Expanding quasiperiodicity in soft matter: Supramolecular decagonal quasicrystals by binary giant molecule blends

The quasiperiodic structures in metal alloys have been known to depend on the existence of icosahedral order in the melt. Among different phases observed in intermetallics, decagonal quasicrystal (DQC) structures have been identified in many glass-forming alloys yet remain inaccessible in bulk-state condensed soft matters. Via annealing the mixture of two giant molecules, the binary system assemblies into an axial DQC superlattice, which is identified comprehensively with meso-atomic accuracy. Analysis indicates that the DQC superlattice is composed of mesoatoms with an unusually broad volume distribution. The interplays of submesoatomic (molecular) and mesoatomic (supramolecular) local packings are found to play a crucial role in not only the formation of the metastable DQC superlattice but also its transition to dodecagonal quasicrystal and Frank–Kasper σ superlattices.

Decagonal random tilings and their quasi-unit cell cluster coverings

Electron microscopy images of decagonal quasicrystals obtained recently have been shown to be related to cluster coverings with a Hexagon–Bow–Tie decagon as single structural unit. Most decagonal phases show more complex structural orderings than models based on deterministic tilings like the Penrose tiling. We analyze different types of decagonal random tilings and their coverings by a Hexagon–Bow–Tie decagon.

Gummelt versus Lück decagon covering and beyond. Implications for decagonal quasicrystals

Specific structural repeat units can be used as quasi-unit cells of decagonal quasicrystals. So far, the most famous and almost exclusively employed one has been the Gummelt decagon. However, in an increasing number of cases Lück decagons have been found to be more appropriate without going into depth. The diversities and commonalities of these two basic decagonal clusters and of some more general ones are discussed. The importance of the type of underlying tiling for the correct classification of a quasi-unit cell is demonstrated.

Insight into the structure of decagonite – the extraterrestrial decagonal quasicrystal

A set of X-ray data collected on a fragment of decagonite, Al71Ni24Fe5, the only known natural decagonal quasicrystal found in a meteorite formed at the beginning of the Solar System, allowed us to determine the first structural model for a natural quasicrystal. It is a two-layer structure with decagonal columnar clusters arranged according to the pentagonal Penrose tiling. The structural model showed peculiarities and slight differences with respect to those obtained for other synthetic decagonal quasicrystals. Interestingly, decagonite is found to exhibit low linear phason strain and a high degree of perfection despite the fact it was formed under conditions very far from those used in the laboratory.