Length attenuation

Another useful quantity for the description of the purity of a liquid is the electron attenuation leng, atf If No electrons start at x = 0 their number is reduced to Ng/e after traversing the distance att. This quantity is equivalent to the schubweg in solid-state physics. 

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The total contribution to the Auger electron signal is then dependent upon the attenuation length (kM) in the matrix before being inelastically scattered, and upon the transmission efficiency of the electron spectrometer as well as the efficiency of the electron detector. Calculated intensities of Auger peaks rarely give an accuracy better than 50%, and it is more reliable to adopt an approach which utilises standards, preferably obtained in the same instrument. 

The attenuation lengths and the back-scattering terms may be calculated from appropriate equations. 

Attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR), 24 111-114 Attenuation, 77 132-133 Attenuation length (AL), 24 87-89 Attrition, catalyst deactivation mechanism, 5 256t... 

Effective atomic number rule, 76 60-61 Effective attenuation length (EAL), 24 88-89... 

Figure 8 shows the attenuation length of electrons in solids as a function of their kinetic energy. The few theoretical calculations available cire in good agreement with these empirical data Only unscattered electrons convey useful information, while scattered electrons contribute to a structureless background (secondary electrons). From Fig. 8, it is clear that photoelectron spectroscopy probes at most a few tens of Angstroms. 

Fig. 8. A universal curve (or band) of electron attenuation length vs. electron kinetic energy, as resulting from an inspection of many experimental results on heavy metals. The energy of different laboratory sources, representing the maximal kinetic energy of the electron, is drawn for comparison in the figure (from Ref. 5)...

A neutron will move through material along a straight line with a constant energy until it encounters a nucleus and induces a nuclear reaction. Thus, neutron attenuation follows an exponential law similar to that for photons. Written in terms of an energy-dependent attenuation length, p, we have... 

Mean free path values are often approximated by a calculating them from a general formula [24], but data which take material properties into account are available also [25]. That this is important is illustrated by the mean free path of Si 2p photoelectrons in SiC>2 (3.7 nm) and in pure silicon (3.2 nm, valid when using A1 Ka radiation) the 2-values differ considerably, although the kinetic energies of the electrons are the same. In a recent review, Jablonski and Powell discussed developments in the understanding of electron attenuation lengths [26]. 

In this formula A and Aj are the spin-dependent hot electron attenuation lengths, which have been measured by various experimental techniques for different ferromagnetic materials [135-145]. The SVT and MTT have also successfully been used to measure Af and for 3d transition metal alloys [146-148], In these experiments the collector current is measured as a function of the ferromagnetic base layer thickness. 

The results show that the attenuation length of minority electrons in NiFe and CoFe is only about 1 nm, while that of majority electrons is a factor 4 to 6 larger. Consequently, thin ferromagnetic films act as efficient spin filters for hot electron currents. For example, the calculated transmission polarization of a 4 nm thick ferromagnetic film with Ai = 1 nm and At = 5 nm amounts already 92%. 

It is not strictly correct to equate the inelastic mean free path with the attenuation length, as we do so essentially in Fig. 1. One would have to assume in the experiment that as many electrons are scattered elastically into as out of the direction of the analyser slits. Because of the net loss due to back scattering this can never be the case in practice. 

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)...

Due to the bonding selectivity of chemisorption, SAM of DNA can be prepared without significant amounts of impurities. Furthermore, molecular orientation within the layer is fairly well defined [19]. Owing to these characteristics, SAM films of DNA have been particularly useful in the determination of absolute yields and cross sections for specific damages. When extracting attenuation lengths (AL) or cross sections from electron-scattering experiments on thin molecular films, by far the most difficult parameter to determine and control, is the film thickness and its... 

Figure 19-10. Dependence of yield of LEE-induced 5 -oligonucleotide fragments on their length for electron energies of 8 ( A), 28 (O), and 68 eV ( ). The curves represent decaying exponential fits. The inset shows the dependence of the attenuation length (AL) on LEE energy. The error bars represent the uncertainty range of the fitting parameter in the exponential...

Table 19-1. Attenuation length and effective cross section for strand breaks (SB) in SAM of oligonu-cleotides chemisorbed on gold as a function of electron energy...

Incident electron energy (eV) Attenuation length (nm) Effective cross section for SB (x 10 17 cm2)1 ... 

The flux (r) of atoms with a velocity va into a plasma integrated over the whole attenuation length, which is assumed to be equivalent to the numbers of ionization events with an ionization rate (apy), is governed by the relation ... 

B. The NEMO Collaboration measured also the value of blue light attenuation length (L,. 1 = L/1 + A 1 j Lc = 35 5 m. Several authors usually quote the water effective scattering length, which is defined as /./, / < cos 1 >, where < cost > is the average cosine of the light scattering distribution in... 

Figure 7. Field attenuation length versus radio frequency for 2004 measurements at the South Pole.

The column-integrated He production at the surface at the present day due to reactions induced by cosmic-ray particles is 23 x 10 atoms He cm y based on 110 atoms He g y at the surface and a mean attenuation length of 160 g cm (Niedermann... 

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