Journal of Phase Equilibria

, Volume 13, Issue 4, pp 365–372 | Cite as

Computer generation of binary and ternary phase diagrams via a convex hull method

  • D. D. Lee
  • J. H. Choy
  • J. K. Lee
Section I: Basic and Applied Research


A rapid computational technique for determining equilibrium phase diagrams of multicomponent systems by constructing the convex hull of the free energy surface is introduced. Rather than calculating tangent lines or planes, this method guarantees a convex representation of the equilibrium free energy surface on a discrete set of points in composition space. Although the accuracy of these phase diagrams is limited by the spacing of points, there are no restrictions on the number or types of free energy functions that may be considered; functions with singular or unknown derivatives may even be used. This method is then applied to generate several model binary and ternary phase diagrams.


Free Energy Free Energy Surface Ternary Phase Diagram Free Energy Function Free Energy Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Cited References

  1. 1.
    L. Kaufman and H. Bernstein, “Computer Calculation of Phase Diagrams,” Academic Press, NY (1970).Google Scholar
  2. 2.
    H. Gaye and C.H.P. Lupis,Met. Trans. A, 6, 1049–1056 (1975).Google Scholar
  3. 3.
    H. Gaye and C.H.P. Lupis,Met. Trans. A, 6, 1057–1064 (1975).Google Scholar
  4. 4.
    M. Hillert, in Calculation of Phase Diagrams and Thermochemistry of Alloy Phases, Y.A Chang and J.F Smith, Ed., TMS-AIME, Warrendale, PA, 1–13 (1979).Google Scholar
  5. 5.
    D. Furman, S. Dattagupta, and R.B. Griffiths,Phys. Rev. B, 15, 441–464 (1977).CrossRefADSGoogle Scholar
  6. 6.
    R.M. Aikin, Jr. and J.K. Lee,Bull. Alloy Phase Diagrams, 4,131–134 (1983).CrossRefGoogle Scholar
  7. 7.
    J.F. Counsell, E.B. Lees, and P.J. Spenser,Metal Sci. J., 5, 210–213 (1971).CrossRefGoogle Scholar
  8. 8.
    D.A. Porter and K.E. Easterling,in Phase Transformations inMetals and Alloys, Van Nostrand, NY, 308 (1981).Google Scholar
  9. 9.
    A.E. Taylor,Advanced Calculus, Ginn and Co., NY, 51(1955).zbMATHGoogle Scholar
  10. 10.
    I. Prigogine and R. Defay,Chemical Thermodynamics, Longmans, London, 239 (1954).Google Scholar
  11. 11.
    T.B. Massalski, J.L. Murray, L.H. Bennett, and H. Baker, Ed.,Binary Alloy Phase Diagrams, Vol. 1 and 2, American Society for Metals, Metals Park, OH (1986).Google Scholar
  12. 12.
    M. Kahlweit, R. Strey, P. Firman, D. Haase, J. Jen, and R. Schomaker,Langmuir, 4, 499–511 (1988).CrossRefGoogle Scholar

Copyright information

© ASM International 1992

Authors and Affiliations

  • D. D. Lee
    • 1
  • J. H. Choy
    • 2
  • J. K. Lee
    • 2
  1. 1.Dept. of PhysicsMassachusetts Institute of TechnologyCambridge
  2. 2.Dept. of Metallurgical and Materials EngineeringMichigan Technological UniversityHoughton

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