TITLE:
Quasicrystals’ Resonant Response with Translational Symmetry
AUTHORS:
Antony J. Bourdillon
KEYWORDS:
Quasicrystal, Icosahedra, Hierarchic, Integral, Periodic, Resonant Response, Harmonic, Irrational, Geometric Series, Metric
JOURNAL NAME:
Journal of Modern Physics,
Vol.12 No.7,
May
25,
2021
ABSTRACT: Diffraction in quasicrystals is in logarithmic order and icosahedral point group symmetry. Neither of these features are allowed in Bragg diffraction, so a special theory is required. The present work displays exact agreement between the analytic metric with a numeric description of diffraction in quasicrystals that is based on quasi-structure factors. So far, we treated the hierarchic structure as ideal; now, we detail the theory by including two significant features: firstly, the steady state wave function of the incident radiation demonstrates how harmonics, in metrical space and time, enable coherent interaction between the periodic wave packet and hierarchic quasicrystal; secondly, mapping of the hierarchic structure for any influence of defects will allow estimation of possible error margins in the analysis. The hierarchic structure has the required logarithmic periodicity: superclusters, containing about 103 atoms, convincingly map phase contrast images; while higher orders leave space for subsidiary speculation. The diffraction is completely explained for the first time.