Single crystals diffraction pattern

The possibility of obtaining single crystal diffraction patterns from regions of very small diameter can obviously be an important addition to the means for investigating the structures of catalytic materials. The difficulty arises that data on individual small particles is usually, at best, merely suggestive and at worst, completely meaningless. What is normally required is statistical data on the relative frequencies of occurrence of the various structural features. For adequate statistics, it would be necessary to record and analyse very large numbers of diffraction patterns. 

In addition to microwave plasma, direct current (dc) plasma [19], hot-filament [20], magnetron sputtering [21], and radiofrequency (rf) [22-24] plasmas were utilized for nanocrystalline diamond deposition. Amaratunga et al. [23, 24], using CH4/Ar rf plasma, reported that single-crystal diffraction patterns obtained from nanocrystalline diamond grains all show 111 twinning. 

The existence of a superstructure was revealed by satellite spots in the XRD single crystal diffraction pattern of partly dehydrated goethite. The superstructure was considered to be an in-... 

Figure 28.5 High-magnification TEM image of a-Fe203 single crystal. Insets show lattice fringes of the (012) plane of hematite and the corresponding single crystal diffraction pattern.

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. 

Figure 2.11 Formation of a single crystal diffraction pattern in transmission electron microscopy. The short wavelength of electrons makes the Ewald sphere flat. Thus, the array of reciprocal lattice points in a reciprocal plane touches the sphere surface and generates a diffraction pattern on the TEM screen. The outer ring may be visible when the Ewald sphere surface touches the reciprocal plane above the original plane.

The crystal orientation with respect to specimen geometry is important information. In Figure 3.30, the NaCl crystal orientation is already revealed by its bright field image, because its cubic shape implies its crystal structure and orientation. In most cases, crystalline materials do not show the geometrical shape representing their crystal structure and orientation. Thus, we need to determine the orientation from single-crystal diffraction patterns. 

Is a zone axis of a single crystal diffraction pattern exactly parallel to the transmitted beam Explain your answer graphically. 

Fourier transformation. The electron density map shows the location of atoms. A 2D electron density map is produced for each angle. The computer program uses the 2D maps plus the rotation angle data to generate the 3D coordinates for atoms (molecules, ions) in the crystal. The mathematical treatment of the experimental data to produce a crystal structure from an unknown single-crystal diffraction pattern is complicated and beyond the scope of this text, but an example of the results will be shown in the following. 

Figure 8.69 Actual single-crystal diffraction pattern of a small molecule collected with a Rigaku XtaLAB mini . (Used by permission of Rigaku Corporation, www.rigaku.com.)...

From the diffuse layer lines observed in the single crystal diffraction pattern the presence of I2 -ions was concluded which form chains however disordered with regard to the cation sublattice normal to (010). 

Figure 6 A single crystal diffraction pattern for KDCO3 (a = 15.2 A, 5 = 5.6 A, c= 3.7 A, = 104.8°). Reproduced courtesy of Fillaux F, Cousson A and Keen DA.

That is to say, peaks are observed in the diffraction data when the momentum transfer vector is equal to a vector of the reciprocal lattice. Such peaks are known as Bragg peaks and Equation [34] is Bragg s law, for diffraction from a single crystal. Figure 6 shows a typical single crystal diffraction pattern for every peak in the observed diffraction pattern the momentum transfer vector, Q, satisfies Bragg s law. Each and every Bragg peak may be identified by a unique combination of indices h, k, /). 

Figure 8 shows the relatively simple powder diffraction pattern of polycrystalline silicon, measured by time-of-flight neutron diffraction. Each allowed Bragg peak for the crystal structure is observed as a sharp peak in the diffraction pattern. A fundamental difference between single crystal and powder diffraction is that the single crystal diffraction pattern has the full directional information described by Equation [28], whereas for the powder diffraction pattern this information has been collapsed down into a onedimensional function. This difference has two important consequences firstly, the loss of directional information makes it very much more difficult to... 

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