Dodecagonal Quasicrystals Still in Progress

The dodecagonal quasiperiodic order is rather rare in the material world, but has been observed in various systems from alloys to aggregates of cylindrical polymers and in a wide range of dimensions. They exhibit uniaxial 12-fold diffraction symmetry, and have common structural properties originating from the arrangement of structural units on a square–triangle tiling. All dodecagonal quasicrystals known so far were classified into the so-called random-tiling type and not into a mathematically ideal quasiperiodic type. The observed dodecagonal quasicrystals deviated from the ideal state with respect to the limited size of their quasicrystalline region and their structural inhomogeniety. This may be caused by the structural metastability that prevents synthesis of high quality quasicrystals. The effort toward an ideal dodecagonal quasicrystal, in particular in alloys, is reviewed here. There may be two key points: one is taking advantage of the entropy for stabilization, namely the tiling configurational entropy, and the other is taking advantage of so-called second generation tiles scaled up by a factor of 2+√3 as observed in Ta_1.6Te quasicrystal and Mn-Si-(Cr, V) approximant systems.