# Small-angle neutron scattering

Entry needed - IN PROGRESS by Sofia.

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:

- <math>\lambda = \frac{h}{p} = \frac{h}{{m}{v}}</math>

where <math>\lambda</math> is the wavelength, <math>\{h}</math> is the Planck constant, <math>{m}</math> is the particle's mass and <math>{v}</math> its velocity.

By Bragg's law of diffraction, the distance d resolvable by radiation of wavelength :<math>\lambda</math> incident on a material with refractive index :<math>{n}</math> at an angle :<math>\theta</math> is

- <math>n\lambda=2d\sin\theta\!</math>.

Typical values for the wavelength of neutrons in a beam are ~

Interacts with nucleus. Neutrons have a small magnetic moment -> interacts with spin and orbital magnetic moments-> more information.

neutrons come from 1. nuclear reactor, fission of Uranium-235; particle accelerators, protons directed at materials with heavy nuclei. Facilities: Grenoble (most steady-state high flux) ILL,

Sources: intro to SANS web pdf. website that linked here

image showing neutrons scattering

## Keyword in references:

Photonic Properties of Strongly Correlated Colloidal Liquids