Structure factor scattering

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... 

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]...

The spatial Fourier transform of the concentration correlation function is the light-scattering structure factor S q,c). The predicted form is then ... 

Measurement of tire light-scattering structure factor, S q), for a rodlike particle in solution is a convenient method for characterizing its structure. It is convenient to introduce the dimensionless variable x = qL. The functional form is given by Berne and Pecora as ... 

As discussed in the earlier section on Construction Methods, the technique of molecular mechanics has been used for investigating structural properties of glassy states of various polymers (70,96-100,131). In spite of the approximations mentioned above, ie, the absence of thermal motion of the atoms, these studies showed that the structural properties, such as X-ray scattering structure factors, radial distribution functions, etc, of the glasses can be very well represented by the simulated structures. 

C. Landron, A. K. Soper, T. Jenkins, G. N. Greaves, L. Heima, and J. P. Coutures, Measuring neutron scattering structure factor for liquid alumina and analysing the radial distribution function by empirical potential structure refinement, J. Non-Ciyst Solids 293, 453-457 (2001). 

In order to confirm whether or not the 3D-phase structure constructed with LSCM truly reflects a real structural entity, we calculated the scattering structure factor from the 3D image [14] and compared it with the structure factor obtained from a TLS experiment. The results are shown in Fig. 2 where the scaled structure factor S(q/qm) (proportional to F x) in Eq. (1)) obtained from LSCM (unfilled circles) is compared with that from... 

The number of scatterers per sphere is of the order of (q o)" The scattering structure factor is then... 

A very sensitive measure of the non-equilibrium structural developments which occur during a phase separation process is provided by the scattering structure factor. In classical spinodal processes one expects to observe a single scattering maximum. The peak position... 

Section 2.30.2 of this chapter characterizes the responses of structure factors obtained from the microscopy images and the scattering structure factors, whereas the rheo-optics in Section 2.30.3 characterizes the responses of the stmcture factors obtained from spectroscopy. 

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