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Figure 6
(a) Coherent merohedral twin of the honeycomb structure: the twin operation [\widehat{h} = \{ {\overline 2}, {\overline 1}, {\overline 5}, {\overline 4}, {\overline 3}\}] is a mirror with an irreducible translation part [t = (0,0,1, {\overline 1},0)]; it transforms the unit cell {A = [ (0,0,1,0,{\overline 1})], B = [ (0,1,0,{\overline 1},0)]} into [\{ A^\prime ] = [ A,\, B^\prime ] =[ ({\overline 1},0,0,1,0)\}]. This interface is perfectly coherent with two rows of common atoms (drawn in purple) and is based on the elementary rhombi of the Penrose tiling drawn in thin lines. (b), (c) The twin variants generated by the decomposition of [10 mm^\prime] on (b) [m^\prime] (bean structure) with [10 mm = \cup_{i = 0}^9 \widehat{C}_{10}^i\, m^\prime] and on (c) [mm^\prime] (honeycomb structure) with [10 mm = \cup_{i = 0}^4 \widehat{C}_{10}^{2i}\, mm^\prime]. As can be clearly seen here, all interfaces are perfectly coherent although there is no two-dimensional coincidence lattice between any two adjacent twin individuals.

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ISSN: 2053-2733
Volume 73| Part 6| November 2017| Pages 427-437
https://doi.org/10.1107/S2053273317013882
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