X-ray diffraction refinement

Figure 1. Architecture of the [Nii2(CO)2iH]3 trianion in Compound 4, as determined from the x-ray diffraction refinement, showing the anisotropic thermal ellipsoids of 20% probability and the atom labeling scheme common to the trianion and three dianions of Compounds 1, 2, 3, and 4.

Figure 3. Analogous views with identical atom labelings and with 30 % anisotropic thermal ellipsoids obtained from the x-ray diffraction refinements of the [Ni 2(CO)2 H2 2 dianion for Compounds 1, 2, and 3> and [Ni 12(00)21 H trianion for Compound 4. The dianions ideally conform...

Watson, Crick, Franklin, Wilkins Secondary Structure from X-ray Diffraction Refined Structure (Figure 4.10)... 

Fu Y, Busing WR, Jin Y, Affholter KA, Wunderlich B (1993) Poly(ethylene Tereph-thalate) Fibers 1. Crystal Structure and Morphology Studies with Full-pattem X-ray Diffraction Refinement. Macromolecules 26 2187-2193. 

The analysis of siUcon carbide involves identification, chemical analysis, and physical testing. For identification, x-ray diffraction, optical microscopy, and electron microscopy are used (136). Refinement of x-ray data by Rietveld analysis allows more precise deterrnination of polytype levels (137). 

The simplest analytical procedure is to oxidize a sample in air below the fusion point of the ash. The loss on ignition is reported as graphitic carbon. Refinements are deterrninations of the presence of amorphous carbon by gravity separation with ethylene bromide, or preferably by x-ray diffraction, and carbonates by loss of weight on treating with nitric acid. Corrections for amorphous carbon and carbonates are appHed to the ignition data, but loss of volatile materials and oxidation may introduce errors. 

The normal mode refinement method is based on the idea of the normal mode important subspace. That is, there exists a subspace of considerably lower dimension than 3N, within which most of the fluctuation of the molecule undergoing the experiment occurs, and a number of the low frequency normal mode eigenvectors span this same subspace. In its application to X-ray diffraction data, it was developed by Kidera et al. [33] and Kidera and Go [47,48] and independently by Diamond [49]. Brueschweiler and Case [50] applied it to NMR data. 

Fig. 6. The X-ray diffraction patterns and calculated best fits from the structure refinement program for the samples MCMB2300, iVICMB2600 and iVfCMB2800.

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

Other single-crystal x-ray diffraction studies of transition element dopants in jS-rh boron are based on the results of a refinement of the /3-rh boron structure that establishes the occurrence of four new low-occupancy (3.7, 6.6, 6.8 and 8.5%) B positions in addition to the earlier known ones. The dopant elements studied, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zr, Nb, Hf and Ta, do not enter B positions in the framework, but they enter the Al, A2, D and E positions. In some cases the doping elements have been studied at several concentrations for each element and for different cooling rates. The percentage occupancies of certain positions are eorrelated with the atomie sizes of the dopants. The bond distances between the polyhedra are shorter than those within the polyhedra. The mechanism of doping for some cases is denoted displacive, rather than interstitial or substitutional, because of competing interactions between the six different partially occupied B positions and dopant atoms. 

Fig. 4.8 Powder X-ray diffraction pattern of pure single-phase Prb-IVand Rietveld refinement.

The performance of a supported metal or metal sulfide catalyst depends on the details of its preparation and pretreatraent. For petroleum refining applications, these catalysts are activated by reduction and/or sulfidation of an oxide precursor. The amount of the catalytic component converted to the active ase cind the dispersion of the active component are important factors in determining the catalytic performance of these materials. This investigation examines the process of reduction and sulfidation on unsupported 00 04 and silica-supported CO3O4 catalysts with different C03O4 dispersions. The C03O4 particle sizes were determined with electron microscopy. X-ray diffraction (XRD), emd... 

Destro,R., Bianchi,R., Gatti,C. andMerati,F. (1991)TotalelectronicchargedensityofL-alaninefrom X-ray diffraction at 23 K, Chem. Phys. Lett., 186, 47-52 Iversen, B.B., Larsen, F.K., Souhassou, M. and Takata, M. (1995) Experimental for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method, Acta Cryst., B51, 580-591 and references therein. 

A preliminary least-squares refinement with the conventional, spherical-atom model indicated no disorder in the low-temperature structure, unlike what had been observed in a previous room-temperature study [4], which showed disorder in the butylic chain at Cl. The intensities were then analysed with various multipole models [12], using the VALRAY [13] set of programs, modified to allow the treatment of a structure as large as LR-B/081 the original maximum number of atoms and variables have been increased from 50 to 70 and from 349 to 1200, respectively. The final multipole model adopted to analyse the X-ray diffraction data is described here. 

Scolecite gave the opportunity to relate the electron density features of Si-O-Si and Si-O-AI bonds to the atomic environment and to the bonding geometry. After the multipolar density refinement against Ag Ka high resolution X-ray diffraction data, a kappa refinement was carried out to derive the atomic net charges in this compound. Several least-squares fit have been tested. The hat matrix method which is presented in this paper, has been particularly efficient in the estimation of reliable atomic net charges in scolecite. 

It is emphasized that revealing the dynamics as well as the structure (or conformation) based on several types of spin-relaxation times is undoubtedly a unique and indispensable means, only available from NMR techniques at ambient temperature of physiological significance. Usually, the structure data themselves are available also from X-ray diffraction studies in a more refined manner. Indeed, better structural data can be obtained at lower temperature by preventing the unnecessary molecular fluctuations, which are major subjects in this chapter, since structural data can be seriously deteriorated for domains where dynamics are predominant even in the 2D or 3D crystalline state or proteoliposome at ambient temperature. It should be also taken into account that the solubilization of membrane proteins in detergents is an alternative means to study structure in solution NMR. However, it is not always able faithfully to mimick the biomembrane environment, because the interface structure is not always the same between the bilayer and detergent system. This typically occurs in the case of PLC-81(1-140) described in Section 4.2.4 and other types of peptide systems. 

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