Materials science

Quasicrystals from nanocrystals

Quasicrystals have a host of unusual physical properties. These intermediates between amorphous solids and regular crystalline materials can now be made to self-assemble from nanoparticles.

The discovery of quasicrystals about 25 years ago1,2 brought about a paradigm shift in solid-state physics. The observation that the arrangement of atoms in these solids exhibited long-range order yet lacked the three-dimensional periodicity and translational symmetry that characterizes conventional crystals puzzled physicists3,4,5 — not least because certain 'forbidden' rotational symmetries occur in these materials. Initially discovered in certain exotic metal alloys, quasicrystals were later found in more common mixtures of elements and even in soft matter3: liquid crystals, surfactants and polymers. Adding to this growing list, Talapin et al.6 (page 964 of this issue) now report that binary colloidal nanoparticle systems, involving mixtures of two kinds of nanocrystal, self-assemble with quasicrystalline order.

Talapin and colleagues' colloidal quasicrystal self-assemblies are dodecagonal — that is, they display a 12-fold 'forbidden' rotational symmetry (a rotation about a particular axis by an angle 360°/12 does not change the material's scattering pattern). The assemblies are aperiodic in a certain plane but periodic in the direction perpendicular to this plane. Larger, micrometre-sized colloidal particles had already been reported to arrange in a decagonal (ten-fold) quasicrystalline pattern, but this was achieved by using laser beams and forcing them to form an interference pattern that conferred the desired symmetry on the system7.

Many of the unique properties of quasicrystals — hardness, low thermal conductivity, low friction and remarkable electronic properties (such as strong anisotropy in electronic transport) — have to do with the interplay between short-range and long-range order in these materials. The short-range order mainly refers to recurrent structural building units, and the long-range order to how these units are arranged in patterns that never repeat themselves. This interplay makes it hard for conventional methods to reconstruct the three-dimensional structure of quasicrystals from their diffraction patterns, although the quality of some of the quasicrystalline diffraction data is as good as the best obtained for periodic crystals. The interplay is also responsible for the lack of positional atomic data of high quality. Finally, it is at the root of the debate about the mechanisms that underlie the growth and stabilization of quasicrystals. All this despite the fact that the number of research papers on quasicrystals is running towards 10,000.

In their experiment, Talapin and colleagues6 used nanoparticles that are large enough to show up clearly in transmission electron micrographs (Fig. 1) but sufficiently small to be considered 'designer atoms', or 'quantum dots'. In binary arrangements of quantum dots, the collective quantum behaviour of the interacting particles can give rise to novel 'metamaterial' properties. For example, a regular arrangement of two sets of different-sized semiconducting nanoparticles has been shown to create a new kind of semiconductor8. Combining the properties of such binary metamaterials with those of quasicrystals would no doubt lead to new opportunities in materials design.

Figure 1: Binary colloidal quasicrystal.

Talapin and colleagues6 demonstrate self-assembly of a binary quasicrystal that involves a mixture of two types of nanoparticle: 13.4-nm Fe2O3 and 5-nm gold colloidal spheres. a, Transmission electron microscopy (TEM) image of the quasicrystal. b, Square–triangular tiling overlaid onto the TEM image. A structural defect ('D') is visible. (Scale bars, 20 nm.)

Talapin et al. resorted to projection transmission electron microscopy, which led, for instance, to the clear identification of a structural defect (Fig. 1). However, the use of transmission electron microscopy tomography on several periodic binary-crystal structures made of similar nanoparticles has previously succeeded in determining the three-dimensional particle locations9. Application of this technique to the dodecagonal quasicrystal structures studied by Talapin and colleagues would allow a full, three-dimensional characterization of the materials, and could provide insight into how these quasicrystals grow.

The authors6 observed that several different binary mixtures of nanoparticles (involving metals, magnetic materials and semiconductors), whose only common trait is a particle-size ratio of 0.43, self-assembled into the same type of quasicrystal. This observation is important both for unravelling some of the many mysteries associated with this type of aperiodic crystal and for our ability to design and fabricate novel materials. Most likely, it means that there is no strict requirement for a specific inter-particle interaction, allowing quasicrystal self-assemblies of many combinations of materials and, possibly, of (much) larger colloidal particles.

In fact, the formation of icosahedral quasicrystals (Fig. 2) made up of silica-coated surfactant spheres about 30 nanometres across, twice the size of Talapin and colleagues' largest nanoparticles, has already been reported10 — although the authors do not actually identify them as quasicrystals. The central part of the underlying formation mechanism, if correct, is that the surfactant/silica composite spheres form before the quasicrystal self-assembles. The size of the beautiful quasicrystal icosahedra formed, roughly 2 micrometres across, is within the colloidal length-scale regime, leading one to daydream that these icosahedra themselves might be made to self-assemble on yet another level of order. The sequence of structural order at which matter could be arranged would then range from an amorphous glass to an aperiodic quasicrystalline solid made of nanoparticles, to finally a periodic structure made of micrometre-sized particles.

Figure 2: Icosahedral quasicrystals.

Scanning electron microscopy image10 of quasicrystal isocahedra (20-faced regular polyhedra displaying five-fold rotational symmetry) formed from composite silica spheres (not shown) about 30 nm across. (Scale bar, 2 μm.)

Lastly, quasicrystals could provide the means to the development of photonic quasicrystals by self-assembly. These materials differ from photonic crystals — materials specially engineered to trap and guide light — in the quasiperiodicity and forbidden symmetries of their crystal structures. These differences could make photonic quasicrystals outperform their conventional analogues. A photonic band gap — the forbidden energy range of photon propagation that characterizes photonic crystals — in the microwave regime has already been demonstrated for quasicrystalline structures made by lithography11. The development of photonic quasicrystals by self-assembly may well be within reach.


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van Blaaderen, A. Quasicrystals from nanocrystals. Nature 461, 892–893 (2009).

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