Metallurgical and Materials Transactions A

, Volume 37, Issue 3, pp 833–839 | Cite as

Edge-to-edge matching—The fundamentals

  • P. M. Kelly
  • M. -X. Zhang
Article

Abstract

The basis of the present authors’ edge-to-edge matching model for understanding the crystallography of partially coherent precipitates is the minimization of the energy of the interface between the two phases. For relatively simple crystal structures, this energy minimization occurs when close-packed, or relatively close-packed, rows of atoms match across the interface. Hence, the fundamental principle behind edge-to-edge matching is that the directions in each phase that correspond to the “edges” of the planes that meet in the interface should be close-packed, or relatively close-packed, rows of atoms. A few of the recently reported examples of what is termed “edge-to-edge matching” appear to ignore this fundamental principle. By comparing theoretical predictions with available experimental data, this article will explore the validity of this critical atom-row coincidence condition, in situations where the two phases have simple crystal structures and in those where the precipitate has a more complex structure.

Keywords

Material Transaction Orientation Relationship Habit Plane Match Model Simple Crystal Structure 
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.
    P.M. Kelly and M.-X. Zhang: Mater. Forum, 1999, vol. 23, pp. 41–62.Google Scholar
  2. 2.
    M.-X. Zhang and P.M. Kelly: Acta Mater., 1998, vol. 46, pp. 4617–28.CrossRefGoogle Scholar
  3. 3.
    J.F. Nie and B.C. Muddle: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2381–89.Google Scholar
  4. 4.
    W.T. Reynolds, Jr., J.F. Nie, W.-Z. Zhang, J.M. Howe, H.I. Aaronson, and G.R. Purdy: Scripta Mater., 2003, vol. 49, pp. 405–10.CrossRefGoogle Scholar
  5. 5.
    J.M. Howe, W.T. Reynolds, Jr., and V.K. Vasudevan: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2391–411.Google Scholar
  6. 6.
    Hume-Rothery Symposium on “Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” 2004 TMS Meeting, Charlotte, NC.Google Scholar
  7. 7.
    G.J. Shiflet and J.H. van der Merwe: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1895–903.Google Scholar
  8. 8.
    F.C. Frank: Acta Metall., 1953, vol. 1, pp. 15–21.CrossRefGoogle Scholar
  9. 9.
    U. Dahmen: Scripta Metall., 1981, vol. 15, pp. 77–81.CrossRefGoogle Scholar
  10. 10.
    U. Dahmen: Acta Metall., 1982, vol. 30, pp. 63–73.CrossRefGoogle Scholar
  11. 11.
    U. Dahmen, P. Ferguson, and K.H. Westmacott: Acta Metall., 1984, vol. 32, pp. 803–10.CrossRefGoogle Scholar
  12. 12.
    U. Dahmen and K.H. Westmacott: Acta Metall., 1986, vol. 34, pp. 475–82.CrossRefGoogle Scholar
  13. 13.
    C.P. Luo and G.C. Weatherly: Acta Metall., 1987, vol. 35, pp. 1963–72.CrossRefGoogle Scholar
  14. 14.
    U. Dahmen: Encyclopedia of Physical Science and Technology, Academic Press Inc., San Diego, CA, 1987, vol. 10, pp. 319–54.Google Scholar
  15. 15.
    C.P. Luo, U. Dahmen, and K.H. Westmacott: Acta Metall. Mater., 1994, vol. 42, pp. 1923–32.CrossRefGoogle Scholar
  16. 16.
    U. Dahmen: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1857–63.Google Scholar
  17. 17.
    C.P. Luo and U. Dahmen: Acta Mater., 1998, vol. 46, pp. 2063–81.CrossRefGoogle Scholar
  18. 18.
    T. Fujii, T. Mori, and M. Kato: Acta Metall. Mater., 1992, vol. 40, pp. 3413–20.CrossRefGoogle Scholar
  19. 19.
    M. Kato, T. Fujii, and T. Mori: Scripta Metall. Mater., 1993, vol. 28, pp. 1167–70.CrossRefGoogle Scholar
  20. 20.
    J.K. Chen and W.T.J. Reynolds: Acta Mater., 1997, vol. 45, pp. 4423–30.CrossRefGoogle Scholar
  21. 21.
    Q. Liang and W.T. Reynolds: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 2059–72.CrossRefGoogle Scholar
  22. 22.
    D.A. Smith and R.C. Pond: Int. Met. Rev., 1976, pp. 61–74.Google Scholar
  23. 23.
    R.C. Ecob and B. Ralph: Acta Metall., 1981, vol. 29, pp. 1037–46.CrossRefGoogle Scholar
  24. 24.
    K.M. Knowles, D.A. Smith, and W.A.T. Clark: Scripta Metall., 1982, vol. 16, pp. 413–16.CrossRefGoogle Scholar
  25. 25.
    M.G. Hall, J.M. Rigsbee, and H.I. Aaronson: Acta Metall., 1986, vol. 34, pp. 1419–31.CrossRefGoogle Scholar
  26. 26.
    M.G. Hall and H.I. Aaronson: Acta Metall., 1986, vol. 34, pp. 1409–18.CrossRefGoogle Scholar
  27. 27.
    Y. Mou: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1905–15.Google Scholar
  28. 28.
    G.R. Purdy and W.-Z. Zhang: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1875–83.Google Scholar
  29. 29.
    G.C. Weatherly and W.-Z. Zhang: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1865–74.Google Scholar
  30. 30.
    W.-Z. Zhang and G.R. Purdy: Scripta Mater., 1997, vol. 37, pp. 543–48.CrossRefGoogle Scholar
  31. 31.
    W.-Z. Zhang and G.R. Purdy: Phil. Mag. A, 1993, vol. 68, pp. 279–90.Google Scholar
  32. 32.
    W.-Z. Zhang and G.R. Purdy: Phil. Mag. A, 1993, vol. 68, pp. 291–303.Google Scholar
  33. 33.
    W.-Z. Zhang and G.C. Weatherly: Progr. Mater. Sci., 2005, vol. 50, pp. 181–292.Google Scholar
  34. 34.
    M.G. Hall, H.I. Aaronson, and K.R. Kinsman: Surface Sci., 1972, vol. 31, pp. 257–74.CrossRefGoogle Scholar
  35. 35.
    J.M. Rigsbee and H.I. Aaronson: Acta Metall., 1979, vol. 27, pp. 351–63.CrossRefGoogle Scholar
  36. 36.
    D.S. Zhou, R.W. Fonda, and G.J. Shiflet: Scripta Metall. Mater., 1991, vol. 25, pp. 2639–44.CrossRefGoogle Scholar
  37. 37.
    G.J. Shiflet and J.H. Van der Merwe: J. Electron. Mater., 1991, vol. 20, pp. 785–91.Google Scholar
  38. 38.
    J.M. Howe and D.A. Smith: Acta Metall. Mater., 1992, vol. 40, pp. 2343–90.CrossRefGoogle Scholar
  39. 39.
    J.H. Van der Merwe and G.J. Shiflet: Acta Metall. Mater., 1994, vol. 42, pp. 1173–87.CrossRefGoogle Scholar
  40. 40.
    J.P. Hirth: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 1885–903.Google Scholar
  41. 41.
    J.F. Nie: Acta Mater., 2004, vol. 32, pp. 795–807.CrossRefGoogle Scholar
  42. 42.
    W. Pitsch: J. Inst. Met., 1959, vol. 87, pp. 444–48; Phil. Mag., 1959, vol. 4, pp. 577–84.Google Scholar
  43. 43.
    G.V. Kurdjumov and G. Sachs: Z. Phys., 1930, vol. 64, pp. 325–43.CrossRefGoogle Scholar
  44. 44.
    Z. Nishiyama: Sci. Rep. Tohoku Univ., 1934, vol. 23, pp. 637–64.Google Scholar
  45. 45.
    G. Wassermann: Arch. Eisenhüttenwes., 1933, vol. 6, pp. 347–51.Google Scholar
  46. 46.
    N.E. Ryan, W.A. Soffa, and R.C. Crawford: Metallography, 1968, vol. 1, pp. 195–220.CrossRefGoogle Scholar
  47. 47.
    E.C. Bain: Trans. AIME, 1924, vol. 70, pp. 25–35.Google Scholar
  48. 48.
    R.G. Baker and J. Nutting: ISI Spec. Rep. No. 64, 1959, pp. 1–22.Google Scholar
  49. 49.
    M.-X. Zhang and P.M. Kelly: Acta. Mater., 2005, vol. 53, pp. 1073–84.CrossRefGoogle Scholar
  50. 50.
    D.I. Potter: J. Less-Common Met., 1973, vol. 31, pp. 299–309.CrossRefGoogle Scholar
  51. 51.
    W. Pitsch and A. Schrader: Arch. Eisenhüttenwes., 1958, vol. 29, pp. 715–21.Google Scholar
  52. 52.
    W. Rong and G.L. Dunlop: Acta Metall., 1984, vol. 32, pp. 1591–99.CrossRefGoogle Scholar
  53. 53.
    W.G. Burgers: Physica, 1934, vol. 1, pp. 561–86.CrossRefGoogle Scholar
  54. 54.
    D. Duly: Acta Metall. Mater., 1993, vol. 41, pp. 1559–66.CrossRefGoogle Scholar
  55. 55.
    W.-Z. Zhang and G.R. Purdy: Acta Metall. Mater., 1993, vol. 41, pp. 543–51.CrossRefGoogle Scholar
  56. 56.
    F. Ye, W.-Z. Zhang, and D. Qiu: Acta Mater., 2005, vol. 52, pp. 2449–60.CrossRefGoogle Scholar
  57. 57.
    M.-X. Zhang and P.M. Kelly: Scripta Mater., 2003, vol. 48, pp. 379–84.CrossRefGoogle Scholar
  58. 58.
    D. Duly, W.-Z. Zhang, and M. Audier: Phil. Mag. A, 1995, vol. 71, pp. 187–204.Google Scholar
  59. 59.
    S. Celotto: Acta Mater., 2000, vol. 48, pp. 1775–87.CrossRefGoogle Scholar
  60. 60.
    J.F. Nie, X.L. Xiao, C.P. Luo, and B.C. Muddle: Micron, 2001, vol. 32, pp. 857–63.CrossRefGoogle Scholar
  61. 61.
    M.-X. Zhang and P.M. Kelly: Scripta Mater., 2003, vol. 48, pp. 647–52.CrossRefGoogle Scholar

Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2006

Authors and Affiliations

  • P. M. Kelly
    • 1
  • M. -X. Zhang
    • 1
  1. 1.the Division of Materials, School of EngineeringUniversity of QueenslandBrisbaneAustralia

Personalised recommendations