Deuterium, coherent scattering

Lithium hydride, LiH, is a rather simple solid there are two atoms in the primitive cell and four electrons. It has the rock salt structure and its primitive cell contains one lithium and one hydrogen atom. Fig. 4.14. There are six dispersion curves of which three are acoustic and three optical. We can compare our calculations with the measured dispersion curves from LiD (rather than LiH because the deuterium coherent scattering cross section is required to measure the relative displacements of pairs of atoms ( 2.1). 

The coherent scattering amplitude used for 96% enriched Li was b — (0.16 + 0.024i) X 10 cm. The glycolate ion was assumed to have 100% deuterium at the position indicated. Quantities in parentheses are the e.s.d. values based on counting statistics alone. 

If the isotope has no spin, then < b > = < b as < b> = b and there is no incoherent scattering for neutrons. Only coherent scattering contains information on the stmcture of the sample. The incoherent cross section contains no information on interference effects and forms an isotropic (flat) background which must be subtracted off in SANS stmctural investigations. While most of the atoms encountered in neutron scattering from polymers are mainly coherent scatterers (e.g., carbon, oxygen, deuterium), there is one important exception [8,22,23]. In the case of hydrogen (H )... 

It may be seen from Table 23.1 that there is a large difference in the coherent scattering length between deuterium and hydrogen and that the latter value is actually negative. This arises from a change of phase of the scattered wave and results in a marked difference in scattering power (contrast) between molecules synthesized with deuterated or protonated monomer units. 

In the case of PED, there is no cancellation between the coherent scattering lengths of carbon and deuterium (Table 23.1), and the incoherent backgrormd is very much smaller than for PEH. Thus, PED should have virtually... 

Neutron Techniques. These include neutron diffraction (ND) and inelastic neutron scattering (INS). Both techniques provide complimentary structural information relative to XRD (44), since the sensitivity of the latter method is proportional to the number of electrons Z, whereas that of the neutron scattering is proportional to the nuclear cross section. Using neutrons makes it possible to detect light elements, such as deuterium, which has a large coherent scattering length In such a case, ND will be much more informative than XRD in the location of that element. In addition, ND allows a better discrimination between different elements with similar Z (45) and spin densities (46). When necessary, this contrast can even be enhanced by the use of specifically prepared samples with different isotopes (47). 

A cleaner situation has been achieved mthdeuterium labeling in neutron scattering. Fortunateily, deuterium and hydrogen have very different coherent scattering amplitudes for thermal neutrons. Thus, it is possible to achieve an isotopic labeling which is efficient for neutrons but leaves the system nearly unperturbed.t... 

The specific advantage of neutrons for biological studies has its basis in the remarkable difference in scattering power, correctly expressed in coherent scattering lengths b, between hydrogen and deuterium (b = -0.374 10 cm = 0.667 10 cm). This... 

In contrast, deuterium scatters neutrons out of phase and in a coherent manner. The concept of coherent scattering length was introduced to account for the phase of the scattered neutrons ... 

To understand the reasons for the differences between the experimental spectra and that predicted by the models, it is necessary to consider the data from which the models are built. The only way to directly measure the dispersion curves of a material is by coherent INS spectroscopy. For hydrogenous polyethylene, this method fails because the background caused by the incoherent scattering from hydrogen completely swamps the coherent signal ( 2.1.1). For perdeuterated polyethylene, the larger coherent and smaller incoherent cross sections of deuterium (see Appendix 1) has allowed the vs acoustic branch to be mapped by coherent INS [11]. 

Fig. 5.8 shows the experimental phonon dispersion relations of a perdeuterated naphthalene crystal (N-dg) determined at a temperature T = 6 K by inelastic neutron scattering [7]. Deuterium (D) has a much higher scattering cross section for coherent inelastic neutron scattering than the isotope H. Nevertheless, to gain a... 

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