Anisotropy of scattering

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

Complex Anisotropy is studied in texture goniometers (p. 193) as a function of sample orientation. If the study is aiming at quantitative analysis of scattering data, the absorption correction may become an issue. Conversely, by choosing a special kind of scanning modus (e.g., symmetrical reflection SAXS SRSAXS), the absorption correction problem can be simplified. 

In a fundamental paper [265] Ruland develops an advanced method for the analysis of scattering patterns showing moderate anisotropy. The deduction is based on a 3D model and the concept of highly oriented lattices. The addition of distortion terms makes sure that the theory is applicable to distorted structures and their scattering. 

The first term on the right corresponds to Raleigh scattering. The second term suggests an energy-exchange interaction that depends on the anisotropy of the polarizability and involves frequencies shifted from that of the incident radiation by an amount which depends on twice the rotational or vibrational frequency of the molecules in the sample. 

Note The phenomenon is due primarily to the anisotropy of the polarizability of the scattering medium. 

Fanchon, E. and Hendrickson, W. A. (1990). Effect of the anisotropy of anomalous scattering on the MAD phasing method. Acta Crystallogr. A 46, 809-820. 

We have discussed intrinsically anisotropic particles—ones with anisotropy originating in their optical constants rather than their shape—in previous chapters. In Section 5.6 we gave the solution to the problem of scattering by an anisotropic sphere in the Rayleigh approximation. From the results of that section and Section 5.5 it follows that the average cross section (C) (scattering or absorption) of a collection of randomly oriented, sufficiently small, anisotropic spheres is... 

Consider a molecule prepared in the absolute ground state in the absence of the field and subjected to microwave field of frequency . If collided with a structureless atom in the absence of the field and at collision energies below the first excitation threshold, the molecule can undergo only elastic scattering. In the presence of the field, the ground state of the molecule becomes a field-dressed state X). And for every field-dressed state X), there is an infinite number of replica states 2 - A ), lower in energy. The states 2 - A ) and X) are coupled by the anisotropy of the atom-molecule interaction potential, so collisions can induce... 

The anisotropy of the diffusion process is most pronounced in the limit of infinite dilution in the absence of intermolecular collisions that scatter... 

Here, a. and a L are the polarizabilities of the diatom parallel and perpendicular to the internuclear separation, R12. The electrostatic theory accounts for the distortions of the local field by the proximity of a point dipole (the polarized collisional partner) and suggests that the anisotropy is given by ft Rn) 6intermolecular interactions). This is the so-called dipole-induced dipole (DID) model, which approximates the induced anisotropy of such diatoms often fairly well. It gives rise to pressure-induced depolarization of scattered light, and to depolarized, collision-induced Raman spectra in general. 

Several types of collision-induced light scattering spectra are known. We have already mentioned the depolarized translational spectra of rare gas pairs and bigger complexes which arise from the anisotropy of the diatom polarizability. Contrary to the infrared inactivity of like pairs, e.g., Ar-Ar like pairs are Raman active. Furthermore, polarized translational spectra... 

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