Russian Journal of Physical Chemistry A

, Volume 84, Issue 4, pp 525–533 | Cite as

A universal method for calculating isobaric-isothermal sections of ternary system phase diagrams

  • A. L. Voskov
  • G. F. Voronin
Chemical Thermodynamics and Thermochemistry


A method for calculating and constructing isobaric-isothermal sections of ternary system phase diagrams with the use of convex hulls was developed. The method is based on the projection of the singularities of the lower part of the Gibbs energy convex hull onto the plane of component mole fractions followed by a geometric analysis of the properties of this projection. The method is applicable to a wide range of ternary systems, it can be used to find tie-line coordinates and determine the phase compositions of all the diagram regions. The quality of the suggested algorithm was estimated, and examples of the construction of several phase diagrams are given.


Phase Diagram Gibbs Energy Convex Hull Ternary System Single Phase Region 
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  1. 1.
    L. E. Baker, A. C. Pierse, and K. D. Luks, Soc. Petrol. Eng. J., No. 5, 731 (1982).Google Scholar
  2. 2.
    G. Xu, W. D. Haynes, and M. A. Stadtherr, Fluid Phase Equilib. 235, 152 (2005).CrossRefGoogle Scholar
  3. 3.
    S. P. Tan and M. Radosz, Fluid Phase Equilib. 216, 159 (2004).CrossRefGoogle Scholar
  4. 4.
    G. F. Voronin, Zh. Fiz. Khim. 77, 1874 (2003) [Russ. J. Phys. Chem. A 77, 1685 (2003)].Google Scholar
  5. 5.
    G. F. Voronin, Zh. Fiz. Khim. 79, 2126 (2005) [Russ. J. Phys. Chem. A 79, 1890 (2005)].Google Scholar
  6. 6.
    G. V. Belov, A. L. Emelina, V. I. Goriacheva, et al., J. Alloys Compd. 452, 133 (2008).CrossRefGoogle Scholar
  7. 7.
    G. F. Voronin and I. V. Pentin, Zh. Fiz. Khim. 79, 1771 (2005) [Russ. J. Phys. Chem. A 79, 1572 (2005)].Google Scholar
  8. 8.
    D. D. Lee, J. H. Choy, and L. K. Lee, J. Phase Equilib. 13, 365 (1992).CrossRefGoogle Scholar
  9. 9.
    J. W. Gibbs, Thermodynamics. Statistical Mechanics (Nauka, Moscow, 1982) [in Russian].Google Scholar
  10. 10.
    F. Preparata and M. Shamos, Computational Geometry, An Introduction (Mir, Moscow, 1989; Springer, New York, 1985).Google Scholar
  11. 11.
    C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Software 22, 469 (1996).CrossRefGoogle Scholar
  12. 12.
    A. V. Skvortsov, Delone Triangulation and Its Use (Tomsk. Univ., Tomsk, 2002) [in Russian].Google Scholar
  13. 13.
    J. Foley and A. Dam, Fundamentals of Interactive Computer Graphics, in 2 vols. (Addison-wesley, Reading, 1982; Mir, Moscow, 1985).Google Scholar
  14. 14.
    J. E. Morral and H. Gupta, J. Chim. Phys. Phys.-Chim. Biol. 90, 421 (1993).Google Scholar
  15. 15.
    L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams (Academic, New York, 1970; Mir, Moscow, 1972).Google Scholar
  16. 16.
    H. Liang, S.-L. Chen, and Y. A. Chang, Metall. Mater. Trans. A 28, 1725 (1997).CrossRefGoogle Scholar
  17. 17.
    P. Liang, T. Tarfa, J. A. Robinson, et al., Thermochim. Acta 314, 87 (1998).CrossRefGoogle Scholar
  18. 18.
    M. Hillert, J. Alloys Compd. 320, 161 (2001).CrossRefGoogle Scholar
  19. 19.
    A. T. Dinsdale, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 15, 317 (1991).Google Scholar
  20. 20.
    T. Jriri, J. Rogez, J. C. Mathieu, and I. Ansara, J. Phase Equilib. 20, 515 (1999).CrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Faculty of ChemistryMoscow State UniversityMoscowRussia

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