Skip to main content

Part of the book series: NATO ASI Series ((NSSB,volume 239))

Abstract

Scaling arguments have contributed a lot to the understanding of the growth of rough surfaces. Usually they are based on the assumption that the size of the surface provides the only characteristic length in the system. However in experiments as well as in computer simulations one generally has to take a second length into account. It is associated with the concept of an intrinsic width or short range roughness of the surface, to be distinguished from its long range fluctuations. Two physical manifestations of such a second length will be discussed: a) The intrinsic width is a major source of corrections to scaling and should be kept small if one wants to measure roughening exponents. In computer simulations this can be achieved by an algorithm called noise reduction, b) At a nonequilibrium roughening transition the second length may diverge, so that the intrinsic width determines the anomalous roughness right at the transition. This is demonstrated for a class of growth models, where analytical as well as numerical results are available.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. An overview is given e.g. by T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989).

    MATH  Google Scholar 

  2. J. G. Zabolitzky and D. Stauffer, Phys. Rev. A34, 1523 (1986).

    ADS  Google Scholar 

  3. D. E. Wolf and J. Kertész, J.Phys. A20, L257 (1987).

    ADS  Google Scholar 

  4. R. Kariotis and M. G. Lagally, Surface Sci. 216, 557 (1989).

    Article  ADS  Google Scholar 

  5. S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. A381, 17 (1982).

    MathSciNet  ADS  Google Scholar 

  6. F. Family and T. Vicsek, J. Phys. A18, L75 (1985).

    ADS  Google Scholar 

  7. F. Family, J. Phys. A19, L441 (1986).

    ADS  Google Scholar 

  8. M. J. Vold, J. Colloid Sci. 14, 168 (1959).

    Article  Google Scholar 

  9. M. Eden, in: Symposium on Information Theory in Biology. H. P. Yockey ed. (Pergamon Press, New York 1958) p. 359.

    Google Scholar 

  10. R. Jullien and R. Botet, J. Phys. A18, 2279 (1985).

    ADS  Google Scholar 

  11. P. Meakin and F. Family, Phys. Rev. A34, 2558 (1986).

    ADS  Google Scholar 

  12. J. Krug and P. Meakin, Phys. Rev. A40, 2064 (1989); P. Meakin and J. Krug, Europhys. Lett. to be published (1989).

    ADS  Google Scholar 

  13. For correlated noise, see e.g. E. Medina, T. Hwa, M. Kardar and Y.-C. Zhang, Phys. Rev. A39, 3053 (1989).

    MathSciNet  ADS  Google Scholar 

  14. M. Kardar, G. Parisi and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).

    Article  ADS  MATH  Google Scholar 

  15. R. Hirsch and D. E. Wolf, J. Phys. A19, L251 (1986).

    ADS  Google Scholar 

  16. D. E. Wolf, J. Phys. A20, 1251 (1987).

    ADS  Google Scholar 

  17. J. Krug, J. Phys. A22, L769 (1989).

    ADS  Google Scholar 

  18. D. Henderson, M. H. Brodsky and P. Chaudhari, Appl. Phys. Lett. 25, 641 (1974).

    Article  ADS  Google Scholar 

  19. J. Krug and H. Spohn, Phys. Rev. A38, 4271 (1988).

    MathSciNet  ADS  Google Scholar 

  20. P. Meakin, P. Ramanlal, L. M. Sander and R. C. Ball, Phys. Rev. A34, 5091 (1986).

    ADS  Google Scholar 

  21. J. Krug, Phys. Rev. A36, 5465 (1987).

    ADS  Google Scholar 

  22. D. E. Wolf and J. Kertész, Phys. Rev. Lett. 63, 1191 (1989).

    Article  ADS  Google Scholar 

  23. M. Plischke and Z. Rácz, Phys. Rev. A32, 3825 (1985).

    ADS  Google Scholar 

  24. D. E. Wolf and J. Kertész, Europhys. Lett. 4, 651 (1987).

    Article  ADS  Google Scholar 

  25. J. Kertész and D. E. Wolf, J. Phys. A21, 747 (1988).

    ADS  Google Scholar 

  26. J. Szép, J. Cserti and J. Kertész, J. Phys. A18, L413 (1985).

    ADS  Google Scholar 

  27. P. Devillard and H. E. Stanley, Phys. Rev. A38, 6451 (1988).

    ADS  Google Scholar 

  28. J. M. Kim and J. M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989).

    Article  ADS  Google Scholar 

  29. M. Kardar and Y.-C. Zhang, Phys. Rev. Lett. 58, 2087 (1987).

    Article  ADS  Google Scholar 

  30. A. J. McKane and M. A. Moore, Phys. Rev. Lett. 60, 527 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  31. T. Halpin-Healy, Phys. Rev. Lett. 62, 442 (1989); T. Nattermann preprint.

    Article  ADS  Google Scholar 

  32. T. Halpin-Healy, Phys. Rev. Lett. 63, 917 (1989).

    Article  ADS  Google Scholar 

  33. D. Liu and M. Plischke, Phys. Rev. B 38, 4781 (1988); P. Devillard and H. E. Stanley, Physica A to be published (1989); L. Tang and B. Forrest, private communication.

    Article  ADS  Google Scholar 

  34. W. Renz, private communication.

    Google Scholar 

  35. J. Kertész and D. E. Wolf, Phys. Rev. Lett. 62, 2571 (1989).

    Article  ADS  Google Scholar 

  36. D. Richardson, Proc. Cambridge Philos. Soc. 74, 515 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. R. Durrett and T. M. Liggett, Ann. Probab. 18, 186 (1981); R. Savit and R. Ziff, Phys. Rev. Lett. 55, 2515 (1985).

    Article  MathSciNet  Google Scholar 

  38. D. E. Wolf, unpublished.

    Google Scholar 

  39. F. C. Frank, J. Cryst. Growth 22, 233 (1974).

    Article  ADS  Google Scholar 

  40. C. Lehner, N. Rajewsky, D. E. Wolf and J. Kertész, Physica A to be published.

    Google Scholar 

  41. W. Kinzel, in: Percolation Structures and Processes. G. Deutscher, R. Zallen and J. Adler, eds. Annals of the Israel Physical Society, Vol. 5 (Hilger, Bristol, 1983).

    Google Scholar 

  42. J. Krug, J. Kertész and D. E. Wolf, to be published.

    Google Scholar 

  43. T. Nattermann, private communication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Plenum Press, New York

About this chapter

Cite this chapter

Wolf, D.E. (1990). Growth of Rough and Facetted Surfaces. In: Lagally, M.G. (eds) Kinetics of Ordering and Growth at Surfaces. NATO ASI Series, vol 239. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0653-5_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0653-5_25

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-7911-2

  • Online ISBN: 978-1-4613-0653-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics