New type of two-dimensional quasicrystal with twelvefold rotational symmetry

Modulated-Crystal Model for the Twelvefold Quasicrystal Ta62Te38

“…We may use a structural framework of the hexagonal Frank-Kasper (FK) phase (Frank & Kasper, 1959;Ye et al, 1984). The so-called twelvefold quasicrystals have been observed to coexist coherently with hexagonal FK phases (Ishimasa et al, 1985;Chen et al, 1988), one of which is called the tr phase. Essential features in the HRTEM images are very similar between both phases.…”

Supramolecular dendritic liquid quasicrystals

“…Ultimately, it leads to quasicrystals. Dodecagonal quasicrystals have been found so far in five transition-metal systems [20][21][22][23] . In all but one case, dodecagonal structures were studied by electron microscopy or electron diffraction.…”

“…As X-ray data can be compared with models more unequivocally than electron diffraction data, we proceed to construct a model of the LQC. We follow the idea that dodecagonal structures can be generated by appropriate 'decoration' of a quasiperiodic square-triangular tiling 18,21,23 .…”

Explaining complex metals with polymers

“…The proposed analogy-valid at the moment only for low-temperature phases where entropy is unimportant-may be irrelevant for most metal-alloy quasicrystals, as they possess mostly 5-fold and 10-fold rotational symmetry, whereas soft-matter quasicrystals are predominantly 12-fold symmetric. Nevertheless, it may help elucidating the physics of those few metallic alloys that do form 12-fold quasicrystals, like NiCr (14) and VNi/VNiSi (15), and perhaps explain why they are so different from the others.…”