Advertisement

Diffusive and subdiffusive step dynamics

  • W. Selke
  • M. Bisani
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 519)

Abstract

The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of the atoms at the steps. The three limiting cases of step-edge diffusion, evaporation-condensation and terrace diffusion are studied in the framework of Langevin descriptions and by Monte Carlo simulations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abraham, D. B., Upton, P. J. (1989): Dynamics of Gaussian interface models. Phys. Rev. B 39, 736CrossRefADSMathSciNetGoogle Scholar
  2. Bartelt, N. C., Einstein, T. L., Williams, E.D. (1994): Measuring surface mass diffusion coefficients by observing step fluctuations. Surf. Sci. 312, 411CrossRefADSGoogle Scholar
  3. Binder, K. (ed.) (1992): The Monte Carlo method in Condensed Matter Physics. (Springer, Berlin, Heidelberg)Google Scholar
  4. Bisani, M. (1998): Zur Theorie wechselwirkender Stufen auf Kristalloberflächen. Diplomarbeit, RWTH AachenGoogle Scholar
  5. Blagojevic, W., Duxbury, P. M. (1997): From atomic diffusion to step dynamics. In: Dynamics of crystal surfaces and interfaces. Eds. Duxbury, P. M., Pence, T. J. (Plenum Press, New York, London), p.1Google Scholar
  6. Bonzel, H. P., Surnev, S. (1997): Morphologies of periodic surface profiles and small particles. In:. Dynamics of crystal surfaces and interfaces. Eds. Duxbury, P. M., Pence, T. J. (Plenum Press, New York, London), p.41Google Scholar
  7. Edwards, S. F., Wilkinson, D. R. (1982): The surface statistics of a granular aggregate. Proc. R. Soc. A 381, 17CrossRefADSMathSciNetGoogle Scholar
  8. Giesen-Seibert, M., Jentjens, R., Poensgen, M., Ibach, H. (1993): Time dependence of step fluctuations on vicinal Cu (1 1 19) surfaces investigated by tunneling microscopy. Phys. Rev. Lett. 71, 3521CrossRefADSGoogle Scholar
  9. Hager, J., Spohn, H. (1995): Self-similar morphology and dynamics of periodic surface profiles below the roughening transition. Surf. Sci. 324, 365CrossRefADSGoogle Scholar
  10. Khare, S. V., Bartelt, N. C., Einstein, T. L. (1996): Brownian motion and shape fluctuations of single-layer adatom and vacancy clusters on surfaces: Theory and simulations. Phys. Rev. B 54, 11752CrossRefADSGoogle Scholar
  11. Khare, S. V., Einstein, T. L. (1998): Unified view of step-edge kinetics and fluctuations. Phys. Rev. B 57, 4782CrossRefADSGoogle Scholar
  12. Kuipers, L., Hoogeman, M. S., Frenken, J. W. M. (1993): Step dynamics on Au(110) studied with a high-temperature, high-speed scanning tunneling microscope. Phys. Rev. Lett. 71, 3517CrossRefADSGoogle Scholar
  13. Lancon, F., Villain, J. (1990): Dynamics of a crystal surface below its roughening. In: Kinetics of ordering and growth at surfaces. Ed. Lagally, M. G. (Plenum Press, New York, London), p.369Google Scholar
  14. Li, J., Berndt, R., Schneider, W.-D., (1996): Tip-assisted diffusion on Ag(110) in scanning tunneling microscopy. Phys. Rev. Lett. 76, 11Google Scholar
  15. Lipowsky, R. (1985): Nonlinear growth of wetting layers. J. Phys. A 18, L 585Google Scholar
  16. Majid, I., Ben-Avraham, D., Havlin, S., Stanley, H. E. (1984): Exact enumeration approach to random walks on percolation clusters in two dimensions. Phys. Rev. B 30, 1626CrossRefADSGoogle Scholar
  17. Mullins, W. W. (1959): Flattening of nearly plane solid surface due to capillarity. J. Appl. Phys. 30, 77CrossRefADSGoogle Scholar
  18. Pimpinelli, A., Villain, J., Wolf, D. E., Metois, J. J., Heyraud, J. C., Elkiani, I., Uimin, G. (1993): Equilibrium step dynamics on vicinal surfaces. Surf. Sci. 295, 143CrossRefADSGoogle Scholar
  19. Selke, W., Duxbury, P. M. (1995): Equilibration of crystal surfaces. Phys. Rev. B 57, 4782Google Scholar
  20. Stauffer, D., Landau, D. P. (1989): Interface growth in a two-dimensional Ising model. Phys. Rev. B 57, 4782Google Scholar
  21. Stebens, A. (1998): Monte-Carlo Simulationen von dynamischen Prozessen auf Kristalloberflächen. Diplomarbeit, RWTH AachenGoogle Scholar
  22. van Beijeren, H., Kehr, K. W., Kutner, R. (1983): Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-diemnsional lattice. Phys. Rev. B 28, 5711CrossRefADSGoogle Scholar
  23. Weeks, J. D., Liu, D.-J., Jeong, H.-C. (1997): Two-dimensional models for step dynamics. In:. Dynamics of crystal surfaces and interfaces. Eds. Duxbury, P. M., Pence, T. J. (Plenum Press, New York, London), p.41Google Scholar
  24. Williams, E. D. (1994): Surface steps and surface morphology: understanding macroscopic phenomena from atomic observations. Surf. Sci. 299/300, 502CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • W. Selke
    • 1
  • M. Bisani
    • 1
  1. 1.Institut für Theoretische PhysikTechnische HochschuleAachenGermany

Personalised recommendations