A five-dimensional model of dodecagonal Ta-Te quasicrystals with fractal occupation domains.

The consideration of two approximants of the first stable dodecagonal Ta-Te quasicrystal shows that the five-dimensional (5D) space group of the dodecagonal phase is P12m2(12(5)mm) and the structure consists of five layers within a 10 A period. A 5D quasicrystal model leading to the two approximate structures by the introduction of appropriate linear phason strains is derived by the section method. The model shows 20 A dodecagonal clusters (DDC) arranged at each vertex of the square-triangle dodecagonal pattern and has fractal occupation domains, suggesting that the quasicrystal has either a deterministic or a random square-triangle packing of the DDC.