Diffraction profile

Fig. 5. Diffraction profile from (a) a single sHt and (c) many sHts. (b) The sampling region from many sHts.

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

X-ray diffraction with facilities for determining the intensity profile of each diffraction line is particularly informative. Criteria which have been adopted as evidence of good bulk homogeneity (54) are (1) a correct lattice constant eto, and (2) a symmetrical X-ray diffraction profile. A method has also been described (30) for determining if a range of lattice... 

Figure 9 shows a selection of (111) diffraction profiles from Pd-Rh alloy films (deposited and annealed at 400°C) which were used to catalyze ethylene oxidation (60) at 150°-200°C. The profile for the film with 24.6% Rh is symmetrical, and inspection of the (222) profile (not illustrated) after resolution of the ai-a doublet showed no evidence of phase... 

Fig. 9. X-ray diffraction profiles from (111) planes of Pd-Rh films, prepared at 400°C and used in catalytic reaction (60).

Fig. 22. X-ray diffraction profiles (111 planes) from 99% Pd-Ag films treated as described in text unresolved trace, solid line K

X-ray diffraction profile, 26 417 X-ray diffractometers commonly used, 26 422 X-ray effect, 20 661 X-ray electromagnetic spectrum,... 

Figure 24 Powder X-ray diffraction profiles for (Si-n-Dec, 90, at different temperatures.260 Reprinted with permission from Chunwachirasiri, W. West, R. Winokur, M. J. Macromolecules 2000, 33, 9720-9731. 2000 American Chemical Society.

FIGURE 5.7 X-ray diffraction profiles of native (ungelatinized), partially gelatinized, and completely gelatinized (amorphous) tapioca starch. Reprinted from Carbohydrate Polymers, Vol. 67, Ratnayake and Jackson (2007), A new insight into the gelatinization process of native starches. Pages 511-529, 2007, with permission from Elsevier. 

Fig. 4. Wide angle x-ray diffraction profile of imide-aryl ether phenylquinoxaline block copolymers (a) 2c and (b) 2d...

In the case of ITPP, Ferro and BrCickner (28) showed that unrestrained minimization of the total energy for a microcrystal corresponding to unstretched fibers yields a structure in very close agreement to the crystallographically refined one. This was in contrast to the earlier results with less accurate calculations. Furthermore, their calculations, which used slightly modified MM2 potentials and a modest restraint on the cartesian coordinates, provided a stereochemically acceptable model that reproduces the powder diffraction profile as accurately as the least-squares fitted model. 

Fig. 16 Experimental (-1- marks), calculated solid line) and difference lower line) powder X-ray diffraction profiles for the three-component material after final Rietveld refinement, as reported by the authors [64]. (Reprinted with permission from Cheung et al. (2003) J Am Chem Soc 125 14658. Copyright 2003 American Chemical Society)...

We can learn the structural change in the crystals during topochemical polymerization by powder X-ray diffraction measurements. X-ray diffraction profiles continuously changed during the polymerization of 1 under the irradiation of an X-ray beam (Fig. 5) [51]. The reflections shifted and approached the reflection position of the polymer. This suggests that the polymerization... 

Fig. 5 Time dependence of X-ray diffraction profiles measured for the powder crystals of 1 at room temperature [51]...

Powder X-ray diffraction has verified that the isomerization occurs via a crys-tal-to-crystal reaction process, and that the diffraction profiles of the crystals after photoirradiation consist of overlapped patterns of diffraction due to the crystals of 10 and 11. This indicates that the crystal domains of each isomer exist simultaneously in the crystals accompanied by crystal phase separation during the photoisomerization. Single crystal structure analysis has disclosed that the crystals of 11 as the photoproduct have a symmetry different from that of the starting crystals of 10 (Fig. 14). 

Immediately after the isolation of macroscopic quantities of Cgo solid [298], highly conducting [299] and superconducting [141] behaviors were verified for the K-doped compounds prepared by a vapor-solid reaction (Haddon, Hebard, et al.). Crystallographic study based on the powder X-ray diffraction profile revealed that the composition of the superconducting phase is KsCeo and the diffraction pattern can be indexed to be a face-centered cubic (fee) structure with a three-dimensional electronic pathway [300]. The lattice parameter (a = 14.24 A) is apparently expanded relative to the undoped cubic Ceo = 14.17 A). The superconductivity has been observed for many A3C60 (A alkali metal), e.g., RbsCeo (Tc = 29 K... 

The ID diffraction profiles are also ideally suited to profile refinement, as illustrated in Figs. 9 and 13 in Sect. 4, from which atomic coordinates can be obtained using standard Rietveld methods. 

Fig. 5 Diffraction profiles collected from the same powdered sample of InSb at 2 GPa, using (top) energy- and (bottom) angle-dispersive diffraction. The angle-dispersive data clearly have higher angular resolution, and are not contaminated by X-ray fluorescence peaks. The tick marks below the angle-dispersive data mark the positions of some of the weak superlattice reflections that were essential to determining the structure of the InSb-IV phase [165]...

Fig. 7 Diffraction profile collected from Te-III at 8.5 GPa. The data were collected on beamline 9.1 at the SRS synchrotron, with an exposure time of 23 min. The tick marks beneath the profile identify those reflections that are explained by the body-centred monoclinic unit cell...

Once Te-III was identified as incommensurate, subsequent analysis was conducted on the previously-collected powder-diffraction data using the formalism of 4D superspace [234], and the JANA2000 software for structure refinement [235]. The Rietveld refinement of the incommensurate Te-III diffraction profile is shown in Fig. 9, and the modulated structure is shown in Fig. 10. Tellurium was only the second element found to have a modulated crystal structure at high-pressure, the... 

Fig. 11 Diffraction profile from Sc-II at 23 GPa obtained on beamline 9.5 at the SRS synchrotron using an exposure time of 25 min. The tick marks show the calculated peak positions for the bestfitting body-centred cubic cell [242]. The inset shows an enlarged view of the low-angle part of the profile, highlighting the doublet peak at 20 11.1° which is not accounted for by the cubic unit cell...

Figure 8.3 Wide angle X-ray diffraction profile of potato starch.

Figure 2.1 X-ray diffraction profile of silicon ferrierite. Difference Profile is also shown. Data from Brookhaven Laboratory.

In order to obtain detailed structure, a knowledge of diffraction intensities is essential, the intensities being related to the structure factor. Computer-controlled single-crystal X-ray diffractometers with structure (software) packages have made structure elucidation a routine matter. The availability of synchrotron X-radiation of continuously variable wavelength has made X-ray diffraction a still more powerful structural tool for the study of solids. A technique of great utility to solid state chemists is the Rietveld treatment of powder X-ray diffraction profiles (Rietveld, 1969 Manohar, 1983). Automated structure packages for the determination of unknown structures by this method are now commercially available (see section 2.2.3). In Fig. 2.1, we show a typical set of profile data. 

Figure 2.3 Neutron-diffraction profile analysis of TIq jPbo.sSrjCuOj. Difference profile and reflection positions are shown. Data from ILL, Grenoble (From Kovatcheva et ai, 1991).

Because neutron beams are much weaker in intensity than X-rays, neutron diffraction requires large single crystals (Iff-lOOmm in volume as compared to the 0.1 mm crystal volume used in X-ray diffraction work). However, it is possible to obtain useful structural data by analysis of neutron-diffraction profiles from polycrystalline materials (Cheetham Taylor, 1977). 

Figure 7.3. (a) In situ X-ray reflectivity vs. time (measured at the anti-Bragg condition, shown in inset at top) during dissolution of orthoclase feldspar, KAlSi308, (001) cleavage surface at extreme pH values. The removal of successive monolayers (ML) is noted for each set of data, (after [100]) (b) in situ crystal truncation rod diffraction profiles for a freshly cleaved orthoclase (001) surface (circles) and after reaction at pH = 2.0 (1 and 15 ML dissolved) (diamond and square) and pH = 12.9 (2 ML dissolved) (triangle) (after [103]). (Figures provided by P. Fenter.)... 

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