TITLE:
Analysis of the Metric in Quasicrystals—Linear Response in Logarithmically Periodic Solids
AUTHORS:
Antony J. Bourdillon
KEYWORDS:
Quasicrystals, Metric, lin-log Response, Measurement, Logarithmic, Periodic, Hierarchic, Structure
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.12,
July
23,
2014
ABSTRACT: The
metric, that enables measurement of structural data from diffraction in
quasicrystals, is analyzed. A modified compromise spacing effect is the
consequence of scattering of periodic electromagnetic or electron waves by
atoms arranged on a geometric grid in an ideal hierarchic structure. This
structure is infinitely extensive, uniquely aligned and uniquely icosahedral.
The approximate analytic factor that converts the geometric terms base τ, into periodic terms modulo 2π, is . It matches the
simulated metric cs=0.947, consistently used in second (Bragg) order, over a
wide scale from atomic dimensions to sixth order superclusters.