Quasi-elastic incoherent structure factors

The elastic (f = 0) and quasi-elastic incoherent structure factors for the isotropic rotation of methane are shown in Fig. 3. It appears from this figure that only the first three terms of the summation in expression 23 have to be considered in the Q range, which is usually covered by QENS instruments. The self-diffusivity will be obtained by first fitting the QENS spectra with expression 23 and then from the broadening of As with Q. 

This elastic scattering term is known as the elastic incoherent structure factor. It decreases from unity at (2 = 0 to 0 at large Q. As the area of S" (Q, (o) in the 00 direction is unity, there is an additional quasi-elastic component that increases from 0 at (2 = 0 to unity at large Q. The form of the quasi-elastic component depends on the nature of the localised diffusion. In the simplest case, where the jumping is between two trapping sites, the quasi-elastic term is a Lorentzian with a (2-independent width which is just 1/t where x is the mean residence time on either site. Two specific models will be noted here (a) random jumping round a ring of sites, the Barnes model [38] and (b)... 

The figure shows that the proportion of elastic scattering decreases as Q increases from zero. In fact the ratio of elastic to total (elastic plus quasi-elastic) scattering intensity provides a very useful quantity which is known as the elastic incoherent structure factor (EISF). It is often experimentally measurable and can be calculated easily from a theoretical model of the molecular motion... 

Fig.3 Elastic ( = 0) and quasi-elastic ( = 1,2,3) incoherent structure factors for the rotational diffusion of methane (R = 1.1 A)...

The prerequisite for an experimental test of a molecular model by quasi-elastic neutron scattering is the calculation of the dynamic structure factors resulting from it. As outlined in Section 2 two different correlation functions may be determined by means of neutron scattering. In the case of coherent scattering, all partial waves emanating from different scattering centers are capable of interference the Fourier transform of the pair-correlation function is measured Eq. (4a). In contrast, incoherent scattering, where the interferences from partial waves of different scatterers are destructive, measures the self-correlation function [Eq. (4b)]. 

Quasi-elastic Neutron Scattering. Coherent and incoherent inelastic neutron scattering are unique experimental techniques to characterize molecular motions on a time scale between 10 and 10 s. The continued development of high resolution inelastic scattering techniques in the past two decades (157-159) enables measurement of the dynamic structure factor S(Q, co) and the... 

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