INDEX refined structure

Several recent examples illustrate how NMR Crystallography can be used to refine structures of Zn-containing coordination compounds [21,31,55]. Martineau et al. used NMR Crystallography to obtain the stmc-ture solution of a fiuorinated inorganic—organic hybrid compound, Zn3Al2Fi2[HAmTAZ]6, where HAmTAZ = 3-amino-1,2,4-triazole [31]. Powder XRD pattern was indexed to obtain unit cell parameters and possible... 

Theoretical and structural studies have been briefly reviewed as late as 1979 (79AHC(25)147) (discussed were the aromaticity, basicity, thermodynamic properties, molecular dimensions and tautomeric properties ) and also in the early 1960s (63ahC(2)365, 62hC(17)1, p. 117). Significant new data have not been added but refinements in the data have been recorded. Tables on electron density, density, refractive indexes, molar refractivity, surface data and dissociation constants of isoxazole and its derivatives have been compiled (62HC(17)l,p. 177). Short reviews on all aspects of the physical properties as applied to isoxazoles have appeared in the series Physical Methods in Heterocyclic Chemistry (1963-1976, vols. 1-6). 

The distance of each reflection from the center of the pattern is a function of the fiber-to-film distance, as well as the unit-cell dimensions. Therefore, by measuring the positions of the reflections, it is possible to determine the unit-cell dimensions and, subsequently, index (or assign Miller indices to) all the reflections. Their intensities are measured with a microdensitometer or digitized with a scanner and then processed.8-10 After applying appropriate geometrical corrections for Lorentz and polarization effects, the observed structure amplitudes are computed. This experimental X-ray data set is crucial for the determination and refinement of molecular and packing models, and also for the adjudication of alternatives. 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

Fig. 13 Rietveld refinement of Sc-II at 23 GPa using the C-centred guest structure. Reflections are indexed using their hklm indices. The upper tick marks show the calculated peak positions for hklG) host reflections and (hkOO) host/guest reflections, and lower ones mark (hkOm) guest-only reflections. The difference between the observed and calculated profiles is shown below the tick marks. The inset shows an enlarged view of the asymmetric peak at 17.5°, showing that it is accounted for by the (4400) and (0002) peaks. The vertical dashed line is a guide to the eye...

The value of r should refine to a value close to + 1 or — 1, where + 1 corresponds to the correct absolute structure and — 1 indicates that the absolute structure has to be inverted. Since rf is accompanied by an estimated standard deviation a(rj). an index of confidence is also available, Rogers rj test has been incorporated into the current versions of the major computer program systems for X-ray structure determination. 

The residual index, or R factor, gives a measure of the difference between the observed and calculated structure factors and therefore of how well the structure has refined. It is defined as... 

The inner coordination spheres of these two complexes are presented in Figure 1. While the Ru-H distance is well defined in the amidinato, it is not in the triazenido complex. Yet reference to Table I indicates that the triazenido structure is better if one uses the unreliable criterion that the lower the R index, the better the structure. In this instance, the low R index in the triazenido complex results from an elaboration of the usual group refinement model (3), allowing for anisotropic motion of the group atoms. This elaboration introduces a large number of additional variables and provides us with an opportunity to lower the R index More importantly, we established that the other features of the structure were virtually unaffected by this elaboration. We conclude that with problems of this type, such an elaboration probably is not justified by the expense involved. Why can t the hydride position be located accurately in the... 

Structure refinements of the AH 200 and AH 300 samples were conducted in the same way. Unit cell constants, final atomic parameters, and R indexes are given in Table I. (Observed and calculated structure factors are available from the authors.) Interatomic distances and angles are given in Table II. Estimated errors on the population and position of the cations may in some cases be greatly underestimated especially for atoms with low occupancy factors. 

The progress of iterative real- and reciprocal-space refinement is monitored by comparing the measured structure-factor amplitudes IFobsl (which are proportional to (/obs ) /2) with amplitudes IFca(c I from the current model. In calculating the new phases at each stage, we learn what intensities our current model, if correct, would yield. As we converge to the correct structure, the measured Fs and the calculated Fs should also converge. The most widely used measure of convergence is the residual index, or R-factor (Chapter 6, Section V.E). 

The Collection is a source of reference patterns for pure crystalline phases. The data may be helpful in identifying known zeolitic materials and indexing their diffraction patterns. Because so many factors related to both the zeolite crystal and the diffraction instrument affect powder diffraction data, phase identification is not always straightforward and frequently requires additional data. Considerable care should be exercised in comparing calculated diffraction patterns to experimental patterns. For example, the use of fixed versus variable incident slits on a powder diffractometer can drastically change the relative intensities of a diffraction pattern, and it should be emphasized that calculated patterns are only as accurate as the structure refinements on which they are based. 

This equation leads to a reductio ad absurdum that may provide a significant refinement of the helical conductor model. It will be noted that as the step helices (ya = 180°) approach the absolutely planar zigzag chain structure (ya = /b = 180°) they acquire very large cross sections. The index of helieity approaches a constant value of about 0.385 but the expected residue rotations approach infinity. (See Table 12). This result is, at least intuitively, absurd. 

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