Segregation of niobium solute in nickel toward grain boundaries and free surfaces

Abstract

The spatial redistribution of niobium atoms near the (100) and (111) free surfaces and selected grain boundaries (GBs) of pure nickel has been considered in the low niobium concentration limit. There is one key difference between the situation for placing a niobium atom at a free surface and at a GB. At the free surface, an energetic compromise is required between having space for the large niobium atom and being able to place that atom at a position of high electron density. For a GB, no such compromise is required. An extremely interesting feature is the presence of a region around the third layer of (111) and the fourth layer of (100) free surfaces where the substitutional internal energy reverses its sign. The authors’ simulations show a significant depletion in concentration of niobium immediately at free surfaces. However, under the first two or three layers of pure nickel, there exists a niobium-enriched region with a strongly temperature-dependent concentration. This predicted nonmonotonic distribution of niobium in the surface region may be important for many applications and calls for experimental confirmation. In contrast, at the grain boundaries, the concentration of niobium, which is pertinent to GB oxidation embrittlement, is predicted to be much higher than in the bulk. It monotonically decreases with the distance from the GB until reaching the bulk value. The calculation of the free energy uses atomistic potentials based on ab initio quantum mechanical calculations, includes lattice relaxation around niobium atoms by using molecular dynamics (with 1440 or 2880 atoms in the modeling cell), and includes vibrational entropy phenomenologically within the local harmonic approximation. The entire approach is ab initio based and does not require any empirical information.

This is a preview of subscription content, access via your institution.

Cited References

  1. 1.

    B .S. Kang, personal communication

  2. 2.

    M. Gao, D.J. Dwyer, and R.P. Wei,Scr. Metall. Mater., 32, 1169 (1995).

    Article  Google Scholar 

  3. 3.

    D.J. Dwyer, X.J. Pang, M. Gao, and R.P. Wei,Appl. Surf. Sci., 81, 229(1994).

    Article  ADS  Google Scholar 

  4. 4.

    P.A. Dowben and A. Miller, Ed.,Surface Segregation Phenomena, CRC Press, Boston (1990).

    Google Scholar 

  5. 5.

    V. Ponec,Studies Surf. Sci. Catal., 95, 175 (1995); “Surface Composition of Alloys,” Chapter 4,Catalysis by Metals and Alloys, Elsevier, Amsterdam, NY (1995).

    Article  Google Scholar 

  6. 6.

    P. Lejcek and S. Hofmann,Crit. Rev. Solid State Mater. Sci., 20, 1 (1995).

    Article  Google Scholar 

  7. 7.

    D. Farkas, “Free Surfaces,”Principles, Vol. 1,Intermetallic Compounds, J.H. Westbrook and L. Fleischer, Ed., 609 (1994)

  8. 8.

    J. Morgan-LÔpez and L. Falicov,Phys. Rev. B, 18, 2542 (1978).

    Article  ADS  Google Scholar 

  9. 9.

    S.H. Overbury, P.A. Bertrand, and G.A. Somorjai,Chem. Rev., 75, 547–560(1975).

    Article  Google Scholar 

  10. 10.

    J.K. Strohl and T.S. King,J. Catalysis, 118, 53 (1989).

    Article  Google Scholar 

  11. 11.

    J.D. Rittner, S.M. Foiles, andD.N.Seidman,Phys.Rev.B, 50, 12004 (1994).

    Article  ADS  Google Scholar 

  12. 12.

    J.D. Rittner and D.N. Seidman,Acta Mater., 45, 3191 (1996).

    Article  Google Scholar 

  13. 13.

    J.D. Rittner, D. Udler, and D.N. Seidman,Interface Sei., 4, 65 (1997).

    Google Scholar 

  14. 14.

    R. Najafabadi and D.J. Srolovitz,Phys. Rev. B, 52, 9229 (1995).

    Article  ADS  Google Scholar 

  15. 15.

    A. Hairie, F. Hairie, B. Lebouvier, G. Nouet, E. Paumier, N. Ralantoson,and A.P. Sutton,Interface Sci., 2, 17(1994).

    Article  Google Scholar 

  16. 16.

    A.P. Sutton,Philos. Mag. A, 63, 793 (1989).

    Article  ADS  Google Scholar 

  17. 17.

    A.P. Sutton,Phibs. Trans. R. Soc. (London) A, 341, 233 (1992).

    Article  ADS  Google Scholar 

  18. 18.

    R. LeSar, R. Najafabadi, and D.J. Srolovitz,Phys. Rev. Lett, 63, 624 (1989).

    Article  ADS  Google Scholar 

  19. 19.

    D.de Fontaine,Solid State Physics, 34, 73 (1979).

    Google Scholar 

  20. 20.

    M.S. Daw and M.I. Baskes,Phys. Rev. Lett., 50, 1285 (1984)

    Article  ADS  Google Scholar 

  21. 21.

    M.S. Daw and M.I. Baskes,Phys. Rev. B, 29, 6443 (1984).

    Article  ADS  Google Scholar 

  22. 22.

    J. Mei, B.R. Cooper, and S.P. Lim,Phys. Rev. B, 54, 178 (1996).

    Article  ADS  Google Scholar 

  23. 23.

    J. Mei, B.R. Cooper, Y.G. Hao, and F.L. Van Scoy,Alloy Modeling and Design,. G.M. Stocks and P.E. A. Turchi, Ed., TMS Publishing, Warrendale, PA, 165 and references therein (1994).

    Google Scholar 

  24. 24.

    L.S. Muratov and B.R. Cooper,Mater. Res. Symp. Proc, 408, 407 (1996).

    Google Scholar 

  25. 25.

    D.L. Price and B.R. Cooper,Phys. Rev. B, 39, 4945 (1989).

    Article  ADS  Google Scholar 

  26. 26.

    D.L. Price, J.M. Wills, and B.R. Cooper,Phys. Rev. B, 46, 11368 (1992).

    Article  ADS  Google Scholar 

  27. 27.

    W.G. Hoover, A.J.C. Ladd, and B. Moran,Phys. Rev. Lett, 48, 1818 (1982).

    Article  ADS  Google Scholar 

  28. 28.

    M. Parrinello and A. Rahman,J. Appl. Phys., 52, 7182 (1981).

    Article  ADS  Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Muratov, L.S., Cooper, B.R. Segregation of niobium solute in nickel toward grain boundaries and free surfaces. JPE 19, 503 (1998). https://doi.org/10.1361/105497198770341671

Download citation

Keywords

  • Free Surface
  • Niobium
  • Monte Carlo
  • Pure Nickel
  • Simulation Cell