Zeitschrift für Physik B Condensed Matter

, Volume 94, Issue 3, pp 311–318

Surface profile evolution above roughening

  • W. Selke
  • P. M. Duxbury
Original Contributions

Abstract

The relaxation of periodic surface profiles above roughening is studied in the framework of one-dimensional (1+1) SOS and Gaussian models, using Monte Carlo techniques. For particle transport by surface diffusion and evaporation-condensation the classical description by Mullins, yielding an exponential temporal decay in the amplitude of a sinusoidal profile, is recovered only when the amplitude is sufficiently small compared to the wavelength. Deviations from the asymptotic behavior are attributed, among other things, to anisotropy of the surface free energy. It is shown analytically that for the 1+1 SOS model, free energy anisotropy should be unimportant providedA/L≫exp(−K) (whereA is amplitude,L is wavelength, andK=J/T withJ the coupling constant andT the dimensionless temperature).

PACS

05.50 05.701 68.30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mullins, W.W.: J. Appl. Phys.30, 77 (1959)Google Scholar
  2. 2.
    Bonzel, H.P., Breuer, U., Voigtländer, B., Zeldov, E.: Surface Sci.272, 10 (1992)Google Scholar
  3. 3.
    Lancon F., Villain, J.: In: Kinetics of ordering and growth at surfaces, p. 369. Lagally, M.G. (ed.) New York: Plenum Press 1990Google Scholar
  4. 4.
    Ozdemir, M., Zangwill, A.: Phys. Rev. B42, 5013 (1990)Google Scholar
  5. 5.
    Spohn, H.: J. Phys. I (France):3, 69 (1993)Google Scholar
  6. 6.
    Selke, W., Oitmaa, J.: Surface Sci.198, L346 (1988)Google Scholar
  7. 7.
    Jiang, Z., Ebner, C.: Phys. Rev. B40, 316 (1989)Google Scholar
  8. 8.
    Selke, W., Bieker, T.: Surface Sci.281, 163 (1993)Google Scholar
  9. 9.
    Selke, W.: In: Metallic alloys: experimental and theoretical perspectives, p. 251. Faulkner, J.S., Jordan, R.G. (eds.) London, New York: Kluwer 1994Google Scholar
  10. 10.
    Falta, J., Imbihl, R., Sander, M., Henzler, M.: Phys. Rev. B45, 6858 (1992)Google Scholar
  11. 11.
    Dubson, M.A., Kalke, M., Hwang, J.: Phys. Rev. B47, 10044 (1993); Dubson, M.A., Jeffers, G.: (Preprint)Google Scholar
  12. 12.
    Weeks, J.D.: In: Ordering of strongly fluctuating condenced matter systems. Riste, T. (ed.) New York: Plenum Press 1980Google Scholar
  13. 13.
    Ehrlich, G., Hudda, F.G.: J. Chem. Phys.44, 1039 (1966)Google Scholar
  14. 14.
    Schwoebel, R.L.: J. Appl. Phys.40, 614 (1969)Google Scholar
  15. 15.
    Krug, J., Plischke, M., Siegert, M.: Phys. Rev. Lett.70, 3271 (1993)Google Scholar
  16. 16.
    Bonzel, H.P., Preuss, E., Steffen, B.: Appl. Phys. A35, 1 (1984); Preuss, E., Freyer, N., Bonzel, H.P.: Appl. Phys. A41, 137 (1986)Google Scholar
  17. 17.
    Burton, W.K., Cabrera, N., Frank, F.C.: Philos. Trans. R. Soc. London Ser. A243, 299 (1951)Google Scholar
  18. 18.
    Rottman, C., Wortis, M.: Phys. Rev. B24, 6274 (1981)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • W. Selke
    • 1
  • P. M. Duxbury
    • 1
  1. 1.Institut für FestkörperforschungForschungszentrum JülichJülichGermany
  2. 2.Department of Physics and Astronomy and center for Fundamental Materials ResearchMichigan State UniversityEast LansingUSA

Personalised recommendations