Mean free path for inelastic scattering

Surface sensitivity in LEED is provided by the limited mean free path for inelastic scattering of slow electrons. This mean fi-ee path is the distance traveled by an electron in the solid before it collides inelastically, loses energy, and thus becomes... 

Fig. 1. Mean free path for inelastic scattering, A, for aluminium [after Refs. (6) and (7)]. Experimental points measured mean attenuation lengths taken from the compilation by Powell (5)...

Fig. I. Photoelectron mean free path for inelastic scattering in Si and Au in the energy range of interest for XANES spectra. The data were obtained from the measurement of electron escape depth in photoemission experiments...

We see that for EELS analysis, the resolution is degraded only linearly with foil thickness. Comparison with the values in Table 3.1 shows that if the collector aperture is about 10 mrad, and the energy losses are 200 eV or more, nanometer resolution can be maintained for foils up to about 100 nm thick. This thickness coincides approximately with the mean free path for inelastic scattering, so that spectra from thicker foils suffer degradation of energy resolution anyway. 

Here denotes the mean free path for inelastic scattering given as... 

Vji, is the drift velocity in the solution at field strength E, AWi is the average inelastic loss, and Aj denotes the mean free path for inelastic scattering (see Equation 10). From Equations 13 and 14 it follows that... 

Up to now we have discussed two extreme limits, the band picture on the one hand, and strong localization associated with interruptions in the metallic chains on the other. In fact, from work on thin metallic films and metallic glasses it is known that there is an intermediate region, that of weak localization. This occurs when the mean free path for elastic scattering (Lel) is only somewhat larger than, or comparable with, that for inelastic processes (Lin). In the first approximation there are corrections to the Boltzmann transport formula which depend on the ratio Lin/Lel in different ways for one-, two-, and three-dimensional materials. Weak localization... 

What Is needed to Interpret electron energy loss spectra of multilayer films Is an expression which can provide, for Incident electrons at a fixed energy, the energy distribution of electrons scattered out of the film In terms of elastic and Inelastic mean free paths (MFF) or scattering probabilities. With such an expression one hopes to obtain an estimate of these MFP and a suitable description of the scattering mechanisms responsible for the spectral features. 

But for inelastic collisions it is not true except in mid-band several scattering processes can take place in one mean free path. An example is given in Chapter 10, Section 1. 

The chemical nature and composition of catalyst surfaces are essential parameters for understanding catalytic reactivity. Electron spectroscopies, mainly Auger Electron Spectroscopy (AES), X-ray Photoelectron Spectroscopy (XPS), Secondary Ion Mass Spectroscopy (SIMS) and Ion Scattering Spectroscopy (ISS) allow such information to be obtained. AES and XPS are most likely to provide meaningful data if the surface region of the solid is homogeneous over a depth several times the inelastic mean free path of the emitted electrons. 

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