Analysis of Transport Phenomena during Bridgman Growth of Calcium Fluoride Doped Crystals

The chemical homogeneity of CaF 2 :Pb crystals, grown by using the vertical Bridgman method, is numerically investigated. The FIDAP commercial code is used to study the heat transfer, convection, and solute transport phenomena during the solidification process. The homogeneity of these doped crystals depends on the solid-liquid interface curvature and the flow intensity. The accurate computation of the thermal field and interface shape for these semitransparent materials requires the modeling of the internal radiative heat transfer. The numerical modeling of the flow field and solute distribution shows a low intensity of the convection and a quasi-diffusive transport regime in the melt. The numerically computed longitudinal solutal profile in the crystal, in agreement with the experimental measurements, shows some significant oscillations of the Pb concentration. For the first time, a correlation between these oscillations and a quasi-diffusive transport regime has been established to explain this phenomenon, which also has been observed in other Bridgman crystal growth experiments. Finally, an optimization of the growth rate to avoid these oscillations and to improve the chemical homogeneity of crystals has been proposed.