Atomic structure of complex quasicrystals

Icosahedral quasicrystals (i-QCs) are long-range ordered solids that show non-crystallographic symmetries such as five-fold rotations. Their detailed atomic structures are still far from completely understood, because most stable i-QCs form as ternary alloys suffering from chemical disorder. Recently, a French-Japanese collaborative team led by Professor A. P. Tsai (Tohoku University, Japan) has succeeded for the first time in obtaining a detailed structure solution for i-YbCd_5.7. Similar to normal crystals, i-QCs exhibit beautiful diffraction patterns, but their lack of periodicity prevents conventional analysis. However, mathematically, i-QCs can be seen as the projection in 3D of a structure that is periodic in a virtual space of higher dimension. This resolves the situation because it allows conventional crystallography to be used in the higher-dimensional space. The obtained result represents an essential starting point for finding the atomic structure of more complex i-QCs. The team's X-ray experiments were done with synchrotron X-rays at D2AM beamline, ESRF in Grenoble, France. For more information about the analysis, see the paper, "Atomic structure of the binary icosahedral Yb-Cd quasicrystal", H. Takakura et al., Nature Materials, 6, 58-63 (2007).