Calculation of Two-Dimensional Sections of Liquidus Projections in Multicomponent Systems
- 137 Downloads
A two-dimensional (2D) section of liquidus projection consists of univariant lines of three-phase equilibria between liquid and other phases. It is useful not only for people’s easy visualization but also for retaining important information about the multicomponent liquidus surface, which is critical for understanding and controlling the solidification microstructure. An algorithm is presented for calculating two-dimensional sections of liquidus projections for multicomponent systems. It can project a liquidus surface onto any given two-dimensional section in the compositional space. A hypothetical quaternary system is designed to illustrate the features of the 2D sectional liquidus projections. Then the Nb-Ti-Si-Cr system is used as an example to demonstrate how to apply a 2D sectional liquidus projection to determine the amount of Cr addition into Nb-Ti-Si alloy to affect the liquidus surface of the quaternary system.
Keywordscomputational studies equilibrium diagram invariant equilibria liquidus surface phase diagram phase equilibria
Y. Austin Chang wishes to thank the Air Force of Scientific Research (Grant No. FA9550-06-1-0229) and the National Science Foundation (FRG grant no. NSF-DMR-03-09468) for financial support, and Kuo-Chih Chou wishes to thank the financial support from Chinese National Natural Science Foundation (No. 50774004).
- 1.F·N. Rhines, Phase Diagrams in Metallurgy. McGraw-Hill, New York, 1956Google Scholar
- 7.M.R. Jackson, B·P. Bewlay, R.G. Rowe, D.W. Skelly, and H.A. Lipsitt, High-Temperature Refractory Metal-Intermetallic Composites, JOM, 1996, 48(1), pp 39-44Google Scholar
- 8.M.G. Mendiratta, J.J. Lewandowski, and D.M. Dimiduk, Strength and Ductile-Phase Toughening in the Two-Phase Niobium/Niobium Silicide (Nb5Si3) Alloys, Metall. Trans., 1991, 22A(7), pp 1573-1583Google Scholar