The Role of Marangoni Convection in Crystal Growth

Tsukada, Takao

doi:10.1016/b978-0-444-63303-3.00022-5

Cited by 5 publications

(5 citation statements)

References 92 publications

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“…Fig. 2 suggests little change of the maximum values of dimensionless temperature T* max at the monitoring point (r=R, θ=0, z=0) in the liquid bridge when the grid amount is larger than 2×10 5 . Considering accuracy and efficiency of calculation, the grid of 40 r ×80 θ ×80 z is finally selected for numerical calculation with a time step of 10 -3 seconds.…”

Section: Methodsmentioning

confidence: 96%

“…Floating zone method is a promising technique to growth single crystals with the advantage of containerless environment, which is widely used for the growth of high-precision silicon, super alloys and other semiconductor material [1][2][3]. Marangoni convection driven by surface tension gradient has a dramatic effect on distribution of impurity concentration in melt, due to existence of free surface in floating zone growth system [4,5]. Experimental [6][7][8][9] and theoretical [10][11][12][13] researches including linear stability analyses and nonlinear direct numerical simulations have been carried out in depth on stability of pure thermocapillary convection.…”

Section: Introductionmentioning

confidence: 99%

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Effect of aspect ratio on coupled solute-thermocapillary convection instability in half-zone liquid bridge

et al. 2022

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Floating zone method is an important technology for growth of high-integrity and high-uniformity single crystal materials due to its free of crucible contamination. However, capillary convection in the melt is a great challenge to floating zone crystal growth. In this paper, numerical simulations are performed to investigate the coupled solute-thermocapillary convection in SixGe1-x system of the half-zone liquid bridge. And the impact of aspect ratio (As) is also investigated on stability of capillary convection. For As=0.5, the results show that pure solute capillary convection is very weak, which presents 2-D axisymmetric structure. The temperature field is mainly determined by thermal diffusion, while the concentration field is dominated by convection and solute diffusion together. Coupled solute-thermocapillary convection exhibits 3-D periodic and rotating oscillatory flow with the azimuthal wavenumber m=4, while the pure thermocapillary convection presents a 3-D steady non-axisymmetric flow while solute capillary convection is absent. This means that instability of convection will increase when two kinds of capillary convection are coupled. When the height of the liquid bridge is changed from 5 mm to 10 mm with a constant radius of 10 mm, azimuthal wave number (m) of coupled capillary convection shows a strong dependence on aspect ratio. The relationship between the azimuthal wave number and aspect ratio can be written as m?As= 2 or m?As=2.2. Further results indicated that when velocity of the monitoring point is large, corresponding concentration is also high at that moment, but the phases of concentration and velocity are not completely synchronized.

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Section: Methodsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Effect of aspect ratio on coupled solute-thermocapillary convection instability in half-zone liquid bridge

et al. 2022

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“…The quartz crucible does not shield the melt from the magnetic field as much as the electrically-conducting graphite crucible, so the strengthening of the vortex near the interface is even greater, convecting more heat toward the interface and driving it further downward while making it more convex. 3 This is an example of a "good" flow driven by an applied field that provides an improved (convex) interface shape 4 .…”

Section: Modifying Interface Shape In Melt Growth Via a Traveling Magmentioning

confidence: 99%

“…The literature on flows in crystal growth is vast, and no attempt will be made to present a comprehensive summary of it. Some recent reviews on this topic include those of Derby et al [1], Kakimoto and Gao [2], Tsukada [3], Vizman [4], and Capper and Zharikov [5]. In this chapter, we will first focus on some essentials on flows and their effects, followed by a series of examples of interesting and important flows in crystal growth systems.…”

Section: Introductionmentioning

confidence: 99%

“…While not discussed here, Marangoni flows can also be quite important in systems with a melt-gas free surface. These flows arise from gradients in surface tension across the free surface and can be very strong; see, e.g.,[3,19,20].2 There is a dimensionless geometric ratio, L/ΔL, that arises from the approximation of ∇ in eq. (8); however, we have ignored it in eq.…”

mentioning

confidence: 99%

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Fluid dynamics in crystal growth: The good, the bad, and the ugly

Derby

2016

Progress in Crystal Growth and Characterization of Materials

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Fluid dynamics are important in processes that grow large crystals from a liquid phase. This chapter presents a primer on fluid mechanics and convection, followed by a discussion of the physics and scaling of flows in such processes. Specific examples of fluid flows in crystal growth systems are presented and classified according to their impact on outcomes, good or bad. Turbulence in crystal growth is discussed within the limited extent of our understanding, which is incomplete, or ugly.

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