Recently, a new solid state related with quasicrystals was discovered by Prof. HE Zhanbing, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Prof. SUN Junliang, College of Chemistry and Molecular Engineering, Peking University, Research Prof. MA Xiuliang, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, and Prof. Walter Steurer, Department of Materials, ETH Zurich, Switzerland. The new solid state appears as a special mosaic of aperiodically distributed unit tiles in translationally periodic structural blocks, which means it contains the structural features both of periodic crystals and of quasicrystals, other than any reported intermediate states between them. In other words, this novel structure accommodates the concordant coexistence of the translational symmetry of conventional crystals and the aperiodicity of quasicrystals, which was previously considered impossible. Therefore, it provides an ingenious solution in designing crystal structures in order to reconcile the contradictions between quasicrystals and conventional crystals. The authors believe that this discovery will trigger wide interest for use in theory, experimentation, and potential applications. For details, please see the original paper by HE Zhanbing, SHEN Yihan, MA Haikun, SUN Junliang, MA Xiuliang, LI Hua, and Walter Steurer, “Quasicrystal-related mosaics with periodic lattices interlaid with aperiodic tiles”,  Acta Cryst. (2020), A76, 137–144. Link：https://doi.org/10.1107/S2053273320000066.

This novel quasicrystal-related solid state was discovered experimentally in Al-Cr-Fe-Si alloys, and the structural characterizations at an atomic resolution were revealed by Cs-corrected transmission electron microscopy. Figure 1 gives a typical example of this new solid state. The yellow hexagonal (H) tiles in Fig. 1a are arranged in a periodic grid (in blue), where the lattice parameters of the periodic grid of yellow H tiles are  a  = 1.90 nm and  c = 3.61 nm, similar to those of the (2/1, 3/2) approximant of quasicrystals. The structural characteristics are revealed intuitively in Fig. 1b when all the structural blocks are colored according to their orientations. In general, the structural blocks inserted in-between the space of periodic H tiles (in yellow in Fig. 1b) are arranged aperiodically through the combination of two oriented star (S) tiles, three oriented H tiles, and four oriented dumbbell-like tetradecagons (DLTs), while also being mixed with some differently oriented boat (B) tiles. Note that a few unit cells of the (2/1, 3/2) approximant could be achieved locally because of the local periodic H and S tiles in the matrix of the mosaic, suggesting the generation of this structure is closely related with the (2/1, 3/2) approximant. In Fig. 1c, ten strong diffraction spots appear in the fast Fourier transform of Fig. 1a, which implies a close structural relationship to the quasicrystals. Although quasicrystal-related nanodomains have been often observed, they are either arranged randomly, in microcrystalline materials or as the crystal nuclei of approximants, or form metadislocations, all of which are clearly different from the structure shown here. This special structure is by no means restricted to the types found experimentally. The combination of different periodic tiles, lattice parameters, and accompanying aperiodic tiles in abundant quasicrystal-related systems can lead to a variety of structures, thereby suggesting their universal properties. For example, another larger example built from a geometric point of view, based on the structural blocks mentioned above, is seen in Fig. 1d.

The authors assert that this special aperiodic crystal is different from procrystalline, incommensurately modulated structures, and quasicrystals. Compared to a one-dimensional nanotubular host–guest structure with aperiodic guest molecules embedded into a periodic host, this aperiodic crystal provides a striking two-dimensional example that accommodates aperiodic and periodic structures simultaneously. Although it was originally found in an alloy, it may exist in other states such as porous materials, and molecular- or nano-assembly systems. The authors believe that this finding might provide insight into the design of materials, especially for those whose properties are closely related to periodicity, including photonic crystals and artistic tiles used in architecture.

Figure1 A new solid state. (a), (b) The structural details of this novel structure are revealed by atomic resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images. The yellow H tiles are positioned periodically on the blue periodic grid with the same  a, and  c parameters of the (2/1, 3/2) approximant, and the aperiodic tiles are displayed in the spaces in-between the periodic H tiles in (a).  (c) Fast Fourier transform of (a), where strong diffraction spots have tenfold symmetry, implying the close structural relationship to the corresponding DQC. (d) A computer-generated structure built from H, S and DLT tiles, where yellow H tiles are periodic. Aperiodic H tiles, S tiles and DLT tiles stack in-between the periodic yellow H tiles. The combination of different periodic tiles, different lattice parameters, and the accompanying aperiodic tiles can lead to a variety of structures, thereby suggesting their universal properties.