# Small-angle neutron scattering

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Small-angle neutron scattering is a technique for probing the internal structure of a material by measuring how neutrons scatter from it. Since neutrons are weakly interacting, when a material is subjected to a beam of them all scattering is elastic. In addition, the weak interaction of neutrons with matter allows them to penetrate deep into the substance under study (sometimes even centimeters), thus providing information about the material bulk.

There are several scattering techniques which share the same operating principle for structural studies: X-ray scattering, neutron scattering, and even optical scattering all come down to illuminating a sample with a beam of particles/waves and recording the resulting scattering pattern. Which one is most appropriate depends on the required resolution and the specific type of information required.

Treating all particles (and photons) as waves, the resolution of these techniques depends linearly on the wavelength, which, in turn, depends, for massive particles, on their momentum, according to de Broglie:

$\lambda = \frac{h}{p} = \frac{h}{{m}{v}}$

where $\lambda$ is the wavelength, $h$ is the Planck constant, $m$ is the particle's mass and $v$ its velocity.

By Bragg's law of diffraction, the distance d resolvable by radiation of wavelength $\lambda$ incident on a material with refractive index $n$ at an angle $\theta$ with respect to the plane perpendicular to the beam is

$d = \frac{{n}{\lambda}}{2\sin\theta}\!$.

Typical values for the wavelength of neutrons in a beam are ~ angstrom; by changing the angle, the resolution of this technique can be varied in the 1-1000nm regime.

Neutrons are not electrically charged and this interact very weakly with matter. This has the advantage that neutron scattering is elastic, which means that the resulting scattering pattern is not convoluted with secondary processes and can be used to extract purely structural information. Moreover, their neutrality allows neutrons to penetrate deeply into a material - sometimes as much as several centimeters - which means that this technique can provide information about the bulk of a material. At the same time, the weakness of the neutron-matter interaction means that high intensity beams are required, which is a practical challenge. Neutrons mostly interact with the nucleus, but they also have a small magnetic moment which sometimes induces them to interact with electrons at large orbits, thus probing part of the electronic structure.

Neutrons can be obtained from nuclear reactors, where they are a byproduct of fission of Uranium-235, or from particle accelerators, as the byproducts of collisions between protons and atoms with heavy nuclei. There are only a few such facilities in the world; the highest-flux neutron beam is maintained at the Institut Laue-Langevin in Grenoble, France, while other SANS facilities are located in Oak Ringe National Lab and Brookhaven National Lab.