A wave has a momentum p = \hbar k and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called
momentum transfer. The
wave number k is the
absolute of the
wave vector k = p / \hbar and is related to the
wavelength k = 2\pi / \lambda. Momentum transfer is given in wavenumber units in
reciprocal space Q = k_f - k_i
Diffraction The momentum transfer plays an important role in the evaluation of
neutron,
X-ray, and
electron diffraction for the investigation of
condensed matter.
Laue-Bragg diffraction occurs on the atomic
crystal lattice, conserves the wave energy and thus is called
elastic scattering, where the
wave numbers final and incident particles, k_f and k_i, respectively, are equal and just the direction changes by a
reciprocal lattice vector G = Q = k_f - k_i with the relation to the lattice spacing G = 2\pi / d . As momentum is conserved, the transfer of momentum occurs to
crystal momentum. The presentation in reciprocal space is generic and does not depend on the type of
radiation and wavelength used but only on the sample system, which allows to compare results obtained from many different methods. Some established communities such as
powder diffraction employ the diffraction angle 2\theta as the independent variable, which worked fine in the early years when only a few
characteristic wavelengths such as Cu-K\alpha were available. The relationship to Q-space is : Q = 2 k \sin \left ( \theta \right ) with k = {2 \pi }/{\lambda} and basically states that larger 2\theta corresponds to larger Q. == See also ==