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The activity coefficient of oxygen in binary liquid metal alloys

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Abstract

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,(∈ j0 )sand j0 )s, are derived in terms of the model parameters. The values of(∈ j0 )s and j0 )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.

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References

  1. C. Wagner:Thermodynamics of Alloys, pp. 51–53, Addison-Wesley, London, England, 1952.

    Google Scholar 

  2. J. Chipman:J. Iron Steel Inst., 1955, vol. 180, p. 97.

    CAS  Google Scholar 

  3. C. B. Alcock and F. D. Richardson:Acta Met., 1958, vol. 6, p. 385.

    Article  CAS  Google Scholar 

  4. C. B. Alcock and F. D. Richardson:Acta Met., 1960, vol. 8, p. 882.

    Article  CAS  Google Scholar 

  5. C. H. P. Lupis and J. F. Elliott:Acta Met., 1966, vol. 14, p. 529, p. 1019.

    Article  CAS  Google Scholar 

  6. C. H. P. Lupis and J. F. Elliott:Acta Met., 1967, vol. 15, p. 265.

    Article  CAS  Google Scholar 

  7. J. F. Elliott, M. Gleiser, and V. Ramakrishna:Thermochemistry for Steelmaking, vol. II, Addison-Wesley, Reading, Mass., 1963.

    Google Scholar 

  8. C. H. P. Lupis:Liquid Metals, Chemistry and Physics, S. Beer, ed., p. 1, Marcel Dekker, New York, 1972.

    Google Scholar 

  9. G. R. Belton and E. S. Tankins:Trans. TMS-AIME, 1965, vol. 233, pp. 1892–98.

    CAS  Google Scholar 

  10. K. T. Jacob and J. H. E. Jeffes:Trans. Inst Mining Met., 1971, vol. C80, pp. 32–41.

    Google Scholar 

  11. E-Hsin Foo and C. H. P. Lupis:Acta Met., 1973, vol. 21, p. 298.

    Article  Google Scholar 

  12. G. K. Sigworth and J. F. Elliott:Metal Sci., 1974, vol. 8, p. 298.

    CAS  Google Scholar 

  13. G. K. Sigworth and J. F. Elliott:Can. Met. Quart., 1974, vol. 13, p. 455.

    CAS  Google Scholar 

  14. K. T. Jacob and C. B. Alcock:Acta Met., 1972, vol. 20, p. 221.

    Article  CAS  Google Scholar 

  15. C. Wagner:Acta Met., 1973, vol. 21, p. 1297.

    Article  CAS  Google Scholar 

  16. N. A. Gokcen:Scr. Met., 1969, vol. 3, p. 157, p. 165.

    Article  CAS  Google Scholar 

  17. F. D. Richardson:Scr. Met., 1969, vol. 3, p. 161.

    Article  CAS  Google Scholar 

  18. W. Eichenauer and G. Müller:Z. Metallic., 1962, vol. 53, p. 321, p. 700.

    CAS  Google Scholar 

  19. H. Rickert and R. Steiner:Z. Phys. Chem., 1966, vol. 49, p. 127.

    CAS  Google Scholar 

  20. R. L. Pastorek and R. A. Rapp:Trans. TMS-AIME, 1969, vol. 245, p. 1711.

    CAS  Google Scholar 

  21. J. H. Swisher and E. T. Turkdogan:Trans. TMS-AIME, 1967, vol. 239, p. 426.

    CAS  Google Scholar 

  22. T. A. Ramanarayanan and R. A. Rapp:Met. Trans., 1972, vol. 3, p. 3239.

    CAS  Google Scholar 

  23. JANAF Thermochemical Tables, 2nd ed., NSRDS-NBS 37, U.S. Department of Commerce, National Bureau of Standards, Washington, D.C., 20402, 1971.

  24. J. Chipman:J. Trans. ASM, 1942, vol. 30, pp. 817–54.

    CAS  Google Scholar 

  25. B. C. H. Steele: Ph.D. Thesis, University of London, 1965.

  26. B. C. H. Steele:Inst. Min. Met., p. 21, London, 1968.

  27. K. Kiukkola and C. Wagner:J. Electrochem. Soc., 1957, vol. 104, pp. 379–87.

    Article  Google Scholar 

  28. N. P. Allen and T. Hewitt:J. Inst. Metals, 1933, vol. 51, pp. 257–72.

    Google Scholar 

  29. D. J. Girardi and C. A. Siebert:J. Metals, 1950, vol. 188, pp. 1168–70.

    CAS  Google Scholar 

  30. K. Sano and H. Sakao:Mem. Fac. Eng. Nagoya Univ., 1956, vol. 8, pp. 137–62.

    CAS  Google Scholar 

  31. A. D. Kulkarni:Met. Trans., 1973, vol. 4, pp. 1713–21.

    CAS  Google Scholar 

  32. D. R. Young and J. W. Tomlinson: Imperial College of Science and Technology, London, as quoted by Kulkarni, Ref. 31.

  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.

  34. K. Azuma and Y. Ogawa:J. Mining Met. Inst., Jap., 1974, vol. 90, pp. 249–52.

    Google Scholar 

  35. W. A. Fischer and W. Ackerman:Arch. Eisenheuttenw., 1966, vol. 37, pp. 43–47.

    CAS  Google Scholar 

  36. M. M. A. El-Naggar and N. A. P. Parlee:Met. Trans., 1970, vol. 1, pp. 2975–77.

    CAS  Google Scholar 

  37. E. S. Tankins:Can. Met. Quart, 1970, vol. 9, pp. 353–57.

    CAS  Google Scholar 

  38. E. S. Tankins and N. Gokcen:High Temp. Sci., 1972, vol. 4, pp. 393–404.

    CAS  Google Scholar 

  39. C. R. Nanda and G. Geiger:Met. Trans., 1970, vol. 1, pp. 1235–43.

    CAS  Google Scholar 

  40. H. Rickert and H. Wagner:Electrochim. Acta, 1966, vol. 11, pp. 83–91.

    Article  Google Scholar 

  41. R. Fruehan and F. D. Richardson:Trans. TMS-AIME, 1969, vol. 245, pp. 1721–26.

    CAS  Google Scholar 

  42. U. Block and H. Stüwe:Z. Metallic., 1969, vol. 60, pp. 709–12.

    CAS  Google Scholar 

  43. T. Wilder:Trans. TMS-AIME, 1966, vol. 236, pp. 1035–40.

    CAS  Google Scholar 

  44. W. Pluschkell and H. Engell:Z. Metallic., 1965, vol. 56, pp. 450–52.

    CAS  Google Scholar 

  45. S. Matoba and T. Kuwana:Tetsu To Hagane Overseas, 1965, vol. 5, no. 3, pp. 187–95.

    Google Scholar 

  46. T. P. Floridis and J. Chipman:Trans. TMS-AIME, 1958, vol. 212, pp. 549–53.

    CAS  Google Scholar 

  47. H. A. Wriedt and J. Chipman:Trans. AIME, 1956, vol. 206, pp. 1195–99.

    Google Scholar 

  48. W. A. Fischer and P. Janke:Arch. Eisenheuttenw., 1968, vol. 39, pp. 89–99.

    CAS  Google Scholar 

  49. E. S. Tankins, N. A. Gokcen, and G. R. Belton:Trans. TMS-AIME, 1964, vol. 230, pp. 820–27.

    CAS  Google Scholar 

  50. B. F. Belov, I. A. Novokhatskiy, and Yu. A. Lobanov:Izv. Akad. Nauk SSSR,Metal, 1967, no. 3, pp. 19–23.

  51. H. Schenck and K. H. Gerdum:Arch. Eisenheuttenw., 1959, vol. 30, pp. 451–60.

    CAS  Google Scholar 

  52. H. Sakao and K. Sano:J. Jap. Inst. Metals, 1962, vol. 26, pp. 30–34.

    Google Scholar 

  53. R. J. Fruehan, L. J. Martonik, and E. T. Turkdogan:Trans. TMS-AIME, 1969, vol. 245, pp. 1501–09.

    CAS  Google Scholar 

  54. H. Schenck, E. Steinmetz, and P. C. Rhee:Arch. Eisenheuttenw., 1969, vol. 40, pp. 619–20.

    Google Scholar 

  55. J. F. Elliott and M. Gleiser:Thermochemistry for Steelmaking, vol. I, Addison- Wesley, Reading, Mass., 1960.

    Google Scholar 

  56. J. E. Bowers:J. Inst. Metals, 1961, vol. 90, pp. 321–28.

    Google Scholar 

  57. V. V. Averin, A. Yu. Polyakov, and A. M. Samarin:Izv. Akad. Nauk SSSR,Otd. Tekh. Nauk, 1957, no. 8, p. 120.

  58. C. Diaz, C. R. Masson, and F. D. Richardson:Trans. Inst. Mining Met., 1965, vol. C75, pp. 183–185.

    Google Scholar 

  59. N. A. P. Parlee and E. M. Sacris:Trans. TMS-AIME, 1965, vol. 233, pp. 1918–19.

    CAS  Google Scholar 

  60. C. B. Alcock and T. N. Bedford:Trans. Faraday Soc., 1964, vol. 60, pp. 822–35.

    Article  CAS  Google Scholar 

  61. F. D. Richardson and L. E. Webb:Trans. Inst. Mining Met., 1954-55, vol. C64, pp. 529–64.

    Google Scholar 

  62. T. N. Bedford and C. B. Alcock:Trans. Faraday Soc., 1965, vol. 61, pp. 443–53.

    Article  Google Scholar 

  63. K. T. Jacob, S. K. Seshardi, and F. D. Richardson:Trans. Inst. Mining Met., 1970,vol. C79, pp. 274–80.

    Google Scholar 

  64. D. W. Marquardt:J. Soc. Ind. Appl. Math., 1963, vol. 2, pp. 431–41.

    Article  Google Scholar 

  65. K. T. Jacob and J. H. E. Jeffes:J. Chem. Thermody., 1973, vol. 5, pp. 365–69.

    Article  CAS  Google Scholar 

  66. I. Tsukahara:Nippon Kinzoku Gakkaishi, 1970, vol. 34, pp. 679.

    CAS  Google Scholar 

  67. T. Oishi, T. Nagahata, and J. Moriyama:Nippon Kinoku Gakkaishi, 1970, vol. 34, p. 1103.

    CAS  Google Scholar 

  68. U. Kuxmann and W. Machens:Erzmetall., 1972, vol. 25, pp. 267.

    CAS  Google Scholar 

  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. E. S. Tankins, J. F. Erthal, and M. K. Thomas, Jr.:J. Electrochem. Soc., 1965, vol. 112, pp. 446–50.

    Article  CAS  Google Scholar 

  71. A. D. Kulkarni and R. E. Johnson:Met. Trans., 1973, vol. 4, pp. 1723–27.

    CAS  Google Scholar 

  72. K. P. Abraham:Trans. Indian Inst. Metals, 1969, vol. 5, pp. 5–7.

    Google Scholar 

  73. G. K. Sigworth and J. F. Elliott: unpublished research, Carnegie-Mellon Uni- versity, Pittsburgh, Pa., and M.I.T., Cambridge, Mass., 1976.

  74. W. A. Fischer, P. Janke, and W. Ackerman:Arch. Eisenheuttenw., 1970, vol. 41, pp. 361–67.

    CAS  Google Scholar 

  75. K. T. Jacob and J. H. E. Jeffes:J. Chem. Thermody., 1971, vol. 3, pp. 433–43.

    Article  CAS  Google Scholar 

  76. W. A. Fischer and M. H. Haussmann:Arch. Eisenheuttenw., 1966, vol.37, pp. 1–3.

    Google Scholar 

  77. E. S. Tankins:Met. Trans., 1970, vol. 1, pp. 538–40.

    CAS  Google Scholar 

  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. 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. L. Pauling:The Nature of the Chemical Bond, 3rd ed., Cornell, Ithaca, 1970.

    Google Scholar 

  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. K. T. Jacob and J. H. E. Jeffes:Trans. Inst. Mining Met., 1971, vol. C80, pp. 181.

    Google Scholar 

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Chiang, T., Chang, Y.A. The activity coefficient of oxygen in binary liquid metal alloys. Metall Trans B 7, 453–467 (1976). https://doi.org/10.1007/BF02652717

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