Numerical modeling of radiative heat transfer in Bridgman solidification of semi-transparent BaF2 crystals

Stelian, Carmen

doi:10.1016/j.jcrysgro.2007.05.026

Cited by 9 publications

(10 citation statements)

References 13 publications

(29 reference statements)

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“…The transparent SLI may be observed for pure materials which are semi-transparent in both phases e.g. : in several papers yttrium aluminum garnet (YAG) and barium fluoride (BaF 2 ) were assumed to be semi-transparent in both phases [28,29]. The semi-transparent SLI is a new idea introduced in this paper, which may account for rejection of dopant at SLI during solidification process of doped and fully semi-transparent materials.…”

Section: Outline Of Combined Fta and Ibt Approachmentioning

confidence: 96%

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

Seredyński

Łapka

Banaszek

et al. 2015

International Journal of Heat and Mass Transfer

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Section: Outline Of Combined Fta and Ibt Approachmentioning

confidence: 96%

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

Seredyński

Łapka

Banaszek

et al. 2015

International Journal of Heat and Mass Transfer

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“…Internal radiation in numerical investigations of heat transfer in the DS-like systems is typically ignored [16,17], or approximated as an artificially enhanced thermal conductivity [18,19]. 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].…”

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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“…This code has been already used for the transient calculation of the solute distribution in Bridgman growth of the semiconductor alloys 3,4 and the modeling of the internal radiative heat transfer during the solidification of semitransparent BaF 2 crystals. 5 CaF 2 belongs to semitransparent materials, which participate in the radiative heat transfer by absorbing and emitting the radiation. The effective thermal conductivity of such materials increases because of the internal radiative heat transport and influences the solid-liquid interface curvature.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Transport Phenomena during Bridgman Growth of Calcium Fluoride Doped Crystals

Stelian

Susan-Resiga

Lighezan

et al. 2008

Crystal Growth & Design

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The chemical homogeneity of CaF 2 :Pb crystals, grown by using the vertical Bridgman method, is numerically investigated. The FIDAP commercial code is used to study the heat transfer, convection, and solute transport phenomena during the solidification process. The homogeneity of these doped crystals depends on the solid-liquid interface curvature and the flow intensity. The accurate computation of the thermal field and interface shape for these semitransparent materials requires the modeling of the internal radiative heat transfer. The numerical modeling of the flow field and solute distribution shows a low intensity of the convection and a quasi-diffusive transport regime in the melt. The numerically computed longitudinal solutal profile in the crystal, in agreement with the experimental measurements, shows some significant oscillations of the Pb concentration. For the first time, a correlation between these oscillations and a quasi-diffusive transport regime has been established to explain this phenomenon, which also has been observed in other Bridgman crystal growth experiments. Finally, an optimization of the growth rate to avoid these oscillations and to improve the chemical homogeneity of crystals has been proposed.

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Numerical modeling of radiative heat transfer in Bridgman solidification of semi-transparent BaF2 crystals

Cited by 9 publications

References 13 publications

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

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

Analysis of Transport Phenomena during Bridgman Growth of Calcium Fluoride Doped Crystals

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