Stable quasicrystals and approximants in Zn-Mg-Zr and Zn-Mg-Hf alloys

Stable icosahedral quasicrystals and an approximant crystal have been found in Zn-Mg-Zr and Zn-Mg-Hf alloys. The formation of primitive (P-type) icosahedral quasicrystals with compositions around Zn85Mg7Zr8 and Zn85Mg7Hf8 has been observed in both the as-cast and the annealed states. A face-centred (F-type) icosahedral phase with a composition around Zn76Mg17Hf7 and its corresponding approximant crystal having a composition around Zn75Mg19Hf6 with a space group of have been identified in a fully annealed Zn79Mg15Hf6 alloy. Chemical ordering between two distinctive icosahedral clusters, Zn54Mg12 and Zn54Hf12 (or Zn54Zr12) are proposed to explain the low content of Hf (or Zr) and the occurrence of superlattice diffraction peaks observed for the F-type icosahedral quasicrystal and its 1/1 approximant. The two icosahedral clusters are equivalent in number in order to satisfy the criterion of an electron-to-atom ratio e/a equal to 2.15. They are randomly arranged for the P-type icosahedral phase and regularly arranged respectively at even- and odd-parity twelvefold vertices in the three-dimensional Penrose tiling for the F-type icosahedral phase.