Crystallization relation

Figure 16-19. A Tt-stacked arrangement of Ooci-OPV5-CN" molecules in the crystal lattice (view at a slight angle with respect to the long molecular axis). B lop-view (lop) and side-view (bottom) of two nearest-neighbor Oocl-OPV5-CN" molecules in the crystal. related by a translation along the ci-axis. The distance of 3.5 A corresponds to the shortest distance between two atoms on different molecules (sec Fig. 16-18 for details).

For obvious reasons, Fourier transformations are widely used to solve problems in X-ray crystallography [129]. With innumerable replications of a molecule in a crystal, all being oriented the same way, approximate periodic boundary conditions are given. Periodic functions become discrete when Fourier transformed. In fact, the diffraction pattern of an X-ray shot on a crystal amounts to the Fourier transform of the square of the absolute values of the real space function [130]. The measurements of intensities and different reflection angles from the crystal relate to the Fourier transform of the electron densities in the crystal. 

The chain of the trans derivative 66t is formed by H-bonded cyclic pairs of carboxyl groups, and possesses but translational symmetry in the a direction"6 (Figure 16). This chain is thus chiral. Both chiral forms are found in the crystal, related by centers of... 

Bonnet, R., Cousineau, E. and Warrington, D.H., (1981), Determination of near-coincident cells for hexagonal crystals. Related DSC lattices , Acta CrystaUogr. A, 37 (2), 184— 189. 

Ribitol, on the other hand, crystallizes in space group P21/c, with left- and right-handed conformers in the same crystal, related by a crystallographic center of symmetry. The choice of these two alternatives depends upon which allows the greatest hydrogen-bonding energy. As yet, theory cannot make this prediction. 

Morphology Target compound Conversion method Conversion condition Crystal relations Reference... 

Gomez, G. Crystallization-Related pH Changes During Freezing of Sodium Phosphate Bufer Solutions. Ph.D. thesis. University of Michigan Ann Arbor, MI, 1995. 

Twinning A nonparallel intergrowth of separate crystals related by a symmetry not possessed by the substance. 

Bennett, M. C. Fentiman, Y. L., Growth Rate of Sucrose Crystals Related to Krypton Surface of Seeds. In Industrial Crystallization The Institute of Chemical Engineers London, U.K. 1969, pp. 217-226. 

For phamraceuticals and special organic chemicals, solution crystallization, in which solvents are used, is the primary method of crystallization compared to other crystallization techniques such as melt or supercritical crystallization. Therefore, the goal of these chapters is to introduce basic properties of solution and crystals related to solution crystallization. The relevance of these basic properties to crystal qualities and crystallization operations will be highlighted with specific examples. 

Hand out copies of Record Sheets 6-A and 6-B to each student. Ask students to choose one of the crystal-related activities to do at home. Explain that an adult must be present when they do these activities. Have students observe their experiments for several days and record observations in their notebooks. Then hold a class discussion about the results. 

Comil, J., Calbert, J.P., and Bredas, J.L., Electronic stracture of the pentacene single crystal Relation to transport properties, J. Am. Chem. Soc, 123, 1250, 2001 Cheng, Y.C., Silbey, R.J., da Silva, D.A. et al.. Three-dimensional band structure and bandlike mobility in oligoacene single crystals A theoretical investigation J. Chem. Phys. 118, 3764, 2003. 

Smectic mesophases have been claimed for other gold(l) 159 carbene complexes based on 1,3-dialkylbenzimi-dazol-2-ylidene and l,3-dialkylimidazol-2-ylidene. However, examination of the X-ray diffraction data in combination with the large clearing enthalpies suggest that these materials are highly ordered and may be better described as crystals. Related Pd(ll) complexes have been described 88. ... 

Table 4.1. Crystal relations for some ice-nucleating materials...

The other two independent modes of linear elastic deformation in cubic single crystals relate to shape changes, in particular to shear on the 100 and 110 planes in the < 100> and < 110> directions, respectively, as depicted in Fig. 2.30. In cubic crystals, these modes have different shear modulus values because they represent two different ways to deform the material and yet conserve volume. For 100 shear, using Eq. (2.53) and Table 2.3, one can show that the shear modulus IIq associated with this deformation is given by... 

There is a structural requirement for ferroelectricity. There are a total of 32 different symmetry point groups, 21 of which do not possess a center of symmetry. Ferro-electrics are part of a small subgroup of noncentrosym-metric crystals. Related properties are piezoelectricity and pyroelectricity. Dielectrics belonging to all but one of the groups of noncentrosymmetric crystals are piezoelectric. Pyroelectric crystals form a further subgroup of 10 types of crystal having especially low symmetry as shown in Table 31.5. 

The different crystalline forms of several polyamides have been examined by infrared spectroscopy. The bands at 936 and 1140cm have been used to measure the crystalline and amorphous contents, respectively, in nylon-6,6 [309], whereas bands at 1198 and 1181 cm were employed for measuring a and y crystalline content [310]. Fluctuations in crystallinity in nylon-6,6 were related to the ratios 1430/2910 and 930/2910 [311,312]. All even-even nylons show an a-crystal-related peak at 690 cm which appears at 725 cm in odd-odd nylons [313]. In nylon-6, there is a crystallinity band at 1260 cm a-crystalline-sensitive bands at 1028, 960, 950, 930, and 830 cm and 7-crystalline-related bands at 1120, 990, and 970 cm [314—316]. A band at 979 cm has been attributed to the amorphous phase [315]. 

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