Skip to main content
SpringerLink
Log in

Archimedean-like colloidal tilings on substrates with decagonal and tetradecagonal symmetry

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

Two-dimensional colloidal suspensions subjected to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction (J. Mikhael et al., Nature 454, 501 (2008)). In experiments as well as in Monte Carlo and Brownian dynamics simulations, we identify a similar phase when the laser field possesses tetradecagonal symmetry. We characterize the structure of both Archimedean-like tilings in detail and point out how the tilings differ from each other. Furthermore, we also estimate specific particle densities where the Archimedean-like tiling phases occur. Finally, using Brownian dynamics simulations we demonstrate how phasonic distortions of the decagonal laser field influence the Archimedean-like tiling. In particular, the domain size of the tiling can be enlarged by phasonic drifts and constant gradients in the phasonic displacement. We demonstrate that the latter occurs when the interfering laser beams are not ideally adjusted.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)

    Article  ADS  Google Scholar 

  2. D. Levine, P.J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984)

    Article  ADS  Google Scholar 

  3. E. Macia, Rep. Prog. Phys. 69, 397 (2006)

    Article  ADS  Google Scholar 

  4. R. McGrath, J. Ledieu, E.J. Cox, R.D. Diehl, J. Phys.: Condens. Matter 14, R119 (2002)

    Article  ADS  Google Scholar 

  5. V. Fourne, Phys. Rev. B 67, 033406 (2003)

    Article  ADS  Google Scholar 

  6. M. Shimoda, T.J. Sato, A.P. Tsai, J.Q. Guo, Phys. Rev. B 62, 11288 (2000)

    Article  ADS  Google Scholar 

  7. K.J. Franke, H.R. Sharma, W. Theis, P. Gille, Ph. Ebert, K.H. Rieder, Phys. Rev. Lett. 89, 156104 (2002)

    Article  ADS  Google Scholar 

  8. J. Ledieu, J.T. Hoeft, D.E. Reid, J.A. Smerdon, R.D. Diehl, T.A. Lograsso, A.R. Ross, R. McGrath, Phys. Rev. Lett. 92, 135507 (2004)

    Article  ADS  Google Scholar 

  9. R.A. Tasca, N. Ferralis, R.D. Diehl, M.W. Cole, J. Phys.: Condens. Matter 16, S2911 (2004)

    Article  ADS  Google Scholar 

  10. S. Curtarolo, W. Setyawan, N. Ferralis, R.D. Diehl, M.W. Cole, Phys. Rev. Lett. 95, 136104 (2005)

    Article  ADS  Google Scholar 

  11. W. Setyawan, N. Ferralis, R.D. Diehl, M.W. Cole, S. Curtarolo, Phys. Rev. B 74, 125425 (2006)

    Article  ADS  Google Scholar 

  12. W. Setyawan, R.D. Diehl, N. Ferralis, M.W. Cole, S. Curtarolo, J. Phys.: Condens. Matter 19, 016007 (2007)

    Article  ADS  Google Scholar 

  13. B. Bilki, M. Erbudak, M. Mungan, Y. Weisskopf, Phys. Rev. B 75, 045437 (2007)

    Article  ADS  Google Scholar 

  14. M. Mungan, Y. Weisskopf, M. Erbudak, Phys. Rev. B 76, 195443 (2007)

    Article  ADS  Google Scholar 

  15. K. Pussi, M. Grierer, R.D. Diehl, J. Phys.: Condens. Matter 21, 474213 (2009)

    Article  ADS  Google Scholar 

  16. M. Schmiedeberg, J. Roth, H. Stark, Phys. Rev. Lett. 97, 158304 (2006)

    Article  ADS  Google Scholar 

  17. M. Schmiedeberg, J. Roth, H. Stark, Eur. Phys. J. E 24, 367 (2007)

    Article  Google Scholar 

  18. J. Mikhael, J. Roth, L. Helden, C. Bechinger, Nature 454, 501 (2008)

    Article  ADS  Google Scholar 

  19. M. Schmiedeberg, H. Stark, Phys. Rev. Lett. 101, 218302 (2008)

    Article  ADS  Google Scholar 

  20. J. Mikhael, M. Schmiedeberg, S. Rausch, J. Roth, H. Stark, C. Bechinger, Proc. Natl. Acad. Sci. U.S.A. 107, 7214 (2010)

    Article  ADS  Google Scholar 

  21. D. Levine, T.C. Lubensky, S. Ostlund, S. Ramaswamym, P.J. Steinhardt, J. Toner, Phys. Rev. Lett. 54, 1520 (1985)

    Article  ADS  Google Scholar 

  22. J.E.S. Socolar, T.C. Lubensky, P.J. Steinhardt, Phys. Rev. B 34, 3345 (1986)

    Article  ADS  Google Scholar 

  23. C.L. Henley, M. de Boissieu, W. Steurer, Philos. Mag. 86, 1131 (2006)

    Article  ADS  Google Scholar 

  24. B. Freedman, R. Lifshitz, J.W. Fleischer, M. Segev, Nature 440, 1166 (2006)

    Article  ADS  Google Scholar 

  25. B. Freedman, R. Lifshitz, J.W. Fleischer, M. Segev, Nat. Mater. 6, 776 (2007)

    Article  ADS  Google Scholar 

  26. S.P. Gorkhali, J. Qi, G.P. Crawford, J. Opt. Soc. Am. B 23, 149 (2005)

    Article  ADS  Google Scholar 

  27. B.V. Derjaguin, L. Landau, Acta Physicochimica (USSR) 14, 633 (1941)

    Google Scholar 

  28. E.J. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948)

  29. W. Strepp, S. Sengupta, P. Nielaba, Phys. Rev. E 66, 056109 (2002)

    Article  ADS  Google Scholar 

  30. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  31. B. Grünbaum, G.C. Shepard, Tilings and Patterns (W.H. Freeman, New York, 1987)

  32. D.V. Talapin, E.V. Shevchenko, M.I. Bodnarchuk, X. Ye, J. Chen, C.B. Murray, Nature 461, 964 (2009)

    Article  ADS  Google Scholar 

  33. A. Patrykiejew, S. Sokołowski, Phys. Rev. Lett. 99, 156101 (2007)

    Article  ADS  Google Scholar 

  34. M. Schmiedeberg, H. Stark, Phys. Rev. Lett. 100, 019601 (2008)

    Article  ADS  Google Scholar 

  35. A. Patrykiejew, S. Sokołowski, Phys. Rev. Lett. 100, 019602 (2008)

    Article  ADS  Google Scholar 

  36. W. Rzysko, A. Patrykiejew, S. Sokołowski, J. Phys.: Condens. Matter 20, 494226 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, 19104, Philadelphia, PA, USA

    M. Schmiedeberg

  2. 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    J. Mikhael, S. Rausch, L. Helden & C. Bechinger

  3. Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    J. Roth

  4. Max-Planck-Institut für Metallforschung, Heisenbergstraße 3, D-70569, Stuttgart, Germany

    C. Bechinger

  5. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623, Berlin, Germany

    H. Stark

Authors
  1. M. Schmiedeberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Mikhael
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Rausch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Roth
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Helden
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. Bechinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. H. Stark
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Schmiedeberg.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schmiedeberg, M., Mikhael, J., Rausch, S. et al. Archimedean-like colloidal tilings on substrates with decagonal and tetradecagonal symmetry. Eur. Phys. J. E 32, 25–34 (2010). https://doi.org/10.1140/epje/i2010-10587-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/i2010-10587-1

Keywords

Search

Navigation