Electron scattering factor

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

The potential is related to the charge density, Fourier transform of electron charge density is commonly known as the X-ray scattering factor. To relate electron scattering factor to the X-ray, which gives... 

After merging of the single zones, data sets of approx. 100-300 independent reflections can be obtained as described in chapter 2.5. In a first step a kinematical structure refinement should be performed using the program SHELXL [13]. The temperature factors for FAPPO were chosen as U = 0.06 for C, N and O as U = 0.10 for H atoms apart from H atoms situated at N with U = 0.12 A (Electron scattering factors [20]). To prevent the molecules from being distorted a refinement, where the whole molecule was kept rigid, was performed. This also improves the usually bad parameter/reflection ratio. In the case of modification I we obtained R-values of 31% (481 unique reflections with I > 2cr) for the 100 kV data and of 25% (385 unique reflections with I > 2a). The sparse 100 kV data of modification II was not analysed quantitatively. From 300 kV data we obtained an R-value of 23% (226 unique reflections with I > 2a). 

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). 

P. A. Doyle, P. S. Turner, Relativistic Hartree-Fock X-ray and Electron Scattering Factors, Acta Cryst, A24, 390-397,1968. 

If unknown, electron scattering factor /fs) may be derived from x-ray scattering factor fx(s) as/(s) = k[Z - f2is)y, where k is constant. ... 

The waves scattered coherently by each of the electrons all have the same wavelength. Therefore, they will interfere. Hence, the total scattered amplitude is the sum of the amplimdes scattered by each electron. The electron scattering factor, which is the amplimde scattered by an electron, was denoted earlier by f. For a given electron it depends on how far its orbital extends (see equation [1.15]). Therefore, the coherent intensity can be written as ... 

Here k = 27t/ f(k) is the usual electron scattering factor, y describes the decay of jjp Oj is the mean square amplitude of the relative displacements of the atoms in the /-th shell around Ay and r (k) is the phase shift of the photoelectron caused by the potential of the absorbing atom. This formula is in excellent agreement with experiments on crystalline metals (Cu, Fe) and semiconductors (Ge). 

When considering scattering by a group of electrons in an atom, it is useful to introduce the concept of the electron scattering factor, / , given by... 



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