Electron escape

Local surface structure and coordination numbers of neighbouring atoms can be extracted from the analysis of extended X-ray absorption fine structures (EXAFS). The essential feature of the method22 is the excitation of a core-hole by monoenergetic photons modulation of the absorption cross-section with energy above the excitation threshold provides information on the distances between neighbouring atoms. A more surface-sensitive version (SEXAFS) monitors the photoemitted or Auger electrons, where the electron escape depth is small ( 1 nm) and discriminates in favour of surface atoms over those within the bulk solid. Model compounds, where bond distances and atomic environments are known, are required as standards. 

Fig. 5. Electron escape depth as a function of electron energy. The energies of several photon sources are shown.

There is a large body of known radiation-physical and radiation-chemical phenomena, the existence or explanation of which requires a track model. With the exception of the consideration of electron escape (ffee-ion yield), these phenomena... 

The fundamental theory of electron escape, owing to Onsager (1938), follows Smoluchowski s (1906) equation of Brownian motion in the presence of a field F. Using the Nemst-Einstein relation p = eD/kRT between the mobility and the diffusion coefficient, Onsager writes the diffusion equation as... 

If an external field is present, the procedure would be the same except that now in place of 0(i) and (n) one would use the corresponding probabilities of electron escape as given by the Onsager equation in the presence of an external field (see Sect. 9.5). 

It should be emphasized that the photoelectron signal is not generated entirely by the surface atoms. The precise definition of X (the escape depth ) is the depth from which a fraction /e of the electrons escape without losing energy through inelastic collisions. This follows from... 

For calculating atomic concentration ratios of the elements, photoionization cross-section by Scofield (4) and apparatus function by VuUi (5) were adopted. Electron escape depth (a) is determined by an experimental equation A =e0 7 (where E is kinetic energy of the electron) proposed by Hirokawa, et. al. (6). 

Charge neutralization in media of low viscosity. Secondary reactions including intertrack reactions. Electron escape time in low-viscosity media. Intratrack reactions completed. Secondary radical formation and reaction. 

In the preceding part of this section, we have concentrated on the electron escape probability, which is an important quantity in the geminate phase of recombination, and can be experimentally observed. However, modern experimental techniques also give us a possibility to observe the time-resolved kinetics of geminate recombination in some systems. Theoretically, the decay of the geminate ion pairs can be described by the pair survival probability, W t), defined by Eq. (4). One method of calculating W t) is to solve the Smoluchowski equation [Eq. (2)] for w r,t) and, then, to integrate the solution over the space variable. Another method [4] is to directly solve Eq. (7) under relevant conditions. 

Figure 1 Electron escape probability as a function of the applied electric field. The solid lines are obtained from Eq. (23) for different values of the initial electron cation distance ro- The broken lines are calculated for ro = 1 nm from the numerical solution of Eq. (16) with the sink term given by k r) = A exp[—a(r—

An important result of the theoretical studies of the multipair effects is that the recombination kinetics in a cluster of ions, in which the initial separation between neighboring cations is 1 nm, is faster than the corresponding decay kinetics of a single ion pair [18]. Furthermore, the escape probability is lower than the Onsager value [Eq. (15)], and decreases with increasing number of ion pairs in the cluster (a relative decrease of about 30% for two ion pairs, and about 50% for five ion pairs). The average electron escape probability in radiation tracks obviously depends on the distribution of ionization events in the tracks, which is determined by the type of radiations and their energy. 

---