Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quasicrystalline structure formation in a classical crystalline thin-film system

Nature volume 502, pages 215–218 (2013)Cite this article

Subjects

Abstract

The discovery of quasicrystals1—crystalline structures that show order while lacking periodicity—forced a paradigm shift in crystallography. Initially limited to intermetallic systems1,2,3,4, the observation of quasicrystalline structures has recently expanded to include ‘soft’ quasicrystals in the fields of colloidal and supermolecular chemistry5,6,7,8,9. Here we report an aperiodic oxide that grows as a two-dimensional quasicrystal on a periodic single-element substrate. On a Pt(111) substrate with 3-fold symmetry, the perovskite barium titanate BaTiO3 forms a high-temperature interface-driven structure with 12-fold symmetry. The building blocks of this dodecagonal structure assemble with the theoretically predicted Stampfli–Gähler tiling10,11 having a fundamental length-scale of 0.69 nm. This example of interface-driven formation of ultrathin quasicrystals from a typical periodic perovskite oxide potentially extends the quasicrystal concept to a broader range of materials. In addition, it demonstrates that frustration at the interface between two periodic materials can drive a thin film into an aperiodic quasicrystalline phase, as proposed previously12. Such structures might also find use as ultrathin buffer layers for the accommodation of large lattice mismatches in conventional epitaxy13.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Electron diffraction from dodecagonal oxide thin film.
Figure 2: STM images of 12-fold structure on local scale.
Figure 3: Dodecagonal tiling as measured by STM.

Notes

  1. The print version states incorrectly that this paper was published online before print; however, the online PDF and HTML versions are correct.

References

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

    Article  ADS  CAS  Google Scholar 

  2. Wang, N., Chen, H. & Kuo, K. H. Two-dimensional quasi-crystal with eightfold rotational symmetry. Phys. Rev. Lett. 59, 1010–1013 (1987)

    Article  ADS  CAS  Google Scholar 

  3. Bendersky, L. Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis. Phys. Rev. Lett. 55, 1461–1463 (1985)

    Article  ADS  CAS  Google Scholar 

  4. Ishimasa, T., Nissen, H. U. & Fukano, Y. New ordered state between crystalline and amorphous in Ni-Cr particles. Phys. Rev. Lett. 55, 511–513 (1985)

    Article  ADS  CAS  Google Scholar 

  5. Dotera, T. Quasicrystals in soft matter. Isr. J. Chem. 51, 1197–1205 (2011)

    Article  CAS  Google Scholar 

  6. Zeng, X. B. et al. Supramolecular dendritic liquid quasicrystals. Nature 428, 157–160 (2004)

    Article  ADS  CAS  Google Scholar 

  7. Hayashida, K., Dotera, T., Takano, A. & Matsushita, Y. Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. Phys. Rev. Lett. 98, 195502 (2007)

    Article  ADS  Google Scholar 

  8. Talapin, D. V. et al. Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461, 964–967 (2009)

    Article  ADS  CAS  Google Scholar 

  9. Mikhael, J., Roth, J., Helden, L. & Bechinger, C. Archimedean-like tiling on decagonal quasicrystalline surfaces. Nature 454, 501–504 (2008)

    Article  ADS  CAS  Google Scholar 

  10. Stampfli, P. A dodecagonal quasi-periodic lattice in two dimensions. Helv. Phys. Acta 59, 1260–1263 (1986)

    Google Scholar 

  11. Gähler, F. in Quasicrystalline Materials (eds Janot, D. & Dubois, J. M. ) 272–284 (World Scientific, 1988)

    Google Scholar 

  12. Smith, A. R., Chao, K.-J., Niu, Q. & Shih, C.-K. Formation of atomically flat silver films on GaAs with a ‘silver mean’ quasi periodicity. Science 273, 226–228 (1996)

    Article  ADS  CAS  Google Scholar 

  13. Franke, K. J., Gille, P., Rieder, K.-H. & Theis, W. Achieving epitaxy between incommensurate materials by quasicrystalline interlayers. Phys. Rev. Lett. 99, 036103 (2007)

    Article  ADS  CAS  Google Scholar 

  14. 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)

    Article  ADS  CAS  Google Scholar 

  15. Li, G. H., Zhang, D., Jiang, H., Lai, W. & Liu, W. Fully oriented decagonal quasicrystalline thin films on crystalline substrates. Appl. Phys. Lett. 71, 897–899 (1997)

    Article  ADS  CAS  Google Scholar 

  16. Förster, S. & Widdra, W. Growth, structure, and thermal stability of epitaxial BaTiO3 films on Pt(111). Surf. Sci. 604, 2163–2169 (2010)

    Article  ADS  Google Scholar 

  17. Förster, S., Huth, M., Schindler, K.-M. & Widdra, W. Epitaxial BaTiO3 (100) films on Pt(100): a low-energy electron diffraction, scanning tunneling microscopy, and x-ray photoelectron spectroscopy study. J. Chem. Phys. 135, 104701 (2011)

    Article  ADS  Google Scholar 

  18. Förster, S., Meinel, K., Schindler, K.-M. & Widdra, W. Oxygen-deficient ordered phases of ultrathin BaTiO3 films on Pt(111). Surf. Interface Anal. 44, 628–634 (2012)

    Article  Google Scholar 

  19. Niizeki, N. & Mitani, H. Two-dimensional dodecagonal quasi-lattices. J. Phys. Math. Gen. 20, L405–L410 (1987)

    Article  ADS  Google Scholar 

  20. Seah, M. P. & Dench, W. A. Quantitative electron spectroscopy of surfaces: a standard data base for electron inelastic mean free paths in solids. Surf. Interface Anal. 1, 2–11 (1979)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank P. A. Thiel for discussions, R. Kulla for technical support, and E. M. Zollner for assisting in sample preparation. Financial support was provided by Deutsche Forschungsgemeinschaft Sonderforschungsbereich 762 ‘Functionality of Oxidic Interfaces’.

Author information

Authors and Affiliations

  1. Institute of Physics, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle, Germany,

    Stefan Förster, Klaus Meinel, René Hammer, Martin Trautmann & Wolf Widdra

  2. Max-Planck-Institut für Mikrostrukturphysik, 06120 Halle, Germany,

    Wolf Widdra

Authors
  1. Stefan Förster
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Klaus Meinel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. René Hammer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Martin Trautmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wolf Widdra
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.F. designed the experiment and performed the sample preparation by radiofrequency magnetron sputtering, room-temperature STM, X-ray photoelectron spectroscopy and LEED measurements. K.M. performed the molecular beam evaporation experiments, Auger electron spectroscopy and spot-profile analysis LEED measurements. R.H. and M.T. contributed the low-temperature STM measurements. S.F., K.M. and W.W. discussed the results and wrote the manuscript.

Corresponding author

Correspondence to Wolf Widdra.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Development of the QC thin film by different preparation steps.

a, LEED pattern of an initially 14 Å thick film of BaTiO3 on Pt(111) after annealing at 1,100 K in O2, showing a BaTiO3(111)-(1 × 1) structure (energy 66 eV). The green hexagons mark the first-order diffraction, and yellow hexagons mark higher-order spots. b, Large-scale STM image of the surface after annealing at 1,250 K in UHV. BaTiO3(111) islands have formed. c–e, Corresponding LEED patterns (energies of 66, 110, and 170 eV, respectively) showing that the area between the BaTiO3(111) islands is completely covered with the QC layer. f, Comparison of the LEED pattern of the QC thin film prepared by magnetron sputtering (left) and the SPALEED data for a QC thin film prepared by MBE (energy 66 eV). The spots marked by black squares are related to 30° rotated BaTiO3 islands, which can appear depending on the preparation conditions.

Extended Data Figure 2 XPS spectra in the regions of the Ba, Ti, and O core levels for the initially 14 Å thick BaTiO3 film on Pt(111).

The black lines show the spectra after the first annealing at 1,100 K in O2; the red lines represent the spectra after the second annealing at 1,250 K in UHV.

Extended Data Figure 3 Bias-dependent high-resolution STM images of the BaTiO3-derived QC layer on Pt(111).

The panels show consecutively recorded STM images of the same surface area at different bias voltage of −0.15 (a), −1.0 (b) and 1.0 V (c). The inset in a shows the FFT of the STM image. The contrast in the outer region of the FFT was enhanced tenfold. For comparison, the colour-coded height scale was kept constant in all three images (0.07 nm).

Extended Data Figure 4 Orientation of the QC layer on the Pt(111) substrate.

a, Simplified model of an idealized dodecagonal structure with an edge length of 0.685 nm (green) on the Pt(111) substrate (grey). Different generations of the dodecagonal tiling are marked with green and red circles. b, Corresponding FFT pattern with the substrate spots drawn in red. The first-order substrate spots are marked with yellow hexagons. In the outer region of b the contrast is enhanced fivefold. c, LEED pattern of the BaTiO3-derived QC layer on Pt(111) on the same reciprocal length scale for comparison.

Extended Data Figure 5 Illustration of the backfolding of the QC layer diffraction at the first-order Pt(111) spots.

a, Scheme of the dodecagonal diffraction pattern of Fig. 1a, extended by the positions of the first-order spots of the Pt(111) substrate as marked by green crosses. b, LEED pattern of the QC layer structure superimposed with red and blue rings indicating the orders of diffraction. For reasons of clarity, the positions of backfolded diffraction spots are indicated by red and blue circles only in the relevant direction and only for the Pt spots in the upper left corner. Backfolding from all six substrate spots finally generates the inner ring of six spots as observed in LEED. Nevertheless, the origin of this ring of six spots is the QC structure.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Förster, S., Meinel, K., Hammer, R. et al. Quasicrystalline structure formation in a classical crystalline thin-film system. Nature 502, 215–218 (2013). https://doi.org/10.1038/nature12514

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature12514

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing