Inelasticity

Studies of inelastic scattering are of considerable interest in heterogeneous catalysis. The degree to which molecules are scattered specularly gives information about their residence time on the surface. Often new chemical species appear, whose trajectory from the surface correlates to some degree with that of the incident beam of molecules. The study of such reactive scattering gives mechanistic information about surface reactions. 

ISS Ion scattering spectroscopy [153, 154] Inelastic backscattering of ions (-1 keV ion beam) Surface composition... 

SANS Small-angle neutron scattering [175, 176] Thermal or cold neutrons are scattered elastically or inelastically Incident-Beam Spectroscopy Surface vibrational states, pore size distribution suspension structure... 

T. Wolfram, ed.. Inelastic Electron Turmeling Spectroscopy, Springer-Verlag, New York, 1978. 

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. 

Figure Al.7.12. Secondary electron kinetic energy distribution, obtained by measuring the scadered electrons produced by bombardment of Al(lOO) with a 170 eV electron beam. The spectrum shows the elastic peak, loss features due to the excitation of plasmons, a signal due to the emission of Al LMM Auger electrons and the inelastic tail. The exact position of the cutoff at 0 eV depends on die surface work fimction.

Seah M P and Dench W A 1979 Quantitative electron spectroscopy of surfaces a standard data base for electron inelastic mean free paths in solids Surf, interface Anai. 1 2... 

Powell C J 1994 Inelastic interactions of electrons with surfaces applications to Auger-electron spectroscopy and x-ray photoelectron spectroscopy Surf. Sc/. 299-300 34... 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

In the next section we discuss linear hydrodynamics and its role in understanding the inelastic light scattering experiments from liquids, by calculating the density-density correlation fiinction,. Spp. 

Out of the five hydrodynamic modes, the polarized inelastic light scattering experiment can probe only the tliree modes represented by equation (A3.3.18), equation (A3.3.19) and equation (A3.3.20). The other two modes, which are in equation (A3.3.17), decouple from the density fluctuations diese are due to transverse... 

Figure A3.9.3. Time-of-flight spectra for Ar scattered from Pt(l 11) at a surface temperature of 100 K [10], Points in the upper plot are actual experimental data. Curve tinough points is a fit to a model in which the bimodal distribution is composed of a sharp, fast moving (lienee short flight time), direct-inelastic (DI) component and a broad, slower moving, trapping-desorption (TD) component. These components are shown...

The site specificity of reaction can also be a state-dependent site specificity, that is, molecules incident in different quantum states react more readily at different sites. This has recently been demonstrated by Kroes and co-workers for the Fl2/Cu(100) system [66]. Additionally, we can find reactivity dominated by certain sites, while inelastic collisions leading to changes in the rotational or vibrational states of the scattering molecules occur primarily at other sites. This spatial separation of the active site according to the change of state occurring (dissociation, vibrational excitation etc) is a very surface specific phenomenon. 

Lykke K R and Kay B D 1990 State-to-state inelastic and reactive molecular beam scattering from surfaces Laser Photoionization and Desorption Surface Analysis Techniquesvo 1208, ed N S Nogar (Bellingham, WA SPIE) p 1218... 

To generalize what we have just done to reactive and inelastic scattering, one needs to calculate numerically integrated trajectories for motions in many degrees of freedom. This is most convenient to develop in space-fixed Cartesian coordinates. In this case, the classical equations of motion (Hamilton s equations) are given... 

Manolopoulos D E 1986 An improved log derivative method for inelastic scattering J. Chem. Phys. 85 6425-9... 

Marcus R A 1970 Extension of the WKB method to wave functions and transition probability amplitudes (S-matrix) for inelastic or reactive collisions Chem. Phys. Lett. 7 525-32... 

The fimdamental kinetic master equations for collisional energy redistribution follow the rules of the kinetic equations for all elementary reactions. Indeed an energy transfer process by inelastic collision, equation (A3.13.5). can be considered as a somewhat special reaction . The kinetic differential equations for these processes have been discussed in the general context of chapter A3.4 on gas kmetics. We discuss here some special aspects related to collisional energy transfer in reactive systems. The general master equation for relaxation and reaction is of the type [H, 12 and 13, 15, 25, 40, 4T ] ... 

Bodo E, Gianturco F A and Paesani F 2000 Testing intermolecular potentials with scattering experiments He-CO rotationally inelastic collisions Z. Phys. Chem., A/F214 1013-34... 

Steinfeld J I, Ruttenberg P, Millot G, Fanjoux G and Lavorel B 1991 Scaling laws for inelastic collision processes in diatomic molecules J. Phys. Chem. 95 9638—47... 

Quack M and Troe J 1975 Complex formation in reactive and inelastic scattering statistical adiabatic channel model of unimolecular processes III Ber. Bunsenges. Phys. Chem. 79 170-83... 

Vibrational spectroscopy provides detailed infonnation on both structure and dynamics of molecular species. Infrared (IR) and Raman spectroscopy are the most connnonly used methods, and will be covered in detail in this chapter. There exist other methods to obtain vibrational spectra, but those are somewhat more specialized and used less often. They are discussed in other chapters, and include inelastic neutron scattering (INS), helium atom scattering, electron energy loss spectroscopy (EELS), photoelectron spectroscopy, among others. 

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