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S C I E N T I F I C H I G H L I G H T S

6 2 H I G H L I G H T S 2 0 2 3 I

X-ray diffraction reveals first 2D columnar liquid quasicrystal

X-ray diffraction has aided the discovery of the first two-dimensional columnar liquid quasicrystal, with dodecagonal symmetry. The discovery opens an approach to creating other strict instead of random quasiperiodic structures in soft matter.

The discovery of quasicrystals in metal alloys in 1984 [1], which won the Nobel prize in chemistry in 2011, changed our preconception that any structure with long-range positional order must be periodic. While a common crystal can be described as a periodic repetition of a single unit cell, a quasicrystal has multiple building blocks (tiles) of different shapes. Such tiles pack locally into clusters with a symmetry such as pentagonal or dodecahedral, which is forbidden in classical crystallography and is incompatible with a periodic lattice. To make such symmetry global while keeping the long-range positional order, strict and often complex tiling rules must be followed.

The first liquid quasicrystal (LQC), discovered in 2004 [2], was formed by dendritic molecules self-assembled into spherical micelles on a dodecagonal quasiperiodic lattice. This was analogous to atomic packing in metallic dodecagonal quasicrystals, but at the nanometre scale instead of atomic (i.e., Angstrom) scale. Since then, more nano- and mesoscale quasicrystals have been found in other soft and hard synthetic systems. The unusual combination of long-range positional order and high rotational symmetry (invariant under a combination of rotational and translational operations) makes nanoscale quasicrystals interesting for applications such as wide band-gap photonics. However, it is still very difficult to control the formation of nanotiles of different shapes through self-assembly, and to guide the packing of such nanotiles into quasiperiodic structures through their intricate interactions.

In this work, grazing incidence X-ray diffraction (GIXRD) experiments carried out at beamline BM28 have resulted in the discovery of the first two-dimensional columnar liquid quasicrystal (CLQC), with dodecagonal symmetry. The discovery is confirmed by the 12-fold rotational symmetry of its GIXRD pattern (Figure 44) from a surface-oriented thin film. The CLQC domains in the film are all oriented with one of their 12 equivalent {1100}

Fig. 44: The GIXRD pattern of CLQC mapped into the q-space, showing the 12-fold rotational

symmetry of the structure. Reciprocal lattice, with four basis vectors, is overlaid on top.