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 ZnMgY alloy system were investigated mainly by transmission electron microscopy. It was found that, although sample rotations of about 1 degrees were required to obtain simple crystallographic relations, the orientation relationship was established among the cubic-Fmm Zn23Y6 structure, the hexagonal-P6(3)/mmc H structure and the F-type IQ; that is, (1) over bar 1 3(c) // the five-fold axis in the IQ // N(2 (1) over bar(1) over bar0)(H), and 1 1 1(c) // the two-fold axis in the IQ // N(0 5 (5) over bar3)(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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