Internal radiative transport in the vertical Bridgman growth of semitransparent crystals

Brandon, Simon; Derby, Jeffrey J.

doi:10.1016/0022-0248(91)90285-d

Cited by 78 publications

(20 citation statements)

References 38 publications

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“…The model allowed the authors to predict deep interface deflections for Y 3 Al 5 O 12 (YAG) and Gd 3 Ga 5 O 12 (GGG) crystals during Czochralski growth but the optical properties of the crystal have not been considered. An even more rigorous model for inner radiation in semi-transparent crystals grown by the Bridgman method was proposed by S. Brandon et al [7,8]. In the model the crystal is considered as grey, absorbing and emitting medium (so-called grey approximation).…”

Section: Introductionmentioning

confidence: 99%

Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Galazka

Schwabe

Wilke

2003

Cryst. Res. Technol.

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Heat and mass transfer taking place during growth of Y 3 Al 5 O 12 (YAG) crystals by the Czochralski method, including inner radiation, is analyzed numerically using a Finite Element Method. For inner radiative heat transfer through the crystal the band approximation model and real transmission characteristics, measured from obtained crystals, are used. The results reveal significant differences in temperature and melt flow for YAG crystals doped with different dopands influencing the optical properties of the crystals. When radiative heat transport through the crystal is taken into account the melt-crystal interface shape is different from that when the radiative transport is not included. Its deflection remains constant over a wide range of crystal rotation rates until it finally rapidly changes in a narrow range of rotation rates.

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Section: Introductionmentioning

confidence: 99%

Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Galazka

Schwabe

Wilke

2003

Cryst. Res. Technol.

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“…Lan et al [20] used both the P1 and the Rosseland approximations to model internal radiation in Bridgman growth of YAG crystals. A detailed analysis of studies taking into account radiative heat transfer in modelling crystal growth was carried out by Brandon and Derby [21] and recently by Mü ller and Friedrich [22]. Jing et al [23] performed a three-dimensional numerical simulation of spoke pattern in a LiNbO 3 oxide melt under a magnetic field but they neglected the internal radiative heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid

Borjini

Aïssia

Halouani³

et al. 2006

International Journal of Heat and Mass Transfer

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“…In some other studies, internal radiation was dealt with by P 1 -approximation [20][21][22] or treated as a surface phenomenon [23,24] assuming that the oxide crystal is totally transparent and internal radiation only acts between surfaces. Some researchers took into account internal radiation rigorously in their simulations [25][26][27][28][29][30][31]. For instance, Brandon and Derby [25,26] performed the first modeling of internal radiation heat transfer in oxide crystal by VB process using a rigorous finite element method and found that the absorption coefficient significantly affects the position and curvature of the melt-crystal interface.…”

Section: Introductionmentioning

confidence: 99%

“…Some researchers took into account internal radiation rigorously in their simulations [25][26][27][28][29][30][31]. For instance, Brandon and Derby [25,26] performed the first modeling of internal radiation heat transfer in oxide crystal by VB process using a rigorous finite element method and found that the absorption coefficient significantly affects the position and curvature of the melt-crystal interface. Xiong et al [27] accounted for internal radiation by the discrete exchange factor method in their numerical investigation of a modified HEM crystal growth process.…”

Section: Introductionmentioning

confidence: 99%

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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Internal radiative transport in the vertical Bridgman growth of semitransparent crystals

Cited by 78 publications

References 38 publications

Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid

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

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