Reflections on symmetry and formation of axial quasicrystals

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Abstract Some ideas are presented on the geometrical factors governing structure and formation of axial quasicrystals with 5- and 7-fold symmetry, respectively. First, the importance of thin atomic layers is discussed for the growth of decagonal quasicrystals. They are the only long-range ordered structural units carrying information on the local non-crystallographic symmetry of the constituent clusters. Second, the consequences of local polysynthetic twinning for the formation of pentagonal and heptagonal quasicrystals are demonstrated. Third, the special relationship of the β-phase, (Co,Ni)1–xAl1+x, to the decagonal phase and its periodic average structure is discussed as well as its role as template for the formation and growth of decagonal Al—Co—Ni.