Growth of lithium triborate crystals. I. Mathematical model

Abstract

A finite element mathematical model for the top seeded solution growth of Li 2O·3B 2O 3 (LBO) crystals, grown from a melt containing the flux MoO 3, is presented. The model is used to calculate the thermal fields and fluid flow in the melt during growth. The thermal boundary conditions used in the model are estimated from temperature measurements made in the melt. The phase diagram of the LBO MoO 3 system is determined experimentally using differential thermal analysis. The physical parameters required in the model are obtained from the literature, when available. Values of the melt viscosity, as a function of the MoO 3 concentration, are determined experimentally. The temperature fields and fluid flow in the melt, particularly below the growing crystal, are calculated for a range of crystal rotations, crucible rotations, crucible sizes, and melt viscosities. The results show that the most effective means of producing fluid flow in this system is by crucible rotation. Fluid flow immediately below the crystal interface determines the movement of the MoO 3 flux rejected by the crystal, away from the interface. This flow is primarily dependent on crucible rotation. If the concentration of MoO 3 at the interface reaches the eutectic composition, MoO 3-rich phases form, terminating the growth of a satisfactory quality LBO crystal.