Periodic Series of Peaks in Diffraction Patterns of Aperiodic Structures

Quasicrystals are aperiodic structures with no periodicity both in direct and reciprocal space. The diffraction pattern of quasicrystals consists however of the periodic series of peaks in the scattering vector space. The intensities of the peaks of all series reduced in a proper way build up the so-called envelope function common for the whole pattern. The Fourier transformed envelope gives the average unit cell which is the statistical distribution of atomic positions in physical space. The distributions lifted to high dimensions correspond to atomic surfaces the basic concept of structural quasicrystals modeling within higher-dimensional approach. DOI: 10.12693/APhysPolA.126.625 PACS: 61.44.