A conical shape-evolution model for the control of sapphire crystal growth in Kyropoulos (KY) method

Generally, the process of sapphire crystal growing in the KY furnace has to be monitored in order to reduce the power of heater continuously as the crystal grows to occupy the crucible. However, it has been difficult to control the heater power as the weight and diameter of crystal change because the solid-liquid interface could not be easily located from on-site measurement. Hence, first, the model was developed to locate the crystal-melt interface and to estimate its dynamic feature during the crystal growth by incorporating the mass and the force balances. This model was applied to analyze the data obtained from the industry-scale crystal growth experiment (for the production of the sapphire crystals in the KY method). Finally, the shape and the dynamic feature of crystallizing front are analytically verified by generating some bands of small bubbles along the crystal-melt interface called a comb-pattern experiment.