Electronic volume dependence

Hie number of Compton scatters occurring in a given volume depends on the number of electrons present and is relatively independent of incident 7-energy. For the lower atomic number elements (excluding hydrogen), the number of electrons present is directly proportional to atomic wt. Thus Compton scattering on a per unit volume basis is a function of density and is independent of chem compn. The density of soils is widely variable and the density of expls falls within the normal range of soil... 

The spatial resolution in quantitative analysis is defined by how large a particle must be to obtain the required analytical accuracy, and this depends upon the spatial distribution of X-ray production in the analysed region. The volume under the incident electron beam which emits characteristic X-rays for analysis is known as the interaction volume. The shape of the interaction volume depends on the energy of the incident electrons and the atomic number of the specimen, it is roughly spherical, as shown in Figure 5.7, with the lateral spread of the electron beam increasing with the depth of penetration. 

When the electron beam enters the sample, it penetrates a small volume, typically about one cubic micron (10-18m3 ). X-rays are emitted from most of this volume, but Auger signals arise from much smaller volumes, down to about 3 x 10 25m3. The Auger analytical volume depends on the beam diameter and on the escape depth of the Auger electrons. The mean free paths of the electrons depend on their energies and on the sample material, with values up to 25 nm under practical analytical conditions. 

For condensed phases of bulk metals, the binding energy can be divided into repulsions between nuclei (see above) and the interaction of the positively charged nuclei with an electron gas. Within this breakdown, the motion of the nuclei can be determined by pair-additive forces with the addition of volume-dependent terms arising from the pressure of the electron gas . While computer simulations based on these types of interactions have been carried out , volume-dependent interactions are difficult to define unambiguously for surfaces. 

An alternate approach, which has proven to be extremely useful for metals, has been developed by Daw, Baskes and Foiles - (and to a lesser extent, by Ercolessi, Tosatti and Parrinello ). Called the embedded atom method (EAM) (or the glue model by the second group), the interactions in this approach are developed by considering the contribution of each individual atom to the local electron density, and then empirically determining an energy functional for each atom which depends on the electron density. This circumvents the problem of defining a global volume-dependent electron density. 

Just as it is useful to have a local ionization energy, so would it be desirable, in the context of reactive behavior, to have a local polarizability, a(r). Reflecting the discussion earlier in this section, we have suggested that 7s(r) be viewed as an inverse measure of as(r) we focus upon the surface local ionization energy and surface local polarizability because the outermost electrons are expected to make the greatest contributions to a. The volume dependence that is so important on a macroscopic scale should not be a factor on the local level, which considers only infinitesimal volume elements dr. We have presented evidence in support of the concept expressed by equation 14 ... 

Simply from symmetry considerations, the electronic structure of any surface, where the atoms or ions are necessarily coordinatively unsaturated, should be different from that of the bulk. The magnitude and type of the differences between surface and bulk electronic structure depend on the particular oxide, of course this is addressed in Chaps. 2, 4 and 14 in this volume. However, a few general observations can be made. 

This view of superconductivity in fullerenes in which T, is dominated by a simple volume-dependent electronic state density suggests that models [17] requiring pairing to be mediated by intermolecular vibrational modes that... 

Both the isomer shift, 5q, and the second-order Doppler shift, 6sod, are pressure dependent through the volume dependence of the electronic charge density at the nucleus. The pressure dependence of the centre shift at constant temperature can be approximated by... 

R505 P. C. Riedi, Cz, Kapusta, Y. Kohori and G. J. Tomka, Volume Dependence of NMR of Ordered Correlated Electron Systems , Hyper-fine Interact., 2000,128, 167... 

Fig.7.5. The volume dependence of the potential parameters and the occupation numbers which enter the first-order pressure expressions (7.46-48) as obtained in calculations on chromium. For s and p electrons the V, t parameters corresponding to (7.47) are shown, while for d electrons we give the C, u parameters corresponding to the central expression (7.46). In the lowest panels pressures calculated by the first-order expressions (7.46-48) are shown and decomposed into SV or SC terms indicated by a, and bandwidth terms indicated by b...

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