Page 64 - Neutrons for Sciences and Society

Neutrons for Science
are atoms in a regular crystalline lattice this interference will give rise to a diffraction pattern, as in the case of X-rays. In the case
of neutrons there is an added complication due to the interaction being with the nucleus. Most atoms have several isotopes having the same number of electrons, but different nuclei, hence the scattering amplitudes for scattered neutrons are different. Isotopes have no effect on diffraction of X-rays (where scattering is a
result of the interaction with the electrons). In contrast there is a major effect with scattered and diffracted neutrons. Isotopes are randomly distributed in the crystal lattice, which blurs the results a little. Scattering includes two parts, one that corresponds to the diffraction pattern, called coherent scattering, and a part which does not contribute called incoherent scattering. There is also a second source of incoherent scattering: the dependence of the cross-section as a function of the relative spins of the neutron and the scattering nucleus. The combination of unpolarised neutrons and an unpolarised target produces a disorder scattering equivalent to that arising from a mixture of isotopes.
If the atoms of the sample are in a gaseous form, the interaction of the neutron is accompanied by recoil of the atom, and a loss of energy from the scattered neutrons. When the atoms are part of a crystal, and hence bound to their neighbours the motions are also connected. These collective movements are described by means
of phonon waves propagating in the crystal with an energy E and a wave vector Q. If a neutron is scattered from one of these atoms the scattering has two components: an elastic part as described above, and one called inelastic. In this second case the neutron can absorb energy, annihilating the phonon, or can create a phonon
(if it possesses sufficient energy). Energy and momentum are
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