Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Jing, Chenrui; Tsukada, Takao; Hozawa, Mitsunori; Shimamura, Kiyoshi; Ichinose, Noboru; Shishido, Toetsu

doi:10.1016/j.jcrysgro.2004.02.078

Cited by 26 publications

(26 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some researchers looked for the onset of the flow instability in oxide melts [9], but the realistic conditions are far beyond the ones considered there. For more realistic Grashof numbers, 3D computations have been performed but only for the melt applying simple boundary conditions at its side, bottom and top [10,11]. The bottom was set adiabatic and a constant temperature was set at the side.…”

mentioning

confidence: 99%

Numerical Modelling of the Czochralski Growth of β-Ga2O3

et al. 2017

View full text Add to dashboard Cite

Our numerical modelling of the Czochralski growth of single crystalline β-Ga 2 O 3 crystals (monoclinic symmetry) starts at the 2D heat transport analysis within the crystal growth furnace, proceeds with the 3D heat transport and fluid flow analysis in the crystal-melt-crucible arrangement and targets the 3D thermal stress analysis within the β-Ga 2 O 3 crystal. In order to perform the stress analysis, we measured the thermal expansion coefficients and the elastic stiffness coefficients in two samples of a β-Ga 2 O 3 crystal grown at IKZ. Additionally, we analyse published data of β-Ga 2 O 3 material properties and use data from literature for comparative calculations. The computations were performed by the software packages CrysMAS, CGsim, Ansys-cfx and comsol Multiphysics. By the hand of two different thermal expansion data sets and two different crystal orientations, we analyse the elastic stresses in terms of the von-Mises stress.

show abstract

mentioning

confidence: 99%

Numerical Modelling of the Czochralski Growth of β-Ga2O3

et al. 2017

View full text Add to dashboard Cite

show abstract

“…The dimensionless governing equations for the melt flow in the Cartesian coordinates can be generally written as [8] …”

Section: Mathematical Formulation and Numerical Methodsmentioning

confidence: 99%

“…In the Czochralski crystal growth system the so-called wave patterns were observed in the 1980s [1][2][3][4][5][6][7][8]. The patterns appear on the free surface of oxide melt in the Czochralski crucible.…”

Section: Introductionmentioning

confidence: 99%

“…The patterns appear on the free surface of oxide melt in the Czochralski crucible. Concerning the wave patterns, Jones made a lot of experimental studies [1][2][3][4], Seidl et al [5], Enger et al [6], Kumar et al [7] and Jing et al [8] reported some theoretical models and numerical simulations. These studies focused on the macroscopic flow patterns.…”

Section: Introductionmentioning

confidence: 99%

“…The general conclusions are that the wave patterns result from the baroclinic instability. Theoretical investigations such as the works of Enger et al [6] and Jing et al [8] mainly focused on the evolution and the three-dimensional spatial structures of the wave patterns by numerical simulations. There are few studies on the characteristic modes of the wave patterns.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Role of characteristic modes in the dynamics of wave pattern in the Czochralski oxide crystal growth

Jing

Chen

et al. 2012

Journal of Crystal Growth

Self Cite

View full text Add to dashboard Cite

a b s t r a c tWave pattern is a flow pattern observed on the free surface of oxide melt in the Czockralski crucible. Wave pattern exhibits regular folds in the azimuthal direction. In this paper three-dimensional flows of the LiNbO 3 melt in a Czockralski crucible of radius r c ¼ 100 mm and crystal radius r s ¼ 50 mm were investigated. The crucible is still and the crystal is rotating at a rate O s . The flow is assumed to be laminar. The governing equations of the melt flows were solved by a block-structured boundary-fittedcoordinate method. Massive numerical simulations were first conducted to obtain several stable n-folded wave patterns by changing aspect ratio A¼ h/r c and O s , where h is the depth of the oxide melt. The proper orthogonal decomposition was then applied to extract the characteristic modes of the n-folded original wave patterns. The spatial feature of the characteristic modes and the role of the characteristic modes in the dynamic process of the original wave patterns were finally analyzed. Some interesting conclusions are obtained. The characteristic modes of the wave patterns show strong spatial feature. The characteristic modes have more folds in the azimuthal direction than the original wave patterns; the characteristic modes appear in group; with the increase of group order, the number of folds in the azimuthal direction is increased regularly by n for the n-folded original wave pattern. The study of the dynamic process shows that the original wave pattern is a traveling wave, which is formed by the dominant characteristic modes.

show abstract

References

2012

Rotating Thermal Flows in Natural and Industrial Processes

View full text Add to dashboard Cite

Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Cited by 26 publications

References 41 publications

Numerical Modelling of the Czochralski Growth of β-Ga2O3

Numerical Modelling of the Czochralski Growth of β-Ga2O3

Role of characteristic modes in the dynamics of wave pattern in the Czochralski oxide crystal growth

References

Contact Info

Product

Resources

About