On the Fractal Dimension of Rough Surfaces

  • Bo PerssonEmail author
Part of the NanoScience and Technology book series (NANO)


Most natural surfaces and surfaces of engineering interest, e.g., polished or sand blasted surfaces, are self affine fractal over a wide range of length scales, with the fractal dimension \(D_\mathrm{f} = 2.15 \pm 0.15\). We give several examples which illustrate this and a simple argument, based on surface fragility, for why the fractal dimension usually is \(<\)2.3. A kinetic model of sand blasting is presented, which gives surface topographies and surface roughness power spectra in good agreement with experiments.


Power Spectrum Fractal Dimension External Object Capillary Wave Engineering Interest 
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.



I thank J. Krim for useful comments on the text.


  1. 1.
    B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    B.N.J. Persson, Surf. Sci. Rep. 61, 201 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    B.N.J. Persson, O. Albohr, U. Tartaglino, A.I. Volokitin, E. Tosatti, J. Phys. Condens. Matter 17, R1 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    J. Krim, Adv. Phys. 61, 155 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    A.L. Barabasi, H.E. Stanley, Fractal Concept in Surface Growth (Cambridge University Press, Cambridge, 1995)CrossRefGoogle Scholar
  6. 6.
    J. Krim, G. Palasantzas, Int. J. Modern Phys. B 9, 599–632 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    J. Krim, I. Heyvaert, C. Van Haesendonck, Y. Bruynseraede, Phys. Rev. Lett. 70, 57–61 (1993)ADSCrossRefGoogle Scholar
  8. 8.
    D. Berman, J. Krim, Thin Solid Films 520, 6201 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    G. Carbone, B. Lorenz, B.N.J. Persson, A. Wohlers, Eur. Phys. J. 29, 275 (2009)Google Scholar
  10. 10.
    B. Lorenz, PGI, FZ Jülich, GermanyGoogle Scholar
  11. 11.
    A. Wohlers, IFAS, RWTH Aachen, GermanyGoogle Scholar
  12. 12.
    O. Albohr, Pirelli Deutschland AG, 64733 Höchst/Odenwald, GermanyGoogle Scholar
  13. 13.
    A. Kovalev, S.N. Gorb, Department of Functional Morphology and Biomechanics, Zoological Institute at the University of Kiel, GermanyGoogle Scholar
  14. 14.
    B.N.J. Persson, A. Kovalev and S.N. Gorb, Tribology Letters 10.1007/s11249-012-0053-2.Google Scholar
  15. 15.
    C. Ganser, F. Schmied, C. Teichert, Institute of Physics, Montanuniversität Leoben, Leoben, AustriaGoogle Scholar
  16. 16.
    A. Kovalev, S.N. Gorb, Department of Functional Morphology and Biomechanics, Zoological Institute at the University of Kiel, GermanyGoogle Scholar
  17. 17.
    B.N.J. Persson, A. Kovalev, M. Wasem, E. Gnecco, S.N. Gorb, EPL 92, 46001 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    D. Pires, B. Gotsmann, F. Porro, D. Wiesmann, U. Duerig, A. Knoll, Langmuir 25, 5141 (2009)CrossRefGoogle Scholar
  19. 19.
    D.E. Wolf, J. Villain, Europhys. Lett. 13, 389 (1990)ADSCrossRefGoogle Scholar
  20. 20.
    F. Family, J. Phys. A 19, L441 (1986)ADSCrossRefGoogle Scholar
  21. 21.
    C. Campana, B.N.J. Persson, M.H. Muser, J. Phys. Condens. Matter 23, 085001 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    S. Akarapu, T. Sharp, M.O. Robbins, Phys. Rev. Letters 106, 204301 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    B.N.J. Persson, M. Scaraggi, European J. Phys. E 34, 113 (2011)CrossRefGoogle Scholar
  24. 24.
    N. Mulakaluri, B.N.J. Persson, EPL 96, 66003 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    E. Bouchaud, J. Phys. Condens. Matter 9, 4319 (1997)ADSCrossRefGoogle Scholar
  26. 26.
    E. Bouchaud, G. Lapasset, J. Planes, Europhys. Lett. 13, 73 (1990)ADSCrossRefGoogle Scholar
  27. 27.
    T. Kessler, A. Visintin, A.E. Bolzan, G. Andreasen, R.C. Salvarezza, W.E. Triaca, A.J. Arivia, Langmuir 12, 6587 (1996)CrossRefGoogle Scholar
  28. 28.
    J. Krim, private communicationGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Peter Grünberg InstitutForschungszentrum JülichJülichGermany

Personalised recommendations