By using 3D finite element calculations, numerical simulations are performed to predict the thermal field as well as the thermal stress in a c-axis sapphire single crystal grown by Kyropoulos technique. The effects of additional resistive heating (placed under the crucible bottom) and crystal rotation are investigated and a comparison is made between the isotropic and anisotropic analysis. The anisotropy of the elastic constants and thermal expansion coefficients as well as their temperature dependence are considered in the anisotropy calculations while Young's modulus and the Poisson ratio are used in the isotropic analysis. Thermal stress is found to be smaller in the anisotropy analysis than that in the isotropic analysis and significant differences are found in their respective distribution patterns. Additional resistive heating acts to decrease both of the crystal-melt interface convexity and the von Mises stress. In addition, crystal rotation combined with additional resistive heating decreases significantly the thermal stress inside the sapphire crystal and along the melt-crystal interface. Therefore, optimizing the heating conditions and using a suitable crystal rotation rate seem to be favorable to control the growth interface shape and to reduce thermal-stress-related defects during the growth process.
The three dimensional thermal stress field is calculated at different growth stages for LMO crystals grown in an inductively heated Czochralski furnace using the anisotropy and temperature-dependency of the mechanical...
Here, the radiative heat transfer inside a Czochralski furnace and the 3D thermal stress generated in a semitransparent Li2MoO4 crystal are deeply analyzed using anisotropic and temperature‐dependent elasticity and thermal expansion coefficients. The developed global numerical model takes into account induction heating, thermal conduction in all parts of the furnace, convection in the melt and the growth atmosphere, Marangoni convection at the free surface, radiation heat exchange between the furnace elements, internal radiation inside the semitransparent crystal and melt, and phase change at the growth interface. The contribution of each radiation mode is studied separately, then coupled together to clearly explain their roles in heat transfer, stress generation in the as‐grown crystal and in power consumption, and heat loss inside the furnace. Flow and temperature fields in the molten oxide and in the growth atmosphere as well as the thermal stress are presented and discussed for each case. Unrealistic cases are first considered where radiation exchange between the furnace elements and internal radiation in the assumed opaque crystal are neglected. For each case, the relation between temperature gradient and thermal stress is clearly demonstrated. Finally, the effect of the melt opacity on thermal stress is studied and related to temperature gradients in the crystal and at the free surface. The experimental observations are in good agreement.
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