Multiple scattering effects

Angular information is notably absent from the list of structural parameters normally obtained from XAS. One approach to obtaining angular detail is to make use of multiple scattering effects (17). Unfortunately, this technique is only useful for outer shells (non-nearest neighbor atoms) where there are atoms intervening between the absorber and the scatterer. This technique suffers from complications if the shells of interest overlap in distance with other shells of atoms. 

The third explanation is the most likely one, although further measurements and calculations are necessary to establish this with reasonable certainty. In the context of the multiple scattering explanation a statement by Witt et al. (1976) is apposite Although multiple scattering effects within the mesosphere itself need not be considered, the additional source of light from the lower atmosphere must be fully taken into account to allow the proper interpretation of upper-atmospheric polarization measurements. ... 

It is at once obvious that Fourier transformation of equation (2.2) should yield information about all the j shells in direct space that contribute to the EXAFS. The Rjs so obtained are, however, shortened by the k-dependent part of /k). Since the intensity of the outgoing spherical wave decreases very rapidly with increasing R, distant atoms contribute very little to the fine structure. Multiple scattering effects are also relatively unimportant and these have indeed been ignored in the derivation of equation (2.2). EXAFS should contain no information about shadowed or eclipsed atoms, but there are exceptions to this. Other theoretical approaches also use similar effects to explain the EXAFS. 

This result properly accounts for single scattering effects. Equation 14 represents an optical approximation which underestimates the value of E0 because the increase of the electronic kinetic energy associated with multiple scattering effects is not taken into account. 

To obtain a rough estimate of the multiple scattering effects a model proposed by M. H. Cohen is useful (18). This model is based on the application of the Wigner-Seitz scheme to an electron in a helium crystal. Each helium atom is represented as a hard sphere characterized by a radius equal to the scattering length. The electron wave function will then be... 

Detailed knowledge of the orientation of an adsorbed molecule is difficult to obtain by conventional surface scattering techniques such as LEED. The reason is that the electron is such a strongly interacting probe that multiple scattering effects... 

Charge transfer occurs when particles collide with each other or with a solid wall. For monodispersed dilute suspensions of gas-solid flows, Cheng and Soo (1970) presented a simple model for the charge transfer in a single scattering collision between two elastic particles. They developed an electrostatic theory based on this mechanism, to illustrate the interrelationship between the charging current on a ball probe and the particle mass flux in a dilute gas-solid suspension. This electrostatic ball probe theory was modified to account for the multiple scattering effect in a dense particle suspension [Zhu and Soo, 1992]. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

The physical principles of XRD have to be complemented with those underlying radiological imaging in order to complete the description of XDI for extended objects. Attenuation effects are much more significant as a source of signal degradation in XDI than in XRD, which only deals with small samples, and multiple scatter effects have to be explicitly accounted for as described in this section. 

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