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Thi, N.H., Gastaldi, J., Schenk, T., Reinhart, G., Mangelinck-Noel, N., Cristiglio, V., Billia, B., Grushko, B., Hartwig, J., Klein, H. and Baruchel, J. (2006) Physical Review E, 74, Article ID: 021605.
https://doi.org/10.1103/PhysRevE.74.031605

has been cited by the following article:

• 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.