Skip to main content
SpringerLink
Log in

Anisotropy of segregation at grain boundaries and surfaces

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

Abstract

The purpose of this article is to review analytical models of the anisotropy of segregation to grain boundaries (GBs) and surfaces, and to evaluate their predictions. A summary of Gibbsian interfacial thermodynamics is provided as an introduction to the topic. This is followed by a historical overview of previous analytical models. A recently developed model of the dependence of GB segregation on the five macroscopic parameters of GB orientation is outlined, and illustration of how this formulation reduces to the particular cases of segregation to simpler types of interfaces is provided. In addition, some specific aspects of interfacial segregation, which have either been problematic or have lacked satisfactory explanation, are addressed. These include (a) the relationship between the compositions on the two sides of a given GB; (b) the difficulty of meaningful definitions of segregation-free energy (and related thermodynamic quantities such as enthalpy and entropy); (c) the so-called compensation temperature, at which the anisotropy of interfacial segregation seems to vanish; (d) the relationship between surface and GB segregation; and finally (e) an attempt to determine whether segregation increases or decreases interfacial energy anisotropy, and the consequences thereof on the equilibrium crystal shape of alloys. Where possible, comparisons are made with the results of experiments or computer simulations.

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. J.W. Gibbs:The Scientific Papers of J. Willard Gibbs, Dover. New York, NY, 1961, vol. 1, pp. 219–331.

    Google Scholar 

  2. R.H. Fowler and E.A. Guggenheim:Statistical Thermodynamics, Macmillan, New York, NY, 1939, pp. 429–40.

    Google Scholar 

  3. S. Ono and S. Kondo: inEncyclopedia of Physics, S. Flugge, ed., Springer, Berlin, 1960, vol. X, pp. 134–277.

    Google Scholar 

  4. D. McLean:Grain Boundaries in Metals, Oxford Press, London, 1957, pp. 116–22.

    Google Scholar 

  5. R. Defay, I. Prigogine, A. Bellmans, and D.H. Everett:Surface Tension and Adsorption, Wiley, New York, NY, 1966, pp. 158–97.

    Google Scholar 

  6. G.S. Rohrer, D.M. Saylor, B. El Dasher, B. Adams, A.D. Rollett, and P. Wynblatt:Z Metallkd., 2004, vol. 95, pp. 197–214.

    CAS  Google Scholar 

  7. D.N. Seidman:Annu. Rev. Mater. Res., 2002, vol. 32, pp. 235–69.

    Article  CAS  Google Scholar 

  8. Y. Pang and P. Wynblatt:J. Am. Ceram. Soc., 2006, vol. 89, pp. 666–71.

    Article  CAS  Google Scholar 

  9. P. Wynblatt, Z. Shi, Y. Pang, and D. Chatain:Z. Metallkd., 2005, vol. 96, pp. 1142–46.

    CAS  Google Scholar 

  10. D.M. Saylor, A. Morawiec, and G.S. Rohrer:J. Am. Ceram. Soc., 2002, vol. 85, pp. 3081–83.

    Article  CAS  Google Scholar 

  11. D.M. Saylor, A. Morawiec, and G.S. Rohrer:Acta Mater., 2003, vol. 51, pp. 3675–86.

    Article  CAS  Google Scholar 

  12. P. Wynblatt and M. Takashima:Interface Sci., 2001, vol. 9, pp. 265–73.

    Article  CAS  Google Scholar 

  13. P. Wynblatt and Z. Shi:J. Mater. Sci., 2005, vol. 40, pp. 2765–73.

    Article  CAS  Google Scholar 

  14. W.W. Mullins:Metal Surfaces, ASM, Cleveland, OH, 1963, p. 17–66.

    Google Scholar 

  15. J.P. Hirth:Structure and Properties of Metal Surfaces, Honda Memorial Series in Materials Science No. 1, Maruzen Co. Ltd., Tokyo, 1973, pp. 10–33.

    Google Scholar 

  16. E.D. Hondros and M.P. Seah:Metall. Trans. A, 1977, vol. 8A, pp. 1363–71.

    CAS  Google Scholar 

  17. J. Langmuir:J. Am. Chem. Soc., 1916, vol. 38, pp. 2221–95.

    Article  CAS  Google Scholar 

  18. J.J. Burton and E.S. Machlin:Phys. Rev. Lett., 1976, vol. 37, pp. 1433–36.

    Article  CAS  Google Scholar 

  19. P. Wynblatt and R.C. Ku:Surf. Sci., 1977, vol. 65, pp. 511–31.

    Article  CAS  Google Scholar 

  20. P. Wynblatt and R.C. Ku: inInterfacial Segregation, W.C. Johnson and J.M. Blakely, eds., ASM, Metals Park, OH, 1979, pp. 115–36.

    Google Scholar 

  21. J. Friedel:Adv. Phys., 1954, vol. 3, pp. 446–507.

    Article  Google Scholar 

  22. Y.W. Lee and H.I. Aaronson:Surf. Sci., 1980, vol. 95, pp. 227–44.

    Article  CAS  Google Scholar 

  23. Y.W. Lee and H.I. Aaronson:Acta Metall., 1980, vol. 28, pp. 539–48.

    Article  Google Scholar 

  24. W.L. Bragg and E.J. Williams:Proc. R. Soc., 1934, vol. A145, pp. 699–730.

    CAS  Google Scholar 

  25. V. Kumar, D. Kumar, and S.K. Joshi:Phys. Rev. B: Condens. Matter Mater. Phys., 1979, vol. B19, pp. 1954–62.

    Google Scholar 

  26. J.L. Moran-Lopez and L.M. Falicov:Phys. Rev. B: Condens. Matter Mater. Phys., 1978, vol. B18, pp. 2542–48.

    Google Scholar 

  27. J.L. Moran-Lopez and L.M. Falicov:Phys. Rev. B: Condens. Matter Mater. Phys., 1978, vol. B18, pp. 2549–54.

    Google Scholar 

  28. V. Kumar and K.H. Bennemann:Phys. Rev. Lett., 1984, vol. 53, pp. 278–81.

    Article  CAS  Google Scholar 

  29. J.M. Sanchez and J.L. Moran-Lopez:Phys. Rev. B: Condens. Matter Mater. Phys., 1985, vol. B32, pp. 3534–40.

    Google Scholar 

  30. J.M. Sanchez and J.L. Moran-Lopez:Surf. Sci., 1985, vol. 157, pp. L297-L302.

    Article  CAS  Google Scholar 

  31. M. Polak and L. Rubinovich:Surface Sci. Rep., 2000, vol. 38, pp. 127–94;The Chemical Physics of Solid Surfaces, D.P. Woodruff, ed., Elsevier Science, Amsterdam, 2002, vol. 10, pp. 86–117.

    Article  CAS  Google Scholar 

  32. K. Lehovec:J. Chem. Phys., 1953, vol. 21, pp. 1123–28.

    Article  CAS  Google Scholar 

  33. K.L. Kliewer and J.S. Koehler:Phys. Rev., 1965, vol. 140, pp. 1226–40.

    Article  CAS  Google Scholar 

  34. P. Wynblatt and R.C. McCune: inSurfaces and Interfaces in Ceramic and Metal-Ceramic Systems, J.A. Pask and A.G. Evans, eds., Plenum, New York, NY, 1981, pp. 83–95.

    Google Scholar 

  35. P. Wynblatt and R.C. McCune: inSurface and Near-Surface Chemistry of Oxide Materials, J. Nowotny and L.-C. Dufour, eds., Elsevier Science Publishers, Amsterdam, 1988, pp. 247–79.

    Google Scholar 

  36. M. Guttmann:Metall. Trans. A, 1977, vol. 8A, pp. 1383–401.

    CAS  Google Scholar 

  37. M. Guttmann and D. McLean: inInterfacial Segregation, W.C. Johnson and J.M. Blakely, eds., ASM, Metals Park, OH, 1979, pp. 261–348.

    Google Scholar 

  38. M.A. Hoffmann and P. Wynblatt:Metall. Trans. A, 1989, vol. 20A, pp. 215–23.

    CAS  Google Scholar 

  39. P. Wynblatt and S.A. Dregia:Coll. Phys. (suppl. J. Phys.), 1990, vol. 51-C1, pp. 757–66.

    Google Scholar 

  40. S.A. Dregia and P. Wynblatt:Acta Metall. Mater., 1991, vol. 39, pp. 771–78.

    Article  CAS  Google Scholar 

  41. G. Rao and P. Wynblatt:Mater. Res. Soc. Symp. Proc., 1992, vol. 205, pp. 369–74.

    CAS  Google Scholar 

  42. D.A. Steigerwald, S.J. Miller, and P. Wynblatt:Surf. Sci., 1985, vol. 155, pp. 79–100.

    Article  CAS  Google Scholar 

  43. D. Wolf:Acta Metall., 1989, vol. 37, pp. 1983–93.

    Article  CAS  Google Scholar 

  44. D. Wolf:Act Metall., 1989, vol. 37, pp. 2823–33.

    Article  CAS  Google Scholar 

  45. D. Wolf:Acta Metall. Mater., 1990, vol. 38, pp. 781–90.

    Article  CAS  Google Scholar 

  46. P. Wynblatt, A. Saùl, and D. Chatain:Acta Mater., 1998, vol. 46, pp. 2337–47.

    Article  CAS  Google Scholar 

  47. D. Udler and D.N. Seidman:Phys. Status Solidi, 1992, vol. B172, pp. 267–85.

    Google Scholar 

  48. D. Udler and D.N. Seidman:Acta Metall. Mater., 1994, vol. 42, pp. 1959–72.

    Article  CAS  Google Scholar 

  49. S.M. Foiles, M.I. Baskes, and M.S. Daw:Phys. Rev. B: Condens. Matter Mater. Phys., 1986, vol. B33, pp. 7983–91.

    Google Scholar 

  50. D. Chatain, N. Eustathopoulos, and P. Desré:J. Coll. Interface Sci., 1981, vol. 83, pp. 384–92.

    Article  CAS  Google Scholar 

  51. T.E. Faber:Introduction to the Theory of Liquid Metals, University Press, Cambridge, United Kingdom, 1972, pp. 128–29

    Google Scholar 

  52. A. Landa, P. Wynblatt, H. Hakkinen, R.N. Barnett, and U. Landman:Phys. Rev. B: Condens. Matter Mater. Phys., 1995, vol. B51, pp. 10972–80.

    Google Scholar 

  53. F.L. Williams and D. Nason:Surf. Sci., 1974, vol. 45, pp. 377–408.

    Article  CAS  Google Scholar 

  54. C. Serre, P. Wynblatt, and D. Chatain:Surf. Sci., 1998, vol. 415, pp. 336–45.

    Article  CAS  Google Scholar 

  55. H. Shim, D. Chatain, and P. Wynblatt:Surf. Sci., 1998, vol. 415, pp. 346–50.

    Article  CAS  Google Scholar 

  56. P. Lejcek and S. Hofmann:Crit. Rev. Solid State Mater. Sci., 1995, vol. 20, pp. 1–85.

    CAS  Google Scholar 

  57. S. Hofmann and P. Lejcek:Interface Sci., 1996, vol. 3, pp. 241–67.

    Article  CAS  Google Scholar 

  58. Y. Pang and P. Wynblatt:J. Am. Ceram. Soc., 2005, vol. 88, pp. 2286–91.

    Article  CAS  Google Scholar 

  59. P. Wynblatt and M. Takashima:Proc. HTC-2000, N. Eustathopoulos, K. Nogi, and N. Sobczak, eds.,Trans. JWRI, 2001, vol. 30, pp. 11–20.

  60. M. Ramamoorthy, D. Vanderbilt, and R.D. King-Smith:Phys. Rev. B: Condens. Matter Mater. Phys., 1994, vol. B49, pp. 16721–27

    Google Scholar 

  61. C.L. White and W.A. Coghlan:Metall. Trans. A, 1977, vol. 8A, pp. 1403–12.

    CAS  Google Scholar 

  62. P. Lejcek and S. Hofmann:Interface Sci., 2002, vol. 9, pp. 221–30.

    Article  Google Scholar 

  63. A.N. Aleshin, R.G. Faulkner, D.A. Molodov, and L.S. Shvindlerman:Interface Sci., 2002, vol. 10, pp. 5–12.

    Article  CAS  Google Scholar 

  64. M.P. Seah and C. Lea:Philos. Mag., 1975, vol. 31, pp. 627–45.

    CAS  Google Scholar 

  65. H.J. Grabke:Steel Res., 1986, vol. 57, pp. 178–85.

    CAS  Google Scholar 

  66. T. Muschik, S. Hofmann, W. Gust, and B. Predel:Appl. Surf. Sci., 1989, vol. 37, pp. 439–55.

    Article  CAS  Google Scholar 

  67. G.A. Lopez, W. Gust, and E.J. Mittemeijer:Scripta Mater., 2003, vol. 49, pp. 747–53.

    Article  CAS  Google Scholar 

  68. H. Mykura:Acta Metall., 1961, vol. 9, pp. 570–76.

    Article  CAS  Google Scholar 

  69. M. McLean and B. Gale:Phil. Mag., 1969, vol. 20, pp. 1033–45.

    CAS  Google Scholar 

  70. G. Wulff:Z. Krist. Mineral, 1901, vol. 34, pp. 449–531.

    CAS  Google Scholar 

  71. C. Herring: inStructure and Properties of Solid Surfaces, R.G. Gomer and C.S. Smith, eds., University of Chicago Press, Chicago, IL, 1953, pp. 5–72.

    Google Scholar 

  72. J.C. Heyraud and J.J. Metois:Surf. Sci., 1983, vol. 128, pp. 334–42.

    Article  CAS  Google Scholar 

  73. J.C. Heyraud and J.J. Metois:Acta Metall., 1980, vol. 28, pp. 1789–97.

    Article  CAS  Google Scholar 

  74. J.C. Heyraud and J.J. Metois:J. Cryst. Growth, 1980, vol. 50, pp. 571–74.

    Article  CAS  Google Scholar 

  75. Z. Wang and P. Wynblatt:Surf. Sci., 1998, vol. 398, pp. 259–66.

    Article  CAS  Google Scholar 

  76. D. Chatain, V. Ghetta, and P. Wynblatt:Interface Sci., 2004, vol. 12, pp. 7–18.

    Article  CAS  Google Scholar 

  77. E.D. Hondros and M. McLean:Structures et Propriétés des Surfaces, Editions du CNRS, Paris, 1970, pp. 219–29.

    Google Scholar 

  78. D. Chatain, P. Wynblatt, and G.S. Rohrer:Acta Mater., 2005, vol. 53, pp. 4057–64.

    Article  CAS  Google Scholar 

  79. W.-C. Cheng and P. Wynblatt:J. Cryst. Growth, 1997, vol. 173, pp. 513–27.

    Article  CAS  Google Scholar 

  80. J.C. Heyraud and J.J. Metois:J. Cryst. Growth, 1987, vol. 82, pp. 269–73.

    Article  CAS  Google Scholar 

  81. H.L. Meyerheim, H. Zajonz, W. Moritz, and I.K. Robinson:Surf. Sci., 1997, vol. 381, pp. L551–57.

    Article  CAS  Google Scholar 

  82. H.L. Meyerheim, M. DeSantis, W. Moritz, and I.K. Robinson:Surf. Sci., 1998, vol. 418, pp. 295–302.

    Article  CAS  Google Scholar 

  83. R. Roosen, R.P. McCormack, and W.C. Carter:Comput. Mater. Sci., 1998, vol. 11, pp. 16–26.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. the Department of Materials Science and Engineering, Carnegie Mellon University, 15213, Pittsburgh, PA

    Paul Wynblatt (Professor Emeritus)

  2. CRMCN-CNRS, Campus de Luminy, 13288, Marseille, Cedex 9, France

    Dominique Chatain (Directeur de Recherches)

Authors
  1. Paul Wynblatt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dominique Chatain
    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

Wynblatt, P., Chatain, D. Anisotropy of segregation at grain boundaries and surfaces. Metall Mater Trans A 37, 2595–2620 (2006). https://doi.org/10.1007/BF02586096

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02586096

Keywords

Search

Navigation