title: Average unit cell for Penrose tiling and its Gaussian approximation.
abstract: In this paper, the average unit cell for a quasicrystal is constructed by a statistical approach. For the Penrose tiling, it is shown that such a unit cell is fully equivalent to the oblique projection of the atomic surface onto physical space. The obtained statistical distributions can be easily extended to imperfect structures by using a Gaussian approximation. This leads to simple analytical expressions for diffraction intensities, which can be very useful in structure refinement.
authors.affiliation: Faculty of Physics and Nuclear Techniques, The University of Mining and Metallurgy, al. Mickiewicza 30, PL-30-059 Kraków, Poland. wolny@novell.ftj.agh.edu.pl
authors.forename: Janusz
authors.initials: J
authors.lastname: Wolny
authors.forename: Bartłomiej
authors.initials: B
authors.lastname: Kozakowski