Effects of Melt Convection on YBa₂Cu₃O_7−x Single Crystal Growth by Pulling Method

Abstract

The melt convection phenomena in YBa₂Cu₃O_7−x (YBCO) single crystal growth by the modified pulling method (Solute Rich Liquid-Crystal Pulling method; SRL-CP method) have been investigated by using a numerical calculation. The finite difference method was used to calculate the steady state of the axisymmetric 2-dimensional incompressible viscous fluid system. In order to clarify the property of the melt convection, the dimensional analysis was performed with changing various parameters for the calculation, such as the crystal rotation rate, the melt viscosity, etc. The intensity ratio of the forced to the natural convection in the melt could be expressed by Re^1.5Dsc^0.7/Gr, where Re, Gr and Dsc were the Renolds number, the Grashof number and the diameter ratio of the crystal to the crucible, respectively. And also, the dimensionless crystal growth interface temperature, Θ could be expressed by Θ=C Re^0.028Pr^0.041Gr^0.019Dsc^0.064, where Pr was the Prandtl number and C was a constant. These results agreed well with the experimental results, and indicated that in this system, the heat transport was mainly dominated by the forced convection.
On the basis of these calculated results, the YBCO single crystal which was 14.5mm×14.5mm×13mm could be grown along the c-axis by the pulling method.