Scattering elastic and inelastic

Fig. 3. Geometric arrangement of a RHEED system showing zeroth- and first-order diffracted beams. Primary electron energy range 10—50 keV (X = 0.12—0.055 A). Incident beam angle 1—3. In most cases, all of the electrons which are scattered (elastic and inelastic) into the angular range of observation are allowed to reach the screen.

Finally, the two components of the total cross section can be still subdivided further. Thus, there are two types of scattering, elastic and inelastic ... 

Electrons interact with solid surfaces by elastic and inelastic scattering, and these interactions are employed in electron spectroscopy. For example, electrons that elastically scatter will diffract from a single-crystal lattice. The diffraction pattern can be used as a means of stnictural detenuination, as in FEED. Electrons scatter inelastically by inducing electronic and vibrational excitations in the surface region. These losses fonu the basis of electron energy loss spectroscopy (EELS). An incident electron can also knock out an iimer-shell, or core, electron from an atom in the solid that will, in turn, initiate an Auger process. Electrons can also be used to induce stimulated desorption, as described in section Al.7.5.6. 

Both conventions are identical only for direct collisions A (a) + B((3) A(a )+B(P ). This nonnalization is customary [5] for elastic and inelastic scattering processes. 

In tenns of the phase shifts h associated with potential scattering by U, tlie amplitudes for elastic and inelastic scattering are then... 

The volume of analysis, i.e., the diameter and depth of the analyzed region, is limited by a combination of the elastic and inelastic scattering.The maximum depth of the interaction volume is described by the Kanaya-Okayama electron range ... 

Thru 1967, emphasis was given to the use of neutrons as the bombarding source of radiation. Almost all possible neutron reactions were considered including moderation of fast neutrons by hydrogen in the expl, thermal capture reactions, elastic and inelastic scattering of neutrons and neutron activation reactions. These neutron reactions are listed as follows ... 

The terms elastic and inelastic scattering of electrons describe that which results in no loss of energy and some measureable loss of energy respectively. If the incident electron beam is coherent (i.e. the electrons are in phase) and of a fixed wavelength, then elastically scattered electrons remain coherent and inelastic electrons are usually incoherent. 

The dynamical elastic and inelastic scattering ofhigh-energy electrons by solids may be described by three fundamental equations [5]. The first equation determines the wave amplitude G ( r, r, E), or the Green function, at point r due to a point source of electrons at r in the averaged potential (V (r)) ... 

The third equation is the kinetic equation, which describes the evolution of the one-particle density matrix p(r, r, E) of the electron in the process of multiple elastic and inelastic scattering in a solid... 

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. 

Fig. 1. Schematic of the information from elastically and inelastically scattered electrons during the electron beam-sample interactions.

Figure 3 Elastic and inelastic scattering cross sections for scattering into an annular detector of inner collection angle 0i, for lOOkV electrons.

If the sample is thin enough, for example a specially prepared thin section, electrons may go straight through and be detected, as well as elastically and inelastically scattered electrons which are scattered in a forward direction. These form the basis of transmission electron microscopy (TEM). 

Figure 8.3 The vibrational elastic and inelastic differential cross sections for electron scattering off LiF at = 5.44 eV (Alhassid and Shao, 1992b, where the source of the data is given). Solid lines with an improved dipole interaction [which breaks the 0(4) symmetry]. Long dashed lines the calculations by Bijker and Amado (1986). The short dashed lines are the Bom approximation.

Z.L. Wang, Elastic and Inelastic Scattering in Electron Diffraction and Imaging, Plenum, New York (1995)... 

Fig. 4.25 Elastic and inelastic contribution to the incoherent scattering function for jump motion between two sites separated by 1.5 A...

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