Inelastic scattering factor

In summary, the movement of a high-energy electron in a solid may be described by a set of three Equations (1), (4) and (6). From these equations we may conclude that for high-energy electron diffraction the problem of multiple elastic and inelastic scattering by a solid is entirely determined by two functions, i.e. (1) the Coulomb interaction potential averaged over the motion of the crystal particles (V(r)> and (2) the mixed dynamic form factor S(r, r, E) of inelastic excitations of the solid. 

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

A reasonable approximation for the pair correlation function of the j8-process may be obtained in the following way. We assume that the inelastic scattering is related to imcorrelated jumps of the different atoms. Then all interferences for the inelastic process are destructive and the inelastic form factor should be identical to that of the self-correlation function, given by Eq. 4.24. On... 

The intensities of the infrared absorptions and of the inelastic scattered light (Raman) are determined by such electrical factors as dipole moments and polarizabilities. At the time of the pioneering studies on the infrared spectra of carbohydrates by the Birmingham school,7"11 calculations of the vibrational frequencies had been performed only for simple molecules of fewer than ten atoms.27,34,35 However, many tables of group frequencies, based on empirical or semi-empirical correlations between spectra and molecular structure, are available.32,34"37... 

This intensity now depends on two factors the concentration CN of the nitrogen in the compound and the attenuation S by inelastic scattering ... 



Figure 4.37 Spectrum of electrons ejected from helium after photoionization with mono-chromatized Al Ka radiation. The main Is photoline and (magnified by a factor of 20) discrete (n = 2, 3,4) and continuous satellites (above the threshold indicated at 79 eV) are shown as well as structures resulting from the inelastic scattering of Is photoelectrons in the source volume. Reprinted from J. Electron Spectrosc. Relat. Phenom. 47, Svensson et al., 327 (1988) with kind permission from Elsevier Science - NL, Sara Burgerhartstraat 25, 1005 KV Amsterdam, The Netherlands.

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