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.
Highlights
Introduction“Physical” theories degenerate to common myth when the basic norms of physical practice are ignored
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
Summary
“Physical” theories degenerate to common myth when the basic norms of physical practice are ignored. When a reflection grating is rotated by a small angle α, the diffracted beam rotates specularly by 2α; whereas the diffraction from a 3-D crystal switches sharply on and off as it rocks about the Bragg condition. In this strong sense, diffraction is described by Bragg’s law: at wavelength λ, light is re-. Bourdillon flected from regular interplanar spacings of width d at the Bragg angle θ (the complement to the angle of incidence) which is constrained such that nλ = 2dsin(θ), where n represents the diffraction order
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