Electron beams, diffraction

The problems associated with quantitative studies of structure based upon this viewpoint of X ray absorption-edge spectra may be similar to those encountered using electron beams of comparable energy, 3 to 100 ev., to carry out electron diffraction studies of crystal structure. Qualitatively, this analogy can be carried further, as both the X ray spectra and the electron beam diffraction in this energy range are influenced by only the first few atom layers. 

The contrast observed on the micrographs results essentially from the variations in intensity of the electron beam diffracted by the 002 interferences as a function of the direction of the C-axis, both in bright field where the diffracted rays are stopped by the contrast diaphragm and in dark field where the image is formed by these rays alone. This result has been demonstrated theoretically, at least, in the case of elastic diffusion. It is found that the energy scattered in a given direction by a pregraphitic structure depends on the orientation of the lattice in relation to the incident beam (17). 

Figure 15.8. Cross-sectional surface of TEM images and the electron beam diffraction patterns of crystal lattice in ZrO Ny prepared at 50, 500 and 700 C [86]. (Reproduced by permission of ECS—The Electrochemical Society, from Doi S, Ishihara A, Mitsushima S, Kamiya N, Ota KI. Zirconium-based compounds for cathode of polymer electrolyte fuel ceU.)...

In dark-field electron microscopy it is not the transmitted beam which is used to construct an image but, rather, a beam diffracted from one facet of the object under investigation. One method for doing this is to shift the aperture of the microscope so that most of the beam is blocked and only those electrons... 

Particle Size. Wet sieve analyses are commonly used in the 20 )J.m (using microsieves) to 150 )J.m size range. Sizes in the 1—10 )J.m range are analyzed by light-transmission Hquid-phase sedimentation, laser beam diffraction, or potentiometric variation methods. Electron microscopy is the only rehable procedure for characterizing submicrometer particles. Scanning electron microscopy is useful for characterizing particle shape, and the relation of particle shape to slurry stabiUty. 

The X-rays generated when an electron beam strikes a crystal also can be diffracted by the specimen in which they are produced. If a photograph is made of this diffracdon pattern (the Kossel pattern) using a special camera, localized crystallographic information can be gleaned. 

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. 

In bright-field microscopy, a small objective aperture is used to block all diffracted beams and to pass only the transmitted (undiffracted) electron beam. In the... 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

The simplest diffraction measurement is the determination of the surface or overlayer unit mesh size and shape. This can be performed by inspection of the diffraction pattern at any energy of the incident beam (see Figure 4). The determination is simplest if the electron beam is incident normal to the surface, because the symmetry of the pattern is then preserved. The diffraction pattern determines only the size and shape of the unit mesh. The positions of atoms in the surface cannot be determined from visual inspection of the diffraction pattern, but must be obtained from an analysis of the intensities of the diffracted beams. Generally, the intensity in a diffracted beam is measured as a fimction of the incident-beam energy at several diffraction geometries. These intensity-versus-energy curves are then compared to model calculations. ... 

Surface atomic structure. The integrated intensity of several diffracted beams is measured as a fimction of electron beam energy for different angles of incidence. The measurements are fitted with a model calculation that includes multiple scattering. The atomic coordinates of the surfiice atoms are extracted. (See also the article on EXAFS.)... 

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