X-ray and neutron diffraction patterns

X-ray and neutron diffraction patterns can be detected when a wave is scattered by a periodic structure of atoms in an ordered array such as a crystal or a fiber. The diffraction patterns can be interpreted directly to give information about the size of the unit cell, information about the symmetry of the molecule, and, in the case of fibers, information about periodicity. The determination of the complete structure of a molecule requires the phase information as well as the intensity and frequency information. The phase can be determined using the method of multiple isomor-phous replacement where heavy metals or groups containing heavy element are incorporated into the diffracting crystals. The final coordinates of biomacromolecules are then deduced using knowledge about the primary structure and are refined by processes that include comparisons of calculated and observed diffraction patterns. Three-dimensional structures of proteins and their complexes (Blundell and Johnson, 1976), nucleic acids, and viruses have been determined by X-ray and neutron diffractions. 

Izumi, F., "A Software Package for the Rietveld Analysis of X-ray and Neutron Diffraction Patterns", KEK Report, National Laboratory for High Energy Physics, Tsukuba... 

In this chapter, we shall not discuss the methods of obtaining information on molecular distribution functions. There are essentially three sources of information analyzing and interpreting x-ray and neutron diffraction patterns solving integral equations and simulation of the behavior of liquids on a computer. Most of the illustrations for this chapter were done by solving the Percus-Yevick equation. This method, along with some comments on the numerical solution, are described in Appendices B—F. 

The measurements must be performed with the utmost care, because the effects are comparable to the standard deviations. X-ray and neutron diffraction patterns should be recorded at the lowest possible temperatures, to minimize thermal motion. 

M. Wilson and P. F. McMillan. Interpretation of X-ray and neutron diffraction patterns for amorphous yttrium and lanthanum aluminium oxides from computer simulation, Phjs. Rev. B 69, 54206-54217 (2004). 

Small angle X-ray- and neutron-diffraction patterns obtained for the annulus fibrosus of porcine invertebral disc have highlighted differences between the collagen in this tissue and that in tendon. ... 

The basic foundation of modeling any crystalline solid lies in the definition of its unit cell. Generally, structures derived from X-ray and neutron diffraction patterns provide good starting points for the structural optimization and subsequent determination of any property of interest. To simulate bulk systems, the model cell is tessellated in space to form an infinite lattice as shown in Figure 15.1. This replication of the ion positions or the so-called periodic boundary condition, produces mirror images of the ions at positions defined by the equation... 

Liquid structure is revealed by X-ray and neutron diffraction patterns. The measured diffraction is proportional to weighted sums of spatial Fourier transforms of the site-site pair correlation functions. The experimentally determined structure factors, are related to the pair functions by a... 

Refined parameters as well as atomic positions and displacements are presented in Table 8.13. Experimental and calculated X-ray and neutron diffraction patterns with this... 

The structure of a liquid is conventionally described by the set of distributions of relative separations of atom pairs, atom triplets, etc. The fundamental basis for X-ray and neutron diffraction studies of liquids is the observation that in the absence of multiple scattering the diffraction pattern is completely determined by the pair distribution function. 

Similar to X-Ray and neutron diffraction analysis, electron dilFraction structure analysis consists of such main stages as the obtaining of appropriate diffraction patterns and their geometrical analysis, the precision evaluation of diffraction-reflection intensities, the use of the appropriate formulas for recalculation of the reflection intensities into the structure factors, finally the solution of the phase problem, Fourier-constructions. 

The future for electron diffraction is very bright for two reasons. First, electron diffraction pattern can be reeorded seleetively from individual nanostrueture at sizes as small as a nanometer using the electron probe forming lenses and apertures, while eleetron imaging provides the selectivity. Second, electrons interact with matter mueh more strongly than X-ray and Neutron diffraction. These advantages, eoupled with quantitative analysis, enable the structure determination of small, nonperiodic, structures that was not possible before. 

For the pyranoses and pyranosides, a relatively large number of high precision X-ray and neutron diffraction results are available. Both a metrical analysis [58] and a pattern recognition analysis [59] were carried out based on a combination of neutron and normalized X-ray structure data. The results of the metrical analysis of the 0H---0 hydrogen-bond geometry are described in Part IB, Chapters 6 and 7. 

Several techniques have been used to derive information about the structure and stability of an aquaion. The most powerful from the structural viewpoint are X-ray and neutron diffraction. At the level of total diffraction patterns, sophisticated modeling techniques are usually required to interpret experimental data in general, for stable ions, these methods have been successful. 

Just as in the case of full pattern decomposition, we will use two freely available software codes (LHPM-Rietica and GSAS ) to carry out Rietveld refinements using either or both x-ray and neutron diffraction data. Many... 

Henderson et al. [223] presented a detailed pattern of the structure of bacteriorhodopsin using high-resolution cryoelectron microscopy. Using X-ray and neutron diffraction techniques, Dencher et al. [224—227] could decode the... 

Henderson et al. [223] presented a detailed pattern of the structure of bacteriorhodopsin using high-resolution cryoelectron microscopy. Using X-ray and neutron diffraction techniques, Dencher et al. [224—227] could decode the secondary and tertiary structure of bacteriorhodopsin during the photocycle. Nevertheless, we should emphasize that the resolution still shows transitions in the active site (protonation of counterions, deprotonation of Schiff base, and reprotonation of counterions), leading to a metastable state of the protein. 

Lazy Pulverix LAZY PULVERIX, a computer program, for calculating X ray and neutron diffraction powder patterns, K. Yvon, W. Jeitschko and E. Parthe, J. Appl. Crystallogr., 1977, 10, 73 74 Lazy Pulverix... 

X-ray diffracLion, Lhe X-rays are scattered by the electron clouds around individual atoms. Since the atoms and molecules of the liquid sample are not fixed in space, the information resulting from the diffraction experiment must be interpreted in terms of statistical averages. The neutrons used in a neutron diffraction experiment are scattered by the nuclei of the atoms in the liquid sample so that the scattering pattern is quite different from that for X-rays. In electron diffraction, the electrical potential, which depends on the spatial configuration of the nuclei and electronic density distribution, determines the diffraction pattern. Early experiments involved simple monoatomic liquids such as the inert gases and liquid metals. However, many molecular liquids have also been studied, including polar liquids such as water, the alcohols, and amides [5]. In this section, attention is focused on two of these techniques, namely. X-ray and neutron diffraction. 

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