Solidification Simulation Using Scheil Model in Multicomponent Systems
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Basic and Applied Research: Section I
Solidification Simulation Using Scheil Model in Multicomponent Systems Shuang-Lin Chen, Ying Yang, Sinn-Wen Chen, Xiong-Gang Lu, and Y. Austin Chang
(Submitted March 19, 2009; in revised form July 6, 2009) Solidification paths simulated by Scheil model have been analyzed. Since the Scheil model assumes that the already solidified solid phases are ‘‘frozen,’’ the simulated solidification paths must follow the eutectic type paths and cross over the peritectic type boundaries to satisfy the mass balance requirement. Examples are given for comparison between the Scheil simulation results and the experimental observations for alloys in Mo-Ti-Si system.
Keywords
calculation, phase diagram, solidification simulation
1. Introduction We have learnt that in an isobaric binary system two basic types of reactions exist during solidification: eutectic and peritectic. Binary eutectic and peritectic reactions can be easily understood from the binary phase diagrams. However, reactions become much more complex in multicomponent systems and it is not so easy to understand the reactions in multi-component systems, even in a ternary system. This article details geometrically the eutectic and peritectic types of reactions in a ternary system during solidification simulation with Scheil model and then extends it to multi-component systems. Examples will be presented to compare the prediction from simulation with experimental results. We start from binary system so that the similarity among binary, ternary, and higher order systems can be revealed. The phase formation during solidification is a kinetic process. In this article, a simple solidification model, the Scheil model,[1] is employed. The major assumptions in this This article is an invited paper selected from participants of the 14th National Conference and Multilateral Symposium on Phase Diagrams and Materials Design in honor of Prof. Zhanpeng Jin’s 70th birthday, held November 3-5, 2008, in Changsha, China. The conference was organized by the Phase Diagrams Committee of the Chinese Physical Society with Drs. Huashan Liu and Libin Liu as the key organizers. Publication in Journal of Phase Equilibria and Diffusion was organized by J.-C. Zhao, The Ohio State University; Yong Du, Central South University; and Qing Chen, Thermo-Calc Software AB. Shuang-Lin Chen, CompuTherm, LLC, Madison, WI 53719 and School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China; Ying Yang, CompuTherm, LLC, Madison, WI 53719; and Xiong-Gang Lu, School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China; Sinn-Wen Chen, Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan, ROC; Y. Austin Chang, Department of Materials Science and Engineering, University of Wisconsin, Madison, WI 53706, USA. Contact e-mail: [email protected].
model are: the solidified phases are ‘‘frozen,’’ i.e., no back diffusion is considered in the solid phases; diffusion in liquid phase is so fast that liquid pha
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