X-ray diffraction by a crystal

FIGURE 2.2 X-ray diffraction by a crystal of beryl using tbe Laue method. 

X-ray diffraction by a crystal arises from X-ray scattering by individual atoms in the crystal. The diffraction intensity relies on collective scattering by all the atoms in the crystal. In an atom, the X-ray is scattered by electrons, not nuclei of atom. An electron scatters the incident X-ray beam to all directions in space. The scattering intensity is a function of the angle between the incident beam and scattering direction (26). The X-ray intensity of electron scattering can be calculated by the following equation. 

Three types of detector are available for measuring the X rays diffracted by a crystal Point detectors, linear and area detectors. The film method involves a two-dimensional detector, which can provide simultaneous information about every point in the region of reciprocal space investigated. The measurements are not immediately available in digital form, but powerful computer-controlled photometers can digitize them. 

Rgure 28.5 Diagram Showing the Bragg Condition for X-Ray Diffraction by a Crystal Lattice. 

The radiation may also be reemitted as scattered radiation in all directions with the same wavelength as the incident beam. In the case of periodic stmctures in which atoms, molecules, or particles are organized in regular arrays, scattering will be observed only at specified angles because of destructive interference by the radiation scattered by different parts of the array at all other angles. In this case the radiation is said to be diffracted. X-ray diffraction by a crystal is an important example. 

Except for in house preliminary studies, the intensities of X-rays diffracted by hydrogenase crystals are now usually obtained with synchrotron radiation (Fig. 6.2) and detected by image plate or charge coupled device (CCD) detectors. To limit the damage induced by the powerful photon flux of synchrotrons, the crystals are usually mounted in a small loop, flash cooled in either liquid propane or nitrogen and stored... 

Fontell, K. (1974) X-ray diffraction by liquid crystals- amphiphilic systems. In G.W. Gray and P.A. Winsor (eds), Liquid Crystals and Plastic Crystals. Ellis Horwood Publishers, Chichester,... 

Although x-ray diffraction by single crystals is a useful technique for determining crystal structure, a more useful analytical technique is powder diffraction the sample crystals are ground to a powder, after which the diffraction pattern can readily be used to identify unknown substances, based on tables of known diffraction patterns. 

X-ray diffraction (XRD) pattern reveals information about the crystal structure, chemical composition, and physical properties of a material. X-rays diffracted by a set of crystallographic planes interfere constructively or distractively depending on the path difference [73]. The X-ray beam is scanned over a wide range of incident angle. The incident angle vs intensity plot is further analyzed to derive a verity of information. 

X-ray diffractions from a crystal can only occur in directions defined by the reciprocal lattice points and with intensities that are governed by a structure factor of the form... 

Think About It The distance between layers of atoms in a crystal should be similar in magnitude to the wavelength of the X rays diffracted by the crystal (compare 0.154 mn with 0.233 nm). 

How is the diffraction pattern obtained in an x-ray experiment such as that shown in Figure 18.5b related to the crystal that caused the diffraction This question was addressed in the early days of x-ray crystallography by Sir Lawrence Bragg of Cambridge University, who showed that diffraction by a crystal can be regarded as the reflection of the primary beam by sets of parallel planes, rather like a set of mirrors, through the unit cells of the crystal (see Figure 18.6b and c). 

In X-Ray Fluorescence (XRF), an X-ray beam is used to irradiate a specimen, and the emitted fluorescent X rays are analyzed with a crystal spectrometer and scintillation or proportional counter. The fluorescent radiation normally is diffracted by a crystal at different angles to separate the X-ray wavelengths and therefore to identify the elements concentrations are determined from the peak intensities. For thin films XRF intensity-composition-thickness equations derived from first principles are used for the precision determination of composition and thickness. This can be done also for each individual layer of multiple-layer films. 

TEM offers two methods of specimen observation, diffraction mode and image mode. In diffraction mode, an electron diffraction pattern is obtained on the fluorescent screen, originating from the sample area illuminated by the electron beam. The diffraction pattern is entirely equivalent to an X-ray diffraction pattern a single crystal will produce a spot pattern on the screen, a polycrystal will produce a powder or ring pattern (assuming the illuminated area includes a sufficient quantity of crystallites), and a glassy or amorphous material will produce a series of diffuse halos. 

Wavelength Spectrometry (WDS) is based upon the phenomenon of Bragg diffraction of X rays incident on a crystal. The difiraction phenomenon is described by the expression ... 

X-rey diffraction. Knowing the angles and intensities at which X-rays are diffracted by a crystal, it is possible to calculate the distances between layers of atoms. 

Structural characteristics of compounds with X Me = 8 are collected in Table 17. Na3NbF8 and Na3TaF8 compounds that form similar crystal structure [77], The structure of Na3TaF8 was determined by Hoard et al. [136], by means of X-ray diffraction of a single crystal. Na3TaF8 is composed of sodium cations and isolated complex ions TaF83, in an Archimedean antiprism configuration, as shown in Fig. 23. 

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. 

This chapter deals with single crystal x-ray diffraction as a tool to study marine natural product structures. A brief introduction to the technique is given, and the structure determination of PbTX-1 (brevetoxin A), the most potent of the neurotoxic shellfish poisons produced by Ptychodiscus brevis in the Gulf of Mexico, is presented as an example. The absolute configuration of the brevetoxins is established via the single crystal x-ray diffraction analysis of a chiral 1,2-dioxolane derivative of PbTX-2 (brevetoxin B). 

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