Scattering diffraction experiments

On a microscopic scale, neutron spectroscopy has proved to be a very powerful tool for the determination of the positions (diffraction) and of the dynamics of hydrogen (inelastic and quasi-elastic scattering). Diffraction experiments on LaNi -H and related systems have been... 

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]... 

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. ... 

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. 

Unlike the wave function, the electron density can be experimentally determined via X-ray diffraction because X-rays are scattered by electrons. A diffraction experiment yields an angular pattern of scattered X-ray beam intensities from which structure factors can be obtained after careful data processing. The structure factors F(H), where H are indices denoting a particular scattering direction, are the Fourier transform of the unit cell electron density. Therefore we can obtain p(r) experimentally via ... 

Because of the inverse relationship between interatomic distances and the directions in which constructive interference between the scattered electrons occurs, the separation between LEED spots is large when interatomic distances are small and vice versa the LEED pattern has the same form as the so-called reciprocal lattice. This concept plays an important role in the interpretation of diffraction experiments as well as in understanding the electronic or vibrational band structure of solids. In two dimensions the construction of the reciprocal lattice is simple. If a surface lattice is characterized by two base vectors a and a2, the reciprocal lattice follows from the definition of the reciprocal lattice vectors a and a2 ... 

In contrast to XRD, the background is rather high in electron diffraction experiments. The size of the background can partially be attributed to the poorer spectral resolution. Presence of electrons scattered on the apertures can not be completely neglected either. 

The theoretical basis of isomorphous replacement can be found in Blundell and Johnson (1976), Drenth (1999), and was recently summarized by Taylor (2003). Here, I will only give a brief overview. As indicated above, an X-ray diffraction experiment only gives us intensities of waves scattered from planes (hkl) in the crystal, but the phase shift associated with each hkl is lost during data measurement. 

Diffuse scattering, which nearly always occurs during a diffraction experiment however, represents a potentially rich source of dynamic information supplementary to that obtainable from the Bragg reflections. Many protein crystals exhibit diffuse... 

Whereas the values of h, k, l in theory should span from — oo to + oo, they are limited in practice to those finite values which are accessible to the diffraction experiment for a given radiation. The structure factor Fhkl is the resultant of N waves scattered in the direction of the reflection hkl by the N atoms in the unit cell, as expressed by equations 2 or 3 ... 

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