Tribology Letters

, Volume 48, Issue 1, pp 33–39 | Cite as

Anisotropy Effects in Atomic-Scale Friction

  • Enrico Gnecco
  • Oscar Y. Fajardo
  • Carlos M. Pina
  • Juan J. Mazo
Original Paper


The static and kinetic friction experienced by a point mass elastically driven at different angles on surface lattices with square, hexagonal, and honeycomb symmetries are estimated by analytical and numeric calculations based on the Prandtl–Tomlinson (PT) model. Assuming a strong surface coupling, the anisotropy of static friction increases from 3.7 up to 46.3% when the density of packing of the surface atoms is reduced, but this is not the case for kinetic friction, the anisotropy of which is maximal on a square lattice. Although these results have not been supported by accurate experimental verifications so far, the PT model was successfully applied to interpret anisotropy effects in the friction force profiles measured, among other surfaces, on rectangular lattices with complex unit cells and on stepped crystal surfaces.


Nanotribology Friction mechanisms Stick-slip Static friction AFM 



Prof. Riccardo Ferrando from the University of Genova is gratefully acknowledged for scientific discussion. Our collaboration was promoted thanks to the EUROCORES programme ‘Friction and Adhesion in Nanomechanical Systems’ (FANAS) of the European Science Foundation. OYF and JJM acknowledge Spain MICINN under Projects No. FIS2008-01240 and FIS2011-25167 cofinanced by FEDER funds.


  1. 1.
    Overney, R.M., Takano, H., Fujihira, M., Paulus, W., Ringsdorf, H.: Anisotropy in friction and molecular stick-slip motion. Phys. Rev. Lett. 72, 3546–3549 (1994)CrossRefGoogle Scholar
  2. 2.
    Takano, H., Fujihira, M.: Study of molecular scale friction on stearic acid crystals by friction force microscopy. J. Vac. Sci. Technol. B 14, 1272–1275 (1996)CrossRefGoogle Scholar
  3. 3.
    Liley, M., Gourdon, D., Stamou, D., Meseth, U., Fischer, T.M., Lautz, C., Stahlberg, H., Vogel, H., Burnham, N.A., Duschl, C.: Friction anisotropy and asymmetry of a compliant monolayer induced by a small molecular tilte. Science 280, 273–275 (1998)CrossRefGoogle Scholar
  4. 4.
    Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimber, J.A., Zandbergen, H.W.: Superlubricity of graphite. Phys. Rev. Lett. 92(1–4), 126101 (2004)CrossRefGoogle Scholar
  5. 5.
    Park, J.Y., Ogletree, D.F., Salmeron, M., Ribeiro, R.A., Canfield, P.C., Jenks, C.J., Thiel, P.A.: High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface. Science 309, 1354–1356 (2005)CrossRefGoogle Scholar
  6. 6.
    Kalihari, V., Haugstad, G., Frisbie, C.D.: Distinguishing elastic shear deformation from friction on the surfaces of molecular crystals. Phys. Rev. Lett. 104(1–4), 086102 (2010)CrossRefGoogle Scholar
  7. 7.
    Campione, M., Fumagalli, E.: Friction anisotropy of the surface of organic crystals and its impact on scanning force microscopy. Phys. Rev. Lett. 105(1–4), 166103 (2010)CrossRefGoogle Scholar
  8. 8.
    Fessler, G., Zimmermann, I., Glatzel, T., Gnecco, E., Steiner, P., Roth, R., Keene, T.D., Liu, S.X., Decurtins, S., Meyer, E.: Orientation dependent molecular friction on organic layer compound crystals. Appl. Phys. Lett. 98(1–3), 083119 (2011)CrossRefGoogle Scholar
  9. 9.
    Verhoeven, G.S., Dienwiebel, M., Frenken, J.W.M.: Model calculations of superlubricity of graphite. Phys. Rev. B 70(1–10), 165418 (2004)CrossRefGoogle Scholar
  10. 10.
    Filippov, A.E., Vanossi, A., Urbakh, M.: Origin of friction anisotropy on a quasicrystal surface. Phys. Rev. Lett. 104(1–4), 074302 (2010)CrossRefGoogle Scholar
  11. 11.
    Müser, M.H.: Velocity dependence of kinetic friction in the Prandtl-Tomlinson model. Phys. Rev. B 84(1–13), 125419 (2011)CrossRefGoogle Scholar
  12. 12.
    Fajardo, O.Y., Mazo, J.J.: Effects of surface disorder and temperature on atomic friction. Phys. Rev. B 82(1–7), 035435 (2010)CrossRefGoogle Scholar
  13. 13.
    Fajardo, O.Y., Mazo, J.J.: Surface defects and temperature on atomic friction. J. Phys.: Condens. Matt. 23, 355008 (2011)CrossRefGoogle Scholar
  14. 14.
    Kerssemakers, J., De Hosson, J.T.M.: Atomic-force microscopy imaging of transition-metal layered compounds—a 2-dimensional stick–slip system. Appl. Phys. Lett. 67, 347–349 (1995)CrossRefGoogle Scholar
  15. 15.
    Hölscher, H., Schwarz, U.D., Wiesendanger, R.: Modelling of the scan process in lateral force microscopy. Surf. Sci. 375, 395–402 (1997)CrossRefGoogle Scholar
  16. 16.
    Hölscher, H., Raberg, W., Schwarz, U.D., Hasbach, A., Wandelt, K., Wiesendanger, R.: Imaging of sub-unit-cell structures in the contact mode of the scanning force microscope. Phys. Rev. B 59, 1661–1664 (1999)CrossRefGoogle Scholar
  17. 17.
    Steiner, P., Gnecco, E., Filleter, T., Gosvami, N.N., Maier, S., Meyer, E., Bennewitz, R.: Atomic friction investigations on ordered superstructures. Trib. Lett. 39, 321–327 (2010)CrossRefGoogle Scholar
  18. 18.
    Steiner, P., Roth, R., Gnecco, E., Baratoff, A., Meyer, E.: Angular dependence of static and kinetic friction on alkali halide surfaces. Phys. Rev. B 82(1–9), 205417 (2010)CrossRefGoogle Scholar
  19. 19.
    Gnecco, E.: Quasi-isotropy of static friction on hexagonal surface lattices. Europhys. Lett. 91(1–6), 66008 (2010)CrossRefGoogle Scholar
  20. 20.
    Braun, O.M., Ferrando, R.: Role of long jumps in surface diffusion. Phys. Rev. E 65(1–11), 061107 (2002)CrossRefGoogle Scholar
  21. 21.
    Pina, C.M., Miranda, R., Gnecco, E.: Anisotropic surface coupling while sliding on dolomite and calcite crystals. Phys. Rev. B 85(1–4), 073402 (2012)CrossRefGoogle Scholar
  22. 22.
    Hölscher, H., Ebeling, D., Schwarz, U.D.: Friction at atomic-scale surface steps: Experiment and theory. Phys. Rev. Lett. 101(1–4), 246105 (2008)CrossRefGoogle Scholar
  23. 23.
    Steiner, P., Gnecco, E., Krok, F., Budzioch, J., Walczak, L., Konior, J., Szymonski, M., Meyer, E.: Atomic-scale friction on stepped surfaces of ionic crystals. Phys. Rev. Lett. 106(1–4), 186104 (2011)CrossRefGoogle Scholar
  24. 24.
    Ehrlich, G., Hudda, F.G.: Atomic view of surface self-diffusion: Tungsten on tungsten. J. Chem. Phys. 44, 1039–1049 (1966)CrossRefGoogle Scholar
  25. 25.
    Schwöbel, R.L., Shipsey, E.J.: Step motion on crystal surfaces. J. Appl. Phys. 37, 3682–3686 (1966)CrossRefGoogle Scholar
  26. 26.
    Campione, M., Trabattoni, S., Moret, M.: Nanoscale mapping of frictional anisotropy. Trib. Lett. 45, 219–224 (2012)CrossRefGoogle Scholar
  27. 27.
    Zhao, X., Phillpot, S.R., Sawyer, W.G., Sinnott, S.B., Perry, S.S.: Transition from thermal to athermal friction under cryogenic conditions. Phys. Rev. Lett. 102(1–4), 186102 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Enrico Gnecco
    • 1
  • Oscar Y. Fajardo
    • 2
  • Carlos M. Pina
    • 3
  • Juan J. Mazo
    • 2
  1. 1.Instituto Madrileño de Estudios AvanzadosIMDEA NanocienciaMadridSpain
  2. 2.Departamento de Física de la Materia Condensada and Instituto de Ciencia de Materiales de AragónCSIC-Universidad de ZaragozaZaragozaSpain
  3. 3.Departamento de Cristalografía y MineralogíaUniversidad Complutense de MadridMadridSpain

Personalised recommendations