Properties of X-Rays and Neutrons

The x-ray wavelength of around 1 A is of the same order of magnitude as most interatomic distances of interest in condensed matter, and this is why x-rays play such an important role in probing the structure, that is, the arrangement of atoms in matter. 

X-Rays, like light, exhibit a wave-particle duality. Certain properties of x-rays are better understood when a beam of x-rays is regarded as a stream of photons. Whereas a wave is characterized by wavelength X and frequency v, a photon is characterized by its energy E and momentum p, which are related to X and v by 

A neutron is an uncharged elementary particle, possessing a mass m equal to 1.675 x 10 24 g and spin 1/2. Its kinetic energy E and momentum p are 

Neutrons also exhibit wave-like behavior, with the wavelength k given by the de Broglie relation 

In Table 1.1 the most probable velocity v in the. Maxwell-Boltzmann distribution, given by Equation (1.7), the corresponding kinetic energy E = mv2/2 = kT, and wavelength k are listed for the three typical moderator temperatures 25, 330, and 2000 K. It is significant that the wavelengths of these neutrons are again of the 

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The very existence of the powder diffraction pattern, which is an experimentally measurable function of the crystal structure and other parameters of the specimen convoluted with various instrumental functions, has been made possible by the commensurability of properties of x-rays and neutrons with properties and structure of solids. As in any experiment, the quality of structural information, which may be obtained via different pathways (two possibilities are illustrated in Figure 2.62 as two series of required steps), is directly proportional to the quality of experimental data. The latter is usually achieved in a thoroughly planned and well executed experiment as will be detailed in Chapter 3. Similarly, each of the data processing steps, which were described in this chapter and are summarized in Figure 2.62, requires knowledge, experience and careful execution, and we will describe them in practical terms in Chapters 4 through 7. 

In this chapter diffraction and in particular X-ray and neutron diffraction will be described in general, with an emphasis on powder diffraction techniques. The specific properties of X-ray and neutron diffraction and a description of sources and instruments for powder diffraction studies will be presented. Furthermore the use of powder diffraction data, from the simple use for phase identification to structure solution and refinements with the Rietveld methods, will be described. Two examples showing the potential for powder... 

Table 5.1 Comparison of some of the properties of X-ray and neutron diffraction...

The spectroscopic techniques that have been most frequently used to investigate biomolecular dynamics are those that are commonly available in laboratories, such as nuclear magnetic resonance (NMR), fluorescence, and Mossbauer spectroscopy. In a later chapter the use of NMR, a powerful probe of local motions in macromolecules, is described. Here we examine scattering of X-ray and neutron radiation. Neutrons and X-rays share the property of being found in expensive sources not commonly available in the laboratory. Neutrons are produced by a nuclear reactor or spallation source. X-ray experiments are routinely performed using intense synclirotron radiation, although in favorable cases laboratory sources may also be used. 

Such defects can give rise to unusual physical and chemical properties as discussed more fully in the following chapters. Here it is worth pointing out that bond valences can be used to explore the local environments around defects which are difficult to observe using the standard techniques of X-ray and neutron diffraction. 

The stress state, where the stress can be both applied and residual, and the associated strain influence many different material properties, which is especially important in engineering and technological applications. The residual stress and strain can be advantageous or, on the contrary, can provoke a faster failure of machine parts or other manufactured materials. There are different methods to determine the strain and stress in materials mechanical, acoustical, optical and the diffraction of X-ray and neutrons. The diffraction method is applicable for crystalline materials and is based on the measurements of the elastic strain effects on the diffraction lines. There are two kinds of such effects, a peak shift and a peak broadening. The strain modifies the interplanar distances d. In a polycrystalline specimen a peak shift is produced if the average of the interplanar distance modifications on the crystallites in reflection is different from zero. If the dispersion of interplanar distance modifications is different from zero, then a peak broadening occurs. The effect of the strain on the peak breadth is described in Chapter 13. Here we deal only with the peak shift effect caused by the macroscopic, or Type I strain/stress. There is a substantial amount of literature on this subject. The comprehensive... 

The electron denstiy distribution p(r) of an atom or molecule is an observable property that can be measured by a combination of X-ray and neutron diffraction experiments [22]. Also, it is easy to calculate p(r) once the MOs and the wave function of a molecule have been determined. The distribution p(r) is invariant with regard to any unitary transformation of the MOs. It has been shown by Hohenberg and Kohn that the energy of a molecule in its (nondegenerate) ground state is a unique functional of p(r) [23]. In other words, the physical and chemical properties of a molecule can be related to p(r). Thus, p(r) represents the best starting point for an analysis of chemical bonding. 

The chemistry of hydrolysis and condensation of silicon alkoxides is now understood in considerable detail, as indicated in the chapter by Coltrain and Kelts (Eastman Kodak Co.). Extensive use of nuclear magnetic resonance has revealed the influence of factors such as pH on the kinetics of the competing reactions. With this information it is possible to rationalize the structures of the aggregates, as revealed by studies of small-angle scattering of X-rays and neutrons. This level of understanding opens the possibility for deliberate control of gel structure and properties. Nonsilicate systems have received less... 

X-ray and neutron imaging are complementary techniques for materials research. X-rays interact mainly with the electronic shell of atoms whereas neutrons as charge-neutral particles interact with the nuclei (Figure 18.1a,b). The different interaction mechanisms yield different beam attenuation properties. Figure 18.1c shows the values for the attenuation coefficients of X-rays and neutrons for different element numbers. In the case of X-rays, the attenuation increases with the number of electrons in the atom and, therefore, with the element number. In case of neutrons, no clear dependence on the amount of nuclei within the atomic core can be found. In contrast to X-rays, some light elements such as H and Li have a very... 

The equilibrium properties of a fluid are related to the correlation fimctions which can also be detemrined experimentally from x-ray and neutron scattering experiments. Exact solutions or approximations to these correlation fiinctions would complete the theory. Exact solutions, however, are usually confined to simple systems in one dimension. We discuss a few of the approximations currently used for 3D fluids. 

Compared to other biomolecular systems, lipid bilayer membranes and lyotropic lipid mesophases in general have been shown to respond most sensitively to hydrostatic pressure. The methods used in the high pressure studies have mainly included X-ray and neutron diffraction, fluorescence, IR and Raman spectroscopy, light transmission and volumetric measurements. Only a small amount of work has been performed using NMR techniques combined with high-pressure, a field which was pioneered by Jonas and co-workers " although the method is very powerful, non-invasive and allows the study of a series of structural and dynamic properties of the systems in detail and with atomic resolution. 

In addition to X-ray and neutron-diffraction structural characterization, the physical properties of iron oxides have been studied by a wide variety of techniques. Most common are conventional transport, optical, dielectric, calorimetric and magnetic measurements. In addition, NMR and Mossbauer are widely used. 

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