Phase Equilibria and Phase Diagrams

  • N. A. Gokcen


The phase equilibria constitute a vast area of interest in metallurgy, geology, chemistry, physics, and related fields. In a single-component system, such equilibria occur between two phases, or three phases. The two-phase equilibria and the corresponding Gibbs energy relations for a component A are
$$A(PhaseI) = A(PhaseII);\Delta G = {G^{II}} - {G^I} = 0,or{G^I} = {G^{II}} $$
A rigorous derivation of equation (2.1) will be given later in this chapter.


Phase Diagram Gibbs Energy Phase Equilibrium Phase Boundary Binary Phase Diagram 
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  1. 1.
    N. A. Gokcen, Thermodynamics, Techscience, Hawthorne, California (1975).Google Scholar
  2. 2.
    A. Alper, editor, Phase Diagrams, three volumes, Academic Press, New York (1970); H. C. Yeh in Volume I, p. 167; T. B. Massalski and H. Pops in Volume II, p. 221.Google Scholar
  3. 3.
    A. G. Guy and J. J. Hren, Elements of Physical Metallurgy, Third edition, Addison-Wesley, Reading, Massachusetts (1974).Google Scholar
  4. 4.
    A. Reisman, Phase Equilibria, Academic Press, New York (1970).Google Scholar
  5. 5.
    Bulletin of Alloy Phase Diagrams, Vols. 1–5, ASM, Metals Park, Ohio (1978–1984).Google Scholar
  6. 6.
    I. Prigogine and R. Defay, Chemical Thermodynamics, translated by D. H. Everett, Longmans, Green, New York (1954).Google Scholar
  7. 7.
    S. Wagner and D. A. Rigney, Metall Trans. 5, 2115 (1974).Google Scholar
  8. 8.
    M. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York (1958).Google Scholar
  9. 9.
    R. P. Elliott, Constitution of Binary Alloys, First Supplement, McGraw-Hill, New York (1965).Google Scholar
  10. 10.
    F. A. Schunk, Constitution of Binary Alloys, Second Supplement, McGraw-Hill, New York (1969);Google Scholar
  11. 10a.
    J. F. Smith and Z. Moser, J. Nuclear Mater., 59, 158 (1976).CrossRefGoogle Scholar
  12. 11.
    R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, and K. K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, Ohio (1973).Google Scholar
  13. 12.
    M. Hillert, Physics 103B, 31 (1981).Google Scholar
  14. 13.
    See, e.g., the articles by (a) M. Hillert, (b) P. J. Spencer, and (c) P. L. Lin, C. W. Bale, and A. D. Pelton, in Calculation of Phase Diagrams and Thermochemistry of Alloy Phases, edited by Y. A. Chang and J. F. Smith, Metall. Soc. AIME (1979).Google Scholar
  15. 14.
    L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams, Academic Press, New York (1970).Google Scholar
  16. 15.
    H. Gaye and C. H. P. Lupis, Metall. Trans. 6A, 1049 (1975).Google Scholar
  17. 16.
    C. W. Bale, A. D. Pelton, and W. T. Thompson. An online computer program (F*A*C*T) is available for phase-diagram calculations through McGill University/Ecole Polytechnique de Montreal, Canada.Google Scholar
  18. 17.
    I. Ansara, Int. Metals Rev. No. 1, p. 20, Metals Society and ASM (1979).CrossRefGoogle Scholar
  19. 18.
    W. Hume-Rothery, R. E. Smallman, and C. W. Haworth, The Structure of Metals and Alloys, The Institute of Metals, London (1969).Google Scholar
  20. 19.
    W. Hume-Rothery, in Phase Stability in Metals and Alloys, edited by P. S. Rudman, J. Stringer, and R. I. Jaffee, McGraw-Hill, New York, p. 3 (1967).Google Scholar
  21. 20.
    T. B. Massalski, in Theory of Alloy Phase Formation, edited by L. H. Bennett, AIME, Warrendale, Pennsylvania (1980).Google Scholar
  22. 21.
    K. A. Gschneidner, Ref. 20, p. 36.Google Scholar
  23. 22.
    K. A. Gschneidner, Ref. 20, p. 1.Google Scholar
  24. 23.
    J. Friedel, Trans. Metall. Soc. AIME 230, 632 (1964); see also pp. 8–9, and 38–39, in Ref. 20.Google Scholar
  25. 24.
    T. B. Massalski, in Physical Metallurgy, edited by R. W. Cahn, North-Holland, Amsterdam (1965);Google Scholar
  26. 24a.
    see also C. S. Barrett and T. B. Massalski, Structure of Metals, McGraw-Hill, New York (1980).Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • N. A. Gokcen
    • 1
  1. 1.Bureau of Mines, U.S. Department of the InteriorAlbany Research CenterAlbanyUSA

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