Beams diffraction

Figure Bl.8.7. A convergent beam diffraction pattern of the fivefold axis of a quasicrystal, as in figure Bl.8.6. The diffraction rings show that the synnnetry is fivefold, not tenfold. (Courtesy of L Bendersky.)...

Engel T and Rieder K H 1982 Structural studies of surfaces with atomic and molecular beam diffraction Structural Studies of Surfaces With Atomic and Molecular Beam Scattering (Springer Tracts in Modern Physics vol 91) (Berlin Springer) pp 55-180... 

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. 

Lattice parameters to four significant figures using convergent beam diffraction... 

As mentioned above, the formalism of the reciprocal lattice is convenient for constructing the directions of diffraction by a crystal. In Figure 3.4 the Ewald sphere was introduced. The radius of the Ewald sphere, also called the sphere of reflection, is reciprocal to the wavelength of X-ray radiation—that is, IX. The reciprocal lattice rotates exactly as the crystal. The direction of the beam diffracted from the crystal is parallel to MP in Figure 3.7 and corresponds to the orientation of the reciprocal lattice. The reciprocal space vector S(h k I) = OP(M/) is perpendicular to the reflecting plane hkl, as defined for the vector S. This leads to the fulfillment of Bragg s law as S(hkI) = 2(sin ())/X = 1 Id. 

In crystallography, the difiiraction of the individual atoms within the crystal interacts with the diffracted waves from the crystal, or reciprocal lattice. This lattice represents all the points in the crystal (x,y,z) as points in the reciprocal lattice (h,k,l). The result is that a crystal gives a diffraction pattern only at the lattice points of the crystal (actually the reciprocal lattice points) (O Figure 22-2). The positions of the spots or reflections on the image are determined hy the dimensions of the crystal lattice. The intensity of each spot is determined hy the nature and arrangement of the atoms with the smallest unit, the unit cell. Every diffracted beam that results in a reflection is made up of beams diffracted from all the atoms within the unit cell, and the intensity of each spot can be calculated from the sum of all the waves diffracted from all the atoms. Therefore, the intensity of each reflection contains information about the entire atomic structure within the unit cell. 

Dealing with the (2D+T) problem of TE wave propagation, one has to take into account some additional terms responsible for light beam diffraction in the waveguide with linear refractive index profile nfc) ... 

Gjonnes, J., Hansen, V., Berg, B. S., Runde, P., Cheng, Y. F., Gjonnes, K., Dorset D. L., Gilmore, C. J. (1998) Structure Model for the Phase Al Ee Derived from Three-Dimensional Electron Diffraction Intensity Data Collected by a Precession Technique. Comparison with Convergent-Beam Diffraction.", Hcta Cryst. A54, 306-319. 

Figure 8.1 Orientation contrast from a monochromatic, collimated X-ray beam. Diffraction occurs only in region A for a particular angular setting of the specimen...

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. 

Diffraction, by X-rays or neutrons, has been the standard method for determining the structures of crystals. The mean free path of X-rays and neutrons is very long, and thus is not sensitive to surfaces. To probe the structures of surfaces, the probing particles must have a very short mean free path in solids. Two methods are extensively used for determining surface structures low-energy electron diffraction (LEED) and atomic-beam diffraction. A helium... 

Atomic-beam diffraction was first demonstrated in 1930, as a verification of the concept of the de Broglie wave (Estermann and Stem, 1930). In the 1970s, it was developed into an extremely informative method for determining topography and atomic structure of solid surfaces (Steele, 1974 Goodman and Wachman, 1976). 

Fig. 4.12. Atomic-beam diffraction. A nearly monochromatic beam of helium, generated by a nozzle, falls on the solid surface with an angle of incidence. The diffracted beam is collected at an outgoing angle. The angular distribution of the diffracted helium beam contains the information about the topography and structure of the...

On surfaces of some d band metals, the 4= states dominated the surface Fermi-level LDOS. Therefore, the corrugation of charge density near the Fermi level is much higher than that of free-electron metals. This fact has been verified by helium-beam diffraction experiments and theoretical calculations (Drakova, Doyen, and Trentini, 1985). If the tip state is also a d state, the corrugation amplitude can be two orders of magnitude greater than the predictions of the 4-wave tip theory, Eq. (1.27) (Tersoff and Hamann, 1985). The maximum enhancement factor, when both the surface and the tip have d- states, can be calculated from the last row of Table 6.2. For Pt(lll), the lattice constant is 2.79 A, and b = 2.60 A . The value of the work function is c() w 4 cV, and k 1.02 A . From Eq. (6.54), y 3.31 A . The enhancement factor is... 

Lapujoulade, J., Salanon, B., and Gorse, D. (1984). Surface structure analysis by atomic beam diffraction. In The Structure of Surfaces, edited by Van Hove, M. A., and Tong, S. Y., Springer-Verlag, Berlin. 

See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

Figure 13 SADP in [001] orientation for (a) the sample annealed in (a) N2 (b) in 02. The patterns are at the same magnification, (c) [001] convergent beam diffraction pattern of the sample annealed in oxygen. HOLZ is arrowed.

Fig. 5 a Diffraction in a DOE. b Nine-beam diffraction pattern obtained by laser illumination of a DOE made of silica 0 =3.82°). c Shear interferometry image made by interference from the front and back side of the DOE shown in (b)... 

A finely ground crystalline powder contains a very large number of small crystals, known as crystallites, which are oriented randomly to one another. If such a sample is placed in the path of a monochromatic X-ray beam, diffraction will occur from planes in those crystallites which happen to be oriented at the correct angle to fulfill the Bragg condition. 

Hitherto only the positions of the X-ray beams diffracted by crystals have been considered unit cell dimensions are determined from the positions of diffracted beams without reference to their intensities. To discover the arrangement and positions of the atoms in the unit cell it is necessary to consider the intensities of the diffracted beams. 

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). 

The data consist of intensities I (hklI. where h. k. and I (the Miller indices represent a vector triplet which conveniently identifies the beam diffracted from a single crystal. In a typical determination, there may be... 

In brief, determining the structure of a protein by X-ray crystallography entails growing high-quality crystals of the purified protein, measuring the directions and intensities of X-ray beams diffracted from the crystals, and using a computer to simulate the effects of an objective lens and thus produce an... 

Atomic beams are suitable for diffraction experiments. The repulsive interaction with the surface is so strong that low-energy atoms are already reflected by the topmost atomic layer. Due to its pronounced sensitivity to the topmost surface layer, the method of atomic beam diffraction is especially useful for the study of adsorbates and superlattices. Typical energies of the incident atoms are under 0.1 eV. At such low energies no radiation damage occurs. In... 

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