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A columnar liquid quasicrystal with a honeycomb structure that consists of triangular, square and trapezoidal cells

Abstract

Quasicrystals are intriguing structures that have long-range positional correlations but no periodicity in real space, and typically with rotational symmetries that are ‘forbidden’ in conventional periodic crystals. Here, we present a two-dimensional columnar liquid quasicrystal with dodecagonal symmetry. Unlike previous dodecagonal quasicrystals based on random tiling, a honeycomb structure based on a strictly quasiperiodic tessellation of tiles is observed. The structure consists of dodecagonal clusters made up of triangular, square and trapezoidal cells that are optimal for local packing. To maximize the presence of such dodecagonal clusters, the system abandons periodicity but adopts a quasiperiodic structure that follows strict packing rules. The stability of random-tiling dodecagonal quasicrystals is often attributed to the entropy of disordering when strict tiling rules are broken, at the sacrifice of the long-range positional order. However, our results demonstrate that quasicrystal stability may rest on energy minimization alone, or with only minimal entropic intervention.

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Fig. 1: Quasiperiodic tilings and their differences to conventional periodic tilings.
Fig. 2: T-shaped polyphilic molecules and their self-assembly.
Fig. 3: X-ray diffractograms of the CLQC and p4gmL phases of compound 1.
Fig. 4: Reconstructed electron-density maps.
Fig. 5: Model of the CLQC on the basis of a quasiperiodic tiling of plane using triangles, squares and trapezoids.
Fig. 6: Tiling and inflation rules that lead to the dodecagonal quasiperiodic tiling of the CLQC.

Data availability

Source data are provided with this paper. All data generated or analysed in this study are available in this article and its Supplementary Information. The datasets generated and analysed during the current study are publicly available in the Figshare repository at https://doi.org/10.6084/m9.figshare.21626570 (ref. 48).

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Acknowledgements

For support with the experiments we thank O. Shebanova and N. Terrill at station I22, Diamond Light Source, O. Bikondoa and P. Thompson at XMaS beamline (BM28), ESRF, and S. Sasaki and H. Masunaga at BL40B2, Spring-8. Financial support is acknowledged from EPSRC (EP-P002250 and EP-T003294), DFG (436494874-RTG 2670), the 111 Project 2.0 of China (BP0618008) and National Natural Science Foundation of China (92156013, 21761132033, 21374086).

Author information

Authors and Affiliations

Authors

Contributions

C.T. and G.U. conceived and directed the project. B.G., U.B. and B.C., under the supervision of C.T., synthesized the compound and carried out the differential scanning calorimetry, polarized optical microscopy and initial X-ray diffraction characterizations. X.Z. and F.L., supervised by G.U., carried out the powder and GIXRD experiments, and data analysis that led to reconstruction of the electron density maps. All the authors contributed to the construction of the structural model of the CLQC phase. Simulation of the CLQC diffraction pattern was carried out by X.Z. X.Z. wrote the manuscript with written contributions from all the co-authors.

Corresponding author

Correspondence to Xiangbing Zeng.

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Peer review information

Nature Chemistry thanks Marianne Imperor-Clerc, Shiki Yagai, Slobodan Zumer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Sections 1 (Synthesis and analytical data), 2 (Simulation of diffraction intensities of CLQC) and 3 (Additional data), Figs. 1–13 and Tables 1–5.

Supplementary Data 1

DSC source data for supplementary Figure 4.

Supplementary Data 2

SAXS source data for supplementary Figure 7.

Supplementary Data 3

WAXS source data for supplementary Figure 7.

Supplementary Data 4

SAXS source data for supplementary Figure 10.

Supplementary Data 5

SAXS experimental and fitted data for supplementary Figure 12.

Supplementary Data 6

Peak widths and standard errors source data for supplementary Figure 13.

Source data

Fig. 3a

SAXS source data of p4gmL and CLQC phases for Fig. 3a.

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Zeng, X., Glettner, B., Baumeister, U. et al. A columnar liquid quasicrystal with a honeycomb structure that consists of triangular, square and trapezoidal cells. Nat. Chem. 15, 625–632 (2023). https://doi.org/10.1038/s41557-023-01166-5

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  • DOI: https://doi.org/10.1038/s41557-023-01166-5

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