The experimental patterns

Although it is rarely possible to study any particular unimolecular reaction all the way from the first order (high pressure) limit to the second order (low pressure) limit, many genuine unimolecular reactions have now been characterised over at least part of the fall-off region [72.R]. Thus, we can easily compare the observed shape of the fall-off curve, and its position on the pressure axis with the behaviour suggested by the Lindemann mechanism. 

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A further point is that for a multiply-twinned particle of diameter 1 nm, for example, the constituent single crystal regions are half of this size or less and so contain only two or three planes of atoms. One can not expect, under these circumstances, that the diffraction pattern will be made up merely by addition of the intensities of the single crystal regions. Coherence interference effects from atoms in adjacent regions will become important. It is then necessary to compare the experimental patterns with patterns calculated for various model structures. 

Fig.7 shows an example of the type of fit we obtain between experiment and theory. The experiment pattern was recorded in a CCD camera, and energy filtering was not used. The experimental and theoretical patterns are processed by a line detection program. To save computation times, only selected areas of the experimental pattern are matched. The areas are selected based on their sensitivity to lattice parameters. 

The experimental data on fractionation by molecular weight are given in 52,53). Fig. 2 b shows changes in the MWD of PVPD (oligomer) after binding part of it in a polycomplex with PAA (polymer)S2) it is clear that the experimental pattern (Fig. 2b) corresponds to the theoretical one (Fig. 2a), i.e., the high-molecular fraction binds in a polycomplex while the low molecular one remains in the solution. 

Recently, in a theoretical study using TD-DFT, it was shown that the exciton CD for [M(phen)3]2+ (M = Fe, Ru, Os) complexes and related complexes is reproduced in good agreement with the experimental pattern, though for the latter two complexes the calculated charge transfer CD bands are in agreement with the experimental one, but not for the corresponding iron(II) complex.135,136... 

The direction of a HOLZ line is normal to the reciprocal lattice vector and its position is decided by the Bragg condition. In diffraction analysis, it is useful to express HOLZ lines using line equations in an orthogonal zone-axis coordinate system (x, y, z), with z parallel to the zone-axis direction. The x direction can be taken along the horizontal direction of the experimental pattern and y is normal to x. The Bragg diffraction equation (2) expressed in this coordinate is given by... 

Figure 9 An example of the best fit obtained from an electron structure factor refinement. The experimental intensities are from a few selected line scans across the experimental pattern shown in (a). The fit was obtained using Si(lll) and (222) strucmre factors as adjustable parameters together with parameters describing the electron diffraction geometry...

Figure 4.20. Experimental powder diffraction pattern of NiMnOaCOH) (top) compared with the digitized PDF records 49-1170 (middle, solid lines) and 43-0318 (bottom, dashed lines). Downward arrows indicate peaks present in the latter record but absent in the measured pattern. Upward arrows shown on the experimental pattern indicate observed Bragg peaks that are missing in the nickel manganese oxide hydroxide, ICDD record No. 43-0318.

Careful analysis of Figure 4.20 indicates that six peaks in this card (43-0318) are clearly missing and three weak to medium intensity peaks have no match in the experimental pattern. The second record 49-1170, is almost a perfect match, but a hydrogen atom is missing in its chemical formula, as was determined later from neutron diffraction data. ... 

The starting model of the crystal structure with all of the necessary parameters is found on the CD in files Ch7Ex05a.exp and Ch7Ex05a.cif the experimental pattern is located in the file Ch7Ex05 CuKa.raw. ... 

The experimental pattern was collected with a 0.02° step from 7 to 50° 20 and a counting time of 60 sec/step, and from 50 to 69° 20 with a counting time of 90 sec/step. The high Bragg angle intensities were scaled to the 60 sec/step counting time for all calculations. The following initial parameters were used in the model completion and refinement ... 

To give a practical example, Figure 7.3 shows a small 26 interval of the experimental pattern of a P2]/n crystal structure. The three vertical bars, generated in the Laue group P2lm, correspond to the positions of the reflections (20-1), (210) and (201). The reflection (20-1) corresponds to a systematically absent reflection, but its intensity is ambiguous because it is overlapped with (210). 

Figure 7.4 (i iii) Histogram plots of METYL corresponding to the symmetry oper ators /, a, and c. Part (iv) shows the experimental pattern the ellipse emphasizes the presence of the reflection (101). 

Other modules support the structural characterization of the mixed-layer minerals. The STRUCMIX module determines the mean abundance of each layer and the range of interaction between these layers. CALCMIX proposes experimental data for reflections located in different diffraction domains and allows the nature and structure of the mixed-layer minerals to be confirmed by calculating theoretical XRD patterns and matching them with the experimental pattern. 

Although this method is efficient, it cannot directly tell us whether the result actually corresponds to the crystal stmcture that is being studied, since the number of mathematical solutions that minimize the gaps between the experimental pattern and the calculated one is very large. In order to properly deal with this problem, it is important to work according to a carefully planned refinement strategy. 

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