Solute redistribution in Bridgman crystal growth under purely diffusive and full convective conditions

Abstract

Solute distribution in crystals grown under purely diffusive or convective conditions is computed by numerical modeling. The numerically computed solutal profiles for Bridgman growth under diffusion limited conditions cannot be described by the classical formulae of Tiller (W. A.Tiller, K. A. Jackson, J. W. Rutter and B. Chalmers, Acta Metall., 1953, 1, 428.) or Smith (V. G. Smith, W. A. Tiller and J. W. Rutter, Can. J. Phys., 1955, 33, 723) and show significant axial and radial variations of concentration. The axial composition homogeneity could be theoretically improved by increasing the growth rate, but in this case the radial segregation is augmented and significant oscillations of the concentration could appear in the longitudinal direction. Numerical modeling shows no improvement on the chemical homogeneity of crystals grown under purely diffusive conditions. The analysis of the growth under convective transport conditions shows smaller axial variations of the concentration and significantly improved radial homogeneity of the crystals. The numerical results compared to the theoretical predictions of Scheil (E. Scheil, Z. Metallkd., 1942, 34, 70) for a full convective regime, show a better agreement for an horizontal Bridgman (P. W. Bridgman, Proc. Am. Acad. Arts Sci., 1925, 60, 305) arrangement where the flow is extended to the whole melt volume than for a vertical Bridgman configuration with a single flow cell located near to the interface.