Phase formation and structures of quasicrystals and approximants in the Zn–Mg–(Ti, Zr, Hf) system

The compositional regions for primitive (P) and face-centered (F) icosahedral quasicrystals (iQc) have been determined to be around Zn₈₄Mg₉Zr₇ and Zn₇₅Mg₁₈Zr₆, respectively. A 1/1 approximant of the F-type iQc was found to have a composition around Zn₇₇Mg₁₈Zr₅. A similar tendency has been verified for the Zn–Mg–Hf system. No stable iQc was observed in the Zn–Mg–Ti system. High-resolution X-ray measurements performed with synchrotron radiation showed that the stable iQcs are highly ordered and contain less phason disorder. High-angle annular dark field (HAADF) scanning transmission electron microscopy observation of the 1/1 Zn–Mg–Hf approximant effectively revealed the Hf positions in the structure, whose local contrasts can be reasonably interpreted by a structural model where icosahedral and dodecahedral Hf clusters are mutually interpenetrated. Similar appearances of local contrasts were frequently observed in HAADF images of the F-type iQc, indicating that the iQc structure is also build up of icosahedral clusters that are almost identical to those in the 1/1 approximant.