Determination of Solid/Melt Interface Shape and Growth Rate during Gradient Freeze Solidification on a Centrifuge Using Current Interface Demarcation

Abstract

Since the experiments conducted by Regel and Rodot¹ on the Star City and Nantes centrifuges, several attempts have been made to explain their surprising results. A few numerical models of Bridgman growth on a centrifuge have been developed, the most notable being those of Arnold² and of Friedrich et a1. ³ Arnold² developed a non-linear, three-dimensional model for convection in the melt during crystal growth by the “thermally stable” gradient freeze technique on a centrifuge. The parameters used were those of the Ag-doped PbTe experiments on the Star City centrifuge in Reference 1. The effects of the average resultant acceleration, the acceleration gradient and the Coriolis force were studied separately and together. Arnold predicted that thermal stability (no convection) would occur when the acceleration is orthogonal to the isotherms and the density increases in the direction of the acceleration. From numerical simulations, he found that the rotation rate for uniform impurity doping is strongly influenced by the interface shape and the growth rate. A higher concave curvature of the interface corresponds to a larger radial temperature gradient, and requires a higher rotation rate to induce thermal stability. A lower growth velocity leads to a longer diffusive length and causes the impurity segregation to be more sensitive to convection near the interface. From computer simulation, Arnold also found that the temperature gradient along the axis of the charge in the PbTe experiment was only ~20% of that measured on the steel cartridge holding the ampoule and so the freezing rate was about 5 times larger than previously thought.