Welberry, Thomas Richard and Sing, Bernd
(2007).
Deformed Penrose tilings.
Philosophical Magazine, 87(1821) pp. 2877–2886.
Full text available as:
Abstract
Monte Carlo (MC) simulation of a model quasicrystal (2D Penrose rhomb tiling) shows that the kinds of local distortions that result from sizeeffectlike relaxations are in fact very similar to mathematical constructions called deformed model sets. Of particular interest
is the fact that these deformed model sets are pure pointdiffractive, i.e. they give diffraction patterns that have sharp Bragg peaks and no diffuse scattering. Although the aforementioned MC simulations give diffraction patterns displaying some diffuse scattering, this can be attributed to the fact that the simulations include a certain amount of unavoidable randomness. Examples of simple deformed
model sets have been constructed by simple prescription and hence contain no randomness. In this case the diffraction patterns show no diffuse scattering. It is demonstrated that simple deformed model sets can be constructed, based on the 2D Penrose rhomb tiling, by using deformations which are defined in terms of the local environment of each vertex. The resulting model sets are all topologically equivalent to the Penrose tiling (same connectedness), are perfectly quasicrystalline but show an enormous variation in the Bragg peak intensities. For the examples described, which are based on nearestneighbour environments, 12 deformation parameters may be chosen independently. If more distant neighbours are taken into account further sets of parameters may be defined. One example of these simple deformed tilings, which shows great similarity to the sizeeffectdistorted tiling, is discussed in detail.
Item Type: 
Journal Article

ISSN: 
14786435 
Extra Information: 
Article includes 9 figures. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Philosophical Magazine. 
Keywords: 
quasicrystals; diffraction patterns; Penrose tilings; deformation; nearestneighbour interaction 
Academic Unit/Department: 
Mathematics, Computing and Technology > Mathematics and Statistics 
Item ID: 
8294 
Depositing User: 
Bernd Sing

Date Deposited: 
02 Aug 2007 
Last Modified: 
07 Dec 2010 05:17 
URI: 
http://oro.open.ac.uk/id/eprint/8294 
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