Forward scattering,

A general relation associates the limiting value of the structure factor in the forward direction, S q — 0), with the fluctuation of the number of particles in a given volume V and, furthermore, based on thermodynamics, with the isothermal compressibility of the sample. 

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Egelhoff W F Jr 1990 X-ray photoelectron and Auger electron forward scattering a new tool for surface crystallography CRC Crit. Rev. Soiid State Mater. Sc/. 16 213... 

Figure Bl.24.1. Schematic diagram of the target chamber and detectors used in ion beam analysis. The backscattering detector is mounted close to the incident beam and the forward scattering detector is mounted so that, when the target is tilted, hydrogen recoils can be detected at angles of about 30° from the beam direction. The x-ray detector faces the sample and receives x-rays emitted from the sample.

The optical theorem relates the integral cross section to the unaginary part of the forward scattering amplitude by... 

Figure 1 Simplistic schematic illustration of the scattering mechanism upon which X-ray photoelectron diffraction (XPD) is based. An intensity increase is expected in the forward scattering direction, where the scattered and primary waves constructively interfere.

Rgure 3 Experimental and calculated results (a) for epitaxial Cu on Ni (001). The solid lines represent experimental data at the Cu coverage indicated and the dashed lines represent single-scattering cluster calculations assuming a plane wave final state for the Cu IMM Auger electron A schematic representation lb) of the Ni (010) plane with 1-5 monolayers of Cu on top. The arrows indicate directions in which forward scattering events should produce diffraction peaks in (a). 

FIGURE 13.45 Schematic of pardcie size anaiysia based on the diffraction of forward-scattered laser light. 

Momentum conservation implies that the wave vectors of the phonons, interacting with the electrons close to the Fermi surface, are either small (forward scattering) or close to 2kp=7i/a (backward scattering). In Eq. (3.10) forward scattering is neglected, as the electron interaction with the acoustic phonons is weak. Neglecting also the weak (/-dependence of the optical phonon frequency, the lattice energy reads ... 

In this test, haze of a specimen is defined as the percentage of transmitted light that, in passing through the specimen, deviates more than 2.5° from the incident beam by forward scattering. Basically it is defined as the ratio of transmitted to incident light. 

Obviously, experiments designed to measure cross-sections as a function of energy are needed. At present, tandem experiments are not capable of high precision at low energies because one must assume details of collision mechanics and because it is difficult to estimate collection efficiencies in forward scattering geometry (15). The extension of all known techniques to lower energy (64, 65) and the further development of pulse methods (58) offer the possibility for advances in this area. 

Figure 2. Probability density plots of the ethyl cation product, (a) from the unlabeled reaction, (b) CH2CH3 from the labeled reaction, and (c) CD3CH2 from the labeled reaction. The backward scattered ethyl cation is more probable in (b), while the forward scattered ethyl cation is more probable in (c). Reprinted from [39] with permission from Elsevier.

The use of nuclear techniques allows the determination of C, N, H, O, and heavier contaminants relative fractions with great accuracy, and of the elements depth profile with moderate resolution (typically 10 nm). Rutherford backscattering spectroscopy (RBS) of light ions (like alpha particles) is used for the determination of carbon and heavier elements. Hydrogen contents are measured by forward scattering of protons by incident alpha particles (ERDA) elastic recoil detection analysis [44,47]. 

Relaxation phenomena can also be studied by nuclear forward scattering of synchrotron radiation [16, 30]. This is discussed in Chap. 9. 

Leupold et al. were the first to report on coherent nuclear resonant scattering of synchrotron radiation from the 67.41 keV level of Ni. The time evolution of the forward scattering was recorded by employing the so-called nuclear lighthouse... 

Fig. 7.17 Time evolution of the nuclear forward scattering for metallic Ni foil. All measurements except for the upper curve were performed with external magnetic field B = 4 T. The solid lines show the fit. The arrows emphasize stretching of the dynamical beat structure by the applied magnetic field. The data at times below 14.6 ns had to be rescaled (from [34])...

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