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Archimedean-like tiling on decagonal quasicrystalline surfaces


Monolayers on crystalline surfaces often form complex structures with physical and chemical properties that differ strongly from those of their bulk phases1. Such hetero-epitactic overlayers are currently used in nanotechnology and understanding their growth mechanism is important for the development of new materials and devices. In comparison with crystals, quasicrystalline surfaces exhibit much larger structural and chemical complexity leading, for example, to unusual frictional2, catalytical3 or optical properties4,5. Deposition of thin films on such substrates can lead to structures that may have typical quasicrystalline properties. Recent experiments have indeed showed 5-fold symmetries in the diffraction pattern of metallic layers adsorbed on quasicrystals6,7. Here we report a real-space investigation of the phase behaviour of a colloidal monolayer interacting with a quasicrystalline decagonal substrate created by interfering five laser beams. We find a pseudomorphic phase that shows both crystalline and quasicrystalline structural properties. It can be described by an archimedean-like tiling8,9 consisting of alternating rows of square and triangular tiles. The calculated diffraction pattern of this phase is in agreement with recent observations of copper adsorbed on icosahedral Al70Pd21Mn9 surfaces10. In addition to establishing a link between archimedean tilings and quasicrystals, our experiments allow us to investigate in real space how single-element monolayers can form commensurate structures on quasicrystalline surfaces.

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Figure 1: Experimental realization of colloidal quasicrystals.
Figure 2: Real and reciprocal space structure of the adsorbate.
Figure 3: Substrate–adsorbate correlations.


  1. Barth, J. V., Costantini, G. & Kern, K. Engineering atomic and molecular nanostructures at surfaces. Nature 437, 671–679 (2005)

    ADS  CAS  Article  Google Scholar 

  2. Park, J. Y. et al. High frictional anisotropy of periodic and aperiodic directions on a quasicrystal surface. Science 309, 1354–1356 (2005)

    ADS  CAS  Article  Google Scholar 

  3. Tsai, A. P. & Yoshimura, M. Highly active quasicrystalline Al-Cu-Fe catalyst for steam reforming of methanol. Appl. Catal. A 214, 237–241 (2001)

    CAS  Article  Google Scholar 

  4. Zoorob, M. E., Charlton, M. D. B., Parker, G. J., Baumberg, J. J. & Netti, M. C. Complete photonic bandgaps in 12-fold symmetric quasicrystals. Nature 404, 740–743 (2000)

    ADS  CAS  Article  Google Scholar 

  5. Matsui, T., Agrawal, A., Nahata, A. & Vardeny, Z. V. Transmission resonances through aperiodic arrays of subwavelength apertures. Nature 446, 517–521 (2007)

    ADS  CAS  Article  Google Scholar 

  6. Franke, K. J. et al. Quasicrystalline epitaxial single element monolayers on icosahedral Al-Pd-Mn and decagonal Al-Ni-Co quasicrystal surfaces. Phys. Rev. Lett. 89, 156104 (2002)

    ADS  CAS  Article  Google Scholar 

  7. Sharma, H. R., Shimoda, M., Ross, A. R., Lograsso, T. A. & Tsai, A. P. Real-space observation of quasicrystalline Sn monolayer formed on the fivefold surface of icosahedral Al-Cu-Fe quasicrystal. Phys. Rev. B 72, 045428 (2005)

    ADS  Article  Google Scholar 

  8. Pearce, P. Structure in Nature is a Strategy for Design (MIT Press, Cambridge, MA, 1978)

    Google Scholar 

  9. David, S., Chelnokov, A. & Lourtioz, J. M. Isotropic photonic structures: Archimedean-like tilings and quasi-crystals. IEEE J. Quantum Electron. 37, 1427–1434 (2001)

    ADS  CAS  Article  Google Scholar 

  10. Ledieu, J. et al. Copper adsorption on the fivefold Al70Pd21Mn9 quasicrystal surface. Phys. Rev. B 72, 035420 (2005)

    ADS  Article  Google Scholar 

  11. Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)

    ADS  CAS  Article  Google Scholar 

  12. Engel, M. & Trebin, H.-R. Self-assembly of monoatomic complex crystals and quasicrystals with a double-well interaction potential. Phys. Rev. Lett. 98, 225505 (2007)

    ADS  Article  Google Scholar 

  13. Keys, A. S. & Glotzer, S. C. How do quasicrystals grow? Phys. Rev. Lett. 99, 235503 (2007)

    ADS  Article  Google Scholar 

  14. Janot, C. Quasicrystals—A Primer (Oxford Univ. Press, New York, 1994)

    MATH  Google Scholar 

  15. Dubois, J. M. Quasicrystals. J. Phys. Condens. Matter 13, 7753–7762 (2001)

    ADS  CAS  Article  Google Scholar 

  16. Fournee, V. et al. Nucleation and growth of Ag films on a quasicrystalline AlPdMn surface. Phys. Rev. B 67, 033406 (2003)

    ADS  Article  Google Scholar 

  17. Curtarolo, S., Setyawan, W., Ferralis, N., Diehl, R. D. & Cole, M. W. Evolution of topological order in Xe films on a quasicrystal surface. Phys. Rev. Lett. 95, 136104 (2005)

    ADS  Article  Google Scholar 

  18. Sharma, H. R., Shimoda, M. & Tsai, A. P. Quasicrystal surfaces: structure and growth of atomic overlayers. Adv. Phys. 56, 403–464 (2007)

    ADS  CAS  Article  Google Scholar 

  19. Ashkin, A. Optical trapping and manipulation of neutral particles using lasers. Proc. Natl Acad. Sci. USA 94, 4853–4860 (1997)

    ADS  CAS  Article  Google Scholar 

  20. Burns, M. M., Fournier, J. M. & Golovchenko, J. A. Optical matter—crystallization and binding in intense optical fields. Science 249, 749–754 (1990)

    ADS  CAS  Article  Google Scholar 

  21. Roichman, Y. & Grier, D. G. Holographic assembly of quasicrystalline photonic heterostructures. Opt. Express 13, 5434–5439 (2005)

    ADS  Article  Google Scholar 

  22. Bechinger, C., Brunner, M. & Leiderer, P. Phase behavior of two-dimensional colloidal systems in the presence of periodic light fields. Phys. Rev. Lett. 86, 930–933 (2001)

    ADS  CAS  Article  Google Scholar 

  23. Yethiraj, A. Tunable colloids: control of colloidal phase transitions with tunable interactions. Soft Matter 3, 1099–1115 (2007)

    ADS  CAS  Article  Google Scholar 

  24. Guinier, A. X-ray Diffraction—In Crystals, Imperfect Crystals and Amorphous Bodies (Dover, New York, 1994)

    Google Scholar 

  25. Bilki, B., Erbudak, M., Mungan, M. & Weisskopf, Y. Structure formation of a layer of adatoms on a quasicrystalline substrate: Molecular dynamics study. Phys. Rev. B 75, 045437 (2007)

    ADS  Article  Google Scholar 

  26. Ledieu, J. et al. Tiling of the fivefold surface of Al70Pd21Mn9 . Surf. Sci. 492, L729–L734 (2001)

    CAS  Article  Google Scholar 

  27. Yethiraj, A. Tunable colloids: control of colloidal phase transitions with tunable interactions. Soft Matter 3, 1099–1115 (2007)

    ADS  CAS  Article  Google Scholar 

  28. Ledieu, J. et al. Pseudomorphic growth of a single element quasiperiodic ultrathin film on a quasicrystal substrate. Phys. Rev. Lett. 92, 135507 (2004)

    ADS  CAS  Article  Google Scholar 

  29. Freedman, B., Lifshitz, R., Fleischer, J. W. & Segev, M. Phason dynamics in nonlinear photonic quasicrystals. Nature Mater. 6, 776–781 (2007)

    ADS  CAS  Article  Google Scholar 

  30. Brunner, M., Bechinger, C., Strepp, W., Lobaskin, V. & v Grünberg, H. H. Density-dependent pair-interactions in 2D colloidal suspensions. Europhys. Lett. 58, 926–932 (2002)

    ADS  CAS  Article  Google Scholar 

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We thank J. Baumgartl, S. Rausch, H.-H. v. Grünberg, M. Schmiedeberg and H. Stark for technical support and helpful discussions. This work is financially supported by the Deutsche Forschungsgemeinschaft.

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Correspondence to Clemens Bechinger.

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Mikhael, J., Roth, J., Helden, L. et al. Archimedean-like tiling on decagonal quasicrystalline surfaces. Nature 454, 501–504 (2008).

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