Diffraction patterns, of crystals

Geometrically, electron diffraction patterns of crystals can be approximated as sections of the reciprocal lattice, since the Ewald sphere can be regarded as a plane (i.e. the radius of the Ewald sphere, 1/2, is much larger than the lengths of low-index reciprocal lattice vectors). 

In fact, a tremendous amount of information is available on the structures of biological macromolecules descriptions of structures of proteins and nucleic acids make up major portions of modern textbooks in biochemistry and molecular biology. The Protein Data Bank and the Nucleic Acid Database are online archives that contain sequence and structural data on thousands of specific molecules and complexes of molecules. This structural information comes from in vitro experiments, with structures inferred from the x-ray diffraction patterns of crystallized molecules, spectroscopic measurements using multi-dimensional nuclear magnetic resonance, and a host of other methodologies. 

FIGURE 7.15. Diffraction patterns of crystals that have been (a) partly ground up and (b) totally ground up to a powder. Note that the rings in (a) show some spots which are evidence of crystallinity. 

Figure 8.61. Electron microscO diffraction pattern of crystals of carbohydrate residues in a — add glycoprotein progesterone complex. The spots constitute crosses indicating the presence of a helical structure.

The Watson-Crick model was based on molecular modeling and two lines of experimental observations chemical analyses of DNA base compositions and mathematical analy ses of X-ray diffraction patterns of crystals of DNA. 

Figure 15.8. Cross-sectional surface of TEM images and the electron beam diffraction patterns of crystal lattice in ZrO Ny prepared at 50, 500 and 700 C [86]. (Reproduced by permission of ECS—The Electrochemical Society, from Doi S, Ishihara A, Mitsushima S, Kamiya N, Ota KI. Zirconium-based compounds for cathode of polymer electrolyte fuel ceU.)...

Studies of diffraction patterns of crystallized immunoglobulins, in the presence or absence of ligands of low molecular weight bound in the active site, have so far not revealed any significant conformational changes (Chapter 5). 

B and B" ions over the actual lattice sites. X-ray diffraction patterns of crystals of solid solutions (and compounds within the homogeneity range in the phase diagram) differ from the X-ray diffraction patterns of perfect crystals [[7]-[13]. In particular, an X-ray diffraction... 

Figure 1 shows the decomposition sequence for several hydrous precursors and indicates approximate temperatures at which the activated forms occur (1). As activation temperature is increased, the crystal stmctures become more ordered as can be seen by the x-ray diffraction patterns of Figure 2 (2). The similarity of these patterns combined with subtie effects of precursor crystal size, trace impurities, and details of sample preparation have led to some confusion in the Hterature (3). The crystal stmctures of the activated aluminas have, however, been well-documented by x-ray diffraction (4) and by nmr techniques (5).

Eig. 1. Laue x-ray diffraction pattern of a single natural graphite crystal. 

Figure 12.12 X-ray diffraction pattern from crystals of a membrane-bound protein, the bacterial photosynthetic reaction center. (Courtesy of H. Michel.)...

Figure 16-17. Left transmission electron micrograph of small single crystals of Ooct-OPV5 scale bar 5 pnt. The arrows indicate the 6-axis direction. Right electron diffraction pattern of the same single crystals. The arrow indicates the 613 relteclion spot (crysial dimensions 5x40 pm2 Philips STiiM CM 12 operated at 120 kV. lnslilul Charles Sudron, Strasbourg).

The mechanism responsible for the formation of gas hydrates became clear when von Stackelberg and his school 42 49 in Bonn succeeded in determining the x-ray diffraction patterns of a number of gas hydrates and Claussen6 helped to formulate structural arrays fitting these patterns. Almost simultaneously Pauling and Marsh26 determined the crystal structure of chlorine hydrate. 

Just as an example, the X-ray diffraction patterns of compression moulded samples of PVDF, poly(vinylfluoride), and of some VDF-VF copolymers of different compositions are shown in Fig. 17 [90]. The degrees of crystallinity of the copolymer samples (40-50%) are high and analogous to those of the homopolymer samples. This indicates a nearly perfect isomorphism between the VF and VDF monomeric units [90, 96], The diffraction patterns and the crystal structures of the copolymers are similar to those of PVF, which are in turn similar to the X-ray pattern and crystalline structure of the P form of PVDF. On the contrary, the X-ray pattern of a PVDF sample crystallized under the same conditions (Fig. 17 a) is completely different, that is typical of the non-piezoelectric a form [90]. 

The diffraction pattern of the sample of chlorine hydrate consisted of powder lines on which were superimposed a large number of more intense single-crystal reflections for some planes only the latter were visible. The intensities of the lines were estimated by comparison with a previously calibrated powder photograph, and were averaged for several films pre-... 

Table 1 Analysis of X-ray diffraction pattern of icosahedrally twinned cubic crystals of MnAl6...

Fig. 7. A typical X-ray diffraction pattern of the Fepr protein fromZJ. vulgaris (Hil-denborough). The pattern was recorded on station 9.6 at the Synchrotron Radiation Source at the CCLRC Daresbury Laboratory using a wavelength 0.87 A and a MAR-Research image-plate detector system with a crystal-to-detector distance of 220 nun. X-ray data clearly extend to a resolution of 1.5 A, or even higher. The crystal system is orthorhombic, spacegroup P2i2i2i with unit cell dimensions, a = 63.87, b = 65.01, c = 153.49 A. The unit cell contains four molecules of 60 kDa moleculEu- weight with a corresponding solvent content of approximately 48%.

The dichlorodibenzo-p-dioxin component was isolated by passing a dioxane solution of the mixture through acetate ion exchange resin to remove phenolics. The eluted product was recrystallized from benzene. The x-ray powder diffraction pattern of the precipitate was identical with that of 2,7-dichlorodibenzo-p-dioxin. Analysis of the mother liquor by GLC showed a singular peak consistent with 2,7-dichlorodibenzo-p-dioxin. The mother liquor was cooled to 5°C and yielded transparent crystals. This material had an x-ray diffraction pattern congruent to a sample of 2,8-dichlorodibenzo-p-dioxin obtained from A. E. Pohland (FDA). The two patterns were quite distinct from each other 14, 15). 

On the other hand, in.the case of the nonionic surfactants C-15, NP-15 and 0-15 (the nonionic surfactant/cyclohexane system), mono-dispersed silicalite nanocrystals were obtained as shown in Fig. 1(c), 1(d) and 1(e), respectively. The X-ray diffraction patterns of the samples showed peaks corresponding to pentasile-type zeolite. The average size of the silicalite nanocrystals was approximately 120 nm. These results indicated that the ionicity of the hydrophilic groups in the surfactant molecules played an important role in the formation and crystallization processes of the silicalite nanocrystals. 

As a typical example of topochemically prepared polymers, the nmr speetrum of the polymer derived from ethyl 4-[2-(2-pyrazyl)ethenyl]-cinnamate [l OEt] crystals by reaction (2), and the X-ray diffraction patterns of the same monomer and polymer are illustrated in Figs 1 and 2 (Hasegawa et al., 1989a). 

Other hand, when an equimolar mixture of 2,5-DSP and l OEt is recrystallized from benzene, yellow crystals, comprising 2,5-DSP and l OEt in a molar ratio of 1 2, deposit. In the DSC curve of this crystal, a single endothermic peak is observed at 166°C, which is different from the melting point of either 2,5-DSP (223°C) or l OEt (156°C). Furthermore, the X-ray powder diffraction pattern of the crystal is quite different from those of the homocrystals 2,5-DSP and l OEt. Upon irradiation the cocrystal 2,5-DSP-l OEt affords a crystalline polymer (77i h = 1.0 dl g in trifluoroacetic acid). The nmr spectrum of the polymer coincides perfectly with that of a 1 2 mixture of poly-2,5-DSP and poly-1 OEt. In the dimer, only 2,5-DSP-dimer and l OEt-dimer are detected by hplc analysis, but the corresponding cross-dimer consisting of 2,5-DSP and l OEt is not detected at all (Hasegawa et al., 1993). These observations by nmr and hplc indicate that the photoproduct obtained from the cocrystal 2,5-DSP-l OEt is not a copolymer but a mixture of poly-2,5-DSP and poly-l OEt in the ratio 1 2. 

Fig. 5. Image and optical diffraction pattern of praseodymium-induced crystals, (A). Crystallization was induced with 8 PrCU. Doublet tracks so prominent in vanadate-induced crystals are not evident in crystals induced with lanthanides. This results in an approximate halving of the A-axis of the unit cell. Magnification x 222000. (B) The image of the superimposed top and bottom lattices of the flattened cylinder give rise to two separate diffraction patterns. (C) Projection map of praseodymium-induced crystals. Map scale 0.55 mm per A. From Dux et al. [119].

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