3D unsteady computer modeling of industrial scale Ky and Cz sapphire crystal growth

Demina, S.E.; Kalaev, V.V.

doi:10.1016/j.jcrysgro.2011.01.101

Cited by 41 publications

(17 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Liu

2017

Crystals

View full text Add to dashboard Cite

show abstract

“…During the last decade, there has been much interest in growing sapphire crystals for LED and optical applications by the Kyropoulos (Ky) and other techniques [1,2]. Knowledge of vortex structure of melt convection is important for crystal growth for technology optimization and improvements of crystal quality.…”

Section: Introductionmentioning

confidence: 99%

“…On the free surface of sapphire melt in a cylindrical crucible with axisymmetric heating, a spoke pattern is observed under particular growth parameters. For Ky crystal growth, the spoke patterns were obtained by Demina et al [2] in industrial furnace. Similar spoke patterns are sometimes observed in other crystal growth cases and in fundamental experimental studies of natural convection.…”

Section: Introductionmentioning

confidence: 99%

3D melt convection in sapphire crystal growth: Evaluation of physical properties

Timofeev¹,

Kalaev²,

Иванов

2015

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

“…There are studies focusing on modeling and simulation of coupled phenomena together. 8,9 However, for control and estimation purposes and specially for model-based control/estimation, reduced order models are required. Reduced order models are used for both radius and temperature control purposes.…”

Section: Introductionmentioning

confidence: 99%

Temperature distribution reconstruction in Czochralski crystal growth process

2014

View full text Add to dashboard Cite

A mechanical geometric crystal growth model is developed to describe the crystal length and radius evolution. The crystal radius regulation is achieved by feedback linearization and accounts for parametric uncertainty in the crystal growth rate. The associated parabolic partial differential equation (PDE) model of heat conduction is considered over the timevarying crystal domain and coupled with crystal growth dynamics. An appropriately defined infinite-dimensional representation of the thermal evolution is derived considering slow time-varying process effects. The computational framework of the Galerkin's method is used for parabolic PDE order reduction and observer synthesis for temperature distribution reconstruction over the entire crystal domain. It is shown that the proposed observer can be utilized to reconstruct temperature distribution from boundary temperature measurements. The developed observer is implemented on the finite-element model of the process and demonstrates that despite parametric and geometric uncertainties present in the model, the temperature distribution is reconstructed with the high accuracy.

show abstract

3D unsteady computer modeling of industrial scale Ky and Cz sapphire crystal growth

Cited by 41 publications

References 9 publications

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

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

3D melt convection in sapphire crystal growth: Evaluation of physical properties

Temperature distribution reconstruction in Czochralski crystal growth process

Contact Info

Product

Resources

About