Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals,Crystal Research and Technology

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Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals
Crystal Research and Technology ( IF 1.5 ) Pub Date : 2020-11-05 , DOI: 10.1002/crat.202000106
Klaus Böttcher ₁ , Wolfram Miller ₁ , Steffen Ganschow ₁

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The Czochralski growth of NdScO₃ single crystals along the [110]‐direction is numerically analyzed with the focus on the influence of the optical thickness on the shape of the crystal–melt interface and on the generation of thermal stresses. Due to lack of data, the optical thickness (i.e., the absorption coefficient) is varied over the entire interval between optically thin and thick. While the thermal calculation in the entire furnace is treated as axisymmetric, the stress calculation of the crystal is done three‐dimensionally in order to meet the spatial anisotropy of thermal expansion and elastic coefficients. The numerically obtained values of the deflection of the crystal/melt interface meet the experimental ones for absorption coefficients in the range between 40 and 200 m⁻¹. The maximum values of the von Mises stress appear for the case of absorption coefficient between 20 and 40 m⁻¹. Applying absorption coefficients in the range between 3 and 100 m⁻¹ leads to local peaks of high temperature in the shoulder region and the tail region near the end of the cylindrical part.

中文翻译：

Scan酸钕单晶在直拉晶体生长时传热和热应力的数值模拟

对NdScO ₃单晶沿[110]方向的Czochralski生长进行了数值分析，重点是光学厚度对晶体-熔体界面形状和热应力产生的影响。由于缺乏数据，光学厚度（即吸收系数）在光学厚度和光学厚度之间的整个间隔内变化。当整个炉子的热计算被视为轴对称时，晶体的应力计算是在三维上完成的，以满足热膨胀和弹性系数的空间各向异性。在40至200 m ^-1范围内的吸收系数，通过数值计算得出的结晶/熔体界面的挠度值符合实验值。。对于吸收系数在20和40 m ^-1之间的情况，会出现von Mises应力的最大值。在3至100m ^-1之间的范围内施加吸收系数导致在圆柱形部分的末端附近的肩部区域和尾部区域中出现局部高温峰值。

更新日期：2021-01-07

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