Analysis of the Metric in Quasicrystals—Linear Response in Logarithmically Periodic Solids

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 2 π , is . It matches the simulated metric c s =0.947, consistently used in second (Bragg) order, over a wide scale from atomic dimensions to sixth order superclusters.