Scattering structures

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

Figure 9 Fit of an incoherent neutron scattering structure factor, S(Q, O)), computed for iipid H atom motion in the piane of the biiayer in a simuiation of a DPPC biiayer, by the sum of an eiastic iine, a naiTow Lorentzian with width T , and a broad Lorentzian with width T2, convoiuted with a Gaussian resoiution function with AE = 0.050 meV.

The coherent tunneling case is experimentally dealt with in spectroscopic studies. For example, the neutron-scattering structure factor determining the spectral line shape is... 

Lipfert, J., Ouellet, J., Norman, D. G., Doniach, S., and Lilley, D. M. (2008). The complete VS ribozyme in solution studied by small-angle X-ray scattering. Structure 16, 1357-1367. 

The high concentration method is used, here, to extract single-chain, interchain and total scattering structure facrtors. The scattering cross section for each sample is given by ... 

The quantity Q[S(Q) - 1] is referred to as the reduced structure function. The total scattering structure function is related to the coherent part of the total diffracted intensity by ... 

X-ray scattering structural studies of very small single crystals, phase transition in powders, local order in amorphous solids, glasses. . . ... 

As discussed in Section 3.3.2, there is an inverse relationship between scattering angle 0 and the ratio of the size of the scattering structure to the wavelength of radiation which is used. Most scattering equations may be expressed in terms of a reduced variable of the form ... 

Table 9.1 r -r are the radii of the different scattering structures observed ... 

Fig. 3 Neutron and X-ray scattering structure factors of [C4mim][PF6] obtained from CG simulation (IL-MSl) and experiment at 200 K. The inset shows the positions of the two major peaks of the X-ray scattering structure factors of [C4mim][PF6] for the two mapping schemes (IL-MSl and IL-MS2) at different temperatures. Neutron and X-ray scattering data are from [23]...

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