• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2367-2374
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• 1996

A generalized Scheil equation for the solute redistribution in the absence of the back diffusion during the dendritic solidification of binary alloys is derived, in which coarsening of the secondary dendrite arms is taken into account. The obtained equation essentially includes the original Scheil equation as a subset. Calculated results for typical cases show that the coarsening affects the microsegregation significantly. The eutectic fraction predicted for coarsening is considerably smaller than that for fixed arm spacing. The most important feature of the present equation in comparison with the Scheil equation lies in the fact that there exists a lower limit of the initial composition below which the eutectic is not formed. Based on the generalized Scheil equation and the lever rule, a new regime map of the eutectic formation on the initial composition-equilibrium partition coefficient plane is proposed. The map consists of three regimes: the eutectic not formed, conditionally formed and unconditionally formed, bounded by the solubility and diffusion controlled limit lines.

• Journal of the Korean Society for Heat Treatment
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• v.32 no.1
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• pp.17-28
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• 2019

Jominy hardenability curves of low alloy steel containing less than 5 wt.% of alloying elements in total were calculated by applying Scheil's rule of additivity to pre-calculated isothermal transformation curve. Isothermal transformation curve for each phase in steel was approximated as a simple mathematical equation by using Kirkaldy's approach and all coefficients in the equation were estimated from experimental temperature-time-transformation (TTT) and/or continuous cooling transformation (CCT) data in the literature. Then jominy test with simple boundary conditions was performed in computer by applying the finite difference scheme. The resultant cooling curves at each location along a longitudinal direction of Jominy bar were applied to calculate phase fractions as well as mechanical properties such as micro Vickers hardness. The simulated results were compared with experimental CCT data and Jominy curves in the literature.

• Resources Recycling
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• v.30 no.4
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• pp.20-26
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• 2021

Solar grade silicon (SoG-Si) has been commercially supplied mainly from off-grade high-purity silicon manufactured for electronic-grade Si (EG-Si). Therefore, for wider application of solar cells, the development of a refining process at a considerably lower cost is required. The most cost-effective and direct approach for producing SoG-Si is to purify and upgrade metallurgical-grade Si (MG-Si). In this study, directional solidification of molten MG-Si was conducted in a high-frequency induction furnace to remove iron from molten Si. The experimental conditions and results were also discussed with respect to the effective segregation coefficient, Scheil equation, and Peclet number. The study showed that when the descent velocity of the specimen decreased, the macro segregations of impurities and ingot purities increased. These results were derived from the decrease in the effective segregation coefficient with the decrease in the rate of descent of the specimen.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.10
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• pp.3361-3370
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• 1996

Micro-Macro approach is conducted for the mixture solidification to handle the closely linked phenomena of microscopic solute redistribution and macroscopic solidification behavior. For this purpose, present work combines the efficiency of mixture theory for macro part and the capability of microscopic analysis of two-phase model for micro part. The micro part of present study is verified by comparison with experiment of Al-4.9 mass% Cu alloy. The effect of back diffusion on the macroscopic variables such as temperature and liquid concentration, is appreciable. The effect, however, is considerable on the mixture concentration and eutectic fraction which are indices of macro and micro segregation, respectively. According to the diffusion time, the behavior near the cooling wall where relatively rapid solidification permits short solutal diffusion time, approaches Scheil equation limit and inner part approaches lever rule limit.