Skip to main content
SpringerLink
Log in

An Analytical Model for Solute Segregation at Liquid Metal/Solid Substrate Interface

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

Abstract

In this paper, we present an analytical model for describing the equilibrium solute segregation at the interface between metallic liquid (an A–B solution, where A is solvent and B is solute) and a solid substrate (S) using approaches of thermodynamics and statistical mechanics. This analytical model suggests that the interfacial solute segregation is governed by the difference in interfacial energies between the pure B/S and pure A/S interfaces, the heat of mixing of the A–B solution and the difference in entropies of fusion between pure solute and solvent. The calculated solute segregations at the interface in the liquid Al-Ti/TiB2 and liquid Sn-Al/Al2O3 systems are in qualitative agreement with the experimental observations. It is demonstrated that the present analytical model can be used to predict the solute segregation at the liquid/substrate interface, at least qualitatively.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. P.A. Dowben and A. Miller: Surface segregation phenomena, CRC Press, Boca Raton, Florida, 1990.

    Google Scholar 

  2. P. Wynblatt: Annu. Rev. Mater. Res., 2008, vol. 38, pp. 173-96.

    Article  Google Scholar 

  3. W.D. Kaplan, D. Chatain, P. Wynblatt, and W.C. Carter: J. Mater. Sci., 2013, vol. 48, pp. 5681-717.

    Article  Google Scholar 

  4. J. Luo, H.K. Cheng, K.M. Asl, C.J. Kiely, and M.P. Harmer: Science, 2011, vol. 333, pp. 1730-3.

    Article  Google Scholar 

  5. J.W. Christian: The theory of transformations in metals and alloys, 3rd ed., Pergamon, Oxford, 2002.

    Google Scholar 

  6. B. Cantor: Phil. Trans. R. Soc. Lond. A, 2003, vol. 361, pp. 409-17.

    Article  Google Scholar 

  7. Z. Fan: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 1409-18.

    Article  Google Scholar 

  8. B. Derby and S. Holt: Interface Sci., 2004, vol. 12, pp. 29-37.

    Article  Google Scholar 

  9. H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter: Nature, 2000, vol. 408, pp. 839-41.

    Article  Google Scholar 

  10. S.H. Oh, M.F. Chisholm, Y. Kauffmann, W.D. Kaplan, W. Luo, M. Rühle, and C. Scheu: Science, 2010, vol. 330, pp. 489-93.

    Article  Google Scholar 

  11. B.M. Gallois: JOM, 1997, vol. 49, pp. 48-51.

    Article  Google Scholar 

  12. G. Levi and W.D. Kaplan: Acta Mater., 2002, vol. 50, pp. 75-88.

    Article  Google Scholar 

  13. S. Hofmann: J. Chim. Phys., 1987, vol. 84, pp. 141.

    Google Scholar 

  14. J.W. McBain and G.F. Mills: Rep. Prog. Phys., 1938, vol. 5, pp. 30-45.

    Article  Google Scholar 

  15. D. McLean: Grain boundaries in metals, Clarendon Press, Oxford, 1957.

    Google Scholar 

  16. E.D. Hondros and M.P. Seah: in Physical Metallurgy, 4th ed., P. Haasen and R.W. Cahn, eds., North Holland, Amsterdam, 1983.

  17. M.P. Seah: J. Vac. Sci. Technol., 1980, vol. 17, pp. 16-24.

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. P. Wynblatt and R.C. Ku: in Interfacial Segregation, W.C. Johnson and I.M. Blakely, eds., American Society for Metals, Metal Park, OH, 1979.

  20. M.P. Seah: J. Catalysis, 1979, vol. 57, pp. 450-7.

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. R.H. Ewing and B. Chalmers: Surf. Sci., 1972, vol. 31, pp. 161-71.

    Article  Google Scholar 

  23. P. Lejček and S. Hofmann: Interface Sci., 2001, vol. 9, pp. 221-30.

    Article  Google Scholar 

  24. P. Lejček and S. Hofmann: Crit. Rev. Solid State Mater. Sci., 2008, vol. 33, pp. 133-63.

    Article  Google Scholar 

  25. P. Wynblatt and D. Chatain: Metall. Mater. Trans., 2006, vol. 37, pp. 2595-620.

    Article  Google Scholar 

  26. G. Levi, D.R. Clarke, and W.D. Kaplan: Interface Sci., 2004, vol. 12, pp. 73-83.

    Article  Google Scholar 

  27. S.H. Oh, Y. Kauffmann, C. Scheu, W.D. Kaplan, and M. Rühle: Science, 2005, vol. 310, pp. 661-3.

    Article  Google Scholar 

  28. S.B. Lee and Y.M. Kim: Acta Mater., 2011, vol. 59, pp. 1383-8.

    Article  Google Scholar 

  29. A. Hashibon, J. Adler, M.W. Finnis, and W.D. Kaplan: Interface Sci., 2001, vol. 9, pp. 175-81.

    Article  Google Scholar 

  30. J.P. Palafox-Hernandez, B.B. Laird, and M. Asta: Acta Mater., 2011, vol. 59, pp. 3137-44.

    Article  Google Scholar 

  31. H. Men and Z. Fan: IOP Conference Serials: Mater. Sci. Eng., 2011, vol. 27, pp. 012007.

    Article  Google Scholar 

  32. G.P. Jones and J. Pearson: Metall. Trans. B, 1976, vol. 7, pp. 223-34.

    Article  Google Scholar 

  33. G.P. Jones: in Solidification Processing 1987, J. Beech and H. Jones, eds., The Institute of Metals, London, 1988.

  34. J.G. Li, L. Coudurier, and N. Eustathopoulos: J. Mater. Sci., 1989, vol. 24, pp. 1109-16.

    Article  Google Scholar 

  35. W.T. Kim and B. Cantor: Acta Metall. Mater., 1994, vol. 42, pp. 3115-27.

    Article  Google Scholar 

  36. P.G. Shewmon: in Physical Metallurgy, 2nd ed., R.W. Cahn, ed., North Holland, Amsterdam, 1970.

  37. L. Granasy, M. Tagze, and A. Ludwig: Mater. Sci. Eng. A, 1991, vol. 133, pp. 577-80.

    Article  Google Scholar 

  38. R.A. Swalin: Thermodynamics of solids, J. Wiley, New York, 1972.

    Google Scholar 

  39. A. Takeuchi and A. Inoue: Mater. Trans., 2005, vol. 46, pp. 2817-29.

    Article  Google Scholar 

  40. W.D. Kaplan and Y. Kauffmann: Annu. Rev. Mater. Res., 2006, vol. 36, pp. 1-48.

    Article  Google Scholar 

  41. D.C. Wallace: Proc. R. Soc. Lond. A, 1991, vol. 433, pp. 631-61.

    Article  Google Scholar 

  42. F. Spaepen: Acta Metall., 1975, vol. 23, pp. 729-43.

    Article  Google Scholar 

  43. A.L. Greer, A.M. Bunn, A. Tronche, P.V. Evans, and D.J. Bristow: Acta Mater., 2000, vol. 48, pp. 2823-35.

    Article  Google Scholar 

  44. P. Schumacher and A.L. Greer: in Light Metals, W. Hale, ed., TMS, Warrendale PA, 1996.

  45. P.S. Mohanty and J.E. Gruzleski: Acta Metall. Mater., 1995, vol. 43, pp. 2001-12.

    Article  Google Scholar 

  46. E.A. Brandes: Smithhells metals reference book, 6th ed., Butterworths, London, 1983.

    Google Scholar 

  47. N. Eustathopoulos, M.G. Nicholas, and B. Drevet: Wettability at high temperature, Pergamon, Amsterdam, 1999.

    Google Scholar 

  48. B.C. Allen: in Liquid Metals: Chemistry and Physics, S.Z. Beer, ed., Dekker, New York, NY, 1972.

  49. M.E. Hyman, C. McCullough, C.G. Levi, and R. Mehrabian: Metall. Trans. A, 1991, vol. 22, pp. 1647-62.

    Article  Google Scholar 

  50. Y.F. Han, Y.B. Dai, D. Shu, J. Wang, and B.D. Sun: J. Phys.: Condens. Matter., 2006, vol. 18, pp. 4197-205.

    Article  Google Scholar 

  51. Y.O. Esin, N.P. Bobrov, M.S. Petrushevskiy, and P.V. Gel’d: Izv Akad Nauk SSR Met., 1974, vol. 5, pp. 104-8.

    Google Scholar 

  52. J.G. Li, D. Chatain, L. Coudurier, and N. Eustathopoulos: J. Mater. Sci. Lett., 1988, vol. 7, pp. 961-3.

    Article  Google Scholar 

  53. N. Wang and B. Wei: Appl. Phys. Lett., 2002, vol. 80, pp. 3515-7.

    Article  Google Scholar 

  54. T. Sritharan and H. Li: Scr. Mater., 1996, vol. 35, pp. 1053-6.

    Article  Google Scholar 

  55. M. Tang, W.C. Carter, and R.M. Cannon: Phys. Rev.B, 2006, vol. 73, pp. 024102.

    Article  Google Scholar 

  56. M. Tang, W.C. Carter, and R.M. Cannon: Phys. Rev. Lett., 2006, vol. 97, pp. 075502.

    Article  Google Scholar 

  57. A.L. Greer, P.S. Coper, M.W. Meredith, W. Schneider, P. Schumacher, J.A. Spittle, and A. Tronche: Adv. Eng. Mater., 2003, vol. 5, pp. 81-91.

    Article  Google Scholar 

Download references

Acknowledgments

EPSRC is gratefully acknowledged for providing financial support under Grant EP/H026177/1 for the EPSRC Centre - LiME.

Author information

Authors and Affiliations

  1. The EPSRC Centre-LiME, BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, U.K.

    Hua Men (Senior Research Fellow) & Zhongyun Fan (Professor)

Authors
  1. Hua Men
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongyun Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hua Men.

Additional information

Manuscript submitted January 6, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Men, H., Fan, Z. An Analytical Model for Solute Segregation at Liquid Metal/Solid Substrate Interface. Metall Mater Trans A 45, 5508–5516 (2014). https://doi.org/10.1007/s11661-014-2525-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11661-014-2525-5

Keywords

Search

Navigation