Metallurgical Transactions B

, Volume 7, Issue 3, pp 453–467 | Cite as

The activity coefficient of oxygen in binary liquid metal alloys

  • T. Chiang
  • Y. A. Chang
Physical Chemistry


The Wagner model with one energy parameter,h, for describing the effect of alloying elements on the activity coefficients of nonmetallic solutes in liquid metals is extended to have two energy parameters,h 1andh 2. The validity of both the Wagner one-parameter equation and the newly derived two-parameter equation is tested using data available in the literature for twelve ternary metal-oxygen systems. In order to have consistent thermodynamic data, all the relevant binary, as well as the twelve ternary metal-oxygen systems are evaluated using the same thermodynamic values for the reference materials which were used in carrying out the experimental measurements. It is found that the twoparameter equation is capable of quantitatively accounting for the compositional dependences of the activity coefficients of oxygen in all twelve ternary systems while the Wagner one-parameter equation is not. A correlation between the Wagner parameter,h, and the thermodynamic properties of the respective binary metal-oxygen and binary metals systems is found, from which the value of this parameter may be predicted without referring to any ternary data. Accordingly, the two-parameter equation is more useful in evaluating ternary experimental data while the Wagner one-parameter equation in connection with the correlation betweenh and binary data is capable of predicting ternary data without any experimental investigation in the ternary region. Based on the one-parameter and the two-parameter equations, theoretical equations for the first-order and second-order free energy interaction parameters,(∈ 0 j )sand 0 j )s, are derived in terms of the model parameters. The values of(∈ 0 j )s and 0 j )s for all the systems are derived and are found to vary linearly with the reciprocal of temperature. Furthermore, linear relationships between these two interaction parameters and their slopes with 1/T are found, from which the temperature dependence of the interaction parameters may be estimated in the absence of experimental data.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Wagner:Thermodynamics of Alloys, pp. 51–53, Addison-Wesley, London, England, 1952.Google Scholar
  2. 2.
    J. Chipman:J. Iron Steel Inst., 1955, vol. 180, p. 97.Google Scholar
  3. 3.
    C. B. Alcock and F. D. Richardson:Acta Met., 1958, vol. 6, p. 385.CrossRefGoogle Scholar
  4. 4.
    C. B. Alcock and F. D. Richardson:Acta Met., 1960, vol. 8, p. 882.CrossRefGoogle Scholar
  5. 5.
    C. H. P. Lupis and J. F. Elliott:Acta Met., 1966, vol. 14, p. 529, p. 1019.CrossRefGoogle Scholar
  6. 6.
    C. H. P. Lupis and J. F. Elliott:Acta Met., 1967, vol. 15, p. 265.CrossRefGoogle Scholar
  7. 7.
    J. F. Elliott, M. Gleiser, and V. Ramakrishna:Thermochemistry for Steelmaking, vol. II, Addison-Wesley, Reading, Mass., 1963.Google Scholar
  8. 8.
    C. H. P. Lupis:Liquid Metals, Chemistry and Physics, S. Beer, ed., p. 1, Marcel Dekker, New York, 1972.Google Scholar
  9. 9.
    G. R. Belton and E. S. Tankins:Trans. TMS-AIME, 1965, vol. 233, pp. 1892–98.Google Scholar
  10. 10.
    K. T. Jacob and J. H. E. Jeffes:Trans. Inst Mining Met., 1971, vol. C80, pp. 32–41.Google Scholar
  11. 11.
    E-Hsin Foo and C. H. P. Lupis:Acta Met., 1973, vol. 21, p. 298.CrossRefGoogle Scholar
  12. 12.
    G. K. Sigworth and J. F. Elliott:Metal Sci., 1974, vol. 8, p. 298.Google Scholar
  13. 13.
    G. K. Sigworth and J. F. Elliott:Can. Met. Quart., 1974, vol. 13, p. 455.Google Scholar
  14. 14.
    K. T. Jacob and C. B. Alcock:Acta Met., 1972, vol. 20, p. 221.CrossRefGoogle Scholar
  15. 15.
    C. Wagner:Acta Met., 1973, vol. 21, p. 1297.CrossRefGoogle Scholar
  16. 16.
    N. A. Gokcen:Scr. Met., 1969, vol. 3, p. 157, p. 165.CrossRefGoogle Scholar
  17. 17.
    F. D. Richardson:Scr. Met., 1969, vol. 3, p. 161.CrossRefGoogle Scholar
  18. 18.
    W. Eichenauer and G. Müller:Z. Metallic., 1962, vol. 53, p. 321, p. 700.Google Scholar
  19. 19.
    H. Rickert and R. Steiner:Z. Phys. Chem., 1966, vol. 49, p. 127.Google Scholar
  20. 20.
    R. L. Pastorek and R. A. Rapp:Trans. TMS-AIME, 1969, vol. 245, p. 1711.Google Scholar
  21. 21.
    J. H. Swisher and E. T. Turkdogan:Trans. TMS-AIME, 1967, vol. 239, p. 426.Google Scholar
  22. 22.
    T. A. Ramanarayanan and R. A. Rapp:Met. Trans., 1972, vol. 3, p. 3239.Google Scholar
  23. 23.
    JANAF Thermochemical Tables, 2nd ed., NSRDS-NBS 37, U.S. Department of Commerce, National Bureau of Standards, Washington, D.C., 20402, 1971.Google Scholar
  24. 24.
    J. Chipman:J. Trans. ASM, 1942, vol. 30, pp. 817–54.Google Scholar
  25. 25.
    B. C. H. Steele: Ph.D. Thesis, University of London, 1965.Google Scholar
  26. 26.
    B. C. H. Steele:Inst. Min. Met., p. 21, London, 1968.Google Scholar
  27. 27.
    K. Kiukkola and C. Wagner:J. Electrochem. Soc., 1957, vol. 104, pp. 379–87.CrossRefGoogle Scholar
  28. 28.
    N. P. Allen and T. Hewitt:J. Inst. Metals, 1933, vol. 51, pp. 257–72.Google Scholar
  29. 29.
    D. J. Girardi and C. A. Siebert:J. Metals, 1950, vol. 188, pp. 1168–70.Google Scholar
  30. 30.
    K. Sano and H. Sakao:Mem. Fac. Eng. Nagoya Univ., 1956, vol. 8, pp. 137–62.Google Scholar
  31. 31.
    A. D. Kulkarni:Met. Trans., 1973, vol. 4, pp. 1713–21.Google Scholar
  32. 32.
    D. R. Young and J. W. Tomlinson: Imperial College of Science and Technology, London, as quoted by Kulkarni, Ref. 31.Google Scholar
  33. 33.
    J. Osterwald: Thesis, Technical University of Berlin, 1965; and J. Osterwald, G. Reimann, and W. Stickel:Z. Phys. Chem. Neue Folge, 1969, vol. 66, pp. 1-7.Google Scholar
  34. 34.
    K. Azuma and Y. Ogawa:J. Mining Met. Inst., Jap., 1974, vol. 90, pp. 249–52.Google Scholar
  35. 35.
    W. A. Fischer and W. Ackerman:Arch. Eisenheuttenw., 1966, vol. 37, pp. 43–47.Google Scholar
  36. 36.
    M. M. A. El-Naggar and N. A. P. Parlee:Met. Trans., 1970, vol. 1, pp. 2975–77.Google Scholar
  37. 37.
    E. S. Tankins:Can. Met. Quart, 1970, vol. 9, pp. 353–57.Google Scholar
  38. 38.
    E. S. Tankins and N. Gokcen:High Temp. Sci., 1972, vol. 4, pp. 393–404.Google Scholar
  39. 39.
    C. R. Nanda and G. Geiger:Met. Trans., 1970, vol. 1, pp. 1235–43.Google Scholar
  40. 40.
    H. Rickert and H. Wagner:Electrochim. Acta, 1966, vol. 11, pp. 83–91.CrossRefGoogle Scholar
  41. 41.
    R. Fruehan and F. D. Richardson:Trans. TMS-AIME, 1969, vol. 245, pp. 1721–26.Google Scholar
  42. 42.
    U. Block and H. Stüwe:Z. Metallic., 1969, vol. 60, pp. 709–12.Google Scholar
  43. 43.
    T. Wilder:Trans. TMS-AIME, 1966, vol. 236, pp. 1035–40.Google Scholar
  44. 44.
    W. Pluschkell and H. Engell:Z. Metallic., 1965, vol. 56, pp. 450–52.Google Scholar
  45. 45.
    S. Matoba and T. Kuwana:Tetsu To Hagane Overseas, 1965, vol. 5, no. 3, pp. 187–95.Google Scholar
  46. 46.
    T. P. Floridis and J. Chipman:Trans. TMS-AIME, 1958, vol. 212, pp. 549–53.Google Scholar
  47. 47.
    H. A. Wriedt and J. Chipman:Trans. AIME, 1956, vol. 206, pp. 1195–99.Google Scholar
  48. 48.
    W. A. Fischer and P. Janke:Arch. Eisenheuttenw., 1968, vol. 39, pp. 89–99.Google Scholar
  49. 49.
    E. S. Tankins, N. A. Gokcen, and G. R. Belton:Trans. TMS-AIME, 1964, vol. 230, pp. 820–27.Google Scholar
  50. 50.
    B. F. Belov, I. A. Novokhatskiy, and Yu. A. Lobanov:Izv. Akad. Nauk SSSR,Metal, 1967, no. 3, pp. 19–23.Google Scholar
  51. 51.
    H. Schenck and K. H. Gerdum:Arch. Eisenheuttenw., 1959, vol. 30, pp. 451–60.Google Scholar
  52. 52.
    H. Sakao and K. Sano:J. Jap. Inst. Metals, 1962, vol. 26, pp. 30–34.Google Scholar
  53. 53.
    R. J. Fruehan, L. J. Martonik, and E. T. Turkdogan:Trans. TMS-AIME, 1969, vol. 245, pp. 1501–09.Google Scholar
  54. 54.
    H. Schenck, E. Steinmetz, and P. C. Rhee:Arch. Eisenheuttenw., 1969, vol. 40, pp. 619–20.Google Scholar
  55. 55.
    J. F. Elliott and M. Gleiser:Thermochemistry for Steelmaking, vol. I, Addison- Wesley, Reading, Mass., 1960.Google Scholar
  56. 56.
    J. E. Bowers:J. Inst. Metals, 1961, vol. 90, pp. 321–28.Google Scholar
  57. 57.
    V. V. Averin, A. Yu. Polyakov, and A. M. Samarin:Izv. Akad. Nauk SSSR,Otd. Tekh. Nauk, 1957, no. 8, p. 120.Google Scholar
  58. 58.
    C. Diaz, C. R. Masson, and F. D. Richardson:Trans. Inst. Mining Met., 1965, vol. C75, pp. 183–185.Google Scholar
  59. 59.
    N. A. P. Parlee and E. M. Sacris:Trans. TMS-AIME, 1965, vol. 233, pp. 1918–19.Google Scholar
  60. 60.
    C. B. Alcock and T. N. Bedford:Trans. Faraday Soc., 1964, vol. 60, pp. 822–35.CrossRefGoogle Scholar
  61. 61.
    F. D. Richardson and L. E. Webb:Trans. Inst. Mining Met., 1954-55, vol. C64, pp. 529–64.Google Scholar
  62. 62.
    T. N. Bedford and C. B. Alcock:Trans. Faraday Soc., 1965, vol. 61, pp. 443–53.CrossRefGoogle Scholar
  63. 63.
    K. T. Jacob, S. K. Seshardi, and F. D. Richardson:Trans. Inst. Mining Met., 1970,vol. C79, pp. 274–80.Google Scholar
  64. 64.
    D. W. Marquardt:J. Soc. Ind. Appl. Math., 1963, vol. 2, pp. 431–41.CrossRefGoogle Scholar
  65. 65.
    K. T. Jacob and J. H. E. Jeffes:J. Chem. Thermody., 1973, vol. 5, pp. 365–69.CrossRefGoogle Scholar
  66. 66.
    I. Tsukahara:Nippon Kinzoku Gakkaishi, 1970, vol. 34, pp. 679.Google Scholar
  67. 67.
    T. Oishi, T. Nagahata, and J. Moriyama:Nippon Kinoku Gakkaishi, 1970, vol. 34, p. 1103.Google Scholar
  68. 68.
    U. Kuxmann and W. Machens:Erzmetall., 1972, vol. 25, pp. 267.Google Scholar
  69. 69.
    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
  70. 70.
    E. S. Tankins, J. F. Erthal, and M. K. Thomas, Jr.:J. Electrochem. Soc., 1965, vol. 112, pp. 446–50.CrossRefGoogle Scholar
  71. 71.
    A. D. Kulkarni and R. E. Johnson:Met. Trans., 1973, vol. 4, pp. 1723–27.Google Scholar
  72. 72.
    K. P. Abraham:Trans. Indian Inst. Metals, 1969, vol. 5, pp. 5–7.Google Scholar
  73. 73.
    G. K. Sigworth and J. F. Elliott: unpublished research, Carnegie-Mellon Uni- versity, Pittsburgh, Pa., and M.I.T., Cambridge, Mass., 1976.Google Scholar
  74. 74.
    W. A. Fischer, P. Janke, and W. Ackerman:Arch. Eisenheuttenw., 1970, vol. 41, pp. 361–67.Google Scholar
  75. 75.
    K. T. Jacob and J. H. E. Jeffes:J. Chem. Thermody., 1971, vol. 3, pp. 433–43.CrossRefGoogle Scholar
  76. 76.
    W. A. Fischer and M. H. Haussmann:Arch. Eisenheuttenw., 1966, vol.37, pp. 1–3.Google Scholar
  77. 77.
    E. S. Tankins:Met. Trans., 1970, vol. 1, pp. 538–40.Google Scholar
  78. 78.
    E. G. King, A. D. Mah, and L. B. Pankratz: INCRA Monograph II, Thermody- namic Properties of Copper and Its Inorganic Compounds, International Cop- per Research Association, Inc., New York, 1973.Google Scholar
  79. 79.
    A. Luraschi and J. F. Elliott: inExtractive Metallurgy of Copper, J. C. Yannopoulos and J. C. Agarwal, eds., vol. I, pp. 90–114, Pyrometallurgy and Electrolytic Refining, The Metallurgical Society of AIME, New York, 1976.Google Scholar
  80. 80.
    L. Pauling:The Nature of the Chemical Bond, 3rd ed., Cornell, Ithaca, 1970.Google Scholar
  81. 81.
    J. Chipman and D. A. Corrigan: inApplications of Fundamental Thermodynam- ics to Metallurgical Process, G. R. Fitterer, ed., p. 23, Gordon and Breach, New York, 1967.Google Scholar
  82. 82.
    K. T. Jacob and J. H. E. Jeffes:Trans. Inst. Mining Met., 1971, vol. C80, pp. 181.Google Scholar

Copyright information

© American Society for Metals, The Melallurgical Society of AIME 1976

Authors and Affiliations

  • T. Chiang
    • 1
  • Y. A. Chang
    • 1
  1. 1.Materials Department, College of Engineering and Applied ScienceUniversity of Wisconsin-MilwaukeeMilwaukee

Personalised recommendations