Diffraction methods disorder

Surface reconstructions have been observed by STM in many systems, and the teclmique has, indeed, been used to confmn the missing row structure in the 1 x 2 reconstruction of Au(l 10) [28]. As the temperature was increased within 10 K of the transition to the disordered 1 1 phase (700 K), a drastic reduction in domain size to -20-40 A (i.e. less than the coherence width of LEED) was observed. In this way, the STM has been used to help explain and extend many observations previously made by diffraction methods. 

Table 8.53 shows the main features of XAS. The advantages of EXAFS over diffraction methods are that the technique does not depend on long-range order, hence it can always be used to study local environments in amorphous (and crystalline) solids and liquids it is atom specific and can be sensitive to low concentrations of the target atom (about 100 ppm). XAS provides information on interatomic distances, coordination numbers, atom types and structural disorder and oxidation state by inference. Accuracy is 1-2% for interatomic distances, and 10-25 % for coordination numbers. 

The location of boron or aluminum sites in zeolites is of utmost importance to an understanding of the catalytic properties. Due to the inherent long-range disorder of the distribution of these sites in most zeolites, it is difficult to locate them by diffraction methods. The aforementioned methods to measure heteronuclear dipolar interactions can be utilized to determine the orientation between the organic SDA and A1 or B in the framework. The SDA location may be obtained by structure refinement or computational modeling. For catalytic reactions, the SDA must be removed from the pores system by calcination. 

The basic modem data describing the atomic stmcture of matter have been obtained by the using of diffraction methods - X-ray, neutron and electron diffraction. All three radiations are used not only for the stmcture analysis of various natural and synthetic crystals - inorganic, metallic, organic, biological crystals but also for the analysis of other condensed states of matter - quasicrystals, incommensurate phases, and partly disordered system, namely, for high-molecular polymers, liquid crystals, amorphous substances and liquids, and isolated molecules in vapours or gases. This tremendous... 

Recently, the PDF method was extended to describe the local dynamics of disordered materials (Dmowski W, Vakhrushev SB, Jeong I-K, Hehlen M, Trouw F, Egami T (2006) Abstracts American conference on neutron scattering, St. Charles, IL, 18-22 June 2006, unpublished). The total PDF is obtained by the powder diffraction method so that S(Q) includes both elastic and inelastic intensities. To determine the dynamics we have to use an inelastic neutron scattering spectrometer and measure the dynamic structure factor, S(Q,a>), over a large Q and co space, and Fourier-transform along Q to obtain the dynamic PDF (DPDF). While the interpretation of the DPDF is a little... 

As a result of static disorder, often alternate positions of atoms can be resolved in electron density maps. In macromolecular crystals, some of the flexible regions possess variable conformers and as a consequence none of the individual ones can be detected in electron density maps. Thus, dynamics between several energetically similar states and/or larger amplitude makes to vanish more mobile sequential subunits. In practice, more than two or three conformer makes detection and/ or assignment impossible. In other words lower than 25-33% of relative population of conformers is unseen by diffraction methods. 

It should be stressed that the diffraction methods do not provide complete characterization of lattice distortions and ionic shifts in relaxors due to the compositional disorder of these materials and nanometric scale of polar order. Thus, local methods such as magnetic resonance and, in particular, NMR can be extremely useful in this case. In NMR experiments, the nuclei are sensitive to their local environment at a distance less than 1-2 nm. In addition, NMR operates at a much longer time scale (105-108 s) in comparison with the neutron or X-ray... 

However, diffraction methods have severe drawbacks. Disordered crystals are often difficult to tackle. If the disorder is of dynamic nature, e.g. arising from small-or large-amplitude motions in the crystal, the use of devices for variable-temperature measurements is compulsory and can also yield very useful information (see below for some examples) on the existence of enantiotropic systems related by phase transitions. In some, not frequent, cases the crystals are sufficiently robust to be used for direct phase transition measurements on the diffractometer. Figure 3 shows an example of multiple diffraction data sets collected on the same specimen... 

While it is to some extent arbitrary, a classification of this kind provides a means of discussing some of the general features now emerging from studies of metallic oxides. We have stressed the evidence that a nonstoichiometric phase is disordered, but may be related to chemically similar phases of fixed composition where an anomaly of structure is ordered and identifiable by x-ray diffraction methods. Where such ordered phases are found, it is possible that features of them are retained as blocks or domains with short range order in the related berthollide. Efforts should be directed towards order-disorder effects, with a view to reconsidering the status of the nonstoichiometric compound with a very wide composition range. 

In all instances where this disorder was actually observed by X-ray or neutron diffraction methods, X and A are hydroxyl oxygen atoms, as in the ices Ih and Ic, in certain of the high pressure ices, and in the cyclodextrin hydrates, see Parts III and IV. In ice Ih the disorder gives rise to the well-known residual entropy of 0.82 0.05 cal deg-1 [114 to 117]. 

The driving force behind the rapid development of powder diffraction methods over the past 10 years is the increasing need for structural characterization of materials that are only available as powders. Examples are zeolite catalysts, magnets, metal hydrides, ceramics, battery and fuel cell electrodes, piezo- and ferroelectrics, and more recently pharmaceuticals and organic and molecular materials as well as biominerals. The emergence of nanoscience as an interdisciplinary research area will further increase the need for powder diffraction, pair-distribution function (PDF) analysis of powder diffraction pattern allows the refinement of structural models regardless of the crystalline quality of the sample and is therefore a very powerful structural characterization tool for nanomaterials and disordered complex materials. 

Investigation of the structure of disordered systems can be performed directly by diffraction methods. The reduced radial distribution fimction d(r) is related to the structure fiictor S(K) as follows ... 

Thermal motion and disorder are two of the main factors limiting our ability to obtain accurate distances and angles by X-ray diffraction methods. As quoted earlier in this Chapter, if only the atoms kept still it would make the task much easier. An understanding of the effects of thermal motion and disorder is necessary so that they may be corrected for when determining bond distances. In order to obtain the most accurate set of bond distances, the X-ray diffraction experiment should be performed at as low a temperature as possible, thus reducing all atomic motion. 

Another example of crystals containing more than one component is provided by the clathrates. In clathrates of, 3-quinol, three quinol molecules are hydrogen bonded together to form an approximately spherical cavity of radius 4 A (Figure 15.13). Any molecule of appropriate size such as oxygen, nitrogen, krypton, xenon, methane, sulfur dioxide, or methyl alcohol can be trapped, and if it is not disordered within the clathrate, its location and orientation can be determined in the crystalline state by X-ray diffraction methods. In most cases, when a clathrate is... 

Powder diffraction techniques can be used to study solid-state reactions as a function of timeJ This is done by scanning 26 as a function of diffraction intensity at regular intervals of time, and plotting the result in a manner such as that shown in Figures 18.14 and 18.15. Powder neutron diffraction methods have been used to study orientational order-disorder transitions as a function of time. ... 

The evolution of molecular models for disordered porous carbons is strongly connected with the advance of experimental techniques such as diffraction methods and electron microscopy. First, X-ray studies on carbon blacks revealed that these materials consist of a wealth of small graphitic crystallites. 

An interesting feature of XANES for structure determination in condensed matter is that it can be used to study the local structure both in crystalline and disordered materials. Therefore once a local structure has been solved for a crystalline material also the similar structure in amorphous, liquid or complex materials, where diffraction methods cannot be applied, can be solved. 

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