plate with Different Wettability

Nguyen

Khanh

2018

Metals

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This paper presents a direct numerical simulation of solidification of a molten metal drop on a cold plate with various wettability by an axisymmetric front-tracking method. Because of the plate kept at a temperature below the fusion value of the melt, a thin solid layer forms at the plate and evolves upwards. The numerical results show that the solidifying front is almost flat except near the triple point with a high solidification rate at the beginning and final stages of solidification. Two solid-to-liquid density ratios ρ sl = 0.9 (volume change) and 1.0 (no change in volume), with two growth angles φ 0 = 0 • and 12 • are considered. The presence of volume change and a non-zero growth angle results in a solidified drop with a conical shape at the top. The focusing issue is the effects of the wettability of the plate in terms of the contact angle φ 0 . Increasing the contact angle in the range of 45 • to 120 • increases time for completing solidification, i.e., solidification time. However, it has a minor effect on the conical angle at the top of the solidified drop and the difference between the initial liquid and final solidified heights of the drop. The effects of the density ratio and growth angle are also presented.

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Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling

Cited by 47 publications

References 18 publications

Shape evolution of detached Bridgman crystals grown in microgravity

Shape evolution of detached Bridgman crystals grown in microgravity

A Front-Tracking Method for Three-Phase Computations of Solidification with Volume Change

Direct Numerical Study of a Molten Metal Drop Solidifying on a Cold Plate with Different Wettability

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