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Quasicrystalline structure formation in a classical crystalline thin-film system


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.

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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.


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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’.

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Authors and Affiliations



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.

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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. ce, 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.

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

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