Single crystal structure recorded

Powder XRD patterns of the products were recorded using Cu Ka radiation (Rich-Seifert, 3000TT). The patterns agreed with those calculated for single-crystal structure determination. Thermogravi-metric analysis (TGA) was carried out (Metler-Toledo) in an oxygen... 

Figure 4.16 (a) Crystal structure recorded on a single crystal of Si(OEt)3-lmPV and (b) J-stacks running along the fe-axis. (Reprinted (adapted) with permission from Ref. [86], Copyright 2006, American Chemical Society.)... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

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. 

Most polymers do not form crystals suitable for single crystal X-ray diffraction, so powder or film methods are usually employed. X-ray and LJV data recorded at various temperatures provide the detailed information required to correlate conformational and electronic properties, since the former is sensitive to the inter- and intrachain packing, and the latter is sensitive to the conformation. DSC provides further evidence for any phase transitions. Detailed studies have been performed by Winokur and West,260 261 who reported a comparison of the polymorphism, structure, and chromism in poly(di- -octylsilylene), (Si- -Oct2), 89, and poly(di- -dccylsilylcnc)(Si- -Dcc2) , 90. These investigations will be described in detail for the useful insights into polysilane structures that they afford. 

A single crystal Raman spectrum of NaRe04 recorded at low temperatures has recently been published by Johnson et al. (200). The measured phonons of this scheelite structure and their assSinment are listed in Table 35. 

Peak positions. Shifts in the positions of the peaks in an experimental powder XRD pattern may arise due to a number of instrumental factors. Furthermore, comparison of powder XRD patterns recorded at different temperatures may show differences in appearance (particularly in regions with significant peak overlap) as a result of anisotropic thermal expansion/contraction. This issue is particularly relevant when an experimental powder XRD pattern recorded at ambient temperature is compared with simulated powder XRD patterns for known crystal structures determined from single-crystal XRD data at low temperature. 

The technique of single crystal X-ray diffraction is quite powerful. In this technique an individual crystal is oriented so that each hkl plane may be examined separately. In this manner it becomes a simple matter to determine the unit cell parameters and symmetry elements associated with the crystal structure. Furthermore, it is also possible to record the intensity for each reflection from a given hkl plane and from this determine the location of atoms in the crystal, i.e. the crystal structure. While the data derived from single crystal X-ray diffraction are very valuable, the experiments are sometimes quite time consuming and so the technique is limited in its appeal as a day to day analytical tool. 

In some systems for which there are known phases and even single crystal studies, the powder patterns for the known phases have not been deposited in the PDF. In this case there are at least three methods for obtaining the necessary patterns. The first is obvious the known phase is prepared and the powder diffraction pattern is recorded. However, it is not always possible to prepare single phase material of the known phase and so other methods must be employed. These other methods depend on the availability of crystal structure data for the desired phase. If the crystal structure is known, the complete powder pattern can be calculated. If only unit cell data are known, the rf-spacings of all possible lines for the phase can be determined from the relation-... 

In CBED, zone-axis patterns (ZAP) can be recorded near the relevant zone axis and the pattern may also include a higher-order Laue zone (referred to as a HOLZ). The radius of the first HOLZ ring G is related to the periodicity along the zone axis [c] and the electron wavelength, by = 2/kc. CBED can thus provide reciprocal space data in all three (x,y,z) dimensions, typically with a lateral resolution of a few nanometres. As in any application, corroborative evidence from other methods such as HRTEM and single-crystal x-ray diffraction, where possible, can be productive in an unambiguous structural determination of complex and defective materials such as catalysts. We illustrate some examples in later sections. 

---