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| Fig. 1: An image taken at the ISIS neutron research facility in Oxfordshire, UK. (Source: Wikimedia Commons.) |
Neutrons are subatomic particles with no net electric charge, unlike other particles such as protons and electrons, which have an intrinsic electric charge. It is this distinction that makes the interaction between neutrons and matter particularly interesting when compared to proton-matter or electron-matter interactions. While the latter interactions are dictated by Coulomb forces involving strong charge repulsion or attraction, charge-free neutrons can move through matter undeterred by these factors. This translates to neutrons generally possessing the ability to penetrate deeper into matter than other subatomic particles. When contemplating the application value of this trait, one can imagine that by evaluating the properties of neutrons scattering from matter, information can be gathered about the bulk characteristics of that matter that cannot be gained from the scattering of other subatomic particles with shorter penetration depths. This opens up a whole variety of possible physics knowledge that can be acquired from studying neutron-matter interactions and indeed there is an expansive field in which neutron scattering is utilized as a versatile experimental technique. This report provides a brief overview of the neutron scattering technique and its many applications.
Before diving into how neutrons are used to learn about different characteristics of matter, it should be discussed where the neutrons used for neutron scattering actually come from. There are currently around 30 active neutron research facilities scattered around the globe, each one containing the means to generate thermal neutrons for experimental research. These neutrons are usually produced by either research reactors specifically engineered for releasing neutrons or by a process known as spallation, both of which will now be described.
In essence, research reactors are just like most other nuclear reactors and depend highly on the process of fission. In these fission processes, a nucleus, usually U-235 or Pu- 239 [1], captures a neutron and then splits into fragments including neutrons with kinetic energy, beta radiation, and photons. Each fission reaction produces on average 2.5 neutrons [1], one of which ends up being used to incite further fission, a half of which is produced delayed and is essential for reactor control, and the last one actually collected for experimental research.
As an alternative to the use of research reactors, some neutron research facilities that have a high-powered particle accelerator can produce neutrons in a process called nuclear spallation. Here, accelerated high-energy protons are directed toward a dense and high-mass- number target such as tungsten, uranium, tantalum, or mercury whereby the collision leaves the nuclei of the target in a highly excited state. The array of products that emerge from this interaction includes various high-energy neutrons and protons that proceed to collide with other yet-to-be excited target nuclei along with lower energy evaporation neutrons [2] that end up being collected for scattering experiments. In terms of yield, for each proton-target nuclei collision, an average of 20 neutrons are produced [3] with the majority of those being evaporation ones.
For neutron production in both the cases of research reactors and spallation, the immediate low-energy neutrons outputted still possess too much energy for practical experimental usage. Thus, a moderation stage is necessary in order to slow them down to become so-called thermal neutrons. Typically this involves surrounding the neutron source with a large volume of an apt moderator such as heavy water, water, or beryllium [4] where fast neutrons will enter and gradually lose their energy in a series of collisions with the nuclei of the moderators. It should be mentioned that at many neutron research facilities today, there are also cold neutron sources in which the moderator used is liquid hydrogen, which allows neutrons to cool to cryogenic temperatures for sub-room temperature experiments. After tens of collisions per neutron [4], the resulting thermal neutrons leak out of the moderator through a designated beam tube and are ready to be utilized for scattering experiments.
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.
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 [5]. 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.
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| Fig. 2: A very basic schematic of an inelastic neutron scattering experiment. |
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 like that shown in Fig. 2 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.
Based on the fundamental aspects behind both types of neutron scattering, there are many different applications for the techniques. For neutron diffraction, most of the applications focus on obtaining static crystal structure information. On the other hand, for inelastic neutron scattering, the applications are geared toward understanding dynamic crystal activity. Both types of scattering thus provide separate important information and justify the use of neutrons for experimental research.
To begin, recall that one of the notable properties of neutron diffraction is that in comparison to x-ray diffraction, neutrons are more sensitive to low atomic number atoms due to interactions with atomic nuclei as opposed to electron clouds. This leads to the special ability for neutrons to probe the structure of compounds that have typically inaccessible low atomic number compounds such as hydrogen. For instance, classes of compounds containing hydrogen such as transition metal hydrides have been successfully characterized structurally with the aid of elastic neutron scattering [7]. Following along the same lines of characterizing materials with low atomic number atoms and the ability to probe hydrogen-containing matter, neutron scattering applications in biology is particularly notable. Since many biological specimens and elements such as proteins contain hydrogen and other low atomic number atoms, the use of neutron scattering techniques is fitting. As an example, small-angle neutron scattering (SANS) is a widely-used neutron diffraction technique in which a highly-collimated neutron beam is focused onto a biological sample, often in some sort of solution, and the collected scattered light provides a wealth of information on the structural properties of the sample [8].
Another application of neutron diffraction is in a technique called neutron reflectometry, which is specifically used for measuring the structures of thin, flat films. Here, a once again highly-collimated neutron beam reflects off an extremely flat-surfaced thin film and the characteristics of the reflected beam are gathered as a function of the neutron wavelength and/or the incident angle. The shape and profile of the reflected neutron beam ends up revealing detailed information about the structure of the film including parameters for roughness, thickness, density, etc. In the end, neutron diffraction is a very useful scattering technique if attempting to accurately determine the static structural properties of a particular material, especially if it contains low atomic number atoms.
In contrast to the applications of neutron diffraction, as mentioned earlier, inelastic neutron scattering specializes in providing dynamic atomic information due to energy exchanges between neutrons and materials under investigation. This leads to many possibilities for systems that can be studied using this type of scattering. All applications of inelastic neutron scattering rely on acquiring momentum and energy information with very fine resolution so instruments associated with this type of scattering must have those characteristics. One common form of inelastic neutron scattering is called triple-axis spectrometry, whose associated spectrometer instrument allows detectors to gather scattered neutrons at any point in both energy and momentum space that are physically accessible to the instrument. This allows for a complete construction of the previously mentioned dynamic structure factor function S(k,w) for a particular material. Another form of inelastic neutron scattering, called time-of-flight scattering, is familiar since it involves the same concepts mentioned earlier for keeping track of the specific energies of neutrons produced in research reactors or through spallation. With this technique, the position and time of each incident neutron on a sample is accurately tagged and fixed along with the same coordinates of the neutrons after scattering off the material. With this information at hand, a simple mathematical transformation yields both the momentum and energy transfers of each neutron, which also builds S(k,w).
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| Fig. 3: A phonon dispersion curve mapped out for GaAs. (Source: Wikimedia Commons) |
Since inelastic neutron scattering can so accurately describe the atomic dynamics of a material in terms of energy and momentum, the most natural description of such components that springs to mind is a phonon dispersion curve. Phonons, as briefly discussed earlier, are representations of quantized vibration modes of atoms in a material's lattice. More specifically, they are coherent movement of atoms in a lattice rather than just random thermal motion. Different phonon modes will end up being associated with different energies/frequencies depending on the momentum shifts of the lattice atoms. This translates to an ability to map out the energies of various phonon modes in a material (w) as a function of the shifts in momentum of the atoms (k), most commonly known as phonon dispersion curves. Given the energy and momentum resolution of inelastic neutron scattering experiments, they end up being used quite frequently for mapping out these phonon dispersion relations for various materials [9]. Fig. 3 provides an example of a phonon dispersion plot (for gallium arsenide here) with the different curves corresponding to different phonon modes, the y-axis being energy, the x-axis being momentum, and the labels above the x-axis just standing as conventions for naming different points in momentum space. Plots such as this contain a great deal of information describing the activity of atoms in a particular material and their dynamics and relation to each other.
As an experimental technique, neutron scattering provides the opportunity to learn plenty of information about atomic structure and dynamics. All of this traces back to the fundamentally unique interaction between neutrons and matter. It is no wonder that there are so many neutron research facilities around the globe with active research reactors and spallation-based sources.
© Mason Jiang. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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