Diffraction scattering length

Figure 8 Behavior of the first sharp diffraction peak of PB with experimental scattering lengths for carbon and deuterium. The deuterium atoms are placed at their mechanical equilibrium positions determined by the positions of the united atom centers and the equilibrium CH bond length and HCH and HCC bond angles along a united atom MD trajectory. With increasing pressure (values given in the legend, simulation performed at T = 293 K), the first sharp diffraction peak shifts to larger q as expected but unexpectedly decreases in height.

Neutron diffraction has been successfully used for structure determinations of aqua complexes of some metal ions, which have isotopes with sufficient differences in scattering lengths to be used for isotopic substitution methods. Not only bond lengths but also coordination numbers and the orientation of the water molecules in the first coordination sphere can then be determined. Several review articles have summarized these results (2-6). 

Koester L, Yelon WB (1983) Summary of low energy scattering lengths and cross sections. Neutron diffraction Newsletter, IUCr. 

Although the formalism for X-ray and neutron diffraction is essentially the same, it is appropriate to treat them separately because of the nature of the basic interaction. For the case of neutron diffraction, neutrons are scattered isotropically by all the nuclei of the system. The degree to which this takes place is determined by the coherent neutron scattering length b, which varies from isotope to isotope (Table I). Because the scattering is isotropic, the results of a given experiment can readily be presented in terms of a total radial distribution function. 

It should be emphasized that the calculation of the number of electrons described above is not exact since x-ray scattering factors are only directly proportional to the number of electrons at 20 = 0° and the proportionality becomes approximate at sinG/A, > 0. The population parameter(s) refinement results are usually more reliable in neutron diffraction because neutron scattering lengths are independent of the Bragg angle. 

Figure 2.59. The electron (left) and nuclear (right) density distributions in the xOz plane of the unit cell of CeRhGcs calculated from x-ray and neutron powder diffraction data, respectively Figure 2.58). The contour of the unit cell is shown schematically as the rectangle under each Fourier map. The peaks correspond to various atoms located in this plane and are so marked on the figure. The volumes of the peaks are proportional to the scattering ability of atoms for x-rays the scattering power decreases in the series Ce(58 e) Rh(45 e) Ge(32 e) for neutrons, the coherent scattering lengths decrease in the reverse order Ge(8.19 fm)...

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