Skip to main content
SpringerLink
Log in

Application of the cluster variation method to ordering in an interstitial solid solution: the γ-Fe[N]/γ′-Fe4N1−x equilibrium

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

Abstract

The tetrahedron approximation of the cluster variation method (CVM) was applied to describe the ordering of N atoms on the fcc interstitial sublattice of γ-Fe[N] and γ′-Fe4N1−x . A Lennard-Jones potential was used to describe the dominantly strain-induced interactions, caused by the misfitting of the N atoms in the interstitial octahedral sites. The γ-Fe[N]/γ′-Fe4N1−x miscibility gap, short-range ordering (SRO), and long-range ordering (LRO) of nitrogen in γ-Fe[N] and γ′-Fe4N1−x , respectively, and lattice parameters of γ and γ′ were calculated. For the first time, N distribution parameters, as calculated by CVM, were compared directly to Mossbauer data for specific surroundings of Fe atoms.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Hillert and L.I. Staffansson: Acta Chem. Scand., 1970, vol. 24 (10), pp. 3618–26.

    CAS  Google Scholar 

  2. H. Harvig: Acta Chem. Scand., 1971, vol. 25 (9), pp. 3199–3204.

    Article  CAS  Google Scholar 

  3. L. Kaufman and H. Bernstein: Computer Calculations of Phase Diagrams, Academic Press, New York, NY, 1970.

    Google Scholar 

  4. O. Redlich and A.T. Kister: Ind. Eng. Chem., 1948, vol. 40, p. 345.

    Article  Google Scholar 

  5. K.H. Jack: Proc. R. Soc., 1948, vol. A195, pp. 34–55.

    CAS  Google Scholar 

  6. K.H. Jack: Acta Cryst., 1952, vol. 5, pp. 404–11.

    Article  Google Scholar 

  7. M. Hillert and M. Jarl: Metall. Trans. A, 1975, vol. 6A, pp. 553–59.

    CAS  Google Scholar 

  8. J. Agren: Metall. Trans. A, 1979, vol. 10A, pp. 1847–52.

    CAS  Google Scholar 

  9. J. Kunze: Steel Res., 1986, vol. 57 (8), pp. 361–67.

    CAS  Google Scholar 

  10. J. Kunze: Nitrogen and Carbon in Iron and Steels; Thermodynamics, Physical Research, Akademie Verlag, Berlin, 1990, vol. 16, pp. 76–85.

    Google Scholar 

  11. K. Frisk: CALPHAD, 1987, vol. 11 (2), pp. 127–34.

    Article  CAS  Google Scholar 

  12. K. Frisk: CALPHAD, 1991, vol. 15 (1), pp. 79–106.

    Article  CAS  Google Scholar 

  13. H. Du: J. Phase Equil., 1993, vol. 14 (6), pp. 682–93.

    CAS  Google Scholar 

  14. B.J. Kooi, M.A.J. Somers, and E.J. Mittemeijer: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 1063–71.

    CAS  Google Scholar 

  15. N.A. Gokcen: Statistical Thermodynamics of Alloys, Plenum Press, New York, NY, 1986.

    Google Scholar 

  16. B.J. Kooi, M.A.J. Somers, and E.J. Mittemeijer: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 1055–61.

    CAS  Google Scholar 

  17. M.A.J. Somers, B.J. Kooi, L. Maldzinski, E.J. Mittemeijer, A.A. van der Horst, A.M. van der Kraan, and N.M. van der Pers: Acta Mater., 1997, vol. 45 (5), pp. 2013–25.

    Article  CAS  Google Scholar 

  18. R.B. McLellan and K. Alex: Scripta Metall., 1970, vol. 4, pp. 967–70.

    Article  CAS  Google Scholar 

  19. I. Fall and J.-M.R. Genin: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 2160–77.

    CAS  Google Scholar 

  20. R. Kikuchi and D. de Fontaine: Proc. Workshop at NBS Gaithersburg, Application of Phase Diagrams in Metallurgy and Ceramics, 1977, pp. 967–79.

  21. D. de Fontaine and R. Kikuchi: Proc. Workshop at NBS Gaithersburg, Application of Phase Diagrams in Metallurgy and Ceramics, 1977, pp. 999–1027.

  22. C. Zener: Phys. Rev., 1948, vol. 74 (6), pp. 639–47.

    Article  CAS  Google Scholar 

  23. B. Burton and R. Kikuchi: Phys. Chem. Minerals, 1984, vol. 11, pp. 125–31.

    Article  CAS  Google Scholar 

  24. B. Burton: Phys. Chem. Minerals, 1984, vol. 11, pp. 132–39.

    Article  CAS  Google Scholar 

  25. J.M. Sanchez, J.R. Barefoot, R.N. Jarrett, and J.K. Tien: Acta Metall., 1984, vol. 32 (9), pp. 1519–25.

    Article  CAS  Google Scholar 

  26. R. Kikuchi: J. Chem. Phys., 1974, vol. 60, pp. 1071–80.

    Article  CAS  Google Scholar 

  27. R. Kikuchi: Phys. Rev., 1951, vol. 81, pp. 988–1003.

    Article  Google Scholar 

  28. C. Colinet: Theory and Applications of the Cluster Variation Method and Path Probability Methods, J.L. Moran-Lopez and J.M. Sanchez, Plenum Press, New York, NY, 1996, pp. 313–40.

    Google Scholar 

  29. C.M. van Baal: Physica, 1973, vol. 64, pp. 571–86.

    Article  Google Scholar 

  30. C. Sigli and J.M Sanchez: CALPHAD, 1984, vol. 8 (3), pp. 221–31.

    Article  CAS  Google Scholar 

  31. M. Enomoto and H. Harada: Metall. Trans. A, 1989, vol 20A, pp. 649–64.

    CAS  Google Scholar 

  32. R. Kikuchi, J.M. Sanchez, D. De Fontaine, and H. Yamauchi: Acta Metall., 1980, vol. 28, pp. 651–62.

    Article  CAS  Google Scholar 

  33. J.M. Sanchez and D. De Fontaine: Phys. Rev. B, 1980, vol. 21, pp. 216–28.

    Article  CAS  Google Scholar 

  34. J.M. Sanchez and D. De Fontaine: Phys. Rev. B, 1982, vol. 25, pp. 1759–65.

    Article  CAS  Google Scholar 

  35. R. Kikuchi: J. Chem. Phys., 1977, vol. 66, pp. 3352–62.

    Article  CAS  Google Scholar 

  36. B. Burton and R. Kikuchi: Am. Min., 1984, vol. 69, pp. 165–75.

    CAS  Google Scholar 

  37. C. Colinet, G. Inden, and R. Kikuchi: Acta Metall. Mater., 1993, vol. 41 (4), 1109–18.

    Article  CAS  Google Scholar 

  38. R. Kikuchi, D. de Fontaine, M. Murakami, and T. Nakamura: Acta Metall., 1977, vol. 25, pp. 207–19.

    Article  CAS  Google Scholar 

  39. D. de Fontaine and C. Wolverton: Ber. Bunsenges. Phys. Chem., 1992, vol. 96 (11), pp. 1503–12.

    Google Scholar 

  40. R. Kikuchi: Acta Metall., 1977, vol. 25, pp. 195–205.

    Article  CAS  Google Scholar 

  41. O. Kubaschewski, C.B. Alcock, and P.J. Spencer: Materials Thermochemistry, 6th ed., Pergomon Press, Oxford, United Kingdom, 1993.

    Google Scholar 

  42. L. Cheng, A. Bottger, T.H. de Keijser, and E.J. Mittemeijer: Scripta Metall. Mater., 1990, vol. 24, pp. 509–13.

    Article  CAS  Google Scholar 

  43. O. Eisenhut and E. Kaupp: Z. Elektrochem., 1930, vol. 36 (6), pp. 392–404.

    CAS  Google Scholar 

  44. E. Lehrer: Z. Elektrochem., 1930, vol. 37 (7), pp. 460–73.

    Google Scholar 

  45. V.G. Paranjpe, M. Cohen, M.B. Bever, and C.F. Floe: Trans. AIME, 1950, vol. 188, pp. 261–67.

    CAS  Google Scholar 

  46. M.A.J. Somers, N.M. van der Pers, D. Schalkoord, and E.J. Mittemeijer: Metall. Trans. A, 1989, vol. 20A, pp. 1533–39.

    CAS  Google Scholar 

  47. L. Rissanen, K.P. Lieb, M. Niederdrenk, O. Schulte, and P. Schaaf: Proc. ICAME-95, 1996, vol. 50, pp. 595–98.

    CAS  Google Scholar 

  48. L. Rissanen, M. Neubauer, K.P. Lieb, and P. Schaaf: J. Alloy Compounds, 1998, vol. 274, pp. 74–82.

    Article  CAS  Google Scholar 

  49. M.J. van Genderen, A. Bottger, and E.J. Mittemeijer: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 63–77.

    Google Scholar 

  50. K. Oda, K. Umezu, and H. Ino: J. Phys. Cond. Mater., 1990, vol. 2, pp. 10147–58.

    Article  CAS  Google Scholar 

  51. D. Atkinson and C. Bodsworth: J. Iron Steel Inst., 1970, vol. 27, pp. 587–93.

    Google Scholar 

  52. J. Foct, R. Rochegude, and A. Hendry: Acta Metall., 1988, vol. 36 (3), pp. 501–05.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. the Laboratory for Materials Science, Delft University of Technology, NL-2628 AL, Delft, The Netherlands

    M. I. Pekelharing (Researcher), A. J. Bottger (Assistant Professor) & E. J. Mittemeijer (Professor)

  2. the IPT Materials Technology, Technical University of Denmark, DK-2800, Lyngby, Denmark

    M. A. J. Somers (Professor)

  3. the Max Planck Institute for Metals Research, D-70174, Stuttgart, Germany

    E. J. Mittemeijer (Professor)

Authors
  1. M. I. Pekelharing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. J. Bottger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. J. Somers
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. J. Mittemeijer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pekelharing, M.I., Bottger, A.J., Somers, M.A.J. et al. Application of the cluster variation method to ordering in an interstitial solid solution: the γ-Fe[N]/γ′-Fe4N1−x equilibrium. Metall Mater Trans A 30, 1945–1953 (1999). https://doi.org/10.1007/s11661-999-0005-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-999-0005-0

Keywords

Search

Navigation