Structure Factor for Quasicrystals - 1D Case

Spectrum of 1D quasicrystals near the periodic chain

Structure in Quasicrystals

The very existence of a quasicrystalline state of matter, which was first discovered by Shecht-man et al. [1] in 1984 and has since been found in an abundance of compounds, poses two intellectual challenges. (1) What are the microscopic mechanisms that make the atoms form a highly ordered, yet not translationally invariant, quasiperiodic state; and (2) what is the nature of the quantum states o...

Structure determinations for random-tiling quasicrystals

How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direc...

Bulk electronic structure of quasicrystals.

We use hard x-ray photoemission to resolve a controversial issue regarding the mechanism for the formation of quasicrystalline solids, i.e., the existence of a pseudogap at the Fermi level. Our data from icosahedral fivefold Al-Pd-Mn and Al-Cu-Fe quasicrystals demonstrate the presence of a pseudogap, which is not observed in surface sensitive low energy photoemission because the spectrum is aff...

The Al3Ni2 Structure as Approximant of Quasicrystals

The present paper discusses the approximant nature of the A13N12 structure from the viewpoint of valence electron concentration (VEC) correspondence as well as from atomic structure correlation. Its VEC is close to that of corresponding quasicrystals and its atomic structure can be descnbed by layers stacked along the direction corresponding to the 10-fold axis of the decagonal phase. A large o...