Role of internal radiation at the different growth stages of sapphire by Kyropoulos method

Fang, Haisheng; Jin, Ziliang; Zhang, M.J.; Zhang, Z.; Zhao, Cheng

doi:10.1016/j.ijheatmasstransfer.2013.08.074

Cited by 18 publications

(11 citation statements)

References 16 publications

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“…Temperature and flow field as well as interface shape are strongly influenced by internal radiation of crystal and melt according to the literatures about the growth of semitransparent oxide crystals. [ 17–19 ] Therefore, the internal radiation in semitransparent materials, which refer to the CaF 2 crystal and melt in this article, is also taken into account in current computation. The effects of the absorption coefficient of crystal and melt to the temperature and flow field were studied.…”

Section: Computational Modelmentioning

confidence: 99%

Numerical Simulation of Heat Transfer and Convection for CaF₂ Crystal Growth by Vertical Bridgman Growth Method

Jiang

Wang

et al. 2020

Crystal Research and Technology

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Herein, simulations of heat transfer and convection for CaF2 crystal growth are performed. Effects of internal radiation of the crystal and the melt are investigated, indicating that the temperature and flow field near the crystal–melt interface are the most affected. The temperature gradient and flow intensity near the interface have a significant change as the absorption coefficient of crystal and melt changes. Simulations at different growth stages for Nd:CaF2 crystal are also conducted to study the evolution of the temperature field and flow field. The interface is slightly convex to the melt during the entire constant‐diameter growth stage, which coincides with the actual crystal growth result. The flow intensity is extremely strong at the top and bottom of the melt, and three different vortexes exist during the entire growth process.

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Section: Computational Modelmentioning

confidence: 99%

Numerical Simulation of Heat Transfer and Convection for CaF₂ Crystal Growth by Vertical Bridgman Growth Method

Jiang

Wang

et al. 2020

Crystal Research and Technology

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“…T cry = T cru (15) where the subscripts cry and cru represent crystal and crucible, respectively. q rad is the radiative heat flux at the crystal side.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…For instance, Tsukada et al [3,7] pointed out that internal radiation decreases the temperature gradient in the oxide crystal in a Cz furnace. Fang et al [15] stated that internal radiation uniforms the temperature distribution and reduces the stress level in the sapphire crystal in a Ky furnace. That is to say, internal radiation does not cause local significant high temperature It is worth noting that the effect of internal radiation in the oxide crystal by HEM shows some differences from that by Cz and Ky processes.…”

Section: With and Without Internal Radiationmentioning

confidence: 99%

“…However, most of the numerical studies in the literature were devoted to Cz [3][4][5][6][7][8][9][10][11] and Kyropoulos (Ky) [11][12][13][14][15] processes, which are not referenced in detail here. Directional solidification (DS) techniques, such as heat exchanger method (HEM), gradient solidification method (GSM) and vertical Bridgman (VB) method, are also widely used to produce oxide single crystals.…”

Section: Introductionmentioning

confidence: 99%

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Role of Internal Radiation in Oxide Crystal Growth by Heat Exchanger Method

Liu

2017

Crystals

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Internal radiation was investigated using the finite volume method for the heat exchanger method (HEM) growth of oxide crystals. Special attention was devoted to the temperature and thermal stress distributions in the bottom region of the grown crystal at the end of the solidification process. The numerical results show that internal radiation strongly strengthens heat transport through the crystal. However, it causes isotherms to intensively concentrate in the crystal bottom region, leading to a significant increase in the temperature gradient and thermal stress in this region. Then, the effect of absorption coefficient on this phenomenon was numerically investigated. It was found that the radiation heat transfer rate at the bottom surface of the crystal monotonically decreases as the absorption coefficient is increased, while the conduction heat transfer rate first increases and then decreases as the absorption coefficient is increased, under the interaction between internal radiation and heat conduction. The variations of the maximum temperature gradient and thermal stress in the crystal bottom show the same tendency as the conduction heat transfer rate. This study indicates that the role of internal radiation on the heat transfer and thermal stress in oxide crystal by HEM process shows some differences from that by Czochralski and Kyropoulos processes.

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“…Kobayashi et al [6] found that the flow and temperature field are strongly affected by the internal radiative heat transfer through the melt. Also the internal radiation is especially important to predict the interface shape during the Kyropoulos crystal growth as demonstrated by Fang et al [9].…”

Section: Introductionmentioning

confidence: 99%

3D melt convection in sapphire crystal growth: Evaluation of physical properties

Timofeev¹,

Kalaev²,

Иванов

2015

International Journal of Heat and Mass Transfer

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Role of internal radiation at the different growth stages of sapphire by Kyropoulos method

Cited by 18 publications

References 16 publications

Numerical Simulation of Heat Transfer and Convection for CaF₂ Crystal Growth by Vertical Bridgman Growth Method

Numerical Simulation of Heat Transfer and Convection for CaF₂ Crystal Growth by Vertical Bridgman Growth Method

Role of Internal Radiation in Oxide Crystal Growth by Heat Exchanger Method

3D melt convection in sapphire crystal growth: Evaluation of physical properties

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Role of internal radiation at the different growth stages of sapphire by Kyropoulos method

Cited by 18 publications

References 16 publications

Numerical Simulation of Heat Transfer and Convection for CaF2 Crystal Growth by Vertical Bridgman Growth Method

Numerical Simulation of Heat Transfer and Convection for CaF2 Crystal Growth by Vertical Bridgman Growth Method

Role of Internal Radiation in Oxide Crystal Growth by Heat Exchanger Method

3D melt convection in sapphire crystal growth: Evaluation of physical properties

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Product

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Numerical Simulation of Heat Transfer and Convection for CaF₂ Crystal Growth by Vertical Bridgman Growth Method

Numerical Simulation of Heat Transfer and Convection for CaF₂ Crystal Growth by Vertical Bridgman Growth Method