Valence electron scattering

As discussed in chapter 3, the valence electrons scatter mainly in the low-order region. Consequently, refinement of high-order data, first proposed by Jeffrey and Cruickshank (1953), yields parameters less biased by bonding effects. The X-X deformation density is calculated with the high-order X-ray parameters, and is defined as... 

Fig. 4 The atomic form factor of a C atom (in ls 2s 2p electronic configuration). Core electron scattering is in blue. Valence electron scattering is in red and total scattering in black...

Figure Bl.6.12 Ionization-energy spectrum of carbonyl sulphide obtained by dipole (e, 2e) spectroscopy [18], The incident-electron energy was 3.5 keV, the scattered incident electron was detected in the forward direction and the ejected (ionized) electron detected in coincidence at 54.7° (angular anisotropies cancel at this magic angle ). The energy of the two outgoing electrons was scaimed keeping the net energy loss fixed at 40 eV so that the spectrum is essentially identical to the 40 eV photoabsorption spectrum. Peaks are identified with ionization of valence electrons from the indicated molecular orbitals.

Inelastic scattering processes are not used for structural studies in TEM and STEM. Instead, the signal from inelastic scattering is used to probe the electron-chemical environment by interpreting the specific excitation of core electrons or valence electrons. Therefore, inelastic excitation spectra are exploited for analytical EM. 

I is the measured intensity, J the Compton profile, M the multiple scattering contribution, K the energy dependent correction factor, B the background, C the normalization constant and Zvai the mean number of valence electrons. Figure 3 shows a valence Compton profile of Cu obtained by this procedure. 

It has been found by Will (2004) from X-ray scattering measurements that valence electrons concentrate along the lines connecting the boron atoms, confirming that the boron layer is a covalently bonded network. The titanium layers are metallic. However, the layers are not characteristic of either pure Ti, or pure B, so the bonding is quite complex. 

Figure 11. Electron-energy-loss spectrum of crystalline boron nitride, showing the boron K-edge (at 190 eV) and the nitrogen K-edge (at 400 eV). The background intensity, delineated by the dashed curve arises from inelastic scattering by valence electrons. The hatched areas represent the measured values required for the quantitative analysis of boron ( see text) (50).

A simple modification of the IAM model, referred to as the K-formalism, makes it possible to allow for charge transfer between atoms. By separating the scattering of the valence electrons from that of the inner shells, it becomes possible to adjust the population and radial dependence of the valence shell. In practice, two charge-density variables, P , the valence shell population parameter, and k, a parameter which allows expansion and contraction of the valence shell, are added to the conventional parameters of structure analysis (Coppens et al. 1979). For consistency, Pv and k must be introduced simultaneously, as a change in the number of electrons affects the electron-electron repulsions, and therefore the radial dependence of the electron distribution (Coulson 1961). 

In inorganic and organometallic solids, the average electron concentration tends to be high. This means that absorption and extinction effects can be severe, and that the use of hard radiation and very small crystals is frequently essential. Needless to say that the advent of synchrotron radiation has been most helpful in this respect. The weaker contribution of valence electrons compared with the scattering of first-row-atom-only solids implies that great care must be taken during data collection in order to obtain reliable information on the valence electron distribution. 

The suitability of light-atom crystals for charge density analysis can be understood in terms of the relative importance of core electron scattering. As the perturbation of the core electrons by the chemical environment is beyond the reach of practically all experimental studies, the frozen-core approximation is routinely used. It assumes the intensity of the core electron scattering to be invariable, while the valence scattering is affected by the chemical environment, as discussed in chapter... 

When an energetic electron scatters inelastically, an electron from the (filled) valence band can be promoted to the (empty) conduction band creating an electron/hole pair. On recombination, the excess energy is released as a photon, the wavelength of which is well defined by the band-gap transition. The technique is powerful in catalysis it is diagnostic of the electronic/chemical state and is sensitive to point defects. It can be used to probe the distribution of dopants in catalytic oxides. 

The incident electrons interact strongly with the valence electrons in the solids, resulting in a high probability of inelastic scattering. 

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