Flow in Czochralski crystal growth melts
Flow in Czochralski crystal growth melts
It is a well-known fact that in the Czochralski crystal growth, as well as in all other crystal growth processes from the liquid phase, the flow in the melt has a strong influence on the chemical and physical properties of the growing crystal. Unlike some other techniques the Czochralski crystal gro...
Saved in:
Personal Name(s): | Mihelcic, M. |
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Wenzl, H. / Wingerath, K. | |
Contributing Institute: |
Publikationen vor 2000; PRE-2000; Retrocat |
Imprint: |
Jülich
Forschungszentrum Jülich GmbH Zentralbibliothek Verlag
1992
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Physical Description: |
II, 54, Anh. |
Document Type: |
Report Book |
Research Program: |
Addenda |
Series Title: |
Berichte des Forschungszentrums Jülich
2697 |
Link: |
OpenAccess |
Publikationsportal JuSER |
It is a well-known fact that in the Czochralski crystal growth, as well as in all other crystal growth processes from the liquid phase, the flow in the melt has a strong influence on the chemical and physical properties of the growing crystal. Unlike some other techniques the Czochralski crystal growth technique, with the view to itsdynamics, represents a rotating systerm,which is rich in many flow phenomena not existing in non-rotating systems. For this reason, some notion of the theory of rotating fluids will be necessary for better understanding of fluid dynamics in the Czochralski crystal growth. This report consists of two parts. In the first part, elements of the theory of rotating fluids are given. It covers, among others, such topics as Taylor-Proudman theorem and its consequences on the fluid flow; Ekman boundary layer; forced oscillations in a rotating fluid which might influence the crystal growth in those cases in which both,the crystal and the crucible, are rotated and the solid-liquid interface is inclined to the rotation axis. In particular, the stability of the flow is of great importance. Many observations during the crystal growth have shown that flow transitions, as the consequence of the flow instability, produce a change of the shape or diameter of the solid-liquid interface. In the second part numerical simulations are presented. We start with the definition of the mathematical model and boundary conditions and present our numerical method. At this point, the problem of choosing the proper model of Cz-crystal growth must be stressed. Even relatively simple questions such as, what, kind of flow and temperature fieldsdo really exist in the bulk, can be properly answered only in a three-dimensional mathematical model. Strong experimental evidence indicates that the flow and temperature field in a real Czcrystal growth are asymmetric and transient(oscillating) and even independent of the scale of experimental set-up. This is not surprising if one recalls for instance, the order of magnitude of Grashof number, Reynolds number etc., as well as the material constants of metallic melts in a real crystal growth.An axisymmetrical model can be used, for instance, when the flow and temperature field in boundary layers(e. g. Ekman boundary layers) are concerned, though the influence of asymmetry in the bulk on the boundary layer remains unsettled. Numerical simulations are performed for (a) axisymmetrical-and (b) three-dimensional models. ln the axisymrnetrical model, Cochran flow and forced oscillations in a rotating fluid are simulated on a fine mesh. In the Cochran flow simulation, the difference between the analytical (infinite disk) and numerical (Czochralski geometry) solution are pointed out. Moreover, the simulations of forced oscillations show an excellent agreement with experimental results. In the three-dimensional model, baroclinic instability, instability of the buoyancy driven convection, and the influence of external magnetic fields on the flow are simulated. The buoyancy driven convection is of particular importance,since it is highly unstable for all nearly real growth conditions. It was found out that the critical Grashof number is approximately 10$^{6}$,which is four orders of magnitude smaller than that for a large (industrial) Czochralski set-up. Simulations of external magnetic fields show the influence of a stationary transverse- and a vertical magnetic field on the flow and temperature distribution in the model. We first force the flow and temperature field to be asymmetric due to an asymmetric temperature boundary condition at the crucible wall and then study the influence of applied magnetic fields. It is found that the vertical magnetic field decreases the thermal asymmetry much better than the transverse magnetic field. Some preliminary results of the influence of rotating transverse magnetic field are also given. |