SynopsisSolute redistribution during solidification has been analyzed by a profile method which has approximately considered the two-dimensional diffusion in solid phase. Derived equations have been compared with conventional equations, numerical analyses and experimental data. It was found that a newly derived simple equation can estimate the liquid concentration better than Brody-Flemings' equation but numerical calculation or further improvement of the analytical treatment is required for estimating the segregation ratio correctly. 7n addition, calculations showed that the dendrite shape, growth mode (parabolic and constant growth) and diffusion in the liquid phase did not affect so much the solute redistribution at least for f<0.9.The diffusion path, which is thought to be a more important factor, has also been discussed and an equation is proposed for the case where diffusion path or the partition coefficient changes stepwise. I. IntroductionIn the solidification of alloys, especially steels, the diffusion of solute into solid phase (back diffusion) affects greatly the microsegregation.Although Brody and Flemingsl~ have firstly analyzed a model which assumed complete diffusion in liquid and incomplete back diffusion, they have not solved the diffusion equation and hence the application of their result is limited to a slow diffusion. Recently Clyne and Kurz2~ derived a better mathematical expression which asymptotically approaches the Scheil's equation and the equilibrium equation for infinitestimal and infinite diffusion coefficient, respectively. Matsumiya et a1.,3~ however, showed that in some cases this equation did not agree so well with numerical results. Further Kobayashi4) has solved Brody-Flemings' model more rigorously.In order to make clear the two-dimensional effect of dendrites and to select a suitable equation for estimating the microsegregation, this paper presents an analysis based on a profile method which does not solve directly the diffusion equation but solves a overall solute mass balance equation and compares derived equations with conventional equations, numerical analyses and experimental data.

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Two phases produced through the liquid-liquid separation gravitationally segregate during solidification of the monotectic alloys. This paper examined reduction of the gravity segregation for the Cu-Pb monotectic alloys by imposing a static magnetic field up to 10 T. The Cu-Pb alloys with compositions ranging from 15.5 to 84.5 at% Pb solidified at a cooling rate of 10 K/s under a magnetic field. The effect of the magnetic field on the macrosegregation was clearly recognized for the Cu-Pb alloys with compositions ranging from 65 to 70 at% Pb, while the magnetic field did not become a dominant factor of the segregation behavior in the other compositions. Furthermore, diameter of the Cu-rich liquid drops under 10 T was smaller than that under 0 T. The static magnetic field reduced not only the rising velocity of the Cu-rich drops but also the coalescence rate of the liquid drops, resulting in the reduction of the macrosegregation. The magnetohydrodynamic estimation suggested that the terminal velocity of the Cu-rich particles with typical diameters is significantly reduced by the imposed static magnetic field. The difficulty of the particle movement due to the electromagnetic force resulted in the homogenous solidified structure for the Cu-Pb alloys.

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