Effect of crucible and crystal rotations on the carbon concentration in large-size sapphire crystals during Czochralski growth

• H.S. Fang, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China, e-mail address: [email protected] • L.L. Zheng, School of Aerospace, Tsinghua University, Beijing 100084, China, e-mail address: [email protected] • J. Derby, Dept. of Chemical Engineering and Material Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN 55455, USA, e-mail address: [email protected] • Lijun Liu, Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China: [email protected] • Koichi Kakimoto, Research Institute for Applied Mechanics, Kyushu University, 6-1, Kasuga-Koen, Kasuga 816-8580, Japan, e-mail address: [email protected] • Daniel Vizman, Department of Physics, West University of Timisoara, 1900 Timisoara, Romania, email address: [email protected] • Jochen Friedrich, Department of Material Science WW6, University Erlangen, D-91058 Erlangen, Germany, email address: [email protected] Graphite is rarely used in CZ sapphire growth furnaces despite its low cost, because chemical reactions with oxygen generate carbon monoxide, which can dissolve into the melt and degrade crystal quality through bubble defects. To address this issue, it is essential to model solute distribution during growth and identify conditions that minimize carbon incorporation. This study numerically investigates the influence of crucible and crystal rotation on carbon concentration in the melt, considering thermal decomposition, graphite–oxygen reactions, and CO re-dissolution. The objective is to determine optimum rotational speeds that suppress carbon accumulation at the solidification front, thereby improving sapphire optical quality. Results show that carbon concentration is strongly affected by melt convection, with the highest values near the free surface adjacent to the crucible wall. At the solidification front, concentration decreases from the triple point toward the centerline. Crystal rotation induces a vortex beneath the interface, enhancing upward flow and solute transport, which increases carbon concentration at higher speeds. Crucible rotation elevates the buoyancy vortex center, thinning velocity and solute boundary layers due to the high Schmidt number (Sc = 190), thus reducing segregation. Concentration at the interface decreases with crucible rotation up to 2 rpm, but beyond this, vortex separation creates a secondary vortex that enhances carbon flux. In counter-rotation, crucible motion elevates the vortex center and lowers concentration, while crystal rotation improves solute delivery. Among all cases, crucible rotation at 2 rpm provides the lowest and most uniform carbon concentration along the solidification front.