Crystal description

The crystal descriptions become increasingly more complex as we move to the monoclinic system. Here all lattice parameters are different, and only two of the interaxial angles are orthogonal. The third angle is not 90°. There are two types of monoclinic space lattices simple monoclinic and base-centered monoclinic. The triclinic crystal, of which there is only one type, has three different lattice parameters, and none of its interaxial angles are orthogonal, though they are all equal. 

Chemical structure, effect on lubricating properties of liquid crystals, 36,37f Cholesteric liquid crystals description, 49 structure, Af ... 

The cluster approach was, for a long time, the only available mechanism for calculating NMR parameters. A crystalline system can be, up to some extent, approximated as a cluster of units (molecules/ions/atoms) whose configuration resembles the crystal. The local environment in the center of this cluster is then an approximation to the bulk solid. The resemblance of the cluster with the true crystal tends to increase as the size of the cluster grows. Therefore, the size of the cluster is critical for the accurate calculation of the desired parameters, as small clusters do not really mimic the crystal environment, whereas big clusters imply heavy computational burdens. When using this approach, the optimal choice resides in a tradeoff between accurate crystal description and acceptable computational cost. 

However, in the low-frequency far-infrared region, this simple concept needs expanding to take into account intramolecular as well as intermolecular coupling because intermolecular interactions lead to collective excitations, similar to phonon in crystals. Description of the low-frequency oanllations would be more adequate if we proceed from spectroscopy of crystals rather than separate molecules. 

This is the method used by the commercial software packages Crystal Ball and RISK . The method is ideally suited to computers as the description of the method will reveal. Suppose we are trying to combine two independent variables, say gross reservoir thickness and net-to-gross ratio (the ratio of the net sand thickness to the gross thickness of the reservoir section) which need to be multiplied to produce a net sand thickness. We have described the two variables as follows ... 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

How are fiindamental aspects of surface reactions studied The surface science approach uses a simplified system to model the more complicated real-world systems. At the heart of this simplified system is the use of well defined surfaces, typically in the fonn of oriented single crystals. A thorough description of these surfaces should include composition, electronic structure and geometric structure measurements, as well as an evaluation of reactivity towards different adsorbates. Furthemiore, the system should be constructed such that it can be made increasingly more complex to more closely mimic macroscopic systems. However, relating surface science results to the corresponding real-world problems often proves to be a stumbling block because of the sheer complexity of these real-world systems. 

The program system COBRA [118, 119] can be regarded as a rule- and data-based approach, but also applies the principles of fragment-based (or template-based) methods extensively (for a detailed description sec Chapter 11, Sections 7.1 and 7.2 in the Handbook). COBRA uses a library of predefined, optimized 3D molecular fragments which have been derived from crystal structures and foi ce-field calculations. Each fi agment contains some additional information on... 

The Fenske-Hall method is a modification of crystal held theory. This is done by using a population analysis scheme, then replacing orbital interactions with point charge interactions. This has been designed for the description of inorganic metal-ligand systems. There are both parameterized and unparameterized forms of this method. 

For transition metal complexes, techniques derived from a crystal-field theory or ligand-field theory description of the molecules have been created. These tend to be more often qualitative than quantitative. 

Sometimes, the system of interest is not the inhnite crystal, but an anomaly in the crystal, such as an extra atom adsorbed in the crystal. In this case, the inhnite symmetry of the crystal is not rigorously correct. The most widely used means for modeling defects is the Mott-Littleton defect method. It is a means for performing an energy minimization in a localized region of the lattice. The method incorporates a continuum description of the polarization for the remainder of the crystal. 

A description of Pasteur s work as part of a broader discussion concerning crystal structure can be found in the article Molecules Crys tals and Chirality in the July 1997 issue of the ioc/rna/ of Chemical Education pp 800-806... 

The crystals are assumed to be circular disks. This geometry is consistent with previous thermodynamic derivations. It has the advantage of easy mathematical description. 

There is extensive Hterature on nitrophosphates (65,66). A description of the Norsk Hydo nitrophosphate process, ie, using calcium adjustment by crystallization of calcium nitrate, emphasizing the environmental advantages is also available (64). 

Epitaxial crystal growth methods such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) have advanced to the point that active regions of essentially arbitrary thicknesses can be prepared (see Thin films, film deposition techniques). Most semiconductors used for lasers are cubic crystals where the lattice constant, the dimension of the cube, is equal to two atomic plane distances. When the thickness of this layer is reduced to dimensions on the order of 0.01 )J.m, between 20 and 30 atomic plane distances, quantum mechanics is needed for an accurate description of the confined carrier energies (11). Such layers are called quantum wells and the lasers containing such layers in their active regions are known as quantum well lasers (12). 

Potassium hydrogen monoperoxosulfate monohydrate [14696-73-2] KHSO 20, related to the triple salt, is not made commercially. The crystal stmcture has been determined and some features of its Raman and ir spectra recorded (69). This compound is more stable under x-rays than the triple salt. The 0—0 distance is 0.1460 nm. The dihedral angle of the 0—0 moiety is about 90°, similar to that ia soHd hydrogea peroxide. This compouad is reported as toxic and irritating to eyes, skin, and mucous membranes (2). Although undoubtedly correct, this description probably better relates to the triple salt. 

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