Patterns of crystallization

If we prescribe rules for one type of cell in Figure 5.6, where the, a, faces form strong bonds with each other, while the, bb, and, ab, junctures are not strong, we anticipate a particular pattern of crystal structure to form. 

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). 

Powder patterns of crystals with axial symmetry yield the value of qQ but do not, of course, give the direction of the axis of symmetry. Line shapes to be expected for the magnetic resonance in this situation have been calculated (95) and for / = %, the shape is illustrated in Fig. 11 for polycrystalline corundum (a-AbOs). 

For powder photographs, the use of the charts described on p. 143 and in Appendix 3 will show whether the substance is cubic, tetragonal, or hexagonal if it is not, the numerical methods of indexing the patterns of crystals of low symmetry may be tried or, if it is. possible to pick out single crystals, or if the specimen can be recrystallized to give suitable crystals, the unit cell dimensions may be determined by the methods described earlier. A search may then be made in the tables of Donnay and Nowacki (1954), in which, for each crystal system, the species are arranged in order of the axial ratios. 

Fig. ]. Types of x-ray patterns of crystals (a) Steel balls in a crystalline lattice (bl Bragg reflections with shape S2...

Slicing, etching, and polishing an iron meteorite reveals a delicate interlocking pattern of crystals. This is called a Widmanstatten structure, and it is the unique fingerprint of each meteorite. These patterns can only form in low gravity environments and are not found in rocks on Earth. 

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. 

These results indicate some obvious patterns of crystallization. High degrees of crystallization occur independently of the initial acetone composition of the solvent at —10°C, and the observed degree of crystallinity decreases significantly as the freeze crystallization temperature is lowered. In addition, at the lower crystallization temperature, the observed degree of crystallinity increases with increasing initial acetone composition of the solvent. This trend is particularly significant at —30°C. 

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. 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

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). 

The role of the inner layer of the colored coating is to produce neutral gray color by adjusting the composition of various transition metal oxides. In order to find the transition metal crystals which give neutral gray color, the XRD patterns of crystals precipitated in the film of various composition have been examined. 

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... 

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