On the effect of natural convection on solute segregation in the horizontal Bridgman configuration: Convergence of a theoretical model with numerical and experimental data

Kaddeche, Slim; Garandet, J.P.; Henry, Daniel; Hadid, H. Ben; Mojtabi, Abdelkader

doi:10.1016/j.jcrysgro.2014.10.009

Cited by 12 publications

(7 citation statements)

References 18 publications

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“…(10)), can provide useful insights regarding local variations for the solute boundary layer. This result confirms that the wall-shear stress at the solid/liquid interface is a very good indicator of the convective transport, not only for averaged values as it was shown by precedent studies [1,13] but also for local variations of the convective transport. This support the fact that the analytical model could be an efficient way to estimate the variations of the interface composition Δ along the solid/liquid front when the convection is not uniform and leads to lateral segregations.…”

Section: Scaling Analysissupporting

confidence: 86%

See 1 more Smart Citation

Solute segregation in directional solidification: Scaling analysis of the solute boundary layer coupled with transient hydrodynamic simulations

Chatelain

Albaric

Pelletier

et al. 2015

Journal of Crystal Growth

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a b s t r a c tThe objective of the present paper is to study the ability of an order of magnitude analysis [1] to give a realistic picture of segregation patterns in vertical Bridgman configurations, on the basis of hydrodynamic simulations. The scaling analysis leads to an analytical formulation of the solute boundary layer, involving the wall-shear stress at the solid/liquid interface. In order to test this analytical model, transient simulations of solute segregation in a 2D lid driven cavity configuration have been performed. The developed analytical model, which involves a quasi-steady approximation, is in good agreement with the numerical time-dependent results. The key results of this work are the correlation of segregation patterns in the solid with flow patterns in the liquid and the ability of the analytical model to describe lateral segregations and to capture unsteadiness in the limit of slow variations associated with Bridgman configurations.

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Section: Scaling Analysissupporting

confidence: 86%

“…More recently, Kaddeche et al [13] compared this model with numerical and experimental results of solute segregation in the horizontal Bridgman configuration. Their aim was to test the model in a configuration with a reliable data base of numerical and experimental results.…”

Section: State Of the Artmentioning

confidence: 99%

Solute segregation in directional solidification: Scaling analysis of the solute boundary layer coupled with transient hydrodynamic simulations

Chatelain

Albaric

Pelletier

et al. 2015

Journal of Crystal Growth

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“…In their study, a steady-state 2D lid driven cavity configuration is used as a reference case for segregation under various convective regimes. Then, Kaddeche et al [18] tested this model on an horizontal Bridgman configuration and compared it with experimental and numerical results. Both studies highlight the ability of the model to predict the mean segregation regime from an averaged value of the wall shear-stress obtained from a hydrodynamic simulation of the melt convection flow.…”

Section: Introductionmentioning

confidence: 99%

Towards wall functions for the prediction of solute segregation in plane front directional solidification

Chatelain

Rhouzlane

Botton

et al. 2017

Journal of Crystal Growth

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The present paper focuses on solute segregation occurring in directional solidification processes with sharp solid/liquid interface, like silicon crystal growth. A major difficulty for the simulation of such processes is their inherently multi-scale nature: the impurity segregation problem is controlled at the solute boundary layer scale (micrometers) while the thermal problem is ruled at the crucible scale (meters). The thickness of the solute boundary layer is controlled by the convection regime and requires a specific refinement of the mesh of numerical models. In order to improve numerical simulations, wall functions describing solute boundary layers for convecto-diffusive regimes are derived from a scaling analysis. The aim of these wall functions is to obtain segregation profiles from purely thermo-hydrodynamic simulations, which do not require solute boundary layer refinement at the solid/liquid interface. Regarding industrial applications, various stirring techniques can be used to enhance segregation, leading to fully turbulent flows in the melt. In this context, the scaling analysis is further improved by taking into account the turbulent solute transport. The solute boundary layers predicted by the analytical model are compared to those obtained by transient segregation simulations in a canonical 2D lid driven cavity configuration for validation purposes. Convective regimes ranging from laminar to fully turbulent are considered. Growth rate and molecular diffusivity influences are also investigated. Then, a procedure to predict concentration fields in the solid phase from a hydrodynamic simulation of the solidification process is proposed. This procedure is based on the analytical wall functions and on solute mass conservation. It only uses wall shear-stress profiles at the solidification front as input data. The 2D analytical concentration fields are directly compared to the results of the complete simulation of segregation in the lid driven cavity configuration. Finally, an additional output from the analytical model is also presented. We put in light the correlation between different species convecto-diffusive behaviour; we use it to propose an estimation method for the segregation parameters of various chemical species knowing segregation parameters of one specific species.

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“…Convection usually dominates dopant transport because of the low values of the diffusion coefficients of the dopant. Effects of forced and natural convection on the solute segregation during crystal growth for different growth configurations have been studied . For example, Burton, Prim and Slichter studied the solute segregation for a Czochralski configuration and obtained an analytical solution of the solute boundary thickness.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Burton, Prim and Slichter studied the solute segregation for a Czochralski configuration and obtained an analytical solution of the solute boundary thickness. Kaddeche et al . studied the effect of natural convection on solute segregation for a horizontal Bridgman configuration.…”

Section: Introductionmentioning

confidence: 99%

Transient Simulation of Dopant Segregation at Facets During Growth of Nd:YAG Crystal

2017

Crystal Research and Technology

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Numerical simulation of faceting and dopant segregation for vertical Bridgman growth of Nd:YAG is presented. The numerical scheme for the interface tracking considers the coupling between kinetic model and thermal transport. Dopant distributes inhomogeneously at the radial direction of the crystal/melt interface and piles up in front of the interface near the crucible. The dopant concentration of faceted portions of the crystal/melt interface is higher than that of unfaceted surface. Effect of natural convection on dopant segregation at facets is studied. The dopant boundary layer thickness decreases with the enhancement of the natural convection. The scaling analysis of the dopant boundary layer thickness for facet surface is obtained. Conflict of InterestThe author has declared no conflict of interest.

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On the effect of natural convection on solute segregation in the horizontal Bridgman configuration: Convergence of a theoretical model with numerical and experimental data

Cited by 12 publications

References 18 publications

Solute segregation in directional solidification: Scaling analysis of the solute boundary layer coupled with transient hydrodynamic simulations

Solute segregation in directional solidification: Scaling analysis of the solute boundary layer coupled with transient hydrodynamic simulations

Towards wall functions for the prediction of solute segregation in plane front directional solidification

Transient Simulation of Dopant Segregation at Facets During Growth of Nd:YAG Crystal

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