Neutron Scattering Principles

In general, scattering of thermal neutrons yields information on the sample by measurement and analysis of the double differential cross section  

The momentum transfer hQ, respectively the wave vector, is given by Q= k -kf where k and kf are the wave vectors of the incoming and outgoing (scattered) neutrons. They relate to the neutron wavelength k j=2Tt/Aij. The neutron momenta a.rep ij=m Vi f=fikif. Therefore  

The energy transfer AE and co can be determined by measurement of the neutron velocities Vi and Vf. Note that for all problems discussed in this article i f and therefore  

The unique features of neutrons that render them into the powerful tool for the investigation of soft matter are  

Typical wavelengths of cold and thermal neutrons that match molecular and atomic distances 

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M Bee. Quasielastic Neutron Scattering Principles and Applications m Solid State Chemistry, Biology and Materials Science. Philadelphia Adam Hilger, 1988. 

In this review we will present the outcome of NSE studies on polymer systems covering results beyond those reported in an earlier review in Advances in Polymer Science [5] eight years ago. Table 1.1 shows the chemical structure and information on the chain dimensions of the systems considered here. In Chap. 2 we will commence with a brief description of neutron scattering principles and a discussion of the two different ways neutron spin echo may be implemented - the traditional NSE approach with precession coils and the neu-... 

Quasi-elastic neutron scattering principles can be found in reference 29. The figures 4 and 5 present for q=l A the dynamic structure factor S(q,co) and the intermediate scattering function I(q,t) of BPTI when increasing pressures at three different values up to 6000 bar and when releasing pressure at 1 bar. 

Bee, M. (1988) Quasi-elastic neutron scattering, principles and applications in solid state chemistry, biology and materials science (Adam Hilger, Bristol, Philadelphia 0... 

H. D. Middendorf, Dynamics of complex fluids by neutron scattering Principles, experimental advances, and recent results... 

The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

These disadvantages are overcome by the so-called dance-floor principle which is supposed to become the major beamline construction principle of the future. Figure 4.11 shows a dance floor during the construction of the beamline hall at the ANSTO neutron-scattering facility at Lucas Heights near Sydney, Australia. The dance floor is featuring an extremely plane and hard floor surface from granite. Optical components, detectors and sample chambers are mounted on supports with a flat lower surface. While compressed air is blown into the gap between the dance floor and the area of support, components are easily moved and adjusted in the optical beam path. 

Even though TEM and SEM played major roles in the study of IPN morphological features, there are various shortcomings, such as staining artifacts, difficulties in sample preparation for very rubbery materials, and the two-dimensional viewing limit for the former. Recently, various scattering techniques have been applied to measure the phase dimensions of IPN s via statistical treatment. The principles of neutron scattering theory as applied to the phase separated materials have been described in a number of papers and review articles [33-36]. 

Table 6.3 provides a summary of the different microscopic techniques that have been applied to hydrate studies and the type of information that can be obtained from these tools. The following discussion provides a brief overview of the application of diffraction and spectroscopy to study hydrate structure and dynamics, and formation/decomposition kinetics. For information on the principles and theory of these techniques, the reader is referred to the following texts on x-ray diffraction (Hammond, 2001), neutron scattering (Higgins and Benoit, 1996), NMR spectroscopy (Abragam, 1961 Schmidt-Rohr and Spiess, 1994), and Raman spectroscopy (Lewis and Edwards, 2001). 

Fig. 8. Difference in the inelastic neutron scattering data between LaFe4Sb 2 and CeFe4Sb 2 vs. energy loss (Keppens et al., 1998). CeFe4Sbi2 was used as a reference compound since the neutron scattering cross section of Ce is much smaller than that of La. The difference spectra therefore reflect the vibrational density of states (DOS) associated with the La atoms. The peak at 7 meV (78 K) corresponds to the quasi-localized La mode. The second broader peak at about 15 meV corresponds to the hybridization of La and Sb vibrational modes. Both peaks can be accounted for using lattice dynamic models based on first-principles calculations (Feldman et al., 2000).

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

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