Skip to main content
Log in

Simultaneous optimization of thermochemical data for liquid iron alloys containing C, N, Ti, Si, Mn, S, and P

  • Published:
Metallurgical and Materials Transactions B Aims and scope Submit manuscript

Abstract

A data base of thermochemical parameters for liquid iron-base alloys containing C, N, Ti, Si, Mn, S, and P is presented. A matrix of linear inequalities describing the experimental data among these elements was constructed. A set of internally consistent thermochemical data permitted by the uncertainties of the experiments was evaluated by means of a linear programming algorithm. Expressions for the interaction parameters of the solutes and the Gibbs energies of formation of the carbides, nitrides, carbonitrides, and sulfides of titanium were simultaneously optimized. It is shown that the resulting thermochemical data base reproduces the experimental data satisfactorily.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C.H.P. Lupis:Chemical Thermodynamics of Materials, Elsevier Science Publishing Co., New York, NY, 1983, p. 524.

    Google Scholar 

  2. T. Mori, E. Ichise, and A. Moro-Oka:Steelmaking Data Sourcebook, The Japanese Society for the Promotion of Science, Gordon and Breach Science Publishers, New York, NY, 1988, pp. 281, 223, and 272.

    Google Scholar 

  3. L. Kaufman:CALPHAD, 1977, vol. 1, pp. 1–6.

    Article  Google Scholar 

  4. D. Bouchard and C.W. Bale:Computer Software in Chemical and Extractive Metallurgy, Proc. 2nd Int. Symp., C.W. Bale and G.A. Irons, eds. Canadian Institute of Mining, Metallurgy and Petroleum, Montréal, 1993, pp. 89–97.

    Google Scholar 

  5. H.J. Greenwood:Geochim. Cosmochim. Acta, 1967, vol. 31, pp. 465–90.

    Article  CAS  Google Scholar 

  6. T.M. Gordon:J. Geol., 1973, vol. 81, pp. 199–208.

    Article  CAS  Google Scholar 

  7. T. Gordon:Short Course in Application of Thermodynamics to Petrology and Ore Deposits, H.J. Greenwood, ed., Mineralogical Association of Canada, Vancouver, 1977, pp. 185–98.

    Google Scholar 

  8. H.W. Day:Am. Mineral., 1979, vol. 64, pp. 809–23.

    CAS  Google Scholar 

  9. R.G. Berman and T.H. Brown:Geochim. Cosmochim. Acta, 1987, vol. 148, pp. 661–78.

    Google Scholar 

  10. M.V. Rao, R. Hiskes, and W.A. Tiller:Acta Metall., 1973, vol. 21, pp. 733–40.

    Article  CAS  Google Scholar 

  11. M.V. Rao and W.A. Tiller:Mater. Sci. Eng., 1974, vol. 15, pp. 87–89.

    Article  CAS  Google Scholar 

  12. I. Barin, O. Knacke, and O. Kubachewski:Thermochemical Properties of Inorganic Substances, Springer-Verlag, Berlin, 1977.

    Google Scholar 

  13. F.D. Rossini:Experimental Thermochemistry, Interscience Publishers Inc., New York, NY, 1956, p. 326.

    Google Scholar 

  14. G.M. Anderson:Short Course in Application of Thermodynamics to Petrology and Ore Deposits, H.J. Greenwood, ed., Mineralogical Association of Canada, Vancouver, 1977, pp. 199–215.

    Google Scholar 

  15. C. Wagner:Thermodynamics of Alloys, Addison-Wesley, Reading, MA, 1952, pp. 51–53.

    Google Scholar 

  16. L.S. Darken:Trans. TMS-A1ME, 1967, vol. 239, pp. 90–96.

    CAS  Google Scholar 

  17. A.D. Pelton and C.W. Bale:Metall. Trans. A, 1986, vol. 17A, pp. 1211–15.

    CAS  Google Scholar 

  18. C.W. Bale and A.D. Pelton:Metall. Trans. A, 1990, vol. 21A, pp. 1997–2002.

    CAS  Google Scholar 

  19. D.B. Evans and R.D. Pehlke:Trans. TMS-AIME, 1965, vol. 233, pp. 1620–24.

    CAS  Google Scholar 

  20. A. Ejima, K. Suzuki, N. Harada, and K. Sanbongi:Trans. Iron Steel Inst. Jpn., 1977, vol. 17, pp. 349–58.

    Google Scholar 

  21. Z. Morita and K. Kunisada:Trans. Iron Steel Inst. Jpn., 1978, vol. 18, pp. 648–54.

    CAS  Google Scholar 

  22. F.M. Donahue III and R.D. Pehlke:Metall. Trans. B, 1987, vol. 18B, pp. 681–85.

    Google Scholar 

  23. P. Duwez and F. Odell:J. Electrochem. Soc., 1950, vol. 97, pp. 299–304.

    CAS  Google Scholar 

  24. M. Hillert and L.L. Staffanson:Acta Chem. Scand., 1970, vol. 24, pp. 3618–26.

    Article  CAS  Google Scholar 

  25. B. Ozturk and R.J. Fruehan:Metall. Trans. B, 1990, vol. 21B, pp. 879–84.

    CAS  Google Scholar 

  26. SAS Institute Inc.:SAS/OR™ User’s Guide, Version 5 ed., SAS Institute Inc., Cary, NC, 1985, pp. 138–209.

    Google Scholar 

  27. W.T. Thompson, C.W. Bale, and A.D. Pelton:F*A*C*T—Facility for the Analysis of Chemical Thermodynamics, User’s Manual, 2nd ed., Ecole Polytechnique/Royal Military College, Montréal, 1985, pp. 1–33.

    Google Scholar 

  28. C.W. Bale, W.T. Thompson, A.D. Pelton, G. Ericksson, P. Talley, and J. Melanpon:Computer Software in Chemical and Extractive Metallurgy, Proc. 2nd Int. Symp., C.W. Bale and G.A. Irons, eds. Canadian Institute of Mining, Metallurgy, and Petroleum, Montréal, 1993, pp. 73–86.

    Google Scholar 

  29. O. Kubaschewski:Iron—Binary Phase Diagrams, Springer-Verlag, New York, NY, 1982, pp. 23–26.

    Google Scholar 

  30. J. Chipman, R.M. Alfred, L.W. Gott, R.B. Small, D.M. Wilson, C.N. Thomson, D.L. Guernsey, and J.C. Fulton:Trans. ASM, 1952, vol. 44, pp. 1215–32.

    Google Scholar 

  31. M. Sumito, N. Tsuchiya, K. Okabe, and K. Sanbongi:Trans. Iron Steel Inst. Jpn., 1981, vol. 21, pp. 3060–68.

    Google Scholar 

  32. E. Schumann and D. Kramer:Giessereiforschung, 1969, vol. 21, pp. 33–47.

    Google Scholar 

  33. F.D. Richardson and W.E. Dennis:Trans. Faraday Soc., 1953, vol. 49, pp. 171–80.

    Article  CAS  Google Scholar 

  34. S. Ban-Ya and S. Matoba:Physical Chemistry of Process Metallurgy, G.R. St. Pierre, ed., Interscience Publishers, New York, NY, 1961, Part I, pp. 373–402.

    Google Scholar 

  35. J. Chipman:Metall. Trans., 1970, vol. 1, pp. 2163–68.

    Article  CAS  Google Scholar 

  36. N.H. El-Kaddah and D.G.C. Robertson:Metall. Trans. B, 1977, vol. 8B, pp. 569–79.

    CAS  Google Scholar 

  37. R.J. Fruehan:Metall. Trans., 1970, vol. 1, pp. 3403–10.

    Article  CAS  Google Scholar 

  38. S. Wagner and G.S. St. Pierre:Metall. Trans., 1974, vol. 5, pp. 887–89.

    Article  CAS  Google Scholar 

  39. T. Furukawa and E. Kato:Tetsu to Hagané, 1975, vol. 61, pp. 22–30.

    Google Scholar 

  40. J.C. Humbert and J.F. Elliot:Trans. TMS-AIME, 1960, vol. 218, pp. 1076–87.

    CAS  Google Scholar 

  41. V.F. Neumann and H. Schenk:Giesserei Tech. Wiss. Beih., 1962, vol. 14, pp. 21–29.

    CAS  Google Scholar 

  42. G. Yuanchang, W. Changzhen, and Y. Hualong:Metall. Trans. B, 1990, vol. 21B, pp. 537–41.

    Google Scholar 

  43. K. Narita, M. Maekawa, T. Onoye, Y. Satoh, and M. Miyamoto:Trans. Iron Steel Inst. Jpn., 1976, vol. 17, pp. 459–68.

    Google Scholar 

  44. R.J. Fruehan:Metall. Trans., 1970, vol. 1, pp. 865–70.

    Article  CAS  Google Scholar 

  45. P.J. Bowles, H.F. Ramstad, and F.D. Richardson:J. Iron Steel Inst., 1964, vol. 202, pp. 113–21.

    CAS  Google Scholar 

  46. G. Smith and J. Taylor:J. Iron Steel Inst., 1964, vol. 202, pp. 577–80.

    CAS  Google Scholar 

  47. N.A. Gokcen and J. Chipman:Trans. AIME, 1952, vol. 194, pp. 171–81.

    Google Scholar 

  48. T.G. Chart:High Temp.-High Pressures, 1970, vol. 2, pp. 461–70.

    CAS  Google Scholar 

  49. R. Schmid:CALPHAD, 1980, vol. 4, pp. 101–108.

    Article  CAS  Google Scholar 

  50. F. Wooley and J.F. Elliot:Trans. TMS-AIME, 1967, vol. 239, pp. 1872–83.

    Google Scholar 

  51. J. Chunlin and Q. Guojun:Trans. Jpn. Inst. Met., 1985, vol. 26, pp. 832–39.

    Google Scholar 

  52. G. Yuanchang and W. Changzhen:Metall. Trans. B, 1990, vol. 21B, pp. 543–47.

    Google Scholar 

  53. D. Bouchard: Ph.D. Thesis, Ecole Polytechnique, Montréal, 1994, pp. 102–16; D. Bouchard and C.W. Bale: unpublished researcher, 1994.

    Google Scholar 

  54. C.W. Schultz, N. Riazance, and S.L. Payne: Report of Investigation 6807, U.S. Bureau of Mines, U.S. Government Printing Office, Washington, DC, 1966.

  55. K. Sanbongi and M. Ohtani:Sci. Rep. Res. Inst. Tohoku, 1955, vol. A7, pp. 204–09.

    Google Scholar 

  56. J.M. Steiler, P. Riboud, M. Onillon, and M. Olette:C. R. Seances Acad. Sci. Sér. C, 1973, vol. 277, pp. 1207–10.

    CAS  Google Scholar 

  57. K. Mukai, H. Aibe, and T. Kitajima:J. Jpn. Inst. Met., 1982, vol. 46, pp. 487–94.

    CAS  Google Scholar 

  58. K.T. Jacob, J.P. Hajra, and M. Iwase:Arch. Eisenhüttenwes., 1984, vol. 55, pp. 421–26.

    CAS  Google Scholar 

  59. M. Ohtani:Sci. Rep. Res. Inst. Tohoku, 1957, vol. A9, pp. 426–33.

    Google Scholar 

  60. F. Ishii, S. Ban-Ya, and T. Fuwa:Tetsu to Hagané, 1982, vol. 68, pp. 946–55.

    CAS  Google Scholar 

  61. R.D. Pehlke and J.F. Elliot:Trans. TMS-AIME, 1960, vol. 218, pp. 1088–101.

    CAS  Google Scholar 

  62. D.W. Gomersall, A. McLean, and R.G. Ward:Trans. TMS-AIME, 1968, vol. 242, pp. 1309–15.

    CAS  Google Scholar 

  63. F. Ishii, S. Ban-Ya, and T. Fuwa:Tetsu to Hagané, 1982, vol. 68, pp. 1551–59.

    CAS  Google Scholar 

  64. V.H. Schenck, M.G. Frohberg, and H. Graf:Arch. Eisenhüttenwes., 1959, vol. 30, pp. 533–37.

    CAS  Google Scholar 

  65. M. Uda and R.D. Pehlke:Cast Met. Res. J., 1974, vol. 10, pp. 30–38.

    CAS  Google Scholar 

  66. O. Opravil and R.D. Pehlke:Trans. Am. Foundrymen’s Soc., 1969, vol. 77, pp. 415–21.

    Google Scholar 

  67. K. Mukai and A. Uchida:Tetsu to Hagané, 1974, vol. 60, pp. 325–36.

    CAS  Google Scholar 

  68. F. Ishii and T. Fuwa:Tetsu to Hagané, 1981, vol. 67, pp. 746–54.

    CAS  Google Scholar 

  69. S. Ban-Ya and J. Chipman:Trans. TMS-AIME, 1968, vol. 242, pp. 940–46.

    CAS  Google Scholar 

  70. J.P. Morris and A.J. Williams:Trans. ASM, 1941, vol. 41, pp. 1425–39.

    Google Scholar 

  71. C.B. Alcock and L.L. Cheng:J. Iron Steel Inst., 1960, vol. 195, pp. 169–73.

    CAS  Google Scholar 

  72. S. Ban-Ya and J. Chipman:Trans. TMS-AIME, 1969, vol. 245, pp. 133–43.

    CAS  Google Scholar 

  73. C.W. Sherman and J. Chipman:J. Met., 1952, vol. 194, pp. 597–602.

    Google Scholar 

  74. P.O. Mellberg and L. Yunzu:Scand. J. Metall., 1981, vol. 10, pp. 94–96.

    CAS  Google Scholar 

  75. E.T. Turkdogan and R.A. Hancock:J. Iron Steel Inst., 1955, vol. 179, pp. 155–59.

    CAS  Google Scholar 

  76. M. Ohtani and N.A. Gokcen:Trans. TMS-AIME, 1960, vol. 218, pp. 380–81.

    CAS  Google Scholar 

  77. P. Spencer and O. Kubaschewski:Arch. Eisenhiittenwes., 1978, vol. 49, pp. 225–28.

    CAS  Google Scholar 

  78. V.H. Schenck, E. Steimetz, and R. Gohhlke:Arch. Eisenhüttenwes., 1966, vol. 37, pp. 775–78.

    CAS  Google Scholar 

  79. M. Yamamoto, K. Yamada, L.L. Meshkov, and E. Kato:Trans. Iron Steel Inst. Jpn., 1982, vol. 22, pp. 262–68.

    Google Scholar 

  80. S. Ban-Ya, N. Maruyama, and S. Fujino:Tetsu to Hagané, 1983, vol. 69, pp. 921–28.

    CAS  Google Scholar 

  81. E.T. Turkdogan and L.E. Leake:J. Iron Steel Inst., London, 1955, vol. 185, pp. 269–71.

    Google Scholar 

  82. E.T. Turkdogan and L.E. Leake:J. Iron Steel Inst. London, 1955, vol. 179, pp. 39–45.

    CAS  Google Scholar 

  83. Y.-D. Yang:Scand. J. Metall., 1992, vol. 21, pp. 194–201.

    CAS  Google Scholar 

  84. S. Ban-Ya, N. Maruyama, and Y. Kawase:Tetsu to Hagané, 1984, vol. 70, pp. 65–72.

    CAS  Google Scholar 

  85. C.H.P. Lupis and J.F. Elliot:Acta Metall., 1966, vol. 14, pp. 529–38.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

DOMINIQUE BOUCHARD, formerly Graduate Student, École Polytechnique de Montréal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouchard, D., Bale, C.W. Simultaneous optimization of thermochemical data for liquid iron alloys containing C, N, Ti, Si, Mn, S, and P. Metall Mater Trans B 26, 467–484 (1995). https://doi.org/10.1007/BF02653863

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02653863

Keywords

Navigation