Dynamics of partially faceted melt/crystal interfaces I: computational approach and single step–source calculations

Weinstein, Oleg; Brandon, Simon

doi:10.1016/j.jcrysgro.2004.04.108

Cited by 41 publications

(85 citation statements)

References 20 publications

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“…[9][10][11] Weinstein simulated the evolution of the melt crystallization interface in a large melt growth system. 12 More recently, numerical simulations of the heat transfer, melt convection and capillary effects problems have been analysed during the HRG process. Rhodes 13 investigated the behavior of the meniscus connecting the crucible lip to the lower surface of the HRG crystal by solving two-dimensional Euler-Laplace capillary equation; however, they did not consider heat transfer effects.Thomas and Brown 14 performed a rigorous analysis of heat transfer in the HRG system by employing the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Simulating the horizontal growth process of silicon ribbon

et al. 2018

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In this paper, we present a solidification growth model that primarily describes the principal components of horizontal ribbon growth process, but also discusses the interaction between fluid flow and heat transfer, crystallization dynamics, and the effects of oxygen impurity distribution in melts, particularly with respect to the morphology of the interface. The effects of the jet cooling rate, pulling speed, and transfer coefficient on solute transport were studied. The results showed that a higher jet velocity produces a sharper temperature gradient at the interface and a stronger Marangoni effect, facilitates solute transport in the silicon melt, and promotes higher oxygen concentration in crystal. The stronger Marangoni convection causes more rapid oxygen transfer in the silicon melt and a higher oxygen concentration. Solidification front increases the downward flow velocity of the eddy current as the pulling speed is increased; this leads to a decrease in solute concentration at the interface. An increase in the downward flow of the vortex confluence facilitates the reduction of solute concentration in the crystal. An increase in the upward flow of the vortex confluence will increase the concentration in the crystal. The oxygen concentration is concentrated at the top and bottom of the silicon ribbon.

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Section: Introductionmentioning

confidence: 99%

Simulating the horizontal growth process of silicon ribbon

et al. 2018

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“…Other studies involve microgravity [JM135], crystal interface [JM136], Bridgman growth [JM137], Czochralski growth [JM67,, FZ growth [JM143], floating crystal growth [JM144], traveling solvent method (TSM) [JM145], modified Markov method [JM146] and LEC growth [JM147]. Heat transfer in scraped eutectic crystallizers was also studied [JM148].…”

Section: Crystal Growthmentioning

confidence: 99%

Heat transfer—A review of 2004 literature

Goldstein

Ibele

Patankar

et al. 2010

International Journal of Heat and Mass Transfer

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“…Another numerical scheme, the kinetic model approach, is similar to the one proposed by Weinstein and Brandon [11][12][13]. It uses Eq.…”

Section: Mathematical Model and Numerical Solutionmentioning

confidence: 99%

“…The first attempt to simulate the faceting coupled with the heat transfer in oxide growth was made in Brandon's group [9,10] using a two-dimensional (2D) finite element approach. Recently, Weinstein and Brandon [11,12] also developed algorithms for faceting, taking into account the coupling of different kinetic mechanisms and extended them to 3D simulation as well [13]. Nevertheless, melt flow and segregation were not considered in their models because the faceting, except {1 1 1}, breaks axisymmetry and a 3D simulation is required.…”

Section: Introductionmentioning

confidence: 99%

“…Ma et al [15] also used a similar approach for the 2D growth of YAG crystals; however, dynamic formation of the facets was further considered. On the other hand, Weinstein and Brandon [11,12] used a kinetic model approach that moves the interface shape according to the local kinetic models related to crystallographic orientation and undercooling. Different mechanisms for facet growth could be considered.…”

Section: Introductionmentioning

confidence: 99%

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