Ph.D. thesis (pdf) - dirac

56 Experimental techniques and observables
probe used. Thermal neutrons and X-ray in the keV range both have Q-vectors
of the order of magnitude 1 Å −1 such that 1/Q is comparable to the characteristic
distances between nearest neighbors in condensed matter. Both probes are therefore
well suited for studying structure in matter unlike for example visible light, which
probes Q values that are 3 orders of magnitude smaller.
The energy loss of the probe is of course limited by the energy of the probe itself,
the neutron can not loose more energy than it has. There is moreover for a given
Q-value an additional limitation because the transfer of energy and momentum are
interdependent. This is the so called kinematic limitation. It is anticipated from
inserting the relation between energy and momentum in equation 4.3.3. This relation
is not the same for neutrons and photons. For neutrons we have
while the relation for photons is
E neutron = 2 Q 2 neutron
2m neutron
(4.3.13)
E photon = c Q photon , (4.3.14)
where c is the speed of light. The difference between the expressions above lead to
different kinematic limitations, even if there are kinematic limitations in both cases.
However, kinematic limitation does not have any practical importance for inelastic
X-ray scattering because the energy transfers of interest when studying dynamics
on an intermolecular scale is of the order of magnitude meV while the energy of the
X-ray is in the keV range. Inelastic X-ray scattering has therefore given access to a
domain in energy-Q-space which where not accessible by neutrons.
The transfer of energy in a real experiment is always given by a certain resolution.
The resolution function is the actual measured signal in a situation where an ideal
experiment would have given a delta function. The measured signal is therefore in
general given by a convolution of the ideal signal and the resolution function. The
shape and width of the resolution is in most cases determined empirically. It depends
on the scattering geometry, the characteristics of the beam (monochromation and
collimation) and on how precisely the change in energy can be measured. The total
energy of thermal neutrons is of the same order of magnitude as the transfer of
energy and this is why neutron scattering is the classical technique for this type of
study. The relative resolution needed in X-ray scattering is on the other hand of
the order of magnitude 10 −7 . The achievement of such a high resolution is amazing,
however the resolution in absolute values is still far from matching that obtained by
high resolution neutron scattering.