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Diffusion and Stability of Large Clusters on Crystal Surfaces

  • Georg Rosenfeld
  • Karina Morgenstern
  • George Comsa
Part of the NATO ASI Series book series (NSSB, volume 360)

Abstract

Diffusion and stability of large two-dimensional clusters (consisting of hundreds to thousands of atoms) are discussed. Scaling laws for the diffusion constant and the decay time of clusters as a function of the cluster size are derived from a microscopic point of view by treating atom diffusion near the cluster edge as a random walk problem of a single particle in the vicinity of an adsorbing boundary. This treatment establishes the connection between the quantities which can be determined by experiment (i.e., the cluster diffusion constant and the decay rate) to the microscopic diffusion processes of single atoms. The results are illustrated by experimental examples for diffusion and decay of adatom and vacancy clusters on a Ag(111) surface.

Keywords

Vacancy Cluster Outer Circle Escape Probability Cluster Decay Cluster Edge 
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.

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References

  1. 1.
    B.K. Chakraverty, J. Phys. Chem. Solids 28, 2401 (1967). Note, however, that on a surface the notion of a screening length is questionable because of the long range of the diffusion field in two dimensions.ADSCrossRefGoogle Scholar
  2. 2.
    e.g., R. Defay and I. Prigogine, Surface Tension and Adsorption, Longmans, London (1966).Google Scholar
  3. 3.
    P. Wynblatt and N.A. Gjostein, Supported metal crystallites, in: Progress in Solid State Chemistry, Vol. 9, Pergamon, Oxford (1975), p. 21.Google Scholar
  4. 4.
    M. Zinke-Allmang, L.C. Feldman, and M.H. Grabow, Surf. Sci. Rep. 16, 377 (1992).ADSCrossRefGoogle Scholar
  5. 5.
    K. Morgenstern, G. Rosenfeld, and G. Comsa, Phys. Rev. Lett. 76, 2113 (1996).ADSCrossRefGoogle Scholar
  6. 6.
    J.G. McLean et al., Phys. Rev. B (in press), and this volume.Google Scholar
  7. 7.
    C. DeW. Van Siclen, Phys. Rev. Lett. 75, 1574 (1995).ADSCrossRefGoogle Scholar
  8. 8.
    J.M. Soler, Phys. Rev. B 53, R10540 (1996).ADSCrossRefGoogle Scholar
  9. 9.
    E.E. Gruber, J. Appl. Phys. 38, 243 (1967).ADSCrossRefGoogle Scholar
  10. 10.
    S.V. Khare, N.C. Bartelt, and T.L. Einstein, Phys. Rev. Lett. 75, 2148 (1995).ADSCrossRefGoogle Scholar
  11. 11.
    J. Villain, J. Phys. I (France) 1, 19 (1991).CrossRefGoogle Scholar
  12. 12.
    N.C. Bartelt, J.L. Goldberg, T.L. Einstein, E.D. Williams, Surf. Sci. 273, 252 (1992).ADSCrossRefGoogle Scholar
  13. N.C. Bartelt, T.L. Einstein, E.D. Williams, Surf. Sci. 312, 411 (1994).ADSCrossRefGoogle Scholar
  14. 13.
    Y.W. Mo, R. Kariotis, B.S. Swartzentruber, J. Vac. Sci. Technol. A 8, 201 (1994).ADSCrossRefGoogle Scholar
  15. 14.
    W. Theis, N.C. Bartelt, R.M. Tromp, Phys. Rev. Lett. 75, 3328 (1995).ADSCrossRefGoogle Scholar
  16. 15.
    D.R. Peale, B. Cooper, J. Vac. Sci. Technol. A 10, 2210 (1992).ADSCrossRefGoogle Scholar
  17. 16.
    J. de la Figuera, J.E. Pristo, O. Ocal, R. Miranda, Solid State Commun. 89, 815 (1994).CrossRefGoogle Scholar
  18. 17.
    J.-M. Wen et al., Phys. Rev. Lett. 73, 2591 (1994), Phys. Rev. Lett. 76, 652 (1996).ADSCrossRefGoogle Scholar
  19. 18.
    See also discussion of available experiments on cluster diffusion by Soler in Ref. 8.Google Scholar
  20. 19.
    K. Morgenstern, G. Rosenfeld, B. Poelsema, and G. Comsa, Phys. Rev. Lett. 74, 2058 (1995).ADSCrossRefGoogle Scholar
  21. 20.
    K. Meinel, M. Klaua, H. Bethge, J. Cryst. Growth 89, 447 (1988).ADSCrossRefGoogle Scholar
  22. 21.
    H.A. van der Vegt et al., Phys. Rev. Lett. 68, 3335 (1992).ADSCrossRefGoogle Scholar
  23. 22.
    K. Besocke, Surf. Sci. 181, 145 (1987).ADSCrossRefGoogle Scholar
  24. 23.
    K. Morgenstern, Dynamik von Nanostrukturen auf Ag(111) — eine rastertunnelmikroskopische Untersuchung mit hoher Zeitauflösung, Berichte des Forschungszentrums Jülich 3278, Jülich (1996).Google Scholar
  25. 24.
    K. Morgenstern et al., to be published.Google Scholar
  26. 25.
    A. Pimpinelli et al., Surf. Sci. 295, 143 (1993).ADSCrossRefGoogle Scholar
  27. 26.
    C. Herring, J. Appl. Phys. 21, 301 (1950).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Georg Rosenfeld
    • 1
  • Karina Morgenstern
    • 1
  • George Comsa
    • 1
  1. 1.Institut für Grenzflächenforschung und VakuumphysikForschungszentrum JülichJülichGermany

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