Characteristics of melt convection during Kyropoulos sapphire crystal growth

Melt flows in the Kyropoulos sapphire growth system include Marangoni convection and buoyancy convection. From the seeding stage to the final growth stage, both the area of the free surface and melt height decrease to zero from initial values, and hence the flow pattern in the melt varies during growth. To study systematically melt convection and its influence on the growth process, a non-dimensional parameter is introduced to denote the relative strength of Marangoni convection to buoyancy convection. Temperature and stream function distributions for the different growth stages are simulated. It is found that Marangoni convection is negligible during the early growth. However, it plays an important role in the late growth. The remelting of the crystal surface starts when Marangoni convection becomes dominant, and thus it may be related to this convection mode. The interface shape is found to be changing during the whole growth process, which reduces the industrial productivity of sapphire. Interface convexity, crystal diameter and the non-dimensional parameter are presented as functions of the melt height. Interface convexity is further described as a function of the non-dimensional parameter. The results are consistent with experimentally observed phenomena.