Anisotropic Scattering

The formalism for X-ray diffraction is the same as that for neutron diffraction. However, because X-rays are scattered anisotropically by the electrons of the system, the form of the total radial distribution Gx(r) is a sum over the individual radial distribution functions convoluted by the X-ray form factor. It is therefore difficult to obtain detailed information regarding ion-water structure from a total G r), and recourse is usually made to models based on solid-state structures. Indeed, this procedure is at the heart of the comprehensive work of the Italian groups of Magini and Licheri 47). 

J. Mattsson, Modelling of Scattering by Surface Breaking Cracks in Anisotropic Materials, Tech. Report 1996 7, Div. Mech., Chalmers University of Technology (1996). 

In the case of anisotropic systems with a cylindrical synnnetry (such as rods or fibres), the scattered intensity can be expressed as (derivation to be made later in section Bl.g.dl ... 

This expression is very similar to (B 1.9.49). If the scattering system is anisotropic, equation (Bl.9.54) can then be expressed in cylindrical polar coordmates (see figure Bl.9.5 ... 

The least recognized fonns of the Porod approximation are for the anisotropic system. If we consider the cylindrical scattering expression of equation (B 1.9.61). there are two principal axes (z and r directions) to be discussed... 

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... 

The thermal strain measurements described above have the common feature of anisotropic behaviour in a supposed isotropic state (cubic structure). These observations go well beyond the short-range, static strain fields associated with the lattice impurities responsible for Huang scattering. This then raises the question of the temperature at which the lattice symmetry changes and the implications of this for the central mode scattering. 

The rotational phase shift 5, which cannot exceed a mean angle of a molecular rotation during collisional time (anc), is certainly small in the case of non-adiabatic collisions. This condition is exactly that needed for anisotropic scattering (or IR absorption) spectrum narrowing, just as vibrational dephasing must be weak for an isotropic spectrum to narrow. 

The lower boundary corresponds to strong collisions, and the upper one to weak collisions. This conclusion can be confirmed by experiment. According to [259], nitrogen dissolved in SF6 has a symmetrical spectrum of isotropic scattering, indicating that collapse of the spectrum has already occurred. At the same densities, the Q-branch of the anisotropic spectrum is still well separated from the side branches, and in [259] the lower bound for its half-width is estimated as 5 cm-1. So,... 

The Hubbard straight line corresponds to rotational diffusion, and quasistatic straight lines (6.65) to quasi-free rotation. One type of motion substitutes for the other in the vicinity of the minimum point of curve xe,2 (tj) and is accompanied by collapse of the anisotropic scattering spectrum. 

Temkin S. I., Burshtein A. I. On the shape of the Q-branch of Raman scattering spectra in dense media. Anisotropic scattering, Chem. Phys. Lett. 66, 62-4 (1979). 

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