Crystal planes, angles between

The diffracted ray coming from the center of the sample and passing through the center of the receiving slit strikes the center of the monochromator crystal. The angle between this ray and the crystal plane is equal to 6. Signs +, — corresponds to the respective clockwise and counter-clockwise rotations of the... 

Figure 4.1.1 shows schematic representation of grazing incidence diffraction from a horizontal surface. The diffraction condition for two-dimensional crystals lying in the xy plane is that the component of the scattering vector in the horizontal plane, labeled q y (q y = (4jt/A,)sin0i, (where 20i, is the in-plane angle between... 

For diffraction studies with monocliromatic radiation, the crystal is connnonly mounted on an Eulerian cradle, which can rotate the crystal so that the nonnal to any set of planes bisects the angle between the incident and reflected beams, which is set for reflection from planes with a particular value of the interplanar spacing, d. 

An alternative, but to some extent complementaty approach to the structure of grain boundaries notes that as the tilt angle between the crystals forming the grain boundary increases, planes of lower atomic concentrations, the high index planes, such as (221), (331) and (115) in the face-centred strucmre, become parallel to the grain boundary. There is therefore a decrease in the number of metal-metal bonds at the boundary as the tilt angle increases. 

X rays and so that the angle between the difiracting plane and the incident X rays is equal to the Bragg angle For a single crystal or epitaxial thin film, there is only one specimen orientation for each (hkl) plane where these difiraction conditions are satisfied. 

The molecular and crystal stmctures of 2-phenylbenzotellurazole were determined by X-ray (89KGS1690). The dihedral angle between the planes of the five-membered heterocycle and 2-phenyl ring is 31.2°. In contrast to benzoisotel-lurazole, no shortened intermolecular Te- N contacts were found in the crystal stmcture of 2-phenylbenzotellurazole. Consequently, no anomalies in solubility and melting point were revealed for this compound as compared with its sulfur and selenium congeners. 

In 1995, Mandal et al. [151] described the crystal structure of N,AT-bis-(p-butoxybenzylidene)-a,a -bi-p-toluidine. They found that the two symmetrical fractions of the molecule are almost planar, but the angle between these planes is 63.5°. The molecules are arranged in tilted layers. This tilted layer-like structure is referred as a precursor to the tilted smectic phase. 

Close approaches of arene. solvents to metalloporphyrins have been observed by crystallography. For example. Mn(TPP) crystallizes as a toluene. solvate with a toluene solvent molecule lying on either side of the porphyrin plane. The dihedral angle between the porphyrin plane and toluene plane is 10.7 (reduced to 6.7 for one of the pyrrole rings). The average perpendicular distance between the toluene ring and the mean 24-atom plane of the porphyrin is 3.30 A. One aromatic C—C bond of toluene approximately eclipses one N—Mn—N axis, with IVln- C distances of 3.05 and 3.25 There has been considerable effort invested in the... 

Although the aminodifluorophosphine (119) is planar about the nitrogen atom in the crystal, electron diffraction shows that in the gaseous phase the molecules are slightly pyramidal, the angle between the RNR plane and the N—P bond being 32° for (119, R = Me), 35° for (119, R = The... 

Fig. 6.12 Mossbauer spectra of a single crystal absorber of Fe(N03)3 9H2O with the absorber plane parallel to the (001) plane. The spectra were obtained at 78 K with a magnetic field of 1.3 T applied in various directions in the absorber plane. B is the angle between the applied field and the [010] direction. (Reprinted with permission from [40] copyright 1974 by Elsevier)...

The information stored in the specimen database is sufficient to identify the particular specimen and the material from which it is made. Other parameters provide information on the orientation of the specimen and on its unit cell parameters. These latter parameters are used by the data collection tasks and the crystal geometry calculation function to determine diffraction angles, the angles between crystal planes, etc. The user can store information on several specimens in the specimen database, thus permitting him to easily remount and rerun a specimen after looking at the collected data. 

The technique is based on Bragg s law, which describes the diffraction of a monochromatic x-ray beam impinging on a plane of atoms [38]. Parallel incident rays strike the crystal planes and are then diffracted at angles that are related to the spacings between planes of molecules in the lattice. 

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