Neutron Scattering

Type of physical science: Neutron Scattering, Scattering; atomic, Elementary particles, Particles, elementary, Particle accelerators, Atomic physics

Field of study: Nonrelativistic quantum mechanics

Neutron scattering is similar, but largely complementary, to other types of scattering such as X-ray, electron, and light scattering. Neutron scattering allows for the nondestructive investigation of the atomic and molecular structure of bulk matter and of the interactions that determine the properties of solid and liquid materials.

Overview

When neutrons collide with a sample of bulk matter, they are, in general, deflected or scattered. Analysis of this neutron scattering enables researchers to determine several properties of the scattering material, including the structure of the material, interactions between constituent particles comprising the material, and bulk properties of the material. Neutron scattering conventionally refers to scattering of low-energy (thermal or epithermal) neutrons. Scattering of neutrons in other energy regimes is similar to, but distinct from, low-energy neutron scattering. Investigations of the atomic or magnetic structure of a condensed-matter system using neutron scattering is conventionally referred to as "neutron diffraction," while studies of the atomic and magnetic dynamics and bulk properties of the system are often referred to as "neutron spectroscopy."

Neutron sources are of three basic types. The most common type is the fission nuclear reactor. Fast neutrons are copiously produced as a part of the fission reactions occurring within the reactor. As a result of collisions with moderating material in the reactor, these are slowed to thermal energies. A hole drilled in the containment vessel of a reactor will therefore be a relatively high-intensity source of thermal neutrons. A second simpler, but more expensive, neutron source consists of a mixture of radium and beryllium. The alpha particles emitted by the radioactive radium react with beryllium nuclei to produce neutrons. The third type of neutron source differs from the first two in that it is typically pulsed rather than continuous. In such a spallation source, an accelerator is used to produce a high-energy beam of electrons or protons that is then directed onto a target (typically uranium, tungsten, or lead), and neutrons are produced as a result; essentially, they are knocked out of the target nuclei.

Neutrons are electrically uncharged and as a result do not experience the electrostatic Coulomb force. However, neutrons do possess a magnetic moment, which causes them to interact with other magnetic particles and with magnetic fields. Also, the neutron is a hadron, meaning that it experiences the strong nuclear force. As a result, neutrons incident on a bulk sample of matter interact only via two mechanisms. One is the short-range nuclear force between the neutron and the atomic nucleus. The other is the interaction between the magnetic moment of the neutron and the spin and orbital magnetic moments of the atom.

When a neutron enters the target material, it may travel a significant distance before being scattered by one of these interactions. Neutrons are therefore useful for investigating the bulk properties of materials. In contrast, electrons and X rays, which interact with the atomic electrons of the target, are scattered primarily near the surface. Because of their interaction with the atomic electrons, the scattering amplitudes for electrons and X rays are roughly proportional to the atomic number of the scattering atom, varying by a factor of about one hundred over the periodic table. By contrast, the scattering amplitude for neutrons on nuclei varies in an erratic and nonmonotonic way from one atomic species to another, indeed from one isotope to another, varying by only a factor of two or three over all isotopes. These neutron-scattering amplitudes are also dependent on the energy of the incident neutron, and there are strong resonances for some nuclei and some energy ranges that result in particularly strong interaction of the neutrons. Similarly, the scattering amplitude for scattering of the neutron by the magnetic moments of the atom will vary depending on the way in which the electrons are distributed and paired within a specific type of atom.

To picture what happens when a neutron encounters a nucleus, the scattering amplitude can be regarded as the probability that the neutron is captured or absorbed by the target nucleus, as a result forming a sort of compound, or transient, nucleus. This transient nucleus may break up in one of several ways. The incident neutron may be re-emitted with its speed unchanged, but in a direction different from the incident direction. Since the energy of the neutron is unchanged in this case, the effect is elastic neutron scattering. Inelastic scattering results when the incident neutron is re-emitted in some direction with increased or decreased energy, the energy difference being supplied by, or deposited in, the target material. Finally, the transient nucleus may emit particles other than a neutron (usually protons, deuterons, or alpha particles), may emit electromagnetic radiation (gamma rays), or may undergo fission, splitting into two large fragments and a number of neutrons. The first two processes of elastic and inelastic scattering are of interest here. In an analogous way, the scattering of a neutron by the magnetic moments of the target material atoms may be either elastic or inelastic. It should be noted that because the neutron mass is comparable to the mass of an atom, a significant fraction of the neutron energy can be imparted to the target material in a single scattering event. This differs from the situation for scattering of X rays and electrons.

Like all subatomic particles, neutrons exhibit a wave-particle dual nature, having both wavelike and particlelike properties. Fast neutrons interact with matter in a predominantly particlelike way. Thus, for example, the scattering of a fast neutron produced in a fission reaction in a reactor with a nucleus of the moderating material can be treated much in the same way as the collision of two billiard balls. For the lower energies of thermal and epithermal neutrons of interest in neutron scattering, the wavelike properties dominate. In particular, thermal neutrons with energies of about 0.025 electronvolt have corresponding de Broglie wavelengths of about 0.2 nanometer, typical of the interatomic spacings in most solids and liquids. As in classical optics, when the wavelength of the incident wave is of the same order as the spacing of the scattering centers, significant diffraction will occur. The resulting diffraction pattern is determined by the location and spacing of the scattering centers. Such is also the case for the elastic scattering of slow neutrons. The lines etched on a diffraction grating in optical diffraction are replaced by the atomic nuclei and magnetic moments of the condensed-matter system, but otherwise the two situations are entirely analogous. Neutron diffraction is therefore able to probe the atomic and magnetic structure of condensed-matter systems. Note that a distinctive advantage of neutron diffraction over X-ray diffraction is the approximate equality of the neutron scattering amplitudes for light nuclei and heavy nuclei, so that neutron diffraction studies "see" light nuclei as well as heavy.

The energies of thermal and epithermal neutrons are of the same order as many of the collective excitation energies in condensed-matter systems, such as phonons, magnons, and rotons. Since a neutron is able to transfer a large fraction of its energy in a single scattering event, inelastic neutron scattering is also an ideal probe of atomic dynamics, magnetic dynamics, and the excitation of these collective modes in solids and liquids. Thus, all neutron scattering can be understood as the scattering of "neutron waves" by moving scattering centers in the form of atomic nuclei and their associated electronic magnetic moments. Elastic scattering gives information about the time-averaged spatial structure of the scattering centers, while inelastic scattering, as a result of the Doppler shifting caused by the motion of the scattering centers, gives information about the dynamics and excitations of the system.

Detection of the scattered neutrons must be accomplished by a two-step process, since the neutron does not directly produce ionization. The neutron must first interact in some way in the detector to form charged particles; the detector must then produce an output signal that is based on the energy deposited by those charged particles. Most major types of (charged) particle detectors can be modified for use as neutron detectors by incorporating a material that serves as a neutron-to-charged-particle conversion medium. Representative examples of such detectors include proportional counters with boron trifluoride gas or helium-3 gas, and scintillation proportional counters with boron or lithium impregnated in the scintillating material. There are also fission-based detectors that utilize proportional counters with fissionable material such as uranium hexafluoride gas in the counter cavity, or uranium-235 or plutonium-239 in a metallic coating on the counter cavity wall.

Often, as in inelastic neutron scattering, information about the energy of the scattered neutrons is needed as well. Three commonly applied methods for determining the neutron energy follow. Because thermal neutrons are traveling slowly, it is actually possible to determine their speed mechanically, by using a time-of-flight method. A pair of disks mounted on a common axle have slightly offset neutron-transparent sectors. When the disks rotate at a speed that allows the neutron to pass through both sectors, the speed of rotation, sector offset, and distance between disks can be used to calculate the neutron speed directly. A second, somewhat more elegant method actually uses diffraction of the scattered neutron beam from a large single crystal. Since the diffraction of the beam through a specific angle by a known crystal is dependent upon the neutron wavelength, the speed of the neutron and its energy may be calculated. The third method of energy determination involves proton recoil. Since the proton and neutron have essentially equal mass, in a head-on collision, a neutron will transfer all of its energy to the proton. The recoil proton energy can then be determined by a variety of methods. The first two of these techniques are also used to select a single energy for the incident neutrons to be used in scattering experiments.

Applications

The range of applications of neutron scattering is wide. Generally speaking, all applications fall into one of four categories: elastic nuclear scattering to determine locations of various types of atoms (atomic structures); elastic magnetic scattering to determine the magnetic topography of a material (magnetic structures); inelastic nuclear scattering to determine the dynamics of vibrational (acoustic) excitations (phonon spectra, as well as excitations of individual atoms); and inelastic magnetic scattering to determine the dynamics of magnetic excitations (magnon spectra). Additionally, some experiments attempt to investigate the interaction between these collective excitations or the relationship of these excitations to phenomena such as superconductivity and phase transitions.

Atomic and magnetic structures of many solids, both crystalline and amorphous, and some liquids have been determined. An initial scattering of a neutron beam from a suitably selected crystal that is properly oriented can be used to produce a completely polarized neutron beam. Such polarized beams are used to make very sensitive measurements of magnetic-spin distributions in various materials. Inelastic neutron scattering is used to determine phonon and magnon dispersion curves for most elements, and for many simple compounds. Dispersion curves describe the relationship between the energy and momentum of a quasiparticle such as a phonon or a magnon. These dispersion relations are intimately connected with the details of the interatomic forces in the specific materials. This information has greatly enhanced the understanding of superconductivity and of phase transitions between various solid-state phases.

A specific application will illustrate the capabilities of modern neutron-scattering techniques. Polymers are large molecules (macromolecules) that consist of chains of identical low-molecular-weight units, or monomers. A longstanding question in polymer science involves the shape assumed by an individual macromolecule in various bulk forms (in solution, melts, gels, or crystals), and under various environmental conditions. Also of interest are the dynamics of such macromolecules in these various circumstances. These questions are of great practical importance, because most animal and plant tissues and most biomolecules are polymers, as are many other materials such as glasses, textiles, paper, rubber, and plastics. A fortunate circumstance makes neutron scattering ideal for studies of polymers. The scattering amplitude for neutrons from hydrogen and from deuterium, an isotope of hydrogen that is chemically identical, are very different, being of about the same magnitude but opposite in sign. Thus, scattering of neutrons by hydrogen is easily distinguishable from scattering by deuterium. A hydrogen-containing macromolecule, or even a selected segment of it, can be "tagged" by replacing hydrogen atoms with chemically identical deuterium atoms. These deuterated sites can be located, and indeed tracked, by scattering neutrons from the sample, a technique known as "isotopic contrast manipulation." Also, because most materials are relatively transparent to neutrons, additional apparatus needed to control environmental conditions such as electric and magnetic fields, ovens, cryostats, and pressure cells can be incorporated without undue difficulty. From such studies, understanding of precise structures, conformations, and dynamics of many macromolecules under a variety of conditions has been obtained.

Early neutron-scattering work was limited primarily by the intensity of the neutron beams that could be obtained from reactors. Initially, only simple materials were studied, but these studies formed the basis for the interpretation of the diffraction patterns of more complex materials. Continuing development of neutron sources and enhanced detection and analysis capabilities have expanded the scope of neutron scattering as an analytical tool. In particular, in addition to higher thermal neutron fluxes from reactors, other neutron sources are now available.

Pulsed-spallation neutron sources are capable of producing much higher peak neutron fluxes than reactors. The energy of the produced neutrons can be tailored to be higher--in the epithermal range, about 1 electronvolt. These characteristics allow for the study of other energy and momentum regions of neutron scattering not accessible to thermal neutrons. These include study of high-frequency vibrations of solids, magnetic excitations (magnons) in solids that are inaccessible to thermal neutrons as a result of the size of the magnetic excitation energies, and improved spatial resolution in structural studies of liquids and amorphous solids that require large momentum transfer from neutron to target in the scattering.

The energy of incident thermal neutrons in inelastic scattering limits the resolution with which they can be used to determine energies of excitations in solids. Improved energy resolution, or high-resolution spectroscopy, requires lower-energy neutrons. Sources of such cold (and even ultracold) neutrons can be designed by using low-temperature moderators to slow the neutrons. Moderators such as liquid deuterium are capable of producing neutron beams that allow energy resolutions of less than 1 microelectronvolt. This improved energy resolution permits the detailed study of widths and line-shapes of the elastic and inelastic scattering patterns that are crudely determined by thermal neutron scattering. Interpretation of these details leads to an improved understanding of the structure and dynamics of condensed matter.

Context

Since its discovery by James Chadwick in 1932, the neutron has played an important role in many areas of physics. Initially, the neutron's crucial role in the structure and stability of the atomic nucleus was the area of greatest interest. As a result of those studies, it became clear that the neutron plays a critical part in nuclear reactions, first in fission and later in fusion. This realization, made urgent by the Manhattan Project, resulted in the development of nuclear-fission reactors, which among other things could be used to produce relatively intense beams of slow neutrons.

While Louis de Broglie had shown much earlier that particles such as the neutron should possess wavelike properties, it was still not known at the time of the development of reactors whether or not this would make neutrons a quantitatively useful probe of matter. Such a probe was desirable, since the existing method of structure determination for solids was X-ray diffraction. While similar in principle, X-ray diffraction cannot determine the positions of low atomic-weight atoms, specifically hydrogen atoms. Hydrogen is an important component of many inorganic materials and of all organic molecules, found in all living things.

Ernest Wollan and Clifford Shull began to investigate the possibility of neutron diffraction in 1946 at Oak Ridge National Laboratory. Incidentally, one of their most important findings from those early studies was that neutron-scattering amplitudes from a given nucleus are independent of the environment of the nucleus. Thus, for example, the nucleus of an aluminum atom always scatters neutrons the same way, regardless of the type of material in which the aluminum is found. It is this property that makes neutron diffraction useful for determining structures of materials. In the late 1940's and early 1950's, Wollan and Shull, along with Wallace Koehler and J. Samuel Smart, began to investigate what could be learned about the magnetic properties of materials by neutron scattering. In the course of these studies, they obtained the first experimental evidence of antiferromagnetism, which had been theoretically predicted earlier, as well as improved understanding of ferromagnetism and paramagnetism. At about the same time that Wollan, Shull, and their colleagues were doing this work, Bertram Brockhouse began neutron research at the Chalk River Laboratories in Ontario, Canada. At this time, the idea of using inelastic neutron scattering to study collective excitations in solids had arisen, and by using an arrangement of his own design known as a "triple-axis spectrometer," Brockhouse and others were able to use inelastic neutron scattering to begin study of phonons and magnons. Brockhouse also found that neutron scattering could be used to study properties of liquids, such as the correlation functions that are basically a measure of the degree of order in the liquid. For this pioneering work, Brockhouse and Shull shared the 1994 Nobel Prize in Physics.

Neutron-scattering techniques have matured to the point that they constitute one of the primary tools for the investigation of a wide range of condensed-matter systems. The relatively complex nature of the experimental setup has limited neutron scattering to a handful of sites. Having been used to understand the structure and properties of solids and liquids in the past, neutron scattering techniques will certainly be increasingly used in the future to increase that understanding and to aid in the design of new materials for specific purposes.

Principal terms

DE BROGLIE WAVELENGTH: The wavelength of the matter wave associated with a subatomic particle; the de Broglie wavelength is inversely proportional to the particle's velocity

ELASTIC SCATTERING: A scattering in which the energy of the scattered particle is unchanged

ELECTRONVOLT: A unit of energy commonly used in atomic and condensed matter physics; one electronvolt is the energy given to an electron when it is accelerated through an electric potential difference of one volt, equal to 1.6 × 10^-19 Joules

EPITHERMAL NEUTRON: A neutron with kinetic energy greater than that of a thermal neutron

FAST NEUTRON: A neutron with kinetic energy more than 1,000 electronvolts

INELASTIC SCATTERING: A scattering in which the scattered particle loses energy to, or gains energy from, the target

MAGNON: A quantized collective disruption of the equilibrium, or ground state, magnetic configuration of a condensed matter system; magnons propagate as quasiparticles

PHONON: A quantized collective vibrational excitation of a condensed matter system; phonons propagate as quasiparticles

SCATTERING AMPLITUDE: A measure of the probability of the occurrence of a specific scattering process

SLOW NEUTRON: A neutron with kinetic energy less than 1 electronvolt

SPALLATION: A nuclear reaction in which particles are ejected from a bombarded target

THERMAL NEUTRON: A neutron that is in thermal equilibrium with the medium in which it moves; typically, thermal neutrons are taken to have kinetic energies of about 0.025 electronvolt

Bibliography

Axe, John D., and Robert M. Nicklow. "Neutron Scattering in Condensed Matter Physics." Physics Today 38, no. 1 (1985). This general survey article is easily accessible to the general reader and considers the range of applications of neutron scattering.

Bacon, G. E. Neutron Diffraction. 3d ed. New York: Oxford University Press, 1975. This is a textbook at an advanced undergraduate level, but it contains comprehensive coverage of the topic, both theoretical and practical. It is very readable and should be accessible to most interested readers.

‗‗‗‗. Neutron Physics. London: Wykeham Publications, 1969. This small book is written in relatively nontechnical language. It contains a wealth of information and examples, many useful diagrams, pictures, and graphs, and covers the subject of neutron physics from sources to detectors to applications of neutrons.

Kittel, Charles. Introduction to Solid State Physics. 5th ed. New York: John Wiley & Sons, 1976. This standard undergraduate text covers all of solid-state physics and contains several chapters devoted to phonons, magnetic structures, and other aspects of solid-state physics that are probed by neutron scattering.

Lander, Gerard H., and David L. Price. "Neutron Scattering with Spallation Sources." Physics Today 38, no. 1 (1985). As the title suggests, this article considers the aspects of neutron scattering that are unique to spallation neutron sources and the epithermal neutrons that they produce.

Larose, A., and J. Vanderwal. Scattering of Thermal Neutrons: A Bibliography. New York: Plenum Press, 1974. A large bibliography of books and journal articles. While some will be at an advanced level, this is a useful reference for anyone interested in the details of this subject.

Moore, Peter B. "Applications of Neutron Scattering to Biology." Physics Today 38, no. 1 (1985). This excellently written cross-disciplinary article surveys what has been done, and what unresolved problems still exist, in the application of neutron scattering, specifically to biological macromolecules.

National Research Council. Condensed Matter Physics. Washington, D.C.: National Academy Press, 1986. One of eight volumes in the "Physics Through the 1990's" series. The field of condensed-matter physics is surveyed, and several portions have direct relevance to neutron scattering. In particular, Appendix E deals specifically with unresolved problems for the understanding of which neutron scattering will be a crucial tool.

Stein, Richard S., and Charles C. Han. "Neutron Scattering from Polymers." Physics Today 38, no. 1 (1985). This article is somewhat on the technical side, but the motivated reader can certainly get a good feel for the ways in which neutron scattering has been applied to enhance the understanding of macromolecules in general.