Elastic peak scattering

Figure Bl.25.12. Excitation mechanisms in electron energy loss spectroscopy for a simple adsorbate system Dipole scattering excites only the vibration perpendicular to the surface (v ) in which a dipole moment nonnal to the surface changes the electron wave is reflected by the surface into the specular direction. Impact scattering excites also the bending mode v- in which the atom moves parallel to the surface electrons are scattered over a wide range of angles. The EELS spectra show the higlily intense elastic peak and the relatively weak loss peaks. Off-specular loss peaks are in general one to two orders of magnitude weaker than specular loss peaks.

L of CO was adsorbed at a pressure of 1 x 10 mbar and T= 200 K. At zero energy loss one observes the highly intense elastic peak. The other peaks in the spectrum are loss peaks. At high energy, loss peaks due to dipole scattering are visible. In this case they are caused by CO vibration perpendicular to the surface. The... 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

Nuclear absorption of incident X-rays (from the synchrotron beam) occurs elastically, provided their energy, y, coincides precisely with the energy of the nuclear transition, Eq, of the Mossbauer isotope (elastic or zero-phonon peak at = E m Fig. 9.34). Nuclear absorption may also proceed inelasticaUy, by creation or annihilation of a phonon. This process causes inelastic sidebands in the energy spectrum around the central elastic peak (Fig. 9.34) and is termed nuclear inelastic scattering (NIS). 

A substantial number of electrons are elastically scattered, and this gives rise to a strong elastic peak in the spectrum. When an electron of low energy (2-5 eY) approaches a surface, it can be scattered inelastically by two basic mechanisms, and the data obtained are dependent upon the experimental geometry - specifically the angles of the incident and the (analysed) scattered beams with respect to the surface (0 and 02 in Figure 5.47). Within a certain distance of the surface the incident electron can interact with the dipole field associated a particular surface vibration, e.g. either the vibrations of the surface atoms of the substrate itself, or one or other... 

Besides the inelastic component, always a certain number of He atoms are elastically scattered in directions lying between the coherent diffraction peaks. We will refer to this scattering as diffuse elastic scattering. This diffuse intensity is attributed to scattering from defects and impurities. Accordingly, it provides information on the degree and nature of surface disorder. It can be used for example to study the growth of thin films or to deduce information on the size, nature and orientation of surface defects Very recently from the analysis of the diffuse elastic peak width, information on the diffusive motion of surface atoms has been obtained. ... 

The Rh(lll) surface was covered with carbon by decomposing 5 x 10 7 torr of either acetylene or ethylene at 1100 K for 10 minutes and subsequent flashing to 1200 K (230. Pre-adsorbed carbon had a very strong inhibiting effect on carbon monoxide chemisorption. This is the same effect it had on the methanation rate (36). The low inelastic scattering intensity indicated relatively small CO coverages while the broad elastic peak and... 

The dynamics of bulk polymers have been approached in two different ways. On one hand, models of localized conformational jumps have been proposed to interpret numerous NMR experiments (see e.g. Ref. or . These models, which are specific of a given polymer assume that a short chain sequence performs conforpia-tional jumps between a few number of sites, the rest of the chain being immobile. Such localized jumps would lead to a well separated elastic peak in neutron quasielastic scattering experiments, in contradiction with all the experimental data obtained from polymer meltsIndeed, these models can in some cases be invoked to describe secondary relaxations in glassy polymers, but they are not sufficient to account for the numerous liquid-like properties of polymer melts. 

For the quasi-elastic region ( 2 meV) that is of concern here, the vibrational motions affect only the elastic intensity through a Debye-Waller factor, exp(-Q (M )), where (u ) is the mean square hydrogen amplitude in the vibrational modes. The scattering law for rotations can be written as a sum of an elastic peak intensity and a quasi-elastic component ... 

Kg. 7. The time-of-ffight distributions of neutrons scattered at 90° from h hly ciystalliue polypropylene at the temperatures indicated. The elastic peaks occur at Channel 73. The frequencies of peaks 2—8 are given in Table 1. Peak 1 is due to the collective contributions of carbon-hydrogen vibrations. The assignment of peak 10 at 35 cm was uncertain... 

Fig. 9. The time-of-fiight spectra of neutrons scattered at 65° from molded poly-tetrafluoroethylene at the indicated temperatures. The rise at Channel 165 is the elastic peak. The arrows indicate the peak energies in cm r...

Fig. 10. The time-of-flight distributions of neutrons scattered from Nylon-6 at 65°. The abscissa corresponds to the number of 28 /4- ec, time-of-flight channels. A scale at the top of the figures shows the energy gain in mev while the arrows give the energies of the observed peaks in cm h The elastic peak occurs at Channel 165...

Scattered electron intensities have been calculated for all 27 normal modes of the propane molecule. The electronic ground state of the molecule was described by the restricted Hartree-Fock wave function within Sadlej s basis set23. Cross sections obtained from DMR calculations were converted to a theoretical band spectrum by assuming Lorentzian shape for all bands with a half-width taken from the width of the observed elastic peak. The bands were centered at the positions of observed vibrational frequencies. 

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