Single crystals diffraction interpretation

Fourier representation of electron density suggests the possibility of direct structure analysis. If all structure factors, F(hkl), are known, p(xyz) can be computed at a large number of points in the unit cell and local maxima in the electron-density function are interpreted to occur at the atomic sites. A typical single-crystal diffraction pattern of the type used for measuring structure factor amplitudes is shown in Figure 6.12. 

C. Diffraction-Crystal simulates powder, fiber, and single-crystal diffraction from crystalline models, which helps interpret the experimental data from molecular, inorganic, and polymeric crystalline materials. 

A single-crystal. X-ray diffraction analysis of the structure has recently been performed that shows that the compound is, in fact, a tin-tin bonded dimer, having an Sn-Sn bond length of 276 pm, similar to that in hexaphenylditin this was interpreted in terms of overlap of a filled spaPy orbital with the vacant p orbitals on the other tin atom resulting in a "bent, weak, Sn-Sn double bond (332). 

Generally, LEED experiments are conducted on specified faces of single crystals. When this is done, the diffraction pattern produced consists of a series of spots with a location, shape, and intensity that can be interpreted in terms of the surface structure. We focus attention on what can be learned from the location and shape of the spots since the study of intensity is beyond the scope of this book. It is generally assumed that the surface examined by LEED is an extension of an already-known bulk crystal structure. The correctness of this assumption can be tested, and results are often expressed in terms of modifications of the three-dimensional structure at the surface. Before we turn to the LEED patterns below, we must first figure out how they are read. 

Allied with the diffraction methods, such as low-energy electron diffraction (LEED) and photoelectron diffraction (PED), which can also be applied in single-crystal research, these advances have led to much better interpretations of the vibrational spectra of chemisorbed hydrocarbons in terms of the structures of the surface species. The new results have in turn led to the possibility of reassessing more reliably earlier interpretations of the infrared or Raman spectra of adsorbed hydrocarbons on the finely divided metal samples (usually oxide supported) that are more closely related to working solid catalysts. Such spectra are more complicated because of the occurrence of a variety of different adsorption sites on the metal particles, with the consequence that the observed pattern of absorption bands frequently arises from overlapping spectra from several different surface species. 

In fibres of some polymers, made under certain conditions, the crystalline regions are found to be tilted with respect to the fibre axis in a well-defined crystallographic direction. This is a very valuable feature, because the diffraction patterns of specimens in which this type of orientation occurs are of precisely the same form as tilted crystal diffraction patterns of single crystals rotated round a direction inclined to a principal axis. The unit cell cannot be obtained directly, for 90° oscillation tilted crystal photographs are required for direct interpretation, but unit cells obtained by trial can be checked by the displacements of diffraction spots from the layer lines this is a severe check, and consistent displacements would leave no doubt of the correctness of a unit cell. This procedure played an effective part in the determination of the unit cell of polyethylene terephthalate (Daubeny, Bunn, and Brown, 1954). 

Comment. All the less- or more-disordered packing modes introduced above are frequently encountered for arrays of helical molecules. The problem of disorder results in an additional (compared with most single crystal analyses) deconvolution problem when X-ray diffraction patterns of such systems are being interpreted. Although complications from disorder effects are not unique to fibrous systems, they are more frequently encountered there. I suspect that this has... 

The ability of boron to coordinate to three and four oxygen atoms enables a wide range of theoretical structural entities to be formulated. An interesting history of early postulates in which only three-coordinate boron was considered has been outlined by Bokii and Kravchenko (56). Several authoritative reviews of the structural chemistry of borates have been published (56, 77, 173, 182, 381, 408, 429), but the most recent and reliable is that by Christ and Clark (80). In their paper they have considered structures determined from X-ray or neutron diffraction studies of single crystals, rather than include interpretations of spectroscopic or dehydration characteristics of bo-... 

X-ray diffraction has been carried out at extreme glancing angles of incidence where total reflection ensures surface sensitivity. This provides structural information that can be interpreted by well-known methods. An extremely high X-ray flux is required to obtain useful data from single-crystal surfaces. Bulk X-ray diffraction is used to determine the structure of organometallic clusters, which provide comparisons to molecules adsorbed on surfaces. 

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