Crystals and quasicrystals: A continuum model

Rhombellanic Crystals and Quasicrystals

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

Photonic crystals, amorphous materials, and quasicrystals

Photonic crystals consist of artificial periodic structures of dielectrics, which have attracted much attention because of their wide range of potential applications in the field of optics. We may also fabricate artificial amorphous or quasicrystalline structures of dielectrics, i.e. photonic amorphous materials or photonic quasicrystals. So far, both theoretical and experimental studies have b...

Continuum elastic sphere vibrations as a model for low-lying optical modes in icosahedral quasicrystals

The nearly dispersionless, so-called “optical” vibrational modes observed by inelastic neutron scattering from icosahedral Al-Pd-Mn and Zn-Mg-Y quasicrystals are found to correspond well to modes of a continuum elastic sphere that has the same diameter as the corresponding icosahedral basic units of the quasicrystal. When the sphere is considered as free, most of the experimentally found modes ...

High-temperature solution growth of intermetallic single crystals and quasicrystals

Solution growth continues to be one of the most powerful techniques for the production of single crystals for basic and applied research. It is a versatile technique that allows for the growth of congruently and incongruently melting materials with equal ease. The primary requirement for growth is that there be an exposed primary solidification surface in the appropriate equilibrium alloy phase...

Continuum Theory for Liquid Crystals