Diffraction on the 2D quasi-periodic Rauzy tiling

Diffraction on scattering centers forming a Rauzy tiling has been theoretically investigated. It is proven that a set of Rauzy points is a model set and it is shown that a Rauzy tiling has a diffraction pattern with narrow Bragg peaks, whose positions and the corresponding intensities are functions of three integer indices. It is also shown that, as a result of the presence of similarity symmetry in the Rauzy tiling, the set of diffraction peaks is divided into nonintersecting classes. Peaks of each class fall on a bilateral spiral, expanding from the origin of coordinates to infinity. The specific features of diffraction in the case of scattering from the quasi-lattice of tiling singularities (Rauzy points) and the geometric centers of tiles are considered separately.