In the figure on the right, a plane incident wave of wavelength λ travelling in the direction specified by the unit vector **S**_{i} is scattered by the particles located at two points, A and B. A detector is placed in the direction specified by the unit vector **S**_{f}. Designating the position of the second scatterer relative to the first as *r*, we have *CB* = **S**_{i} · **r **and *AD* = **S**_{f} · **r **. The path difference is then:

**q** is called the **scattering vector** and completely characterizes the scattering geometry: the incident and scattered beam directions and the wavelength. It is defined as **q **= **k**_{f }- **k**_{i} , with** ****k**_{i(f)} = (2Π/λ)**S**_{i(f)}.

The scattering vector **q** is also sometimes referred to as the **momentum transfer vector** since ħ**q** represents the change in the momentum by the incident neutron upon scattering.

The Bragg's law for diffraction tells that for having diffraction in one direction, the path difference must be an integer of the wave length. The condition to have diffraction thus reads:

**This last equation means that the diffraction condition can be simply expressed by ***the scattering vector q must be a vector of the reciprocal lattice*.

The diffraction pattern will therefore give direct information on the reciprocal lattice and in turn on the crystal lattice. Single-crystal neutron diffraction is a powerful tool:

- In **chemistry** to study molecular structures, the nature of the hydrogen bond and the structures of metal hydrides;

- In **biology** for the crystallography of proteins and the diffraction from fibres and membranes;

- In** physics** for the investigation of magnetic materials – using the interaction of the atomic magnetic moment of the material under study with the magnetic moment of the neutron (performing then* magnetic neutron diffraction*).