Phase Equilibria and Phase Diagrams

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 5)


Crystal growth can be called, in a wide sense, the science and technology of controlling phase transitions that lead to a (single crystalline) solid. Hence thorough knowledge of the thermodynamics of phase transitions and skill in deducing from phase diagrams the consequences for crystal growth are among the keys to efficient work in that area. In this chapter we will familiarize ourselves with the thermodynamic basis of phase diagrams. The discussion will first center upon liquid-solid equilibria and later expand the concepts to vapor-condensed phase equilibria. This general presentation is then illustrated in Chap. 4 with a broad discussion of specific systems and the consequences of their phase equilibria for the selection of specific crystal growth techniques. Large parts of this chapter are structured after a monograph on principles of phase diagrams by GORDON [3.1]. The presentation has also benefited from recent reviews by YEH [3.2] and KRÖGER [3.3]. For supplementary reading a more advanced presentation by PELTON and THOMPSON [3.33] is particularly recommended.


Phase Diagram Triple Point Isothermal Section Liquid Solution Invariant Reaction 
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  1. 3.1
    P. Gordon: Principles of Phase Diagrams (McGraw-Hill, New York 1968 ). The various figures shown from this reference have been reproduced with the permission of McGraw-Hill Book CompanyGoogle Scholar
  2. 3.2
    H.C. Yeh: “Interpretation of Phase Diagrams”, in Phase Diagrams,Vol.1,ed. by A.M. Alper (Academic Press, New York 1970) Chap.4Google Scholar
  3. 3.3
    F.A. Kröger: The Chemistry of Imperfect Crystals, 2nd ed. ( North Hol-land, Amsterdam 1973 ) Chap. 2Google Scholar
  4. 3.4
    R.E. Honig: “Vapor pressure data for the elements”, in The Characteri-zation of High-Temperature Vapors, ed. by J.L. Margrave ( Wiley and Sons, New York 1967 )Google Scholar
  5. 3.5
    K.M. Kim, A.F. Witt, H.C. Gatos: Segregation behavior in a stationary vertical zone with converging interface: pressure induced segregation effects. J. Electrochem. Soc. 121, 448 (1974)CrossRefGoogle Scholar
  6. 3.6
    C.A. Knight, N.C. Knight: Superheated ice: true compression fractures and fast internal melting. Science 178, 613 (1972)CrossRefGoogle Scholar
  7. 3.7
    P.M. Morse: Thermal Physics, 2nd ed. ( W.A. Benjamin, New York 1969 )Google Scholar
  8. 3.8
    W.J. Moore: Physical Chemistry, 3rd ed. ( Prentice Hall, Englewood Cliffs, NJ 1962 ) p. 96Google Scholar
  9. 3.9
    G.J. Abbaschian, S.F. Ravitz: Melting kinetics of gallium single crys-tals. J. Crystal Growth 28, 16 (1975)CrossRefGoogle Scholar
  10. 3.10
    A.B. Pippard: Elements of Classical Thermodynamics ( Cambridge University Press, Cambridge 1966 ) 502Google Scholar
  11. 3.11
    P.G. de Gennes: “Phase transition and turbulence: an introduction”, in Fluctuations, Instabilities, and Phase Transitions, ed. by T. Riste ( Plenum Press, New York 1975 ) pp. 1–18Google Scholar
  12. 3.12
    H.M. Strong, R.H. Wentorf, Jr.: The growth of large diamond crystals, Naturwissenschaften 59, 1 (1972)CrossRefGoogle Scholar
  13. 3.13
    J.C. Angus, H.A. Will, W.S. Stano: Growth of diamond seed crystals by vapor deposition. J. Appl. Phys. 39, 2915 (1968)CrossRefGoogle Scholar
  14. 3.14
    S.P. Chauhan, J.C. Angus, N.C. Gardner: Kinetics of carbon deposition on diamond powder. J. Appl. Phys. 47, 4746 (1976)CrossRefGoogle Scholar
  15. 3.15
    B.V. Deryagin, D.V. Fedoseev: Epitaxial synthesis of diamond in the metastable region. Russ. Chem. Rev. 39, 783 (1970)CrossRefGoogle Scholar
  16. 3.16
    B.V. Deryagin, D.V. Fedoseev: The synthesis of diamond at low pressure. Scient. American 102 (November 1975)Google Scholar
  17. 3.17
    C.D. Thurmond: Equilibrium thermochemistry of solid and liquid alloys of germanium and of silicon. J. Phys. Chem. 57, 827 (1953)CrossRefGoogle Scholar
  18. 3.18
    H. Seltz: J. Amer. Chem. Soc. 56, 307 (1934)CrossRefGoogle Scholar
  19. 3.19
    J. Steininger: Thermodynamics and calculations of the liquidus-solidus gap in homogeneous, monotonic alloy systems. J. Appl. Phys. 41, 2713 (1970)CrossRefGoogle Scholar
  20. 3.20
    F.J. Dunkerley, G.J. Mills: Thermodynamics in Metallurgy (Am. Soc. Metals, Metals Park/Ohio 1950 )Google Scholar
  21. 3.21
    G.M. Wolten, W.R. Wilcox: In Fractional Solidification,ed. by M. Zief, W.R. Wilcox (Marcel Dekker, New York 1967) Chap. 2Google Scholar
  22. 3.22
    W.C. Winegard: An Introduction to the Solidification of Metals ( Institute of Metals, London 1964 )Google Scholar
  23. 3.23
    P.G. Shewmon: Transformation of Metals ( McGraw-Hill, New York 1969 )Google Scholar
  24. 3.24
    M. Hansen: Constitution of Binary Alloys, 2nd ed. ( McGraw-Hill, New York 1958 )Google Scholar
  25. 3.25
    A.H. Cottrell: An Introduction to Metallurgy (St. Martin’s Press, New York 1967 )Google Scholar
  26. 3.26
    H.W. Bakhuis Roozeboom: Die Heterogenen Gleichgewichts, Zweites Heft: Systeme aus zwei Komponenten (Vieweg, Braunschweig 1904 ) p. 125Google Scholar
  27. 3.27
    J. Zernicke: Chemical Phase Theory (Uitgevers-Maatschappij Kluwer, Deventer, Antwerp, Djakarta 1955 )Google Scholar
  28. 3.28
    E.M. Levin, C.R. Robbins, H.F. McMurdie: Phase Diagrams for Ceramists ( American Ceramic Society, Columbus 1964 )Google Scholar
  29. 3.29
    A. Reisman: Phase Equilibria ( Academic Press, New York 1970 )Google Scholar
  30. 3.30
    R. Haase, H. Schönert: Solid—Liquid Equilibrium, Intern. Encyclopedia of Physical Chemistry and Chemical Physics, Topic 13, Vol. 1 ( Permagon, New York 1969 )Google Scholar
  31. 3.31
    G.B. Stringfellow: Calculation of ternary and quaternary III-V phase diagrams. J. Crystal Growth 27, 21 (1974)Google Scholar
  32. 3.32
    L.S. Palatnik, A.I. Landau: Phase Equilibria in Multicomponent Systems (Holt, Rinehart and Winston, New York 1964 )Google Scholar
  33. 3.33
    A.D. Pelton, W.T. Thompson: Phase Diagrams. Progr. Sol. State Chem. 10, 119 (1975).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  1. 1.Department of Physics and Department of Materials Science and EngineeringUniversity of UtahSalt Lake CityUSA

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