Electron Stopping Powers

Ema data can be quantitated to provide elemental concentrations, but several corrections are necessary to account for matrix effects adequately. One weU-known method for matrix correction is the 2af method (7,31). This approach is based on calculated corrections for major matrix-dependent effects which alter the intensity of x-rays observed at a particular energy after being emitted from the corresponding atoms. The 2af method corrects for differences between elements in electron stopping power and backscattering (the correction), self-absorption of x-rays by the matrix (the a correction), and the excitation of x-rays from one element by x-rays emitted from a different element, or in other words, secondary fluorescence (the f correction). 

P. Duncamb, S. j. B. Reed in K. F. J. Heinrich (ed.) The Calculation of Stopping Power and Backscattcr Effects in Electron Probe Microanalysis, NBS Special Publ. 298, Washington, 1968. 

Here Z is the charge of the projectile with velocity v. In order to calculate stopping powers for atomic and molecular targets with reliability, however, one must choose a one-electron basis set appropriate for calculation of the generalized oscillator strength distribution (GOSD). The development of reasonable criteria for the choice of a reliable basis for such calculations is the concern of this paper. 

Figure 1. Electronic and nuclear energy loss function of (a) Au implanted in Si02 and (b) He implanted in Si02. The fraction of the electronic or nuclear 5 stopping power with respect to the total (S tot = S + for Au (c) and He (d). (Reprinted from Ref [1], 2005, with permission from Italian Physical Society.)...

Fs is the stopping power factor. Electron penetration is a function not only of the incident electron energy (which is constant for a given analysis) but also on the stopping power of the sample, which depends somewhat on atomic number. Reed (1993) derives equations for the generated characteristic X-ray intensity, leading to expressions for Fs. 

The electronic stopping power of the 2 MeV Ne+ ions in the palladium acetate films is much larger than that of 2 MeV He ions. The most obvious difference between the effects of the two ions is in the appearance of the films at the high dose limit. A 0.90 nm thick palladium acetate film exposed to 2 MeV Ne+ ion irradiation until no further spectroscopic changes occur looks black, compared with the metallic silvery films produced in the He ion irradiation. However... 

Fermi (1940) pointed out that as /)—-1 the stopping power would power would approach °° were it not for the fact that polarization screening of one medium electron by another reduced the interaction slightly. This effect is important for the condensed phase and is therefore called the density correction it is denoted by adding -Z<5/2 to the stopping number. Fano s (1963) expression for 8 reduces at high velocities to... 

FIGURE 3.1 Stopping power of water for various charged particles over a wide span of energy 1 electron, 2 (positive) muon, 3 proton, 4 carbon nucleus, and 5 fission (light) fragment. See text for details. Reproduced from Mozumder (1969), by permission of John Wiley Sons, Inc. ... 

Thus, the average stopping power is proportional to the initial energy except for corrections due to atomic collisions (electronic excitation) near 108 eV. For a medium of nuclear charge Ze and mass number A, the radiation length is given by (Bethe and Ashkin, 1953)... 

In the region 104-109 eV, where the energy loss is via electronic excitation and ionization, Bethe s formula with corrections (Eq. 2.11) describes the stopping power quite accurately. In the interval 104-106 eV, the decrease of stopping power with energy is attributable to the v-2 term. It reaches a minimum of —0.02 eV/A at -1.5 MeV then it shows a relativistic rise before the restricted part rides to the Fermi plateau at -40 MeV. 

In the interval 25—104 eV, stopping power has been evaluated according to the procedure of Sect. 2.5.2. At lower energies, the computation is neither accurate nor certain. Extrapolation of electron range from 5 to 10 KeV using a power... 

At still lower energies, the loss mechanism is the interaction of the electron with the permanent dipoles of the water molecule. Frohlich and Platzman (1953) estimated a constant time rate of energy loss due to this effect at -1013 eV/s. The stopping power in eV/A is then approximately given by (1.7 x 10 3)E 1/2, where the energy E is in eV... 

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