Diffraction experiment

The structure of a fluid is characterized by the spatial and orientational correlations between atoms and molecules detemiiued through x-ray and neutron diffraction experiments. Examples are the atomic pair correlation fiinctions (g, g. . ) in liquid water. An important feature of these correlation functions is that... 

The correlation functions provide an alternate route to the equilibrium properties of classical fluids. In particular, the two-particle correlation fimction of a system with a pairwise additive potential detemrines all of its themiodynamic properties. It also detemrines the compressibility of systems witir even more complex tliree-body and higher-order interactions. The pair correlation fiinctions are easier to approximate than the PFs to which they are related they can also be obtained, in principle, from x-ray or neutron diffraction experiments. This provides a useful perspective of fluid stmcture, and enables Hamiltonian models and approximations for the equilibrium stmcture of fluids and solutions to be tested by direct comparison with the experimentally detennined correlation fiinctions. We discuss the basic relations for the correlation fiinctions in the canonical and grand canonical ensembles before considering applications to model systems. 

The other type of x-ray source is an electron syncluotron, which produces an extremely intense, highly polarized and, in the direction perpendicular to the plane of polarization, highly collimated beam. The energy spectrum is continuous up to a maximum that depends on the energy of the accelerated electrons, so that x-rays for diffraction experiments must either be reflected from a monochromator crystal or used in the Laue mode. Whereas diffraction instruments using vacuum tubes as the source are available in many institutions worldwide, there are syncluotron x-ray facilities only in a few major research institutions. There are syncluotron facilities in the United States, the United Kingdom, France, Genuany and Japan. 

In a diffraction experiment a quantity F(S) can be measured which follows from equation (B 1.17.8) and equation (B 1.17.9) in Fourier space as... 

Illuminating the sample at grazing angles. The penetration depth of photons depends on the cosine of the incidence angle and, therefore, can be reduced by this procedure. Although such an approach has limited use, it has been successfully employed in a few instances, such as for x-ray diffraction experiments. 

The transition from smectic A to smectic B phase is characterized by tire development of a sixfold modulation of density witliin tire smectic layers ( hexatic ordering), which can be seen from x-ray diffraction experiments where a sixfold symmetry of diffuse scattering appears. This sixfold symmetry reflects tire bond orientational order. An appropriate order parameter to describe tlie SmA-SmB phase transition is tlien [18,19 and 20]... 

Apart from the sheer complexity of the static stmctures of biomolecules, they are also rather labile. On the one hand this means that especial consideration must be given to the fact (for example in electron microscopy) that samples have to be dried, possibly stained, and then measured in high vacuum, which may introduce artifacts into the observed images [5]. On the other, apart from the vexing question of whether a protein in a crystal has the same stmcture as one freely diffusing in solution, the static stmcture resulting from an x-ray diffraction experiment gives few clues to the molecular motions on which operation of an enzyme depends [6]. 

The 3D MoRSE code is closely related to the molecular transform. The molecular transform is a generalized scattering function. It can be used to predict the intensity of the scattered radiation i for a known molecular structure in X-ray and electron diffraction experiments. The general molecular transform is given by Eq. (22), where i(s) is the intensity of the scattered radiation caused by a collection of N atoms located at points r. ... 

The short-range order in a material is important in determining optoelectronic properties. For instance, x-ray and electron diffraction experiments performed on amorphous siHcon (i -Si) and germanium (a-Ge) have revealed that the nearest neighbor environments are approximately the same as those found in their crystalline counterparts (6) photoemission experiments performed on i -Si show that the DOS in valence and conduction bands are virtually identical to the corresponding crystal with the exception that the singularities (associated with periodicity) present in the latter are smeared out in the former. 

Jin x-ray monochromator. A monochromator is a large single crystal (usually graphite) that is oriented so that a very iatense reflection is directed toward the sample. AH wavelengths are absorbed by the monochromator except a small range of wavelengths used for the diffraction experiment. Usually only the characteristic radiation is used if an x-ray tube is the x-ray source. 

The Wealth of Information from Single-Crystal Determinations. The amount of information that is determined from a crystal stmcture experiment is much greater and more precise than for any other analytical tool for stmctural chemistry or stmctural molecular biology. Indeed, almost all of the stmctural information that has been deterrnined for these two fields has been derived from x-ray single crystal diffraction experiments. 

Bragg-Brentano Powder Diffractometer. A powder diffraction experiment differs in several ways from a single-crystal diffraction experiment. The sample, instead of being a single crystal, usually consists of many small single crystals that have many different orientations. It may consist of one or more crystalline phases (components). The size of the crystaUites is usually about 1—50 p.m in diameter. The sample is usually prepared to have a fiat surface. If possible, the experimenter tries to produce a sample that has a random distribution of crystaUite orientations. 

Zeolites and Catalytic Cracking. The best-understood metal oxide catalysts are zeoHtes, ie, crystalline aluminosihcates (77—79). The zeoHtes are well understood because they have much more nearly uniform compositions and stmctures than amorphous metal oxides such as siUca and alumina. Here the usage of amorphous refers to results of x-ray diffraction experiments the crystaUites of a metal oxide such as y-Al202 that constitute the microparticles are usually so small that sharp x-ray diffraction patterns are not measured consequendy the soHds are said to be x-ray amorphous or simply amorphous. 

In diffraction experiments a narrow and parallel beam of x-rays is taken out from the x-ray source and directed onto the crystal to produce diffracted beams (Figure 18.5a). The primary beam must strike the crystal from many different directions to produce all possible diffraction spots and so the crystal is rotated in the beam during the experiment. Rotating the crystal is much easier than rotating the x-ray source, especially when it is a synchrotron. 

Figure 18.5 Schematic view of a diffraction experiment, (a) A narrow beam of x-rays (red) is taken out from the x-ray source through a collimating device. When the primary beam hits the crystal, most of it passes straight through, but some is diffracted by the crystal. These diffracted beams, which leave the crystal in many different directions, are recorded on a detector, either a piece of x-ray film or an area detector, (b) A diffraction pattern from a crystal of the enzyme RuBisCo using monochromatic radiation (compare with Figure 18.2b, the pattern using polychromatic radiation). The crystal was rotated one degree while this pattern was recorded.

Phase information can also be obtained by Multiwavelength Anomalous Diffraction experiments... 

X-ray data are recorded either on image plates or by electronic detectors The rules for diffraction are given by Bragg s law Phase determination is the major crystallographic problem Phase information can also be obtained by Multiwavelength Anomalous Diffraction experiments... 

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 ... 

In a sense, a superconductor is an insulator that has been doped (contains random defects in the metal oxide lattice). Some of the defects observed via neutron diffraction experiments include metal site substitutions or vacancies, and oxygen vacancies or interstituals (atomic locations between normal atom positions). Neutron diffraction experiments have been an indispensable tool for probing the presence of vacancies, substitutions, or interstituals because of the approximately equal scattering power of all atoms. 

One important structural feature on which to focus is whether the nitrogen atom lies in the same plane as the three carbon atoms. Electron diffraction experiments have found the ground state to be slightly non-planar. You can determine the planarity of the structures you compute by examining the sum of the three C-N-C angles (for a planar molecule, the sum will be 360°) and by looking at the values of the C2-N-C4-O and C3-N-C4 Hg dihedral angles (in a planar structure, both will be 0°). 

Bowron et al. [11] have performed neutron diffraction experiments on 1,3-dimethylimidazolium chloride ([MMIM]C1) in order to model the imidazolium room-temperature ionic liquids. The total structure factors, E(Q), for five 1,3-dimethylimidazolium chloride melts - fully probated, fully deuterated, a 1 1 fully deuterated/fully probated mixture, ring deuterated only, and side chain deuterated only - were measured. Figure 4.1-4 shows the probability distribution of chloride around a central imidazolium cation as determined by modeling of the neutron data. 

In the second section a classification of the different kinds of polymorphism in polymers is made on the basis of idealized structural models and upon consideration of limiting models of the order-disorder phenomena which may occur at the molecular level. The determination of structural models and degree of order can be made appropriately through diffraction experiments. Polymorphism in polymers is, here, discussed only with reference to cases and models, for which long-range positional order is preserved at least in one dimension. 

At one extreme, one has the structural models of perfect crystals, which have long-range positional order for all the atoms (apart thermal motion). A diffraction experiment on a set of such crystals oriented in one direction (corresponding, in most real cases of polymeric materials, to an oriented fiber) would result in a pattern of sharp reflections organized in layer lines. 

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