In X-rays and neutrons

A.AUTHIER, in X-ray and neutron dynamical diffraction theory and applications, eds. A.AUTHIER, S.LAGOMARSINO B.K.TANNER (Plenum Press, New York, 1997),p. 1. 

The five years since last considering specifically recent developments in X-ray and neutron diffraction methods for zeolites [1] have witnessed substantial progress. Some techniques, such as high resolution powder X-ray diffraction using synchrotron X-rays, have blossomed from earliest demonstrations of feasibility to widespread and productive application. Others, such as neutron powder diffraction, have shown steady progress. For still others, notably microcrystal diffraction, a variety of circumstances have contributed to extended gestation periods. Additionally, opportunities scarcely considered earlier (such as single crystal Laue diffraction, and certain developments in computer simulations that complement diffraction work) now command broad attention and warrant the commitment of substantial further investment. 

In powder diffraction, x-ray photons or neutrons (in x-ray and neutron diffraction experiments, respectively) are registered by the detector as random events. The measured intensity is directly proportional to the number of counts and therefore, the accuracy of intensity measurements is governed by statistics. Even though below we will refer to x-ray diffraction and photons, all conclusions remain identical when neutron diffraction and neutron count is considered. 

The difficulty in applying Eq. (3.33) lies in finding an appropriate expression for i//(z). An important simplification which has been widely applied in X-ray and neutron reflectivity is obtained if i//(z) is replaced with the free space wavefunction exp(iko2 ). This is known as the Born approximation and provides... 

The pair distribution function leads to the pair correlation function, which illustrates how the local order found near a given molecule is lost as distance from the molecule increases. This quantity is of fundamental theoretical interest and may be determined in X-ray and neutron scattering experiments, as discussed below. The definition of the pair correlation function g r j) is... 

For practical applications in X-ray and neutron-diffraction studies under pressure (and in volumetric or, more, recently in extended X-ray-absorption fine-structure spectroscopy (EXAFS) studies), a single (p-v )-isotherm at ambient temperature is insufficient, so low- and high-temperature isotherms are also required. Thus, the complete (thermal) equation of state (EOS), P - or F = V p,T), must be known for at least one solid to establish... 

The thickness of sample cell holders is optimally given by the reciprocal of the absorption coefficient. While the scattered intensity increases linearly with thickness, the sample absorption, however, increases exponentially. The scattered intensity reaches its maximum value when the incident beam is weakened to /e = 0.37, and this means that 1 mm thick samples are usual in X-ray and neutron work in H2O buffers. For neutron work in H20 buffers, 2 mm thick samples are usual, even though the optimal thickness is now greater than 10 mm. Samples that are too thick may lead to curve artefacts from multiple scattering events. Allowance for... 

S. Neov, I. Gerasimova, P. Mikula In Neutron Diffraction Investigation of the Short-Range Atomic Order in Tellurite Glasses, Proceedings of an International Conference on Advanced Methods in X-Ray and Neutron Structure Analysis of Materials, Czechoslovakia (1987). 

Scattering Techniques. The thickness of adsorbed layers can be determined using light. X-ray, and neutron scattering techniques (3). Quasi-elastic light scattering measurements on dispersion of particles measure the diffusion coefficients of particles in the dispersion. The size of these particles is related to the diffusion coefficient by the Stokes-Einstein equation. This measurement is performed on the dispersion with and without the adsorbed polymer. The difference in the radii in the two measurements is the thickness of the adsorbed layer. In these measurements it should be ensured that the particles in the dispersion are monodisperse and that there is no flocculation. In X-ray and neutron... 

The recoil-free fraction in Mossbauer spectroscopy is equivalent to the fraction of X-ray scattering processes without lattice excitation this fraction of elastic processes in X-ray and neutron diffraction is described by the Debye-Waller factor ... 

Liquid water also has tetrahedral symmetry because the melting process is not disruptive enough to disorder the water molecules fully. This is known from the radial distribution functions for liquid water that are observed in x-ray and neutron-diffraction experiments. Figure 29.6 shows the radial distribution functions of two liquids, water, and argon. 

Leszczynski, M., in X-Ray and Neutron Structure Analysis in Materials Science, Hasek, J., Ed., Plenum Press, New York, 1989, 253. 

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