Diffraction pattern calculated

Figures 2 (b) and (c) show a diffraction pattern obtained from a particle of diameter 1.5 nm and a diffraction pattern calculated for a multiply twinned, decahedral particle. The conclusion drawn from the study of many such observed and calculated patterns obtained from gold particles in the size range of 1.5 to 2 nm contained in a plastic film is that very few particles are multiply twinned, many have one or two twin planes but more than half are untwinned (16). This suggests that, at least for this type of specimen, there is no confirmation of the theoretical prediction that the multiply twinned form is the equilibrium state for very small particles.

The determination of a molecular structure from X-ray diffraction data is of critical importance to modem chemical and biological sciences. For small molecules, the structure is normally determined by direct methods. The X-ray diffraction pattern resulting from the interaction of X-rays with the electron clouds of different elements gives a pattern from which the elements present and their connectivity may be deduced. The expected diffraction pattern calculated for an apparent structure is then compared with the observed data to refine the result. Refinement factors (usually expressed as Rw) of 1-3% are common in modem small molecule structure determinations. 

In the direct-space approach [26-28] for solving crystal structures from powder diffraction data, trial crystal structures are generated in direct space, independently of the experimental powder diffraction data. The powder diffraction pattern for the trial structure is calculated automatically using Eq. (1) in Sect. 2.2 [the structure factor amplitudes F(h) obtained using this equation are used to determine the relative intensities 1(h) of the diffraction maxima in the powder diffraction pattern]. The suitability of each trial structure is then assessed by direct comparison between the experimental powder diffraction pattern and the powder diffraction pattern calculated for the trial structure. The comparison between the experimental and calculated powder diffraction patterns is quanti-... 

Fig. 4.19 X-ray powder diffraction patterns calculated from the crystal structures for the two forms of terephthalic acid. Upper, Form I lower, Form II. (After Davey et al. 1994.)...

Fig. 4.22 X-ray powder diffraction patterns calculated from the crystal structure determinations of the four polymorphs of sul-phapyridine (Bar and Bernstein 1985 Bernstein 1988). For ease of comparison such patterns should be stacked with identical scales on the abscissa. From top to bottom. Forms II, III, IV and V. 

Another approach (common to many strategies of structure generation and polymorph prediction ) is to attempt to match the powder diffraction pattern calculated from the generated trial structure with an experimental one, although this can no longer be justified as a truly predictive procedure. 

Figure 4.22 TEM image of a cutout of cubically organized Au55(PPh3)i2Cl6 on PVP. The insert shows the diffraction pattern calculated from the recorded image.

On the other hand the density function is smoother and broader, the relative minimum around 160 /im is erased by the diffraction pattern calculations and the broader particle size intervals. 

Figure 7.2 The structure of a duck and its diffraction pattern calculated by Fourier transformation. From http //www.ysbl.york.ac.uk/ cowtan/fourier/ fourier.html. (Reprinted with permission from Kevin Cowtan.)...

X-ray diffraction patterns were recorded for the binder portions and analyzed using the quantitative Rietveld refinement. In this method, contents of crystal phases and amorphous component are obtained, by fitting the experimental data with X-ray diffraction patterns calculated for selected phases from the crystallographic data. 

Fig. 5.16. The diffraction patterns calculated by the Debye equation for the boxes in Fig. 5.14(b)-(d).

Figures Measured diffraction patterns, calculated patterns and difference plot At least one figure enabling a visual assessment of the data collection and analysis quality...

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