TITLE:
Hierarchic Computations in Geometric Space—Showing Sharp Diffraction in Quasicrystals
AUTHORS:
Antony J. Bourdillon
KEYWORDS:
Quasicrystals, Geometric Space, Structure Factors, Scattering Factors, Hierarchic
JOURNAL NAME:
Journal of Modern Physics,
Vol.7 No.1,
January
8,
2016
ABSTRACT: A quasi-structure factor method is used to show how sharp diffraction patterns are produced by aperiodic quasicrystals. Icosahedral symmetry is described for the tensor rank 3 solids with edge-sharing unit cells that are pentagonally close packed in hierarchic structures having a geometric reciprocal lattice. The hierarchic symmetry replaces translational symmetry in crystal diffraction. Details in the calculation show how the symmetry is simulated in diffraction.