Scattering element-specific

Phonons are quasiparticles, which are quantized lattice vibrations of all atoms in a solid material. Oscillating properties of the individual atoms in nonequivalent positions in a compound, however, are not necessarily equivalent. The dynamics of certain atoms in a compound influence characteristics such as the vibration of the impurity or doped atoms in metals and the rare-earth atom oscillations in filled skutterudite antimonides. Therefore, the ability to measure the element-specific phonon density of states is an advantageous feature of the method based on nuclear resonant inelastic scattering. Element-specific studies on the atomic motions in filled skutterudites have been performed (Long et al. 2005 Wille et al. 2007 Tsutsui et al. 2008). 

Future trends will include studies of grain-dependent surface adsorption phenomena, such as gas-solid reactions and surface segregation. More frequent use of the element-specific CEELS version of REELM to complement SAM in probing the conduction-band density of states should occur. As commercially available SAM instruments improve their spot sizes, especially at low Eq with field emission sources, REELM will be possible at lateral resolutions approaching 10 nm without back scattered electron problems. 

As micro-analytical techniques (performing direct analysis on a <10 mg sample mass) have a particularly distinct demand for very homogeneous CRMs, it becomes necessary to provide element-specific homogeneity information in the CRM certificates. The distribution of elements in a material can be evaluated experimentally by repetitive analysis. The scattering of results from a method with known intrinsic precision is related to the mass of sample consumed for individual analysis. The... 

Here U is the mean velocity within the scattering volume and not the velocity of a specific scattering element. One finally obtains the following result ... 

A straightforward Fourier transform of the EXAFS signal does not yield the true radial distribution function. First, the phase shift causes each coordination shell to peak at the incorrect distance second, due to the element specific back-scattering amplitude, the intensity may not be correct. The appropriate corrections can be made, however, when phase shift and amplitude functions are derived from reference samples or from theoretical calculations. The phase- and amplitude-corrected Fourier transform becomes ... 

Megaelectron volt (MeV) ion beam techniques offer a number of non-destructive analysis methods that allow to measure depth profiles of elemental concentrations in material surfaces. Elements are identified by elastic scattering, by specific nuclear reaction products or by emission of characteristic X-rays. With nuclear microprobes raster images of the material composition at the surface can be obtained. Particle-induced gamma-ray emission (PIGE) is especially suited for fluorine detection down to the ppm concentration level. 

X-ray photoelectron diffraction is the coherent superposition of a directly photo-emitted electron wave with the elastically scattered waves from near-neighboring atoms. This gives element-specific structural information about the near surface atoms in a single crystal [8-10]. The short inelastic mean free path of the electron waves at the kinetic energies of interest (15 to 1000 eV) leads to surface sensitivity and determination of the atomic geometry of the emitting atom. The known energies of narrow XPS core-level peaks lead to element specificity. The resolution of surface peaks and chemical shifts may even sometimes lead to a chemical state-specific structure determination. 

Figure 2 Schematic for photoelectron diffraction. Photo-emitted electrons are energy-analyzed at different exit angles. Direct photo-emitted electron waves interfere with the scattered waves to give angular intensity variations. These angular variations contain element-specific information about the near-surface structure.

A straightforward Fourier transform of the EXAFS signal does not yield the true radial distribution function. First, the phase shift causes each coordination shell to peak at the incorrect distance. Second, due to the element specific back-scattering amplitude, the intensity may not be correct. Third, coordination numbers of distant shells will be too low mainly because of the term 1/r in the amplitude (10.10) and also because of the small inelastic mean free path of the photoelectron. The appropriate corrections can be made, however, when phase shift and amplitude functions are derived from reference samples or from theoretical calculations. Figure 11.17 illustrates the effect of phase and amplitude correction on the EXAFS of a Rh foil [38]. Note that unless the sample is that of a single element, N is a fractional coordination number, i.e. the product of the real coordination number and the concentration of the element involved. Also, the EXAFS information is an average over the entire sample. As a consequence, meaningful data on supported catalysts are only obtained when the particles have a monodisperse size distribution. 

Fig. 2 Electron-atom interactions. (A) Elastic electron-electron interaction dominates the scattering intensity at low and medium scattering angles (B) Rutherford scattering at the nucleus causes high-angle scattering and (C) electrons can excite atom-bonded electrons from the ground state to higher unoccupied states or to the vacuum level, element specific X-rays are produced when the excited electron returns to the ground state. (View this art in color at www.dekker.com.)...

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