Experimental Diffraction Methods

In the following we will discuss three methods for satisfying Bragg s law in a systematic manner. For other methods, we refer the reader to the specialized literature. 

By making a small modification to the Ewald construction, we obtain a more informative representation of the Laue method. By multiplying all the dimensions of the construction by the wavelength A, we obtain a lattice -h fcb -h /c ) and a sphere of radius 1. Thus, for polychromatic radiation, we obtain a superposition of lattices of variable dimensions intersected by a single 

The reflections derived from a reciprocal lattice plane passing through the origin (000) form a cone whose axis is normal to the plane (Fig. 3.25). This normal is a translation [L/IW] of the crystal lattice U, V, W being coprime integers). The indices of the lattice points (hkl) of the plane satisfy the equation hU + kV IW = 0. Hence the lattice planes (hkl) belong to the zone UVW (Section 1.3.3). The surface of the cone contains the primary beam. 

An important new application of the Laue method has been developed since synchrotrons dedicated to the production of high-intensity X-rays have become available (Section 3.6,3). It is used to rapidly obtain diflractograms of macro-molecular structures. 

If we employ a monochromatic beam of X-rays, Bragg s law is obeyed only for certain orientations of the crystal. There exist a number of methods designed to photograph reciprocal space by movements, more or less complicated, of the crystal. In general, the simpler the method, the more complicated is the interpretation of the dififractogram. 

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In 1962 Olah repotted the NMR spectrum of the t-butyl cation in superacid solution, [1] and NMR was thenceforth the ex rimental method of choice for studies of intermediates in solution acid chemistry. The inhomogeneous nature and diversity of solid acid systems will ensure that no one experimental technique will so completely dominate as NMR has in solution studies, but the contributions and potential of NMR to solid acid studies are clearly such as to put it on an equal footing with reaction studies, infrared, TPD, diffraction methods and calorimetry. 

In this chapter, we have chosen from the scientific literature accounts of symposia published at intervals during the period 1920 1990. They are personal choices illustrating what we believe reflect significant developments in experimental techniques and concepts during this time. Initially there was a dependence on gas-phase pressure measurements and the construction of adsorption isotherms, followed by the development of mass spectrometry for gas analysis, surface spectroscopies with infrared spectroscopy dominant, but soon to be followed by Auger and photoelectron spectroscopy, field emission, field ionisation and diffraction methods. 

Experimental equipment for X-ray diffraction methods has improved enormously in recent years. CCD detectors and focusing devices (Goepel mirror) have drastically reduced the data acquisition time. Cryogenic systems have been developed which allow structural studies to be extended down to the liquid helium temperature range. These developments have had important implications for SCO research. For example, fibre optics have been mounted in the cryostats for exploring structural changes effected by light-induced spin state conversion (LIESST effect). Chaps. 15 and 16 treat such studies. 

ABSTRACT The aim of this study was to test portable infrared spectroscopy for non-destructive analysis of ancient construction mortar. Mortar samples from the House of the Vestals, in Pompeii, Italy, were initially examined with traditional analytical techniques, including X-ray fluorescence, X-ray diffraction and thin section analysis. These techniques were used to establish mineralogical and chemical profiles of the samples and to verify the results of experimental field methods. Results showed the lime-based binder was composed of calcite, and the volcanic sand aggregate contained clinopyroxene, plagioclase, sanidine and olivine crystals. 

Recent developments and prospects of X-ray powder diffraction methods. In the preceding paragraph a few comments have been made about diffractometry and its uses in the analysis of materials. However it is not possible to give here an account of this subject its principles and underlying theories, its experimental techniques and... 

In an opposite way, if we are able to identify the diffraction group from experimental diffraction patterns, then, we can obtain the point group. This is the basis of the point group determination. To reach this aim, two experimental methods are available a method proposed by Buxton et al. [3] and a multi-beam method proposed by Tanaka et. al. [4]. 

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. 

The electrostatic potential y(r) is a physical observable, which can be determined experimentally by diffraction methods as well as computationally. It directly reflects the distribution in space of the positive (nuclear) and the negative (electronic) charge in a system. V (r) can also be related rigorously to its energy and its chemical potential, and further provides a means for defining covalent and ionic radii" ... 

D had a large experimental uncertainty, but is nevertheless close to the later result of 4.16 0.4 D (Kulakowska et al. 1974), obtained from capacitance measurements of a solution in dioxane. The diffraction method has the advantage that it gives not only the magnitude but also the direction of the dipole moment. Gas-phase microwave measurements are also capable of providing all three components of the dipole moment, but only the magnitude is obtained from dielectric solution measurements. 

For further discussion of the already extensive experimental information, the reader is referred to the review by Spackman (1992). Spackman concludes that, while the diffraction method may never become the routine method of choice for... 

Overview of Semi-Empirical and Ab Initio Molecular Orbital Methods. 2.2 Applications of Molecular Mechanics. 3 Experimental Structural Methods. 3.1 X-Ray Diffraction. 3.2 NMR Spectroscopy and. 3.3 Mass Spectrometry. 3.4 UV/Fluorescence. 3.5 IR Spectroscopy. 3.6 Redox Potentials. 4 Thermodynamic Aspects. 4.1 Melting Points. 5 Reactivity of Fully Conjugated Rings 6 Reactivity of Nonconjugated Rings... 

During the last two decades, studies on ion solvation and electrolyte solutions have made remarkable progress by the interplay of experiments and theories. Experimentally, X-ray and neutron diffraction methods and sophisticated EXAFS, IR, Raman, NMR and dielectric relaxation spectroscopies have been used successfully to obtain structural and/or dynamic information about ion-solvent and ion-ion interactions. Theoretically, microscopic or molecular approaches to the study of ion solvation and electrolyte solutions were made by Monte Carlo and molecular dynamics calculations/simulations, as well as by improved statistical mechanics treatments. Some topics that are essential to this book, are included in this chapter. For more details of recent progress, see Ref. [1]. 

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