Neutron Scattering

White" neutrons
from reactor
Sample
Monochromator
Crystal
Figure 5 .2 : Schematic set-up of a diffraction experiment . The inset shows the relation
between incident and final wave vectors k, k' and the scattering vector Q .
5 .2 Experimental Examples : Static Scattering
5 .2 .1 Placzek corrections
Figure 5 .2 shows the schematics of a scattering experiment for the determination of S(Q) .
By using a monochromator the incident neutron energy or the wave vector k is fixed . After
scattering the intensity is recorded as a function of the scattering angle 20 without energy
discrimination . This means that the diffraction setup fixes only the direction of kf but
not its magnitude . Therefore, for a given angle différent scattering vectors Q are mixed
as figure 5 .3 shows .
Strictly speaking, this invalidates thé relation (dQ/dÇZ) coh = IbI ZNS(Q) between (angle)
differential cross section and structure factor .
Nevertheless, for high incident energies it is an excellent approximation as long as thé
energy transfer due to inelastic scattering is small compared to thé incident energy E .
This condition is always fulfilled for x-ray scattering because thé incident energy lies in
thé keV range there and thé inelasticity of scattering is limited mainly to thermal energies
kBT which are of thé order of meV .
5-5