Possible nucleus of the Bergman cluster in the Zn-Mg-Y alloy system

To understand the formation of the Bergman cluster in the F-type icosahedral quasicrystal, crystallographic relations between the quasicrystal and the intermetallic-compound H and Zn${}_{23}$Y${}_6$ 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{\deg} were required to obtain simple crystallographic relations, the orientation relationship was established among the cubic-$Fm\bar{3}m$ Zn${}_{23}$Y${}_6$ structure, the hexagonal-$P{6}_3\mathrm{/}mmc$ H structure, and the F-type icosahedral quasicrystal (IQ); that is, $[\bar{1}13{]}_{\mathrm{c}}$ // the fivefold axis in the IQ // N$(2\overline{1} \overline{1}0){\rm H}$,and$[110]{\rm c}$ // the twofold axis in the IQ // N$(05\bar{5}3{)}_{\mathrm{H}}$, where N(hkml)${}_{\mathrm{H}}$ means the normal direction of the (hkml)${}_{\mathrm{H}}$ plane in the H structure. The correspondences between atomic positions in the Bergman cluster and in the Zn${}_{23}$Y${}_6$ 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.