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The Gummelt decagon as a `quasi unit cell'

The Gummelt decagon as a `quasi unit cell' Steinhardt, Jeong, Saitoh, Tanaka, Abe & Tsai [Nature (London) (1998), 396, 55–57] have demonstrated that the structure of decagonal Al–Ni–Co can be built from overlapping clusters of a single type. The structure arises from a decoration of the decagons of a Gummelt covering. The unit (essentially a decagonal prism) was called by Steinhardt et al. a `quasi unit cell'. In this work, a classification scheme is proposed for `G patterns' – quasiperiodic patterns obtained by decorating a decagonal quasi unit cell. The classification makes use of the fact that G patterns can also be derived from decoration of a tiling. The tiles are analogues, for decagonal quasiperiodic patterns, of the `asymmetric units' of a periodic pattern; they provide a simple mode of description and classification of the `Gummelt‐type structures'. Four existing models for decagonal phases are considered from this viewpoint. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

The Gummelt decagon as a `quasi unit cell'

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Publisher
Wiley
Copyright
Copyright © 2001 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767301007504
Publisher site
See Article on Publisher Site

Abstract

Steinhardt, Jeong, Saitoh, Tanaka, Abe & Tsai [Nature (London) (1998), 396, 55–57] have demonstrated that the structure of decagonal Al–Ni–Co can be built from overlapping clusters of a single type. The structure arises from a decoration of the decagons of a Gummelt covering. The unit (essentially a decagonal prism) was called by Steinhardt et al. a `quasi unit cell'. In this work, a classification scheme is proposed for `G patterns' – quasiperiodic patterns obtained by decorating a decagonal quasi unit cell. The classification makes use of the fact that G patterns can also be derived from decoration of a tiling. The tiles are analogues, for decagonal quasiperiodic patterns, of the `asymmetric units' of a periodic pattern; they provide a simple mode of description and classification of the `Gummelt‐type structures'. Four existing models for decagonal phases are considered from this viewpoint.

Journal

Acta Crystallographica Section A Foundations of Crystallography – Wiley

Published: Sep 1, 2001

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