Journal of Phase Equilibria and Diffusion

, Volume 29, Issue 5, pp 390–397 | Cite as

Calculation of Two-Dimensional Sections of Liquidus Projections in Multicomponent Systems

  • Shuanglin Chen
  • Ying Yang
  • Weisheng Cao
  • Bernard P. Bewlay
  • Kuo-Chih Chou
  • Y. Austin Chang
Basic and Applied Research

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.


computational 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).


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Copyright information

© ASM International 2008

Authors and Affiliations

  • Shuanglin Chen
    • 1
    • 2
  • Ying Yang
    • 1
  • Weisheng Cao
    • 1
  • Bernard P. Bewlay
    • 3
  • Kuo-Chih Chou
    • 2
    • 4
  • Y. Austin Chang
    • 5
  1. 1.CompuTherm, LLCMadisonUSA
  2. 2.School of Materials Science and EngineeringShanghai UniversityShanghaiChina
  3. 3.General Electric Co., GE Global Research CenterNiskayunaUSA
  4. 4.Department of Physical ChemistryUniversity of Science and Technology BeijingBeijingChina
  5. 5.Department of Materials Science and EngineeringUniversity of WisconsinMadisonUSA

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