Advertisement

Critical and multicritical points in fluids and magnets

  • Jean Sivardiere
VI. Lattice Gas
Part of the Lecture Notes in Physics book series (LNP, volume 206)

Abstract

In this article we review the geometrical properties of the phase diagrams of multicomponent fluids. Lattice gas models used to simulate the thermodynamical behaviour of these fluids are presented. We focus on critical and multicritical points, and on the analogies between fluids and magnets.

Spin one-half models are shown to describe systems with a single critical point. Spin one models may describe systems with a symmetrical tricritical point. Spin three half models may describe systems with a symmetrical tetracritical point and non symmetrical tricritical points. The topology of phase diagrams is correctly reproduced within the molecular field approximation, and classes of systems having isomorphic phase diagrams are defined.

Keywords

Phase Diagram Ternary Mixture Critical Line Triple Line Tricritical Point 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    L. TISZA (1966), Generalized thermodynamics, The M.I.T. Press, Boston.Google Scholar
  2. (2).
    H.E. STANLEY (1971), Introduction to phase transitions and critical phenomen, Clarendon Press, Oxford.Google Scholar
  3. (3).
    R.B. GRIFFITHS and J.C. WHEELER (1970), Phys. Rev. A2 1047.ADSGoogle Scholar
  4. (4).
    K. HUANG (1963), Statistical Mechanics, Wiley, New-York.Google Scholar
  5. (5).
    T.D. LEE and C.N. YANG (1952), Phys. Rev. 87, 410.MATHCrossRefADSMathSciNetGoogle Scholar
  6. (6).
    L. LANDAU (1965), Collected papers of L. Landau, edited by D. ter Haar, Pergamon, London.Google Scholar
  7. (7).
    E.H. GRAF, D.M. LEE and J.D. REPPY (1967), Phys. Rev. Letters 19, 417.CrossRefADSGoogle Scholar
  8. (8).
    I.S. JACOBS and P.E. LAWRENCE (1967), Phys. Rev.164, 866.CrossRefADSGoogle Scholar
  9. (9).
    C.W. GARLAND and B.B. WIENER (1971), Phys. Rev. B3 1634.ADSGoogle Scholar
  10. (10).
    A.M. GOLDMAN (1973), Phys. Rev. Letters 30 1038.CrossRefADSGoogle Scholar
  11. (11).
    J.L. FIRPO et al. (1981), J. Chem Phys. 74 2569.CrossRefADSGoogle Scholar
  12. (12).
    C.P. BEAN and D. RODBELL (1962), Phys. Rev. 126, 104.CrossRefADSGoogle Scholar
  13. (13).
    J.L. MEIJERING (1963), Philips Res. Repts 18 318.Google Scholar
  14. (14).
    J.W. DOANE (1972), Phys. Rev. Letters 28, 1694.CrossRefADSGoogle Scholar
  15. (15).
    M. BLUME (1966), Phys. Rev. 141, 517.CrossRefADSGoogle Scholar
  16. (16).
    H.W. CAPEL (1966), Physica 32, 966.CrossRefADSGoogle Scholar
  17. (17).
    M. BLUME, V.J. EMERY and R.B. GRIFFITHS (1971), Phys. Rev. A4, 1071.ADSGoogle Scholar
  18. (18).
    A. HINTERMANN and F. RYS (1969), Helv. Phys. Acta 42 608.Google Scholar
  19. (19).
    J. BERNASCONI and F. RYS (1971), Phys. Rev. B4, 3045.ADSGoogle Scholar
  20. (20).
    M. WORTIS (1974), Phys. Letters 47 A, 445.ADSGoogle Scholar
  21. (21).
    M. PAPOULAR and J.P. LAHEURTE (1973), Solid State Commun. 12, 71.CrossRefADSGoogle Scholar
  22. (22).
    J. LAJZEROWICZ and J. SIVARDIERE (1975), Phys. Rev. All, 2079.ADSGoogle Scholar
  23. (23).
    J. SIVARDIERE (1981), J. Phys. C. 14, 3829.CrossRefADSGoogle Scholar
  24. (24).
    R.B. GRIFFITHS (1970), Phys. Rev. Letters 24, 715.CrossRefADSGoogle Scholar
  25. (25).
    R.B. GRIFFITHS (1973), Phys. Rev. B7, 545.ADSGoogle Scholar
  26. (26).
    D. MUKAMEL and M. BLUME (1974), Phys. Rev. A10, 610.ADSGoogle Scholar
  27. (27).
    J. SIVARDIERE and J. LAJZEROWICZ (1975), Phys. Rev. All, 2090.ADSGoogle Scholar
  28. (28).
    J. SIVARDIERE and J. LAJZEROWICZ (1975), Phys. Rev. All, 2101.ADSGoogle Scholar
  29. (29).
    J.L. MEIJERING (1950), Philips Res. Repts 5, 333.Google Scholar
  30. (30).
    J.L. MEIJERING (1951), Philips Res. Repts 6, 183.Google Scholar
  31. (31).
    D. FURMAN, S. DATTAGUPTA and R.B. GRIFFITHS (1977), Phys. Rev. B15, 441.ADSGoogle Scholar
  32. (32).
    S. KRINSKY and D. MUKAMEL (1975), Phys. Rev.B11, 399.ADSGoogle Scholar
  33. (33).
    S. KRINSKY and D. MUKAMEL (1975), Phys. Rev. B12, 211.ADSGoogle Scholar
  34. (34).
    J.R. FOX (1978), J. Chem. Phys. l69, 2231.CrossRefADSGoogle Scholar
  35. (35).
    H.K. HARDY and J.L. MEIJERING (1955), Philips Res. Repts 10, 358.Google Scholar
  36. (36).
    J. SIVARDIERE (1976), J. Physique 37, 1267.CrossRefGoogle Scholar
  37. (37).
    J. SIVARDIERE (1981), J. Phys. C14, 3845 and (1982), C15, 1611 and 1619.ADSGoogle Scholar
  38. (38).
    B. WIDOM (1973), J. Phys. Chem. 77, 2196.CrossRefGoogle Scholar
  39. (39).
    R.B. GRIFFITHS (1974), J. Chem. Phys. 60, 195.CrossRefADSGoogle Scholar
  40. (40).
    J.P. STRALEY and M.E. FISHER (1973), J, Phys. A6, 1310.ADSGoogle Scholar
  41. (40a).
    See also: D. JASNOW, T. OHTA and J. RUDNICK (1979), Phys. Rev. B20, 2774.ADSGoogle Scholar
  42. (40b).
    M. KAUFMAN et al. (1981), Phys. Rev. B23, 3448.ADSMathSciNetGoogle Scholar
  43. (41).
    J. SIVARDIERE (1980), J. Physique 41, 1081.CrossRefMathSciNetGoogle Scholar
  44. (42).
    J. SIVARDIERE (1981), Phys. Stat. Sol. b103, 823.MathSciNetADSGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Jean Sivardiere
    • 1
  1. 1.Département de Recherche FondamentaleCentre d'Etudes Nucléaires de GrenobleGrenoble CedexFrance

Personalised recommendations