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

Abstract

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.

Oscillations of the longitudinal solutal profile in Bridgman growth of doped crystals

“…Extensive experimental [1][2][3] and numerical studies [4][5][6] have shown that the solute distribution in crystals depends on the physical properties of the given alloy, the growth rate and the flow intensity. Unexpected oscillations in the longitudinal solutal profile have been detected in some Bridgman solidification experiments of doped semiconductors [7,8] and fluoride crystals [9]. The particularity of these experiments consists in a low level of the melt convection as shown by previous numerical simulations [10,11].…”

“…More details about the modeling of doped semiconductor and calcium fluoride crystals are given in Refs. [10,11].…”

“…The general analysis of solutal profile oscillations is performed for doped calcium fluoride crystals, which have also been investigated in Ref. [11]. The modeling of GaInSb crystal growth is performed in order to compare the numerical results to existing experimental data.…”

“…The numerical modeling is performed for an experimental configuration used for the growth of 1% Pb doped CaF 2 crystals [9]. The graphite crucible containing the sample (radius R ¼ 0.55 cm, length L ¼ 7 cm) is pulled in a thermal field characterized by an axial temperature gradient G T ¼ 20 K/cm.…”

“…Unexpected oscillations in the longitudinal solutal profile have been detected in some Bridgman solidification experiments of doped semiconductors [7,8] and fluoride crystals [9]. The particularity of these experiments consists in a low level of the melt convection as shown by previous numerical simulations [10,11]. The effect of the convection on the solute transport in the melt is described by the convectodiffusive parameter D. This parameter varies from values close to zero, in the case of a convective regime, to unity for a purely diffusive regime.…”