# Small Angle Neutron Scattering (SANS)

The equation q ⋅ r = 2Πn gives the reciprocity between q  and r  when neutrons are scattered by a sample. This reciprocity means that information on relatively large r is contained in I(q) at relatively small q. In other words: whenever the sample contains a scattering length density inhomogeneity of dimension larger than ≈ 10 Å, scattering becomes observable in the small-angle region.
The scattering here does not take place from individual atoms but instead from aggregates of atoms. The range of q covered is from about 5·10-3 to 0.5 Å-1, representing a range in real space from 10 to 103 Å. Small-angle scattering provides information about the size, shape and orientation of the components of the sample.
Important differences between neutrons and X-rays will lead the scientist to choose either SAXS or SANS depending on their sample and experiment. The energy of an X-ray photon of 1.5 Å wavelength is more than 105 greater than a neutron of the same wavelength and so radiation damage of biological samples is less of a problem with neutrons than with X-rays. Neutron radiation is very penetrating: it can be used to examine properties of samples several centimeters thick and can probe samples encased in furnaces, cryostats or pressure cells... On the other hand, the neutron beam is relatively weak and thus cannot be collimated in a SANS experiment to a diameter less than a 1 mm. In contrast, X-rays can be focused down to a few μm, and it is possible to measure the scattering much closer to q=0 with X-rays than with neutrons. The small X-ray spot size lends itself more conveniently to rastering of the sample, which is valuable in cases where the sample is inhomogeneous.

An important method by neutron small-angle scattering experiments is called isotopic substitution (e.g. hydrogen by deuterium). Different spectra varying the scattering length density of one phase are then recorded for the same system which represents a severe test to check the validity of the proposed models.

### References

R.-J. Roe, Methods of X-Ray and Neutron Scattering in Polymer Science, Oxford University Press, 2000.
B.T.M. Willis and C.J. Carlile, Experimental Neutron Scattering, Oxford University Press, 2009.