Distributions energy

This expression gives only a rough estimate. It neglects the electronic energy loss, the form of the atomic interaction and replacement collisions. Therefore, in reality, the above formula will give a considerable overestimation of the number of displacements. It is possible to take some of the neglected quantities into account by a correction factor. 

One can calculate the complete profile of the displaced atoms and get in that way a spatial distribution of the deposited energy. Several attempts have been made - ). 

Damage and range In units of Rp Fig. 9. Computed range and damage profiles for different mass ratios (after ) 

There are cases where the range of the displaced atoms exceeds the range of the implanted ions and vice versa, depending on the ratio of the mass M, of the ion to the mass Mj of the displaced atom. Fig. 9 presents the range of the ions and the corresponding energy distribution for 

Looking at this presentation, one should keep in mind that the experimental energy distributions may deviate a good deal from the calculations. 

For a polarized electrode under steady-state current flow, the generalized reaction given by eq. (1.2) can be used to derive the Butler-Volmer equation, which involves energy barriers known as activation eneigies. Only the activation energy change is used for the forward (AG/) (reduction) and reverse (AGr) (oxidation) reactions. For example, the hydrogen reaction, 2e = H2 at 

In general, the electrochemical and chemical rates of reactions due to either anodic or cathodic overpotentials can be predicted using both Faraday and Arrhenius equations, respectively 

At equilibrium, Faraday s and Arrhenius rate equations become equal (i / = Ra) and consequently, the current density becomes 

the term 7 = zF fjAw may be defined as the electroehemical rate constant having unit of current density A/am ). For a reversible electrode at equilibrium, the current density in eq. (3.3) bk omes the exehange eurrent density that is, i = io- In addition. Table 3.1 gives typieal experimental values for io- 

On the other hand, if an electrode is polarized by an overpotential under steady-state conditions, then the rates of reactions are not equal Rp Ra) and consequently, the forward (cathodic) and reverse (anodic) current density components must be defined in terms of the free energy change A( deduced from Figiue 3.1. Hence, 

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ENERGY DISTRIBUTION OF SCATTERED ELECTRONS FROM A c(4x2) MONOLAYER OF C2H3 ON Rh(lll) AT 300K... 

MSS Molecule surface scattering [159-161] Translational and rotational energy distribution of a scattered molecular beam Quantum mechanics of scattering processes... 

We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Fig. XVn-24. Site energy distribution for nitrogen adsorbed on Silica SB. (From Ref. 160.) (Reprinted with permission from J. Phys. Chem. Copyright by the American Chemical Society.)...

Fig. XVII-25. Interaction energy distributions for N2 on BN (a) Langmuir b) Langmuir plus lateral interaction (c) van der Waals. (From Ref. 162.)...

C. Point versus Patch Site Energy Distributions... 

The preceding material has been couched in terms of site energy distributions—the implication being that an adsorbent may have chemically different kinds of sites. This is not necessarily the case—if micropores are present (see Section XVII-16) adsorption in such may show an increased Q because the adsorbate experiences interaction with surrounding walls of adsorbent. To a lesser extent this can also be true for a nonporous but very rough surface. 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

It would seem better to transform chemisorption isotherms into corresponding site energy distributions in the manner reviewed in Section XVII-14 than to make choices of analytical convenience regarding the f(Q) function. The second procedure tends to give equations whose fit to data is empirical and deductions from which can be spurious. 

We have seen various kinds of explanations of why may vary with 6. The subject may, in a sense, be bypassed and an energy distribution function obtained much as in Section XVII-14A. In doing this, Cerefolini and Re [149] used a rate law in which the amount desorbed is linear in the logarithm of time (the Elovich equation). 

Knowing the energy distributions of electrons, (k), and the spatial distribution of electrons, p(r), is important in obtaining the structural and electronic properties of condensed matter systems. 

Figure Al.7.12 shows the scattered electron kinetic energy distribution produced when a monoenergetic electron beam is incident on an A1 surface. Some of the electrons are elastically backscattered with essentially...

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.

Photoelectron spectroscopy provides a direct measure of the filled density of states of a solid. The kinetic energy distribution of the electrons that are emitted via the photoelectric effect when a sample is exposed to a monocluomatic ultraviolet (UV) or x-ray beam yields a photoelectron spectrum. Photoelectron spectroscopy not only provides the atomic composition, but also infonnation conceming the chemical enviromnent of the atoms in the near-surface region. Thus, it is probably the most popular and usefiil surface analysis teclmique. There are a number of fonus of photoelectron spectroscopy in conuuon use. 

This rate coefficient can be averaged in a fifth step over a translational energy distribution P (E ) appropriate for the bulk experiment. In principle, any distribution P (E ) as applicable in tire experiment can be introduced at this point. If this distribution is a thennal Maxwell-Boltzmann distribution one obtains a partially state-selected themial rate coefficient... 

Marcus R A 1977 Energy distributions in unimolecular reactions Ber. Bunsenges. Phys. Chem. 81 190-7... 

Pibel C D, Sirota E, Brenner J and Dai H L 1998 Nanosecond time-resolved FTIR emission spectroscopy monitoring the energy distribution of highly vibrationally excited molecules during collisional deactivation J. Chem. Phys. 108 1297-300... 

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