Radiation, scattering electron

Another problem that can be addressed by theoretical calculations has to do with radical stability. Since radiation scatters electrons from different molecular orbitals at random, one might expect to see a great variety of damaged products. Usually this is not the case, as discussed in Section 18.2. Theoretical calculations are useful here in ranking the energies of the various oxidation and reduction products. It is often possible therefore to predict which products will be observed in a particular system. 

The Maxwell theory of X-ray scattering by stable systems, both solids and liquids, is described in many textbooks. A simple and compact presentation is given in Chapter 15 of Electrodynamics of Continuous Media [20]. The incident electric and magnetic X-ray helds are plane waves Ex(r, f) = Exo exp[i(q r — fixO] H(r, t) = H o exp[/(q r — fixO] with a spatially and temporally constant amplitude. The electric field Ex(r, t) induces a forced oscillation of the electrons in the body. They then act as elementary antennas emitting the scattered X-ray radiation. For many purposes, the electrons may be considered to be free. One then finds that the intensity /x(q) of the X-ray radiation scattered along the wavevector q is... 

For an assembly of several free point electrons, interference occurs between radiation scattered by different centers. If the incident and diffracted beams are defined by two unit vectors, s0 and s, respectively (Fig. 1.1), the phase difference of the radiation scattered by two points, separated by the vector r, equals 27tS-r, where S is the scattering vector, equal to (s — s0)/A. Vector S bisects s and s0, and has the length 2 sin 0/X. In the physics literature, an alternative notion is commonly used. The incident and diffracted beams are defined by the vectors k... 

Techniques of electron spectroscopies have emerged to become the principal means for investigating electronic structures of solids and surfaces (Rao, 1985 Mason et al, 1986). Most of these techniques involve the analysis of the kinetic energy of the ejected or scattered electrons. Some of the important techniques of electron spectroscopy used to study solids are photoelectron spectroscopy using X-rays (XPS) or UV radiation (UVPS), Auger electron spectroscopy (AES) and electron energy loss spectroscopy, (EELS). All these techniques are surface-sensitive and probe 25 A or less of solids. Cleanliness of the surfaces and ultra-high vacuum ( 10 — 10 " torr) are there-... 

The inelastically scattered electrons and the secondary electrons produce charge carriers in the phosphor, which then recombine with emission of luminescent radiation, either directly or after traveling in the lattice. 

For a two-component system (macromolecule, component 2, dissolved in pure solvent, e.g., water, component 1), application of the fluctuation theory of scattering (15, 16) shows that in a volume element of volume SV (of the order of s z at the lowest angles of measurement), the intensity of radiation scattered by the solution in excess of the solvent, I(s) = /(s)solution — I(s)solvent, is proportional to the fluctuations in the number of electrons, n ... 

The structure factor F hkl) is the Fourier transform of the unit cell contents sampled at reciprocal lattice points, hkl. The structure factor amplitude (magnitude) F is the ratio of the amplitude of the radiation scattered in a particular direction by the contents of one unit cell to that scattered by a single electron at the origin of the unit cell under the same conditions (see Chapter 3). The first report of the structure factor expression was given by Arnold Sommerfeld at a Solvay Conference. The structure factor F has both a magnitude F(hkl) and a phase rel-... 

To this point we have assumed that an atom, be it heavy or otherwise, scatters as a point source of scattering power fj having phase 0j. Although the detailed physical explanation is outside the scope of this book and involves quantum mechanical properties, it must be pointed out that this is not entirely true. An atom scatters X rays in a somewhat more complex fashion, in that its scattered radiation is composed of two components. The major component, which arises from normal Thompson scattering, and is by far the largest component, has phase 0 dependent on the atom s position as we have assumed. But there is also a minor component of the scattering that has phase 0 + jt/2. This is because the electrons of the atom also absorb a small amount of radiation due to electron resonance phenomena and re-emit it with a phase change. This second component is called the anomalous dispersion, and to be entirely correct, we should properly describe the radiation scattered by an atom as a complex number,... 

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