Multi-Crystal Diffraction

It is well known that XRD image usually is a reflection of structural characteristics of matters. Researchers generally use powder diffraction pattern to understand the structure of materials. Currently, the XRD is widely used in laboratories for the identification of material phase, the nature of which is a structural analysis. XRD was first used to establish the diffraction image of all materials, or alternatively, the image can be compared with the standard substance. The principle is identical with single crystal diffraction, but the latter is specifically designed to explore the crystal structure of the new materials. By contrast, multi-crystal XRD is much more widely used than the single crystal diffraction in the study of materials. 

According to multi-crystal XRD theory, the diffraction intensity yd of a point in any X-ray diffraction image, can be expressed by the equation ... 

A silver- mercury centered cluster compound was prepared by Peringer etal. [96] (Scheme 12.41). The multi-component reaction led to quantitative formation of the complex 141, which was analyzed by X-ray single crystal diffraction. The Hg-Ag distances in this compound are 2.853(2) and 2.805(2) A, and the Hg-Hg distance is 2.6598(14) A. 

EXAFS (Extended X-ray Absorption Fine Structure) measurements using synchrotron radiation have been successfully applied to the determination of structural details of SCO systems and have been particularly useful when it has not been possible to obtain suitable crystals for X-ray diffraction studies. Perhaps the most significant application has been in elucidating important aspects of the structure of the iron(II) SCO linear polymers derived from 1,2,4-triazoles [56]. EXAFS has also been applied to probe the dimensions of LIESST-generated metastable high spin states [57]. It has even been used to generate a spin transition curve from multi-temperature measurements [58]. 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

The method of strueture analysis developed by the Soviet group was based on the kinematieal approximation that ED intensity is directly related (proportional) to the square of structure factor amplitudes. The same method had also been applied by Cowley in Melbourne for solving a few structures. In 1957 Cowley and Moodie introdueed the -beam dynamical diffraction theory to the seattering of eleetrons by atoms and crystals. This theory provided the basis of multi-sliee ealeulations whieh enabled the simulation of dynamieal intensities of eleetron diffraetion patterns, and later electron microscope images. The theory showed that if dynamical scattering is signifieant, intensities of eleetron diffraetion are usually not related to strueture faetors in a simple way. Sinee that day, the fear of dynamical effects has hampered efforts to analyze struetures by eleetron diffraction. 

Usually many set of lattice planes can simultaneously be exactly or close to the Bragg orientation and give a multi-beam pattern made of several diffracted beams as shown in the example on figure 2c. A special type of multi-beam pattern concerns Zone-Axis Patterns (ZAP). This type of pattern is observed when a high symmetry [uvw] direction of the crystal is parallel to the incident beam. In this case, the spots on the pattern are arranged along Laue zones (Figure 2d). 

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. 

Given the complex nature of the crystal structure and small crystal size with an anisotropic morphology of UZM-5, the normal X-ray diffraction patterns were not sufficient to deduce an unambiguous structure. Thus a multi-technique approach was required to successfully solve the structure, to explain the adsorption properties and by analogy to the structure of other zeolites in order to assess potential applications. 

Tanaka K, Onuki Y (2002) Observation of 4f electron transfer from Ce to Bg in the Kondo crystal CeBe and its mechanism by multi-temperature X-ray diffraction. Acta Crystallogr B 58 423 36... 

As the amount of Fe is increased, the (111) peak shifts to smaller d-spacings, reflecting a contraction of the lattice. The (111) peak positions in Fig. 11.5 show a continuous shift from pure Pt to pure Fe. The Pt-Fe XRD patterns are consistent with a single-phase, substitutional solid solution (disordered alloy) over the entire compositional range. In contrast, Fig. 11.6 clearly displays diffraction from inter-metallic compounds of lower symmetry. Post-deposition annealing has resulted in an ordering of the Pt and Fe atoms, the effect of which is the crystallization of an ordered metal alloy of lower symmetry than 100% Pt. In essence, the applied vacuum deposition method is ideally suited for the preparation of multi-component,... 

Eli Y2O3 nanolayers coated on different dielectric nanoparticles Recently, the structural and optical properties of Eu3+ Y2C>3 films coated on a variety of dielectric nanoparticles have been investigated using transmission electron microscope (TEM), X-rays diffraction (XRD) and site-selective laser spectroscopic methods (Chen, X.Y. et al., 2005 Chen et al., 2003a). Eu3+ ions are employed as probes for the study of crystallization and multi-site structure as well as the luminescent centers in nanolayers. It was found that the luminescent nanolayers exhibit distinct thermodynamics and luminescence properties. 

The strength of electron microscopy as a characterization technique lies not only in its ability to probe at near atomic resolution, the internal structure of minute amounts of material, but also in its capacity to reveal directly structural imperfections of the most subtle kind.(1-4) Other investigative methods such as x-ray or neutron diffraction as well as many spectroscopic techniques possess their own individual merits but they utilize procedures which provide only spatially averaged information. And this is often far less suitable for the characterization of defective, multi-phasic or heterogeneous crystalline (or quasi-crystal 1ine) materials. 

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. 

Hendrickson, W. A., Pahler, A., Smith, J. L., Satow, Y, Merritt, E. A., and Phizackerley, R. P. (1989). Crystal structure of core streptavidin determined from multi-wavelength anomalous diffraction of synchrotron radiation. Proc. Natl. Acad. Sci. USA 86, 2190-2194. 

Single-component solvent evaporation methods depend on the removal of solvent in order to obtain the saturated solution required for crystallization to occur. If single-solvent solutions do not yield diffraction-quality crystals, mixtures of solvents may be tried. Multi-component solvent evaporation methods depend on the difference in the... 

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