3-DIMENSIONAL CONVECTION AND SOLUTE SEGREGATION IN VERTICAL BRIDGMAN CRYSTAL-GROWTH

Perfect axisymmetry is difficult to achieve in the vertical Bridgman c rystal growth. Nonaxisymmetry is, to a certain degree, always present in a real crystal growth configuration. To study how fluid flow and so lute fields in the process are affected by slight deviations from axis ymmetry, a three-dimensional finite-volume/Newton method is developed. Pseudo-steady-state heat and mass transfer, fluid flow, and the growt h front are solved simultaneously. The calculated results for axisymme tric cases are compared with those by two-dimensional finite volume an d finite element methods, and they are in excellent agreement. Calcula ted results also show that three-dimensional flow and solute fields ar e easily induced by imperfect axisymmetry. A slightly tilted ampoule o r a small temperature gradient in the azimuthal direction could break axisymmetry and dramatically affect flow patterns and solute segregati on.