Localization scattering

Landauer R (1957) Spatial variation of currents and fields due to localized scatterers in metallic conduction, IBM. J Res Dev 1 223-231... 

These conditions give rise to local scattering matrices a1 mapping amplitudes (pu onto 4>ij at vertex l having the form... 

The central idea of contrast variation is shown in Fig. 5. The dissolved object is depicted as an assembly of scattering units with different scattering power. The entire object occupies a volume in the system depicted by the shaded area in Fig. 5, left-hand side. The local scattering length density r) is rendered as a product of the shape function T (f) and the local scattering length density inside the object ... 

Fig. 2.2. Schematic diagram, not to scale, of the time-of-flight localized scattering system used by the UCL group for total scattering cross section measurements.

Although the overall count rate limitation with negligible deadtime correction losses is about 10 counts s , experimental expefience shows that it is rather easy to saturate the system, especially for highly localized scattering events (e.g. strong Bragg reflections). This shows the interest in the development of new detection systems. 

We illustrate the formation of coherence in the one-particle DOS again in fig. 9a for the band states. The calculation, like the ones before, is based on the lattice version of the NCA technique (LNCA), which has been outlined above. It leads to temperatiure-dependent spectra for both kinds of electrons, cf. also fig. 4b. The band states do not reflect the enhancement of the DOS, which is due to the local states, but they react simultaneously by the formation of a gap of the same size to the increase of local scattering at all lattice sites with decreasing temperature. Clearly the change in DOS near Ep reflects the characteristic temperature T, which can roughly be determined from the size of the gap. For comparison, a calculation for the IV regime of the periodic Anderson model is in addition shown in fig. 9b. The spectrum is less temperature dependent, due to the... 

In the case of amorphous materials, the reciprocal space does not contain localized scattered beams. It is fuU of intensity with some faint maxima (see Section 1.1.2.4 and Figure 1.3). The objective aperture is thus illuminated in any of its positions. It produces bright dots due to the aperture Airy disc combined with the beams scattered by statistical overlapping of atom pairs. The dots are thus not localized in the real space. 

If Z is the average scattering power and is the local scattering power, then the local fluctuation in the scattering power will be... 

It should be noted that the different seattering and microscopy methods discussed are eomplementary. Although TEM, SEM and STXM provide exquisite detail on the strueture of materials, the information gained is only local. Scattering methods, on the other hand, provide statistically average... 

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