Anisotropic systems, scattering from

Much less is known about the AIP (and IIP) for all other anisotropic systems. In order to extract information from measurements of the orientation dependent part of the total collision cross section under these unfavourable circumstances one proceeds as follows for the IIP one uses an empirical two parameter potential, the Lennard-JOnes 12-6 potential, with the parameters determined from independent scattering experiments. These potentials are implemented by an angle dependent part so that one has, for instance for the case of atom-non-polar diatom collisions (3) with... 

Neutron scattering investigations have been extended from isotropic polymers to oriented systems. Sadler and Odell measured the scattering from two samples of polyethylene, one of which had been extruded and the other pressure-crystallized onto previously extruded fibres. The pressure-crystallized sample was isotropic unlike the extruded sample, which was found to be highly anisotropic. The authors derived a lower limit for the length of the extruded polymer molecule of 3 x 10 A from the width of the meridional streak, although no data analysis was given. 

Equation (8.59) defines the ID interference function of a layer stack material. G (s) is one-dimensional, because p has been chosen in such a way that it extinguishes the decay of the Porod law. Its application is restricted to a layer system, because misorientation has been extinguished by Lorentz correction. If the intensity were isotropic but the scattering entities were no layer stacks, one would first project the isotropic intensity on a line and then proceed with a Porod analysis based on p = 2. For the computation of multidimensional anisotropic interference functions one would choose p = 2 in any case, and misorientation would be kept in the state as it is found. If one did not intend to keep the state of misorientation, one would first desmear the anisotropic scattering data from the orientation distribution of the scattering entities (Sect. 9.7). 

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). 

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