TITLE:
Wave Harmonization in Hierarchic Quasicrystals by the Analytic Metric
AUTHORS:
Antony J. Bourdillon
KEYWORDS:
Quasicrystal, Icosahedra, Hierarchic, Harmonization, Metric, Geometric Series
JOURNAL NAME:
Journal of Modern Physics,
Vol.10 No.11,
October
21,
2019
ABSTRACT: Thirty seven years after the discovery of quasicrystals, their diffraction is completely described by harmonization between the sine wave probe with hierarchic translational symmetry in a structure that is often called quasiperiodic. The diffraction occurs in geometric series that is a special case of the Fibonacci sequence. Its members are irrational. When substitution is made for the golden section τ by the semi-integral value 1.5, a coherent set of rational numbers maps the sequence. Then the square of corresponding ratios is a metric that harmonizes the sine wave probe with the hierarchic structure, and the quasi-Bragg angle adjusts accordingly. From this fact follows a consistent description of structure, diffraction and measurement.