Open AccessA complicated quasicrystal approximant ɛ 16 predicted by the strong‐reflections approach
Author(s) -
Li Mingrun,
Sun Junliang,
Oleynikov Peter,
Hovmöller Sven,
Zou Xiaodong,
Grushko Benjamin
Publication year - 2010
Publication title -
acta crystallographica section b
Language(s) - English
Resource type - Journals
eISSN - 1600-5740
pISSN - 0108-7681
DOI - 10.1107/s0108768109053804
Subject(s) - quasicrystal , high resolution transmission electron microscopy , reciprocal lattice , electron diffraction , diffraction , crystallography , zone axis , fourier transform , space (punctuation) , crystal structure , physics , condensed matter physics , chemistry , optics , quantum mechanics , linguistics , philosophy
The structure of a complicated quasicrystal approximant ɛ 16 was predicted from a known and related quasicrystal approximant ɛ 6 by the strong‐reflections approach. Electron‐diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong‐reflections approach, the structure factors of ɛ 16 were deduced from those of the known ɛ 6 structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ɛ 16 . An electron‐density map of ɛ 16 was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ɛ 6 , the predicted structure of ɛ 16 contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ɛ 16 is built by banana‐shaped tiles and pentagonal tiles; this structure is confirmed by high‐resolution transmission electron microscopy (HRTEM). The simulated precession electron‐diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ɛ 16 with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.