Small-angle neutron scattering

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Small angle neutron scattering (SANS) is a laboratory technique, similar to the often complementary techniques of small angle X-ray scattering (SAXS) and light scattering. These are particularly useful because of the dramatic increase in forward scattering that occurs at phase transitions, known as critical opalescence, and because many materials, substances and biological systems possess interesting and complex features in their structure, which match the useful length scale ranges that these techniques probe. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, defects in materials, surfactants, colloids, ferromagnetic correlations in magnetism, alloy segregation, polymers, proteins, biological membranes, viruses, ribosome and macromolecules. There are numerous SANS instruments available worldwide. While analysis of the data can give information on size, shape, etc., without making any model assumptions a preliminary analysis of the data can only give information on the radius of gyration for a particle using Guinier's equation.[1]



During a SANS experiment a beam of neutrons is directed at a sample, which can be an aqueous solution, a solid, a powder, or a crystal. The neutrons are elastically scattered by changes of refractive index on a nanometer scale inside the sample which is the interaction with the nuclei of the atoms present in the sample. Because the nuclei of all atoms are compact and of comparable size neutrons are capable of interacting strongly with all atoms. This is in contrast to X-ray techniques where the X-rays interact weakly with hydrogen, the most abundant element.

In zero order dynamical theory of diffraction the refractive index is directly related to the scattering length density and is a measure of the strength of the interaction of a neutron wave with a given nucleus. The following table shows the scattering lengths for various elements (in 10−12 cm).[2]

Note that the relative scale of the scattering lengths is the same. Another important point is that the scattering from hydrogen is distinct from that of deuterium. Also, hydrogen is one of the few elements that has a negative scatter, which means that neutrons deflected from hydrogen are 180° out of phase relative to those deflected by the other elements. These features are important for the technique of contrast variation (see below).

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