To understand the formation of the Bergman cluster in the F-type icosahedral quasicrystal (IQ), crystallographic relations between the quasicrystal and the intermetallic-compound H and Zn23Y6 phases in the Zn–Mg–Y alloy system were investigated mainly by transmission electron microscopy. It was found that, although sample rotations of about 1° were required to obtain simple crystallographic relations, the orientation relationship was established among the cubic-Fm 3m Zn23Y6 structure, the hexagonal-P63/mmc H structure and the F-type IQ; that is, [ 11 3]c // the five-fold axis in the IQ // N(2 1 1 0)H, and [1 1 0]c // the two-fold axis in the IQ // N(0 5 5 3)H, where N(h k m l)H means the normal direction of the (h k m l)H plane in the H structure. The correspondences between atomic positions in the Bergman cluster and in the Zn23Y6 structure and between those in the cluster and in the H structure were investigated on the basis of the established relationship. As a result, an assembly of six short-penetrated-decagonal columns was identified as an appropriate nucleus in the formation of the Bergman cluster from these two structures.
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