Advertisement

Study of Surface Diffusion through Langevin Dynamics

  • S. C. Ying
Part of the NATO ASI Series book series (NSSB, volume 360)

Abstract

We present here results from theoretical investigations of adatom diffusion based on Langevin dynamics. We derive a generalized Langevin equation from a microscopic Hamiltonian and discuss its application to the study of surface diffusion. In particular, we focus on how the diffusion constant depends on the friction parameter characterizing the non-adiabatic coupling of the adatom to the substrate excitations. We discuss such topics as the validity of the transition state theory, occurrences of long jumps and memory effects in determining the prefactor and the barrier for surface diffusion.

Keywords

Saddle Point Memory Effect Surface Diffusion Memory Function Diffusion Constant 
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. E. Blöchl, C. G. Van de Walle, and S. T. Pantelides, Phys. Rev. Lett. 64, 1401 (1990).ADSCrossRefGoogle Scholar
  2. 2.
    L. B. Hansen, P. Stoltze, K. W. Jacobsen, and J. K. Norskov, Phys. Rev. B 44, 6523 (1991).ADSCrossRefGoogle Scholar
  3. 3.
    P. J. Feibelman, Surf. Sci. 313, L801 (1994).ADSCrossRefGoogle Scholar
  4. P. J. Feibelman, J. S. Nelson, and G. L. Kellogg, Phys. Rev. B 49, 10548 (1994).ADSCrossRefGoogle Scholar
  5. 4.
    R. Stumpf and M. Scheffler, Surf. Sci. 307, 510 (1994).Google Scholar
  6. 5.
    C. Lee, G. T. Barkema, M. Breeman, A. Pasquarello, and R. Car, Surf. Sci. Lett. 306, L575 (1994).CrossRefGoogle Scholar
  7. 6.
    E. Kaxiras and J. Erlebacher, Phys. Rev. Lett. 72, 1714 (1994).ADSCrossRefGoogle Scholar
  8. 7.
    S. Gladstone, K. Laidler, and H. Eyring in The Theory of Rate Processes McGraw-Hill, New York, (1941).Google Scholar
  9. G. Vineyard, J. Phys. and Chem. Solids 3, 121 (1957).ADSCrossRefGoogle Scholar
  10. A. F. Voter and J. D. Doll, J. Chem. Phys. 80, 5832 (1984).ADSCrossRefGoogle Scholar
  11. 8.
    A. F. Voter and J. D. Doll, J. Chem. Phys. 82, 80 (1985).ADSCrossRefGoogle Scholar
  12. 9.
    C. P. Flynn and G. Jacucci, Phys. Rev. B 25, 6225 (1982).ADSCrossRefGoogle Scholar
  13. 10.
    G. Jacucci in Diffusion in Crystalline Solids, G. E. Murch and A. S. Nowick, eds. Academic, New York, (1984).Google Scholar
  14. 11.
    G. Wahnstrom, Surf. Sci. 159, 311 (1985); 164, 449 (1985); Phys. Rev. B 33, 1020 (1986); J. Chem. Phys. 84, 5931 (1986).ADSCrossRefGoogle Scholar
  15. 12.
    J. R. Banavar, M. H. Cohen, and R. Gomer, Surf. Sci. 107, 113 (1981).ADSCrossRefGoogle Scholar
  16. 13.
    S. C. Ying, Phys. Rev. B 41, 7068 (1989).ADSCrossRefGoogle Scholar
  17. 14.
    T. Ala-Nissila and S. C. Ying, Prog. Surf. Sci. 39, 227 (1992).ADSCrossRefGoogle Scholar
  18. 15.
    L. Y. Chen and S. C. Ying, Phys. Rev. Lett. 71, 4361 (1993); Phys. Rev. B 49, 13838 (1994).ADSCrossRefGoogle Scholar
  19. 16.
    H. Mori, Progr. Theor. Phys. 34, 399 (1965).ADSCrossRefGoogle Scholar
  20. 17.
    D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions, Benjamin, New York, (1975).Google Scholar
  21. 18.
    G. Wahnström, Surf. Sci. 159, 311 (1985).ADSCrossRefGoogle Scholar
  22. 19.
    L. Y. Chen and S. C. Ying, J. Elec. Spec. 64, 797 (1993).ADSCrossRefGoogle Scholar
  23. 20.
    G. Wahnström, Surf. Sci. 164, 449 (1985); Phys. Rev. B 33, 1020 (1986).ADSCrossRefGoogle Scholar
  24. 21.
    R. Ferrando, R. Spadacini, and G. E. Tommei, Surf. Sci., 265, 273 (1992).Google Scholar
  25. 22.
    H. Risken, The Fokker Planck Equation, Springer-Verlag, Berlin, (1984).CrossRefzbMATHGoogle Scholar
  26. 23.
    H. A. Kramers, Physica 7, 284 (1940).MathSciNetADSCrossRefzbMATHGoogle Scholar
  27. 24.
    E. Ganz, S. K. Theiss, I. S. Hwang, and J. Golovchenko, Phys. Rev. Lett. 68, 1567 (1992).ADSCrossRefGoogle Scholar
  28. 25.
    D. C. Senft and G. Ehrlich, Phys. Rev. Lett. 74, 294 (1995).ADSCrossRefGoogle Scholar
  29. 26.
    L. Y. Chen, M. R. Baldan and S. C. Ying, to appear in Phys. Rev. B, Sept. (1996).Google Scholar
  30. 27.
    A. Cucchetti and S. C. Ying, to appear in Phys. Rev. B, Aug. (1996).Google Scholar
  31. 28.
    M. P. Allen, and D. J. Tildesley, Computer Simulation of Liquids, Clarendon, Oxford (1994).Google Scholar
  32. 29.
    J. Ellis and J. P. Toennies, Phys. Rev. Lett. 70, 2118 (1993).ADSCrossRefGoogle Scholar
  33. 30.
    A. Graham, F. Hofmann, J. P. Toennies, L. Y. Chen, and S. C. Ying, to be published.Google Scholar
  34. 31.
    J. W. M. Frenken and B. J. Hinch, in Springer series in Surface Science, vol. 27, p. 287, ed. E. Hulpke (1992).Google Scholar
  35. 32.
    F. Hofmann, W. Schöllkopf, J. P. Toennies in Proceedings of the Welch Foundation Conference on Chemical Research, Chemical Dynamics of Transient Species (1994).Google Scholar
  36. 33.
    S. Lindgren, C. Svensson, and L. Wallden, Phys. Rev. B, 42, 1467 (1990).ADSCrossRefGoogle Scholar
  37. 34.
    C. T. Chudley, and R. J. Elliott, Proc. Phys. Soc. London 77, 353 (1961).ADSCrossRefGoogle Scholar
  38. 35.
    R. Gomer, Rep. Prog. Phys. 53, 917 (1990).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • S. C. Ying
    • 1
  1. 1.Physics DepartmentBrown UniversityProvidenceUSA

Personalised recommendations