Three-dimensional crystals

Diffraction When the wavelength of the incident radiation is much less than the dimension of arrays in the crystals, three-dimensional interference patterns usually called diffraction patterns are generated. The diffraction pattern gives information about the lattice and the constituent molecules of the array. 

Flarker D 1936 The application of the three-dimensional Patterson method and the crystal structures of proustite, Ag,AsS, and pyrargyrite, Ag,SnS, J. Chem. Phys. 4 381-90... 

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

Aluminosilicates. These silicates consist of frameworks of silica and alumina tetrahedra linked at all corners to form three-dimensional networks familiar examples are the common rock-forming minerals quartz and feldspar. Framework silicates generally form blocky crystals, more isotropic... 

The stmcture of Pmssian Blue and its analogues consists of a three-dimensional polymeric network of Fe —CN—Fe linkages. Single-crystal x-ray and neutron diffraction studies of insoluble Pmssian Blue estabUsh that the stmcture is based on a rock salt-like face-centered cubic (fee) arrangement with Fe centers occupying one type of site and [Fe(CN)3] units randomly occupying three-quarters of the complementary sites (5). The cyanides bridge the two types of sites. The vacant [Fe(CN)3] sites are occupied by some of the water molecules. Other waters are zeoHtic, ie, interstitial, and occupy the centers of octants of the unit cell. The stmcture contains three different iron coordination environments, Fe C, Fe N, and Fe N4(H20), in a 3 1 3 ratio. 

The tertiary metal phosphates are of the general formula MPO where M is B, Al, Ga, Fe, Mn, etc. The metal—oxygen bonds of these materials have considerable covalent character. The anhydrous salts are continuous three-dimensional networks analogous to the various polymorphic forms of siHca. Of limited commercial interest are the alurninum, boron, and iron phosphates. Boron phosphate [13308-51 -5] BPO, is produced by heating the reaction product of boric acid and phosphoric acid or by a dding H BO to H PO at room temperature, foUowed by crystallization from a solution containing >48% P205- Boron phosphate has limited use as a catalyst support, in ceramics, and in refractories. 

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