Scattered intensity neutron diffraction

We have seen that the intensities of diffraction of x-rays or neutrons are proportional to the squared moduli of the Fourier transfomi of the scattering density of the diffracting object. This corresponds to the Fourier transfomi of a convolution, P(s), of the fomi... 

The intensities of diffracted beams, or reflections as they ate commonly called, depend upon the strength of the scattering that the material inflicts upon the radiation. Electrons are scattered strongly, neutrons weakly and X-rays moderately. The basic scattering nnit of a crystal is its unit cell, and we may calculate the scattering at any angle by mnltiplying... 

Figure 10. Elastic neutron diffraction pattern from a 0.4-layer nitric oxide film adsorbed on a recompressed graphite powder Papyex (431. Background scattering from the substrate has been subtracted. The molecules are assumed to be lying down as shown in the unit cell (inset). The arrows indicate the position and relative intensities of the Bragg peaks calculated for this structure.

X-ray and neutron diffraction patterns can be detected when a wave is scattered by a periodic structure of atoms in an ordered array such as a crystal or a fiber. The diffraction patterns can be interpreted directly to give information about the size of the unit cell, information about the symmetry of the molecule, and, in the case of fibers, information about periodicity. The determination of the complete structure of a molecule requires the phase information as well as the intensity and frequency information. The phase can be determined using the method of multiple isomor-phous replacement where heavy metals or groups containing heavy element are incorporated into the diffracting crystals. The final coordinates of biomacromolecules are then deduced using knowledge about the primary structure and are refined by processes that include comparisons of calculated and observed diffraction patterns. Three-dimensional structures of proteins and their complexes (Blundell and Johnson, 1976), nucleic acids, and viruses have been determined by X-ray and neutron diffractions. 

It can be shown that what is actually measured in a neutron diffraction experiment is the component of S (or J), which is normal to the scattering vector (which is in turn normal to the scattering plane, hkl), and the total diffiacted intensity is then proportional to... 

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