Author(s)

Antony J. Bourdillon

UHRL, San Jose, CA, USA.

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.

Quasicrystal, Icosahedra, Hierarchic, Integral, Periodic, Resonant Response, Harmonic, Irrational, Geometric Series, Metric

Bourdillon, A. (2021) Quasicrystals’ Resonant Response with Translational Symmetry. Journal of Modern Physics, 12, 1012-1026. doi: 10.4236/jmp.2021.127063.