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

Banerjee, Jyotirmay; Muralidhar, K.

doi:10.1016/j.ijthermalsci.2005.05.007

Cited by 14 publications

(6 citation statements)

References 22 publications

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“…For a beaker diameter of 100 mm and a cylinder diameter of 50 mm, the largest Grashof number Gr was 3.2 × 10 6 , the largest Reynolds number Re of the rotating cylinder being 3.25 × 10 3 . Radius of the crucible is used as the length scale for nondimensionalization (Banerjee and Muralidhar, 2005). The mixed convection parameter, defined as Gr/Re 2 , could be varied.…”

Section: Apparatus and Instrumentationmentioning

confidence: 99%

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Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Banerjee

Bharadwaj

Muralidhar

2006

J Vis

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Steady state temperature distribution in a model Czochralski crucible has been mapped by liquid crystal thermography (LCT). The crucible is a water-filled glass beaker. Water is used as the test fluid because of ease of experimentation, as well as the availability of correct thermo-physical properties. In addition, the Prandtl number of water matches those of molten oxides. A copper cylinder whose diameter is smaller than that of the beaker is placed centrally at the water surface. Convection patterns are set up by applying constant temperature difference between the crucible wall and the cylinder surface, in the temperature range of the liquid crystals. The cylinder is given a fixed rotation, thus creating mixed convection conditions in the test fluid. The LCT images recorded in the present study clearly reveal convective rolls, and the interaction of buoyancy-driven convection in the crucible with cylinder rotation. The resulting temperature distributions match numerical simulation quite well. The pure buoyancy and pure rotation experiments result in axisymmetric temperature fields, while in mixed convection, the field is unsteady and three dimensional.

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Section: Apparatus and Instrumentationmentioning

confidence: 99%

“…The images of the thermal field obtained using LCT are compared with the predictions of a numerical model (Banerjee and Muralidhar, 2005). The model assumes that the temperature and velocity fields are axisymmetric.…”

Section: Numerical Modelmentioning

confidence: 99%

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Banerjee

Bharadwaj

Muralidhar

2006

J Vis

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“…Continuity:

\nabla \cdot u = 0,

Momentum:

u \cdot \nabla u = ν \nabla^{2} u - \frac{\nabla p}{ρ} - g β_{T} (T - T_{0}),

Energy:

\nabla \cdot (T u) = α_{i} \nabla^{2} T + \frac{\nabla \cdot q_{r, i}^{''}}{ρ_{i} C_{p, i}},

where u is the velocity vector, ρ is the density and ν is kinetic viscosity of the fluid; g is the gravitational acceleration vector, β T is the thermal expansion coefficient of the sapphire melt, T is the temperature, and T 0 is the reference temperature; α i and C p,i represent the thermal diffusivity and specific heat, respectively;

q_{r, i}^{''}

is the radiative source term, solved by DO Model as described in Ref. ,

\nabla \cdot q_{r, i}^{''} = κ (4 I_{b} - \int_{2 π} I_{i} d Ω_{i}),

where

Ω_{i}

is the solid angle,

I_{b} = σ n^{2} T^{4}

is the radiation intensity of black body, and κ is absorption coefficient. Radiation intensity I i can be obtained by solving the radiative transfer equation,

\frac{\overset{μ}{true}}{r} \frac{\partial (r I)}{\partial r} + \tilde{ξ} \frac{\partial (I)}{\partial z} - \frac{1}{r} \partial (\tilde{η} I)

…”

Section: Mathematical Modelsmentioning

confidence: 99%

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Fang

Wang

Jin

et al. 2013

Crystal Research and Technology

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Kyropoulos (Ky) method is the most suitable technique for the growth of high‐quality sapphire single crystal for substrate applications. Cracks are often observed in the grown ingot that significantly reduces industrial productivity. In the paper, cracking causes are analyzed by examining crystal shape, thermal stress and three‐dimensional effects during the stable growth of sapphire crystal. It is found that locally induced thermal stress around the shoulder of the crystal is the largest. However, thermal stress is not fully responsible for the cracks, since the predicted stress level is lower than a critical value regarding crystal cracking. Polycrystalline growth or/and other crystal defects must be another factor that degrades the critical value and makes the crystal more fragile. Simulation results further show that crystal shape has less effect on the thermal stress level, although experiments have shown that crack‐free crystals usually have smooth surfaces. The initial cracking position in the ingot predicted in simulation agrees well with experimental observation after considering crystal defects in a qualitative discussion. From the view of three‐dimensional simulation, the variation of heating condition during growth may result in high thermal stress locally that leads to the cracks at one side of the crystal. Additionally, three‐dimensionally unexpected temperature drop of the heater may be responsible for the sticking‐to‐crucible phenomenon at the shoulder region of the grown crystal.

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“…Since LMO single crystals have anisotropic mechanical properties such as elastic constants and thermal expansion coefficients, the exact thermal stress computation has to be performed in three dimensions by taking into account this anisotropy. Furthermore, for semitransparent crystals, such as LMO, internal radiation plays a key role in heat transfer and strongly affects crystal-melt interface convexity [9][10][11][12][13][14][15][16][17][18] . Therefore, temperature distribution inside the crystal is not uniform and, then, accurate computations of the stress inside the crystal requires to take into account the temperature dependence of anisotropic elasticity and thermal expansion tensors.…”

Section: Introductionmentioning

confidence: 99%

Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li₂MoO₄ growth

et al. 2021

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

Cited by 14 publications

References 22 publications

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li₂MoO₄ growth

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

Cited by 14 publications

References 22 publications

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li2MoO4 growth

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Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li₂MoO₄ growth