A quasi-structure factor method is used to show how sharp diffraction patterns are produced by aperiodic quasicrystals. Icosahedral symmetry is described for the tensor rank 3 solids with edgesharing unit cells that are pentagonally close packed in hierarchic structures having a geometric reciprocal lattice. The hierarchic symmetry replaces translational symmetry in crystal diffraction. Details...

The calculation of LEED intensities in a spherical-wave representation can be substantially simplified by symmetry relations. The wave field around each atom is expanded in symmetry-adapted functions where the local point symmetry of the atomic site applies. For overlayer systems with more than one atom per unit cell symmetry-adapted functions can be used when the division of the crystal into m...

A free energy functional for a crystal which contains both the symmetry-conserved and symmetry-broken parts of the direct pair correlation function has been used to investigate the fluid-solid transition in systems interacting via purely repulsive Weeks-Chandler-Anderson Lennard-Jones potential and the full Lennard-Jones potential. The results found for freezing parameters for the fluid-face ce...

The crystal structure of tris-odium potassium dodeca-molybdenum tetra-deca-sulfide, Na2.9 (2)KMo12S14, consists of Mo12S14S6 cluster units inter-connected through inter-unit Mo-S bonds and delimiting channels in which the Na(+) cations are disordered. The cluster units are centered at Wyckoff positions 2d and have point-group symmetry 3.2. The K atom lies on sites with 3.2 symmetry (Wyckoff sit...

The size of absolute band gaps in two-dimensional photonic crystals is often limited by band degeneracies at the lattice symmetry points. By reducing the lattice symmetry, these degeneracies can be lifted to increase the size of existing photonic band gaps, or to create new gaps where none existed for the more symmetric structure. Specifically, symmetry reduction by the addition of different di...

Cyclotron frequency of a crystal electron is, in general, not an easily accessible parameter. Nevertheless, its calculation can be simplified when the symmetry properties of the band structure and those of the motion equations in the magnetic field are simultaneously taken into account. In effect, a combined symmetry of the electron Hamiltonian and that of the Lorentz equation provide us with a...

Although long assumed to have an important role in the suppression of crystallization and the development of glassformers, the effect of local fivefold symmetry has never been directly tested. Here we consider whether such suppression of crystallization has a kinetic or thermodynamic nature and investigate its mechanism. We introduce a model in which the degree of fivefold symmetry can be tuned...

In this paper we introduce a new method to design interparticle interactions to target arbitrary crystal structures via the process of self-assembly. We show that it is possible to exploit the slope of the crystal nucleation free-energy barrier to sample and select optimal interparticle interactions for self-assembly into a desired structure. We apply this method to find interactions to target ...

The hyperthermophilic glycoside hydrolase family endocellulase 12 from the archaeon Pyrococcus furiosus (EGPf; Gene ID PF0854; EC 3.2.1.4) catalyzes the hydrolytic cleavage of the β-1,4-glucosidic linkage in β-glucan in lignocellulose biomass. A crystal of EGPf was previously prepared at pH 9.0 and its structure was determined at an atomic resolution of 1.07 Å. This article reports the crystall...

The X-ray crystallography problem is to reconstruct a crystalline structure from the Fourier magnitude of its diffracted scattering data. This has three major difficulties: (1) Only Fourier magnitude (not phase) data are known; (2) There is no support constraint (since the crystal is periodic); and (3) only low-wavenumber scattering data are available. But it also has two major advantages: (1) ...