Basis crystal structure

Zentel, R., Poths, H., Kremer, F., Schdnfeld, A., Jungbauer, D., Twieg, R., Willson, C. G., and Yoon, D., Polymeric liquid crystals structural basis for ferroelectric and nonlinear optical properties, Polym. Adv. Technol., 3, 211-217 (1992). 

Knowing the lattice is usually not sufficient to reconstruct the crystal structure. A knowledge of the vectors (a, b, c) does not specify the positions of the atoms within the unit cell. The positions of the atoms withm the unit cell is given by a set of vectors i., = 1, 2, 3... u where n is the number of atoms in the unit cell. The set of vectors, x., is called the basis. For simple elemental structures, the unit cell may contain only one atom. The lattice sites in this case can be chosen to correspond to the atomic sites, and no basis exists. 

The empirical pseiidopotential method can be illustrated by considering a specific semiconductor such as silicon. The crystal structure of Si is diamond. The structure is shown in figure Al.3.4. The lattice vectors and basis for a primitive cell have been defined in the section on crystal structures (ATS.4.1). In Cartesian coordinates, one can write G for the diamond structure as... 

Polyethylene. The crystal structure of this polymer is essentially the same as those of linear alkanes containing 20-40 carbon atoms, and the values of Tjj and AHf j are what would be expected on the basis of an extrapolation from data on the alkanes. Since there are no chain substituents or intermolecular forces other than London forces in polyethylene, we shall compare other polymers to it as a reference substance. 

Crystal Structure and Ionic Radii. Crystal stmcture data have provided the basis for the ionic radii (coordination number = CN = 6), which are summarized in Table 9 (13,14,17). For both and ions there is an actinide contraction, analogous to the lanthanide contraction, with increasing positive charge on the nucleus. 

Leucine residues 2, 5, 7, 12, 20, and 24 of the motif are invariant in both type A and type B repeats of the ribonuclease inhibitor. An examination of more than 500 tandem repeats from 68 different proteins has shown that residues 20 and 24 can be other hydrophobic residues, whereas the remaining four leucine residues are present in all repeats. On the basis of the crystal structure of the ribonuclease inhibitor and the important structural role of these leucine residues, it has been possible to construct plausible structural models of several other proteins with leucine-rich motifs, such as the extracellular domains of the thyrotropin and gonadotropin receptors. 

By comparing the crystal structures of these complexes with a further complex of the 434 repressor DNA-binding domain and a synthetic DNA containing the operator region OR3, Harrison has been able to resolve at least in part the structural basis for the differential binding affinity of 434 Cro and repressor to the different 434 operator regions. 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

The ultraviolet and infrared spectra and the crystal structure (as determined by X-rays) of cyanuric acid have been interpreted on the basis of the trioxo structure 157 however, other ultraviolet data have been reported from which it was concluded that approximately 5% of this compound exists in a hydroxy form in solu-tion. The monoanion of cyanuric acid exists as 158. Ultraviolet spectral data suggest that ammelide (159) and ammeline (160) exist as shown (available infrared spectra offer less conclusive evi-... 

The importance of the proximity effect in cyclodextrin catalysis has been discussed on the basis of the structural data. Harata et al. 31,35> have determined the crystal structures of a-cyclodextrin complexes with m- and p-nitrophenols by the X-ray method. Upon the assumption that m- and p-nitrophenyl acetates form inclusion complexes in the same manner as the corresponding nitrophenols, they estimated the distances between the carbonyl carbon atoms of the acetates and the adjacent second-... 

It is not clear why some organisms have two 14-3-3 isoforms while others have up to 12. Binding 14-3-3 inhibits the plant enzyme nitrate reductase and there appears to be no selectivity between plant 14-3-3 isoforms in fact yeast and human isoforms appear to work equally as well in vitro. The best example where selectivity has been demonstrated is human 14-3-3o. 14-3-3o Preferential homodimerizes with itself and crystallization revealed a structural basis for this isoform s dimerization properties as well as for its specific selectivity for target binding proteins. Here partner specificity is the result of amino acid differences outside of the phosphopeptide-binding cleft. 

Kashiwagi et al.10) determined the second moment anisotropy for the one-way drawn polyethylene terephthalate sheets discussed above. The three lattice sums S00, S2q and S4o were calculated from the crystal structure determination of Daubeny et al., the proton positions being calculated on the basis of known bond angles and lengths. The isotropic lattice sum S00 was adjusted to a value consistent with the measured isotropic second moment of 10.3G2. The values for P200, P220 etc. were then used to predict the optical anisotropy. The predicted refractive indices for the sheets of draw ratio 2 1 and 2.5 1 are shown in Fig. 10, together with the experimental... 

Bis(dicyclohexylammonium) bis(2,6-pyridinedicarboxylato)dibutylstannate is concluded to have sevenfold coordination at the Sn on the basis of its Sn CP/ MAS NMR chemical shift ((5 = —424.9 ppm). The assignment has been corroborated by crystal structure determination of its monohydrate, in which the Sn atom has frflMS-C2SnN04 PBP geometry (Sn-C = 204.0,206.7pm, C-Sn-C = 168.9°). One 2,6-pyiidinedicarboxylato group chelates to the Sn atom (Sn-O = 223.4,226.0 pm Sn-N = 227.9 pm), whereas the other binds through only one carboxyl end (Sn-O = 241.6, 244.1pm). The anhydrous compound displays higher in vitro antitumor activity than those of cisplatin and carboplatin (Table 7). ... 

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