Quasicrystalline structure formation in a classical crystalline thin-film system

Journal name:
Nature
Volume:
502,
Pages:
215–218
Date published:
DOI:
doi:10.1038/nature12514
Received
Accepted
Published online

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 0.69nm. 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.

At a glance

Figures

  1. Electron diffraction from dodecagonal oxide thin film.
    Figure 1: Electron diffraction from dodecagonal oxide thin film.

    a, b, LEED patterns of the dodecagonal BaTiO3-derived thin film phase on Pt(111) at electron energies of 66 eV (a) and 8 eV (b). c, Scheme of the 12-fold diffraction pattern, generated by linear combinations of the four lattice vectors, which are indicated by the red arrows. The size of the diffraction spots reflects the diffraction order. Corresponding orders of diffraction are colour-coded identically in all three images. The small green hexagons in a mark diffraction from additional (111)-oriented BaTiO3 islands.

  2. STM images of 12-fold structure on local scale.
    Figure 2: STM images of 12-fold structure on local scale.

    a, b, Low-temperature STM image of the dodecagonal BaTiO3-derived thin film phase on Pt(111) (a), and its Fourier transform (b). The Bragg planes of four first-order diffraction spots (arrows in b) are indicated in a. c, The corresponding LEED pattern, showing all the characteristic features of the FFT in b (electron energy 35eV). The contrast of the outer part of b has been enhanced fivefold.

  3. Dodecagonal tiling as measured by STM.
    Figure 3: Dodecagonal tiling as measured by STM.

    a, Ideal dodecagonal tiling built up from equilateral triangles and squares (green lines). Adjacent dodecagons form a self-similar next-generation tiling (red lines) on a 2+√3 longer length scale, as indicated at the right. The beginning of the third-generation tiling is indicated in blue. b, c, High-resolution STM images of the BaTiO3-derived dodecagonal QC phase. The second-generation (b) and first-generation (c) tilings follow the colour coding in a. To guide the eye, the outer rings of the first-generation dodecagons are coloured yellow. Inside the dodecagons the atomic arrangement as visible in STM is described by triangles, squares and also rhombi, as marked in c.

  4. Development of the QC thin film by different preparation steps.
    Extended Data Fig. 1: Development of the QC thin film by different preparation steps.

    a, LEED pattern of an initially 14Å thick film of BaTiO3 on Pt(111) after annealing at 1,100K in O2, showing a BaTiO3(111)-(1×1) structure (energy 66eV). 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 1,250K in UHV. BaTiO3(111) islands have formed. ce, Corresponding LEED patterns (energies of 66, 110, and 170eV, 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 66eV). The spots marked by black squares are related to 30° rotated BaTiO3 islands, which can appear depending on the preparation conditions.

  5. XPS spectra in the regions of the Ba, Ti, and O core levels for the initially 14[thinsp]A thick BaTiO3 film on Pt(111).
    Extended Data Fig. 2: XPS spectra in the regions of the Ba, Ti, and O core levels for the initially 14Å thick BaTiO3 film on Pt(111).

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

  6. Bias-dependent high-resolution STM images of the BaTiO3-derived QC layer on Pt(111).
    Extended Data Fig. 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 1.0V (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 (0.07nm).

  7. Orientation of the QC layer on the Pt(111) substrate.
    Extended Data Fig. 4: Orientation of the QC layer on the Pt(111) substrate.

    a, Simplified model of an idealized dodecagonal structure with an edge length of 0.685nm (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.

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

References

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Author information

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

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.

Competing financial interests

The authors declare no competing financial interests.

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Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: Development of the QC thin film by different preparation steps. (149 KB)

    a, LEED pattern of an initially 14Å thick film of BaTiO3 on Pt(111) after annealing at 1,100K in O2, showing a BaTiO3(111)-(1×1) structure (energy 66eV). 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 1,250K in UHV. BaTiO3(111) islands have formed. ce, Corresponding LEED patterns (energies of 66, 110, and 170eV, 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 66eV). The spots marked by black squares are related to 30° rotated BaTiO3 islands, which can appear depending on the preparation conditions.

  2. Extended Data Figure 2: XPS spectra in the regions of the Ba, Ti, and O core levels for the initially 14Å thick BaTiO3 film on Pt(111). (77 KB)

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

  3. Extended Data Figure 3: Bias-dependent high-resolution STM images of the BaTiO3-derived QC layer on Pt(111). (146 KB)

    The panels show consecutively recorded STM images of the same surface area at different bias voltage of −0.15 (a), −1.0 (b) and 1.0V (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 (0.07nm).

  4. Extended Data Figure 4: Orientation of the QC layer on the Pt(111) substrate. (144 KB)

    a, Simplified model of an idealized dodecagonal structure with an edge length of 0.685nm (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.

  5. Extended Data Figure 5: Illustration of the backfolding of the QC layer diffraction at the first-order Pt(111) spots. (78 KB)

    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.

Additional data