Hydrogen coherent scattering

Let us take two polymers (one deuterated and one hydrogenated) and dissolve them in a solvent (or another polymer) having a scattering length b. The coherent scattered intensity can be derived from (B 1.9.117), which gives... 

As well as the coherent scattering, which has the same wavelength as the incident waves, an atom scatters waves of reduced wave-length. The intensity of these waves is not included in the formulae (I) and (2). For X-rays falling on a hydrogen atom, the total intensity scattered inelastically, due both to Raman effect and Compton effect, is given by the formula... 

It is easy to see that neutron diffraction experiments on hydrogenous materials are difficult because the coherent scattering is weak and the incoherent scattering is strong. Fortunately the heavier isotope. 

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). 

Here is the momentum transferred from the neutron and x is one of the reciprocal lattice vectors of the palladium lattice. Thus, the incoherent scattering sees all the vibration modes but the coherent scattering selects one particular phonon for a particular experimental value of Q. It is now clear that both the incoherent and coherent one-phonon scattering will depend on the shape of the optical dispersion curves and hence will be influenced by hydrogen-hydrogen interactions. Indeed, one of the first observations of inelastic scattering from a hydride [10] interpreted the shape of the optical peak in terms of a frequency distribution broadened by H-H interactions. 

Hydrogen is the most important example of an incoherently scattering nucleus. Not only is the cross-section for neutron scattering from hydrogen virtually completely incoherent, it is much larger (>4X) than that of any other nucleus so that the cjy(q) are very difficult to determine in hydrogenous materials. Most other nuclei of interest are predominantly coherent scatterers. 

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. 

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