A volume radiation heat transfer model for Czochralski crystal growth processes

Nunes, Edmundo M.; Naraghi, Mohammad H.; Zhang, Hui; Prasad, V.

doi:10.1016/s0022-0248(02)00826-6

Cited by 30 publications

(19 citation statements)

References 26 publications

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“…For CZ crystal growth, several radiation models are available [20] to relate crystal temperature to ramp-down power. For simplification, the effective convection heat transfer coefficient is used to take into account of convection, radiation effects.…”

Section: Cooling Of Crystal From Surfacementioning

confidence: 99%

Optimization of the cooling profile to achieve crack-free Yb:S-FAP crystals

Fang

Qiu

Zheng

et al. 2008

Journal of Crystal Growth

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To suppress cracking during cool down, a numerical simulation of the growth system was used to understand the correlation between the furnace power during cool down and the radial temperature differences within the crystal. The critical radial temperature difference, above which the crystal cracks, has been determined by benchmarking the simulation results against experimental observations. Based on this comparison, an optimal three-stage ramp-down profile was implemented and produced high quality, crack-free Yb:S-FAP crystals.

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Section: Cooling Of Crystal From Surfacementioning

confidence: 99%

Optimization of the cooling profile to achieve crack-free Yb:S-FAP crystals

Fang

Qiu

Zheng

et al. 2008

Journal of Crystal Growth

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“…When the crystal is rotated, all three components of melt velocity are non-zero. As suggested by Prasad et al [7] as well as Nunes et al [6], it is convenient to work with the angular momentum equation rather than the angular velocity. Hence, 2 momentum and 1 angular momentum equation have been solved in the present work.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Nunes et al [6] combined the multi-zone adaptive grid generation and curvilinear finite volume scheme of Prasad et al [7] to a spectral thermal radiation model to predict the temperature distribution in a Czochralski domain for growing a YAG crystal. The radiative transfer model was based on the discrete exchange factor method.…”

Section: Introductionmentioning

confidence: 99%

Role of internal radiation during Czochralski growth of YAG and Nd:YAG crystals

Banerjee

Muralidhar

2006

International Journal of Thermal Sciences

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“…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%

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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A volume radiation heat transfer model for Czochralski crystal growth processes

Cited by 30 publications

References 26 publications

Optimization of the cooling profile to achieve crack-free Yb:S-FAP crystals

Optimization of the cooling profile to achieve crack-free Yb:S-FAP crystals

Role of internal radiation during Czochralski growth of YAG and Nd:YAG crystals

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

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