Atomic X-rays and

Early studies, which did not include many high-order reflections, revealed systematic differences between spherical-atom X-ray- and neutron-temperature factors (Coppens 1968). Though the spherical-atom approximation of the X-ray treatment is an important contributor to such discrepancies, differences in data-collection temperature (for studies at nonambient temperatures) and systematic errors due to other effects cannot be ignored. For instance, thermal diffuse scattering (TDS) is different for neutrons and X-rays. As the effect of TDS on the Bragg intensities can be mimicked by adjustment of the thermal parameters, systematic differences may occur. Furthermore, since neutron samples must be... 

The serpentine group of minerals, which include chrysotile asbestos, are almost identical in composition. The chemical composition of unit cell is Mg6(OH)8Si40io. Chrysotiles have layered or sheeted crystal structure containing a silica sheet of (Si20s) in which silica tetrahedra point one way (Streib 1978). A layer of brucite, Mg(OH)2, joins the silica tetrahedra on one side of the sheet structure. Two out of every three —OH are replaced by oxygen atoms. X-ray and electron microscope studies indicate... 

The most widely used comparisons of optical isotope shifts have been with results from muonic atom X-rays and electron scattering. These have been reviewed recently by Shera. The analysis of several muonic X-ray transitions allows the extraction of various radial moment parameters, as well as of the Barrett radius defined earlier. The experiments are limited to stable isotopes, as targets of the order of 0.1 g or more are required for such muonic X-ray studies. Absolute calibrations of optical measurements for these stable isotopes can thus be made, which in turn allow more precise extraction of nuclear data for the radioisotopes. This has been done recently for barium.The muonic experiments have also allowed the de-... 

The structure of a fluid is characterized by the spatial and orientational correlations between atoms and molecules detemiiued through x-ray and neutron diffraction experiments. Examples are the atomic pair correlation fiinctions (g, g. . ) in liquid water. An important feature of these correlation functions is that... 

Figure Bl.9.1. Diagrams showing that x-ray and light scattering involve extra-nuclear electrons, while neutron scattering depends on the nature of the atomic nucleus.

A number of surface-sensitive spectroscopies rely only in part on photons. On the one hand, there are teclmiques where the sample is excited by electromagnetic radiation but where other particles ejected from the sample are used for the characterization of the surface (photons in electrons, ions or neutral atoms or moieties out). These include photoelectron spectroscopies (both x-ray- and UV-based) [89, 9Q and 91], photon stimulated desorption [92], and others. At the other end, a number of methods are based on a particles-in/photons-out set-up. These include inverse photoemission and ion- and electron-stimulated fluorescence [93, M]- All tirese teclmiques are discussed elsewhere in tliis encyclopaedia. 

The 3D MoRSE code is closely related to the molecular transform. The molecular transform is a generalized scattering function. It can be used to predict the intensity of the scattered radiation i for a known molecular structure in X-ray and electron diffraction experiments. The general molecular transform is given by Eq. (22), where i(s) is the intensity of the scattered radiation caused by a collection of N atoms located at points r. ... 

X-Rays and Annihilation Radiation. The interaction of y-rays with matter produces the x-rays that are characteristic of the atoms in the material in which the interactions take place. Such x-rays appear in measured spectmm. 

In thin sections natural graphite is translucent, strongly pleochroic, and uniaxial. It has a negative sign of birefringence and two extinctions per revolution under crossed Nicol prisms. The atomic number of carbon accounts for its low absorption coefficient for x-rays and electrons. 

The X-ray and neutron scattering processes provide relatively direct spatial information on atomic motions via detennination of the wave vector transferred between the photon/neutron and the sample this is a Fourier transfonn relationship between wave vectors in reciprocal space and position vectors in real space. Neutrons, by virtue of the possibility of resolving their energy transfers, can also give infonnation on the time dependence of the motions involved. 

II. BASIC EQUATIONS RELATING ATOMIC POSITIONS TO X-RAY AND NEUTRON SCATTERING... 

To put the errors in comparative models into perspective, we list the differences among strucmres of the same protein that have been detennined experimentally (Fig. 9). The 1 A accuracy of main chain atom positions corresponds to X-ray structures defined at a low resolution of about 2.5 A and with an / -factor of about 25% [192], as well as to medium resolution NMR structures determined from 10 interproton distance restraints per residue [193]. Similarly, differences between the highly refined X-ray and NMR structures of the same protein also tend to be about 1 A [193]. Changes in the environment... 

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

There is also clear evidence of a change from predominantly class-a to class-b metal charactristics (p. 909) in passing down this group. Whereas cobalt(III) forms few complexes with the heavier donor atoms of Groups 15 and 16, rhodium(III), and more especially iridium (III), coordinate readily with P-, As- and S-donor ligands. Compounds with Se- and even Te- are also known. Thus infrared. X-ray and nmr studies show that, in complexes such as [Co(NH3)4(NCS)2]" ", the NCS acts as an A -donor ligand, whereas in [M(SCN)6] (M = Rh, Ir) it is an 5-donor. Likewise in the hexahalogeno complex anions, [MX ] ", cobalt forms only that with fluoride, whereas rhodium forms them with all the halides except iodide, and iridium forms them with all except fluoride. 

Beryllium is obtained by electrolytic reduction of molten beryllium chloride. The element s low density makes it useful for the construction of missiles and satellites. Beryllium is also used as windows for x-ray tubes because Be atoms have so few electrons, thin sheets of the metal are transparent to x-rays and allow the rays to escape. Beryllium is added in small amounts to copper the small Be atoms pin the Cu atoms together in an interstitial alloy that is more rigid than pure copper but still conducts electricity well. These hard, electrically conducting alloys are formed into nonsparking tools for use in oil refineries and grain elevators, where there is a risk of explosion. Beryllium-copper alloys are also used in the electronics industry to form tiny nonmagnetic parts and contacts that resist deformation and corrosion. 

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