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Figure 1
The NiZr structure (Kirkpatrick et al., 1962BB12) is a CrB-type structure Cmcm with lattice parameters |A| = 0.3268, |B| = 0.9973 and |C| = 0.4101 nm, defined by two Wyckoff positions: Ni at (0, 0.0817, 1/4) and Zr at (0, 0.3609, 1/4). Ni and Zr atoms projected in the [001] plane form hexagons that are the superimposition of two opposite regular pentagons (in red and blue in the figure) sharing the same diagonal with an accuracy better than 1%. The symbols + and − correspond to the z coordinates being equal, respectively, to 1/4 and −1/4. The two usual tiles of the Penrose tiling (rhombi of acute angles [\pi/10] and [\pi/5]) are outlined in light grey. All atomic positions belong to the [{\bb Z}]-module generated by the five vectors in green noted from 1 to 5. The structure can advantageously be described as a tiling of a unique equilateral hexagonal prototile drawn in purple (see Fig. 3[link]).

ISSN: 2053-2733
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