Bernd Sing & T. Richard Welberry
Deformed Model Sets and Distorted Penrose Tilings
(5510K, LaTeX; with 3 Colourplates and 10 Figures (EPS))

ABSTRACT.  In this article, we show how the mathematical concept of a deformed model 
set can be used to gain insight into the diffraction pattern of 
quasicrystalline structures. We explain what a deformed model set is, 
what its characteristic features are and how it relates to certain 
disorder phenomena in solids. We then apply this concept to 
distorted Penrose tilings, i.e., Penrose tilings where we apply 
size-effect-like distortions. While the size effect in crystals only 
operates on the diffuse scattering, there is also an 
intensity transfer on the Bragg peaks in distorted Penrose 
tilings. The persistence of pure point diffraction in distorted 
Penrose tilings can be explained by interpreting such tilings as 
deformed model sets.