Neutron diffraction is the phenomenon observed of neutrons behaving like waves instead of like particles as we would expect. The circumstances have to be just right to observe wave behaviour in neutrons.
In neutron diffraction a beam of neutrons is aimed at a thin sheet of crystalline material. The atomic spacing in the crystal acts like a diffraction grating. The speed of the neutrons has to be right so that their associated wavelength (see below for more information about associated wavelength) is close to the atomic spacing (maximum diffraction is achieved if
After diffraction the neutrons passing through multiple sources will produce an interference pattern. The pattern can be used to provide information about the structure of the crystal.
De Broglie hypothesised that matter particles could behave like waves under the right circumstances. He said that the associated wavelength of those particles would be related to their momentum according to this relationship:
Where λ is called the De Broglie wavelength, h is the Planck constant, and mv is the momentum of the particle.
As you can see it is impossible for a particle to have an associated wavelength if it is stationary because mv would be zero and λ would tend to infinity.