Diffraction techniques

Electron diffraction is an important technique for the study of crystalline materials [64, 65]. It is regularly used to identify crystal structures and local orientation. The directions in which electrons are diffracted from a specimen relate to the atomic spacings and orientation of the material (Section 3.2). A crystal has a regular arrangement of atoms and so in the TEM it will produce a diffraction pattern consisting of sharp spots. 

Polycrystalline materials have many spots, which together form continuous rings. Small or imperfect crystals give fuzzy spots or rings. 

The beam can be focused using the condenser lenses to limit the area irradiated, but the intensity produced by focusing the beam is too high. A strongly excited first condenser lens and a very small second condenser lens aperture reduce the intensity. With these conditions a near focused beam illuminates a small region of the specimen with a near parallel electron beam. Here the diffraction area is selected by the incident beam diameter as the aperture is above the specimen. 

A second powerful use of diffraction is in atomic-scale structure determination, which is especially well known for LEED [127, 163-166]. There the experimental and calculated intensity-voltage (I-V) curves are compared for various surface structures, taking multiple scattering of electrons into account (see Chapter 3.2.1 in Volume 1). However, there is a complication in performing the calculations for QCs because periodic boundary conditions cannot be applied (the same problem noted earlier for DFT). 

The reactions of heterocyclic chalcogen-nitrogen systems often result in substantial reorganization of their structural frameworks. Spectroscopic techniques alone are rarely sufficient to provide decisive structural information, and X-ray crystallography has been of paramount importance in the development of chalcogen-nitrogen chemistry. The structural chemistry of Se-N and Te-N compounds has been reviewed.19 

20) (b) TeN2CH2 (2) (redrawn from crystal data given in ref. 21) 

Electron diffraction studies have also provided structural information for chalcogen-nitrogen compounds that are liquids or gases at room temperature, e.g., the 1,2,3,5-dithiadiazolyl radical [CF3CNSSN] (3)22 and the 1,3,2-di-thiazolyl [CF3CSNSCCF3] (4).23 The structure of the trithiatriazine (NSF)3 (5) has also been determined in the gas phase by a combination of electron diffraction and microwave spectroscopy, which shows that all three fluorine atoms are axial.24 

Some illustrative examples of the application of 14N NMR spectroscopy in sulfur-nitrogen chemistry include (a) studies of the (NSC1)3 - 3NSC1 equilibrium in solution28 and (b) identification of the S-N species present in solutions of sulfur in liquid ammonia.29 

The gas-phase structures of the 12 7r-electron systems 1,3,2,4-benzodithiadiazines X4C6S2N2 (6a, X=H 6b, X=F) were determined by electron diffraction. The parent system 6a is non-planar in the gas phase, whereas the tetrafluoro derivative 6b is planar. Conversely, the solid-state structure of 6a is planar, while that of 6b is non-planar, presumably as a result of packing forces.  

The isotope is quadrupolar (7 = 3/2) and has low natural abundance (0.76%). Therefore, NMR spectroscopy has found very limited application in S-N chemistry. On the other hand, both selenium and tellurium 

Convergent beam microdiffraction is possible from regions that are extremely small, using a convergent rather than a near parallel beam. The 

In accordance with the Fraunhofer theory (which was introduced by Fraunhofer over 100 years ago), the special intensity distribution is given by. 

Most practical suspensions are polydisperse and generate a very complex diffraction pattern. The diffraction pattern of each particle size overlaps with diffraction patterns of other sizes, while the particles of different sizes diffract light at different angles and the energy distribution becomes a very complex pattern. However, the manufacturers of light-dif action instruments (such as Malvern, Coulters and Horriba) have developed numerical algorithms relating diffraction patterns to particle size distribution. 

Several factors can affect the accuracy of Fraunhofer diffraction (i) particles smaller than the lower limit of Fraunhofer theory (ii) nonexistent ghost particles in particle size distribution obtained by Fraunhofer diffraction applied to systems containing particles with edges, or a large fraction of small particles (below 10 pm) (iii) computer algorithms that are unknown to the user and vary with the manufacturer s software version (iv) the composition-dependent optical properties of the particles and dispersion medium and (v) if the density of all particles is not the same, the result may be inaccurate. 

The structures of chalcogen-nitrogen compounds are frequently unpredictable. For example, the reactions of heterocyclic systems often result in substantial reorganization of their structural frameworks, e.g. ring expansion or contraction. The formation of acyclic products from ring systems (or vice versa) is also observed. 

Specific structural information for various classes of chalcogen-nitrogen compounds will be discussed in the appropriate chapters. 

In S-N compounds containing H bonded directly to nitrogen, inverse detection 2D NMR spectroscopy can be applied to give N 

---

The PS-4 ultrasonic examination system provides many new features, which allows the operator to perform several inspections simultaneously. Both pulse-echo and time-of-flight-diffraction technique can be applied together with storage of digital A-scan data at the same time. 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Figure 4.7c illustrates how x-ray diffraction techniques can be applied to the problem of evaluating 6. If the intensity of scattered x-rays is monitored as a function of the angle of diffraction, a result like that shown in Fig. 4.7c is obtained. The sharp peak is associated with the crystalline diffraction, and the broad peak, with the amorphous contribution. If the area A under each of the peaks is measured, then... 

Free Silica. Free siUca down to 1% can be deterrnined with x-ray diffraction techniques (xrd). 

Instrumental Methods for Bulk Samples. With bulk fiber samples, or samples of materials containing significant amounts of asbestos fibers, a number of other instmmental analytical methods can be used for the identification of asbestos fibers. In principle, any instmmental method that enables the elemental characterization of minerals can be used to identify a particular type of asbestos fiber. Among such methods, x-ray fluorescence (xrf) and x-ray photo-electron spectroscopy (xps) offer convenient identification methods, usually from the ratio of the various metal cations to the siUcon content. The x-ray diffraction technique (xrd) also offers a powerfiil means of identifying the various types of asbestos fibers, as well as the nature of other minerals associated with the fibers (9). 

Surface Area. Overall catalyst surface area can be determined by the BET method mentioned eadier, but mote specific techniques are requited to determine a catalyst s active surface area. X-ray diffraction techniques can give data from which the average particle si2e and hence the active surface area may be calculated. Or, it may be necessary to find an appropriate gas or Hquid that will adsorb only on the active surface and to measure the extent of adsorption under controUed conditions. In some cases, it maybe possible to measure the products of reaction between a reactive adsorbent and the active site. Radioactively tagged materials are frequentiy usehil in this appHcation. Once a correlation has been estabHshed between either total or active surface area and catalyst performance (particulady activity), it may be possible to use the less costiy method for quaHty assurance purposes. 

Bleaching Powder. This material, known siace 1798, is made by chlorination of slightly moist hydrated lime, calcium hydroxide [1305-62-0] Ca(OH)2- It has the empirical formula Ca(OCl)2 CaCl2 Ca(OH)2 2H20. Its compositioa, loag a subject of coatroversy, was estabHshed by phase studies, microscopy, and x-ray diffraction techniques (241). The initial chlorination products are monobasic calcium chloride [14031-38-4] and dibasic calcium hypochlorite [12394-14-8] ... 

The STEM instrument itself can produce highly focused high-intensity beams down to 2 A if a field-emission source is used. Such an instrument provides a higher spatial resolution compositional analysis than any other widely used technique, but to capitalize on this requires very thin samples, as stated above. EELS and EDS are the two composition techniques usually found on a STEM, but CL, and even AES are sometimes incorporated. In addition simultaneous crystallographic information can be provided by diffraction, as in the TEM, but with 100 times better spatial resolution. The combination of diffraction techniques and analysis techniques in a TEM or STEM is termed Analytical Electron Microscopy, AEM. A well-equipped analytical TEM or STEM costs well over 1,000,000. 

EXAFS is a nondestructive, element-specific spectroscopic technique with application to all elements from lithium to uranium. It is employed as a direct probe of the atomic environment of an X-ray absorbing element and provides chemical bonding information. Although EXAFS is primarily used to determine the local structure of bulk solids (e.g., crystalline and amorphous materials), solid surfaces, and interfaces, its use is not limited to the solid state. As a structural tool, EXAFS complements the familiar X-ray diffraction technique, which is applicable only to crystalline solids. EXAFS provides an atomic-scale perspective about the X-ray absorbing element in terms of the numbers, types, and interatomic distances of neighboring atoms. 

Solid state NMR is a relatively recent spectroscopic technique that can be used to uniquely identify and quantitate crystalline phases in bulk materials and at surfaces and interfaces. While NMR resembles X-ray diffraction in this capacity, it has the additional advantage of being element-selective and inherently quantitative. Since the signal observed is a direct reflection of the local environment of the element under smdy, NMR can also provide structural insights on a molecularlevel. Thus, information about coordination numbers, local symmetry, and internuclear bond distances is readily available. This feature is particularly usefrd in the structural analysis of highly disordered, amorphous, and compositionally complex systems, where diffraction techniques and other spectroscopies (IR, Raman, EXAFS) often fail. 

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

Intimate information about the nature of the H bond has come from vibrational spectro.scopy (infrared and Raman), proton nmr spectroscopy, and diffraction techniques (X-ray and neutron). In vibrational spectroscopy the presence of a hydrogen bond A-H B is manifest by the following effects ... 

B. N. Brockhouse (McMaster University) and C. G. Schull (Massachusetts Institute of Technology) pioneering contributions to neutron scattering techniques for studies of condensed matter (namely neutron spectroscopy and neutron diffraction techniques, respectively). 

Polyester fibers contain crystalline as well as noncrystalline regions. The degree of crystallinity and molecular orientation are important in determining the tensile strength of the fiber (between 18-22 denier) and its shrinkage. The degree of crystallinity and molecular orientation can be determined by X-ray diffraction techniques. ... 

Investigations based on equation (a) are indirect. Direct structural studies using diffraction techniques (X-ray or neutron), or electron microscopy, while they cannot detect the low concentrations of defects present in NiO or CoO are indispensible to the study of grossly non-stoichiometric oxides like FeO, TiOj, WOj etc., and particularly electron microscopes with a point-to-point resolution of about 0.2 nm are widely used. The first direct observation of a point defect (actually a complex of two interstitial metal atoms, and two oxygen atoms in Nb,2029) was made" using electron microscopy. 

An important conceptual, or even philosophical, difference between the orbital/wavefunction methods and the density functional methods is that, at least in principle, the density functional methods do not appeal to orbitals. In the former case the theoretical entities are completely unobservable whereas electron density invoked by density functional theories is a genuine observable. Experiments to observe electron densities have been routinely conducted since the development of X-ray and other diffraction techniques (Coppens, 2001).18... 

Films on stainless steel, analysis by x-ray emission spectrography, 230 Film thickness, determination, 146-159 by attenuation of monochromatic x-rays from substrate, 149-152 by attenuation of unresolved beam from substrate, 147-149 by x-ray diffraction techniques, 147 intercomparison of three methods used in, 158... 

A New Electron Diffraction Technique, Potentially Applicable to Research in Catalysis L. H. Germer... 

---