12.3. Neutron Spectroscopy 703
Another important quantity is the momentum transfer, which is generally rep-
resented byQ. It can be obtained in terms of the wave vector ̄kby noting that
the magnitude of the wave vector is directly related to the momentum through
p=k. The momentum transfer is generally represented only as a difference
of the two wave vectors, that isQ ̄=k ̄i−k ̄f. (12.3.11)Note that here all the quantities are vectors and should therefore be treated
accordingly (see also Fig.12.3.1(b)). The quantityQis a function of the angle
of reflection and its value depends solely on the structure of the sample. This
implies that it can be used to deduce information about the structure. This
is true but the usual practice is to derive ascattering functionSbased not
only onQbut also onω. The information contained in this function is richer
than the parameterQalone and is therefore able to provide deeper insight
into the structure of the material. To be more specific, the parameterωgives
information about the type of scattering, which is also a function of the material
and its structure. A typical plot ofSwith respect to the energy transfer to the
sample is shown in Fig.12.3.2.
Quasielastic Scattering:The elastic peak shown in Fig.12.3.2 is broadened
at higher values of energy transfer. This broadening is due to the so called
quasielasticscattering process. Note that in an ideal case the elastic peak
should be a delta function, that is, should not have any width. However, due
to crystal imperfections and other effects related to measurements, the peak
assumes a finite width. Further broadening of this peak due to the quasielastic
process is separate from this, though. Quasielastic scattering is a physical
process characterized by small energy transfers of the order of 2meV.A very important point to note here is that in the process of quasielastic and
inelastic scatterings the scattered neutron energy can be lower or higher than the
incident neutron energy. In other words, the incident neutron can also gain energy
during the scattering process.
Now that we understand the basics of neutron scattering, we can move on to the
discussion of the practical aspects of neutron spectroscopy. As mentioned earlier,
there are two parameters, namelyQandω, which can reveal information about the
sample’s internal structure. Therefore the neutron spectroscopy is concerned with
determining the neutron intensity as a function of these two parameters. Since these
parameters depend on the wave vectors and the scattering angle, the spectrometer
should be able to determine the neutron intensity at different angles with respect
to initial direction of neutrons. The wave vector can be determined by a number of
instruments that employ techniques that are conceptually different from one another.
In the following we list the three most commonly used techniques together with their
respective instruments.
Bragg Diffraction- Triple-Axis Spectrometer
- High Flux Backscattering Spectrometer
- Filter Analyzer Spectrometer