Method of X-ray diffraction

In this study, two methods of xrd-rsms and gixrd were applied to ferroelectric thin film. Which xrd-rsm is chosen depends on the orientation of the thin film media. In the following session, details of these two xrd-rsms and the gixrd and the comparison of them to the conventional 20 — 0 scan method are discussed. 

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The methods of X-ray diffraction usually were used to determine the orientation of crystal faces. Low-energy electron diffraction (LEED) gives more accurate results. However, such measurements provide an exact characterization only of the initial surface state of the electrodes. It is more difficult to determine the surface state after the electrochemical studies, and even more so during these studies. 

For purposes of investigation of the micro- and macro-structural characteristics of graphite, we have used methods of X-ray diffraction, SEM and we also studied the pattern of particle distribution by size with the SK laser micron sizer (Horiba, Japan). 

For work with the method of x-ray diffraction two items were necessary to study the theory and to learn to work with x-rays. So Mark studied together with Weissenberg Niggli s book on crystallography thoroughly. To work with soft x-rays, as it is necessary for diffraction work, was rather difficult at those times. X-Ray tubes for these purposes were not available com-... 

During investigations we were analyzing samples by methods of X-ray diffraction, electron scanning microscopy, microprobe analysis, atomic force microscopy, high-resolution transmission electron microscopy with preliminary attracting of the another methods including optical microscopy, Raman spectroscopy, thermal analysis and some of others. 

To shed more light on the structure of DNA, Rosalind Franklin and Maurice Wilkins used the powerful method of x-ray diffraction (see Box A-A) to analyze DNA fibers. They showed in the early 1950s that DNA produces a characteristic x-ray diffraction pattern (Fig. 8-14). From this pattern it was deduced that DNA molecules are helical with two periodicities along their long axis, a primary one of 3.4 A and a secondary one of 34 A The problem then was to formulate a three-dimensional model of the DNA molecule that could account not only for the x-ray diffraction data but also for the specific A = T and G = C base equivalences discovered by Chargaff and for the other chemical properties of DNA. 

The evidence for isomerism varies from the obvious, such as a difference in phase, to the subtle, such as the temperature dependence of an NMR spectrum. These instances illustrate an important point, namely, that the detection of isomerism is dependent upon the existence of an energy barrier between the different forms and upon a method of detection sensitive enough to observe the barrier. A compound that appears to be a single species on one time-scale may prove to be a mixture on another. The relationship between the lifetime of a particular molecular structure and the various physical methods for studying it has been discussed by Muetterties.3 The essentially instantaneous method of X-ray diffraction (10 18s) may be contrasted with NMR techniques (10 1-10 9s) and the time scale for the experimental separation of isomers (>102s). 

The classical valency concept of the tetrahedral carbon atom has been more than fully verified by its success in explaining the chemistry of countless thousands of organic compounds. The first direct physical confirmation of the tetrahedral distribution of carbon valency bonds, however, came with the elucidation of the structure of diamond by W. H. and W. L. Bragg (1913) using the newly discovered method of X-ray diffraction. 

There are a number of excellent texts devoted entirely to the methods of x-ray diffraction and interpretation of the resulting data. This chapter affords only a quick glimpse into the least complex aspects of this important field. Although x-ray studies of noncrystalline material (gases, liquids, and glasses) have led to some interesting results, such studies are far less important than studies of crystals and will not be discussed in this text. 

This example shows how a simple rearrangement of atoms within the unit cell can eliminate a reflection completely. More generally, the intensity of a diffracted beam is changed, not necessarily to zero, by any change in atomic positions, and, conversely, we can determine atomic positions only by observations of diffracted intensities. To establish an exact relation between atom position and intensity is the main purpose of this chapter. The problem is complex because of the many variables involved, and we will have to proceed step by step we will consider how x-rays are scattered first by a single electron, then by an atom, and finally by all the atoms in the unit cell. We will apply these results to the powder method of x-ray diffraction only, and, to obtain an expression for the intensity of a powder pattern line, we will have to consider a number of other factors which affect the way in which a crystalline powder diffracts x-rays. 

The common methods of x-ray diffraction are differentiated by the methods used for bringing reciprocal-lattice points into contact with the surface of the sphere of reflection. The radius of the sphere may be varied by varying the incident wavelength (Laue method), or the position of the reciprocal lattice may be varied by changes in the orientation of the crystal (rotating-crystal and powder methods). 

Planes, crystallographic, 44 et seq. Plastic deformation, 35, 52 et seq. Powder method of X-ray diffraction, 33 Polar bond, 25... 

The method of X-ray diffraction is widely used for the determination of the structures of molecular solids (i.e. sohds composed of discrete molecules) and of non-molecular solids (e.g. ionic materials). As the technique has been developed, its range of applications has expanded to include poljrmers, proteins and other macromolecules. The reason that X-rays are chosen for these experiments is that the wavelength (a 10 m) is of the same order of magnitude as the internuclear distances in molecules or non-molecular solids. As a consequence of this, diffraction is observed when X-rays interact with an array of atoms in a solid (see below). 

Debye-Scherrer method A method of X-ray diffraction in which abeam of X-rays is diffracted by material in the form of powder. Since the powder consists of very small crystals of the material in all possible orienta-... 

Debye-Scherrer pattern A method of x-ray diffraction analysis widely used to identify polycrystalline materials. 

As indicated above, the covalent radius of an element depends on its oxidation state. In a binary ionic compound, MX, containing the positive ion, M. and the negative ion. X, the minimum distance between them is measurable with considerable accuracy by the method of X-ray diffraction. The problem is to divide such a distance into the ionic radii for the individual ions. That ions behave like hard spheres with a constant radius whatever their environment might be is an approximation to the real situation. In compounds which do not exhibit much covalency the approximation is reasonable, and led Shannon and Prewitt to assign radii to O- and F of 140 and 133 pm respectively after their study of many oxides and fluorides. Ionic radii are not assignable to every element, and the generalizations described apply only to those elements which do form ions in compounds, and are subject to their oxidation states (discussed in Chapter 5) and coordination numbers i.e. the number of nearest neighbours they have in the ionic compound). 

The method of x-ray diffraction by crystals has been used to determine the detailed structures of a number of globular proteins. The alpha helix and the two pleated sheets have been found to be the main types of secondary structure in these proteins. The location of the catalytically active region of an enzyme can be discovered by the x-ray study of crystals of the enzyme combined with an inhibitor. 

In recent years a great amount of information about the structure of inorganic complexes has been gathered by the methods of x-ray diffraction, measurement of magnetic susceptibility, magnetic resonance spectroscopy, Mossbauer spectroscopy, and other techniques. This information about the structure of complexes has been correlated with their chemical properties in such a way as to bring reasonable order into this field of chemistry. 

The key in determining the molecular structure (atoms distribution, electronic localization) through the methods of X-ray diffraction consists in the structure factor determination and in the associated electronic density, the relations (5.17) and (5.18), respectively the present discussion follows Putz and Lacrama (2005). 

The size and shape question can be raised either for the bulk phase or for dilute solutions. In the bulk phase, e.g., in a protein crystal, the detailed configuration can be elucidated by the method of X-ray diffraction which, in recent years, has had such phenomenal success in the case of myoglobin (Kendrew et al., 1960) and hemoglobin (Perutz et al., 1960) and promises to yield the structures of other proteins in the near future. Another method which is applicable to molecularly dispersed species in the... 

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