4. Neutron Scattering

Neutron Scattering Experimental Technique

The experimental scattering of neutrons can basically be divided into two categories: elastic neutron scattering (also known as neutron diffraction) and inelastic neutron scattering. Both techniques have their own unique purposes and methods of implementation. Here, basic overviews of these techniques will be provided.

Elastic Neutron Scattering (Neutron Diffraction)

To start, the basis of elastic neutron scattering is fundamentally no different than that of other diffraction processes such as the various forms of light diffraction. Just like all other quantum particles, neutrons can be described from both a particle and wave-like perspective. In this case, the wave-like behavior of neutrons allows it to experience the phenomenon of diffraction typically associated with light, which is more naturally thought of from a wave point of view. Given the usual energies of the neutrons produced at neutron research facilities, the consequent neutron wavelengths fall in the Angstrom range, which happens to be the scale of atomic separation in matter. This means that thermal neutrons impinging on matter can produce diffraction patterns after scattering from atomic layers as governed by the well-known Bragg’s law, which is generally brought up in descriptions of x-ray diffraction.

Since thermal neutrons can so intimately be affected by matter atomically through diffraction, they can reveal a wealth of information about the crystal structure of the target material. This is very analogous to the link between x-ray diffraction patterns and the determination of a material’s crystal structure. However, it must be understood that despite the similarities, the information that can be extracted from neutron diffraction is complementary rather than overlapping with that attained from x-ray diffraction. This is a result of the fact related earlier in the introduction that neutron-matter interactions are inherently very different from other types of particle/radiation-matter interactions. In this case, when encountering matter, x- rays more directly intermingle with the electron clouds surrounding atoms whereas neutrons, not affected by the charged electrons, interact with the atomic nuclei. This significant difference also leads to the selection of materials that can be studied for neutron diffraction based on varying scattering cross sections. While x-rays experience stronger diffraction patterns from materials with large atomic number atoms due to the presence of more electrons, neutron diffraction patterns are actually more sensitive to materials with small atomic number atoms (lighter materials). Although, for neutrons, there is more of a dependence on the type of isotope of the material studied rather than a linear dependence on atomic number.

Given the concept of neutron diffraction, the experimental point of view can now be established for the technique. First, after neutrons are produced either from research reactors or through spallation, their wavelength properties must be defined so that experiments can be accurate and effective. Typically, this is performed using monochromators and filters at research reactors to self-select the neutron wavelength to be used or using the so-called time of flight technique at spallation sources in which individual incident neutrons of different energies are sorted and labeled based on their varying velocity levels and then filtered later on with the aid of that information. After this, the neutron beam is directed to be incident on a sample of choice sitting on a rotating stage (to change the orientation of the sample) and the scattered beam is collected by a detector, also able to rotate in order to find the angle of the scattered beam relative to the sample. As an important side-note, it’s worth mentioning that samples used in any neutron scattering experiment must be either powders or relatively large single crystals in order to match the typical diameters of neutron beams. Single crystals, for instance, need to at least be on the order of 1 cubic-millimeter in size to be studied in most cases. This is a disadvantage compared to x-ray scattering experiments, which do not have such strict requirements on sample size. The resulting neutron diffraction data is usually represented in a plot of scattered neutron intensity as a function of scattering angle, very much like with x-ray diffraction.

Inelastic Neutron Scattering

The inelastic scattering of neutrons, as the name of the technique implies, involves processes in which neutrons incident on a sample experience an exchange of energy with the matter, resulting in a shift in energy/wavelength of the exiting neutrons relative to the incident ones. Ruminating on the origin of energy exchanges between neutrons and matter, one realizes that the collisions between neutrons and atomic nuclei can lead to atomic motion within material lattices and if certain quantized lattice vibrations (phonons) are resonantly excited, then energy will be transferred from the neutrons to the matter. By detecting the energy shifts of the scattered neutrons, then, much knowledge can be acquired about the fundamental atomic and molecular motions taking place in various materials. This is the very basis for all experiments involving inelastic neutron scattering and clearly differs from the concept behind neutron diffraction.

Experimentally, inelastic neutron scattering is more involved and demanding than neutron diffraction. To begin, since experiments involving this sort of scattering search for shifts in energy that may be quite subtle and small, it becomes extremely important to have fine energy resolution. This translates to the need for either good quality monochromatization of the neutron beam or accurate time-of-flight stamping of the produced neutrons in order to confidently establish the wavelength/energy parameters of the experiment. Given this, an inelastic neutron scattering experiment can be carried out with a schematic very much. and with the results bundled into a function called the dynamic structure factor S(k,w) where k is basically a reflection of the change in momentum of the incident neutrons in the material under investigation and w is the energy change of the material. Finally, typical presentations of inelastic neutron scattering data show contour plots of material energy change (w) as a function of neutron momentum shift (k). These images directly reveal atomic motion and activity in matter that can be mapped in the form of a phonon dispersion curve, which will also be briefly described in the next section.

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