'Size-effect'-like distortions in quasicrystalline structures

We show in this paper that by applying size-effect distortions to a perfect Penrose tiling, on the basis that rhomb-edges which connect different types of vertices assume different lengths, we can obtain a diffraction pattern which shows remarkable similarity to the zero-level (h₅ = 0) section observed in decagonal Al₇₁Co₁₃Ni₁₆. In particular a central clearly delineated decagon is observed, on the inside of which there is reduced intensity, and on the outside of which there is enhanced intensity. Such a transfer of intensity is characteristic of size-effect distortions in crystals but for these systems it is necessary to have disorder involving (at least) two types of atoms. In the present case the effect is observed with all vertices occupied by a single scatterer and the system remains topologically equivalent to the Penrose pattern with long range quasicrystallinity.