title: What periodicities can be found in diffraction patterns of quasicrystals?
abstract: The structure of quasicrystals is aperiodic. Their diffraction patterns, however, can be considered periodic. They are composed solely of series of peaks which exhibit a fully periodic arrangement in reciprocal space. Furthermore, the peak intensities in each series define the so-called `envelope function'. A Fourier transform of the envelope function gives an average unit cell, whose definition is based on the statistical distribution of atomic coordinates in physical space. If such a distribution is lifted to higher-dimensional space, it becomes the so-called atomic surface - the most fundamental feature of higher-dimensional analysis.
authors.affiliation: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, Krakow, 30-059, Poland.
authors.forename: Janusz
authors.initials: J
authors.lastname: Wolny
authors.affiliation: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, Krakow, 30-059, Poland.
authors.forename: Bartlomiej
authors.initials: B
authors.lastname: Kozakowski
authors.affiliation: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, Krakow, 30-059, Poland.
authors.forename: Pawel
authors.initials: P
authors.lastname: Kuczera
authors.affiliation: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, Krakow, 30-059, Poland.
authors.forename: Lucjan
authors.initials: L
authors.lastname: Pytlik
authors.affiliation: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, Krakow, 30-059, Poland.
authors.forename: Radoslaw
authors.initials: R
authors.lastname: Strzalka
keywords: Fibonacci sequence; Penrose tiling; average unit cell; diffraction pattern; higher-dimensional analysis; quasicrystals