Diffraction crystalline materials

Electron diffraction patterns have been obtained of myelin and rat central nervous system membranes after osmium tetroxide and formalin fixation. Strongly diffractive crystalline material present in an OSO4 fixed specimen was interpreted as precipitated dye as the observed spotted pattern was much weaker in formalin treated tissue samples. OSO4 easily reacts with ethylenic double bonds. An alternative and more likely explanation therefore is that regular, electron dense crystalline structures are formed due to reaction of OSO4 with a highly organized lattice of unsaturated membrane lipids. 

Transmission electron microscopy (tern) is used to analyze the stmcture of crystals, such as distinguishing between amorphous siUcon dioxide and crystalline quartz. The technique is based on the phenomenon that crystalline materials are ordered arrays that scatter waves coherently. A crystalline material diffracts a beam in such a way that discrete spots can be detected on a photographic plate, whereas an amorphous substrate produces diffuse rings. Tern is also used in an imaging mode to produce images of substrate grain stmctures. Tern requires samples that are very thin (10—50 nm) sections, and is a destmctive as well as time-consuming method of analysis. 

The im< e mode produces an image of the illuminated sample area, as in Figure 2. The imj e can contain contrast brought about by several mechanisms mass contrast, due to spatial separations between distinct atomic constituents thickness contrast, due to nonuniformity in sample thickness diffraction contrast, which in the case of crystalline materials results from scattering of the incident electron wave by structural defects and phase contrast (see discussion later in this article). Alternating between imj e and diffraction mode on a TEM involves nothing more than the flick of a switch. The reasons for this simplicity are buried in the intricate electron optics technology that makes the practice of TEM possible. 

The crystal group or Bravais lattice of an unknown crystalline material can also be obtained using SAD. This is achieved easily with polycrystalline specimens, employing the same powder pattern indexing procedures as are used in X-ray diffraction. ... 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

Since the recognition in 1936 of the wave nature of neutrons and the subsequent demonstration of the diffraction of neutrons by a crystalline material, the development of neutron diffraction as a useful analytical tool has been inevitable. The initial growth period of this field was slow due to the unavailability of neutron sources (nuclear reactors) and the low neutron flux available at existing reactors. Within the last decade, however, increases in the number and type of neutron sources, increased flux, and improved detection schemes have placed this technique firmly in the mainstream of materials analysis. 

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... 

Like X-ray and electron diffraction, neutron diffraction is a technique used primarily to characterize crystalline materials (defined here as materials possessing long-range order). The basic equation describing a diffraction experiment is the Bra equation ... 

X-ray diffraction has been used for the study both of simple molten salts and of binary mixtures thereof, as well as for liquid crystalline materials. The scattering process is similar to that described above for neutron diffraction, with the exception that the scattering of the photons arises from the electron density and not the nuclei. The X-ray scattering factor therefore increases with atomic number and the scattering pattern is dominated by the heavy atoms in the sample. Unlike in neutron diffraction, hydrogen (for example) scatters very wealdy and its position cannot be determined with any great accuracy. 

Other liquid-crystalline materials that have been investigated by X-ray scattering include single- and double-chained pyridinium [33] and N-substituted 4-(5-alkyl-l,3-dioxan-2-yl)pyridinium salts [34]. In the former case, diffraction analysis allowed an explanation for the differences in mono- and di-substituted salts to be proposed. 

Crystalline material will diffract a beam of X-rays, and X-ray powder diffractometry can be used to identify components of mixtures. These X-ray procedures are examples of non-destructive methods of analysis. 

A regularly formed crystal of reasonable size (typically >500 pm in each dimension) is required for X-ray diffraction. Samples of pure protein are screened against a matrix of buffers, additives, or precipitants for conditions under which they form crystals. This can require many thousands of trials and has benefited from increased automation over the past five years. Most large crystallographic laboratories now have robotics systems, and the most sophisticated also automate the visualization of the crystallization experiments, to monitor the appearance of crystalline material. Such developments [e.g., Ref. 1] are adding computer visualization and pattern recognition to the informatics requirements. 

Crystals produce different diffraction patterns when subjected to bombardment of monochromatic X-ray sources and thereby provide unequivocal identification of crystalline materials. 

The use of Equation (22) is very general, but it is also possible, with accurate measurements and data treatment, to perform the quantitative phase analysis in semi-crystalline materials without using any internal standard. This procedure is possible only if the chemical compositions of all the phases, including the amorphous one, are known. If the composition of the amorphous phase is unknown, the quantitative analysis without using any internal standard can still be used provided that the chemical composition of the whole sample is available [51]. This approach, until now, has been developed only for the XRD with Bragg-Brentano geometry that is one of the most diffused techniques in powder diffraction laboratories. 

Zeolites. In heterogeneous catalysis porosity is nearly always of essential importance. In most cases porous materials are synthesized using the above de.scribed sol-gel techniques resulting in so-called amorphous catalysts. Porosity is introduced in the agglomeration process in which the sol is transformed into a gel. From X-ray Diffraction patterns it is clear that the material shows only weak broad lines, characteristic of non-crystalline materials. Silica and alumina are typical examples. Zeolites are an exception they are crystalline materials but nevertheless exhibit high (micro) porosity. Zeolites belong to the class of molecular sieves, which are porous solids with pores of molecular dimensions, i.e., typically the pore diameter ranges from 0.3 to 10 nm. Examples of molecular sieves are carbons, oxides and zeolites. 

For the crystalline materials, high resolution X-ray diffraction experiment is a powerful tool to derive accurate electron density even for large systems like zeolites. In this study, we are interested in the experimental electron density distribution in the scolecite CaAl2Si3O10 3H20 in order to make comparison with its sodium analogue natrolite Na2Al2Si3Oi0 2H20 for which the electron density has been reported recently [1,2],... 

In the phrase "liquid-crystalline", the "crystalline" adjective refers to the fact that these materials are sufficiently ordered to diffract an X-ray beam in a way analogous to that of normal crystalline materials. On the other hand, the "liquid" part specifies that there is frequently sufficient disorder for the material to flow like a liquid [145]. The disorder is typically in one dimension as is the case, for example, with rod-like molecules having their axes all parallel but out of register with regard to their lengths. 

The crystallinity of as-deposited AlSb films steadily increases with increasing deposition temperature. Below 375 °C no crystalline material was present according to X-ray diffraction studies (Fig. 46). 

Although single-crystal x-ray diffraction undoubtedly represents the most powerful method for the characterization of crystalline materials, it does suffer from the drawback of requiring the existence of a suitable single crystal. Very early in the history of x-ray diffraction studies, it was recognized that the scattering of x-ray radiation by powdered crystalline solids could be used to obtain structural information, leading to the practice of x-ray powder diffraction (XRPD). 

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. 

In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a statistical description of the structure may be obtained. The so-called radial distribution function is defined as ... 

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