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Petra Gummelt

Decagon covering model and equivalent HBS-tiling model

Keywords: Cluster covering, Decagonal quasicrystals, Quasi-unit-cell, Penrose tiling, HBS-tiling

For decagonal Al—Co—Ni quasicrystals, coverings based on a single decagonally shaped columnar 20 Å-cluster as well as tilings of so-called hexagon-, boat- and star-tiles are used to model the atomic structure. We introduce geometrically defined local transformation rules which enable us to replace a covering of overlapping congruent decagons by an equivalent HBS-tiling at the same scale and vice versa. Starting from an obvious one-to-one correspondence in case of idealized, perfect Penrose order, we show that there is a very similar relation also for random decagon coverings with slightly relaxed structure. The proofs given here complete our statements announced in previous work.

Zeitschrift für Kristallographie, Oldenbourg Wissenschaftsverlag

Print ISSN: 0044-2968
Volume: 221, 08/2006
Pages: 582 - 588

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