Neutron scattering

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Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. The natural/physical phenomenon is of elemental importance in nuclear engineering and the nuclear sciences. Regarding the experimental technique, understanding and manipulating neutron scattering is fundamental to the applications used in crystallography, physics, physical chemistry, biophysics, and materials research.

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Neutron scattering is practiced at research reactors and spallation neutron sources that provide neutron radiation of varying intensities. Neutron diffraction (elastic scattering) techniques are used for analyzing structures; where inelastic neutron scattering is used in studying atomic vibrations and other excitations.

Scattering of fast neutrons

"Fast neutrons" (see neutron temperature) have a kinetic energy above 1  MeV. They can be scattered by condensed matter—nuclei having kinetic energies far below 1 eV—as a valid experimental approximation of an elastic collision with a particle at rest. With each collision, the fast neutron transfers a significant part of its kinetic energy to the scattering nucleus (condensed matter), the more so the lighter the nucleus. And with each collision, the "fast" neutron is slowed until it reaches thermal equilibrium with the material in which it is scattered.

Neutron moderators are used to produce thermal neutrons, which have kinetic energies below 1 eV (T < 500K). [1] Thermal neutrons are used to maintain a nuclear chain reaction in a nuclear reactor, and as a research tool in neutron scattering experiments and other applications of neutron science (see below). The remainder of this article concentrates on the scattering of thermal neutrons.

Neutron-matter interaction

Because neutrons are electrically neutral, they penetrate more deeply into matter than electrically charged particles of comparable kinetic energy, and thus are valuable as probes of bulk properties.

Neutrons interact with atomic nuclei and with magnetic fields from unpaired electrons, causing pronounced interference and energy transfer effects in neutron scattering experiments. Unlike an x-ray photon with a similar wavelength, which interacts with the electron cloud surrounding the nucleus, neutrons interact primarily with the nucleus itself, as described by Fermi's pseudopotential. Neutron scattering and absorption cross sections vary widely from isotope to isotope.

Neutron scattering can be incoherent or coherent, also depending on isotope. Among all isotopes, hydrogen has the highest scattering cross section. Important elements like carbon and oxygen are quite visible in neutron scattering—this is in marked contrast to X-ray scattering where cross sections systematically increase with atomic number. Thus neutrons can be used to analyze materials with low atomic numbers, including proteins and surfactants. This can be done at synchrotron sources but very high intensities are needed, which may cause the structures to change. The nucleus provides a very short range, as isotropic potential varies randomly from isotope to isotope, which makes it possible to tune the (scattering) contrast to suit the experiment.

Scattering almost always presents both elastic and inelastic components. The fraction of elastic scattering is determined by the Debye-Waller factor or the Mössbauer-Lamb factor. Depending on the research question, most measurements concentrate on either elastic or inelastic scattering.

Achieving a precise velocity, i.e. a precise energy and de Broglie wavelength, of a neutron beam is important. Such single-energy beams are termed 'monochromatic', and monochromaticity is achieved either with a crystal monochromator or with a time of flight (TOF) spectrometer. In the time-of-flight technique, neutrons are sent through a sequence of two rotating slits such that only neutrons of a particular velocity are selected. Spallation sources have been developed that can create a rapid pulse of neutrons. The pulse contains neutrons of many different velocities or de Broglie wavelengths, but separate velocities of the scattered neutrons can be determined afterwards by measuring the time of flight of the neutrons between the sample and neutron detector.

Magnetic scattering

The neutron has a net electric charge of zero, but has a significant magnetic moment, although only about 0.1% of that of the electron. Nevertheless, it is large enough to scatter from local magnetic fields inside condensed matter, providing a weakly interacting and hence penetrating probe of ordered magnetic structures and electron spin fluctuations. [2]

Inelastic neutron scattering

Generic layout of an inelastic neutron scattering experiment Inelastic-neutron-scattering-basics.png
Generic layout of an inelastic neutron scattering experiment
Inelastic Neutron Scattering

Inelastic neutron scattering is an experimental technique commonly used in condensed matter research to study atomic and molecular motion as well as magnetic and crystal field excitations. [3] [4] It distinguishes itself from other neutron scattering techniques by resolving the change in kinetic energy that occurs when the collision between neutrons and the sample is an inelastic one. Results are generally communicated as the dynamic structure factor (also called inelastic scattering law) , sometimes also as the dynamic susceptibility where the scattering vector is the difference between incoming and outgoing wave vector, and is the energy change experienced by the sample (negative that of the scattered neutron). When results are plotted as function of , they can often be interpreted in the same way as spectra obtained by conventional spectroscopic techniques; insofar as inelastic neutron scattering can be seen as a special spectroscopy.

Inelastic scattering experiments normally require a monochromatization of the incident or outgoing beam and an energy analysis of the scattered neutrons. This can be done either through time-of-flight techniques (neutron time-of-flight scattering) or through Bragg reflection from single crystals (neutron triple-axis spectroscopy, neutron backscattering). Monochromatization is not needed in echo techniques (neutron spin echo, neutron resonance spin echo), which use the quantum mechanical phase of the neutrons in addition to their amplitudes.[ citation needed ]

History

The first neutron diffraction experiments were performed in the 1930s. [1] However it was not until around 1945, with the advent of nuclear reactors, that high neutron fluxes became possible, leading to the possibility of in-depth structure investigations. The first neutron-scattering instruments were installed in beam tubes at multi-purpose research reactors. In the 1960s, high-flux reactors were built that were optimized for beam-tube experiments. The development culminated in the high-flux reactor of the Institut Laue-Langevin (in operation since 1972) that achieved the highest neutron flux to this date. Besides a few high-flux sources, there were some twenty medium-flux reactor sources at universities and other research institutes. Starting in the 1980s, many of these medium-flux sources were shut down, and research concentrated at a few world-leading high-flux sources.

Facilities

Today, most neutron scattering experiments are performed by research scientists who apply for beamtime at neutron sources through a formal proposal procedure. Because of the low count rates involved in neutron scattering experiments, relatively long periods of beam time (on the order of days) are usually required for usable data sets. Proposals are assessed for feasibility and scientific interest. [5]

Techniques

See also

Related Research Articles

Neutron Subatomic particle

The neutron is a subatomic particle, symbol
n
or
n0
, which has a neutral charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave similarly within the nucleus, and each has a mass of approximately one atomic mass unit, they are both referred to as nucleons. Their properties and interactions are described by nuclear physics.

Neutron activation analysis

Neutron activation analysis (NAA) is the nuclear process used for determining the concentrations of elements in a vast amount of materials. NAA allows discrete sampling of elements as it disregards the chemical form of a sample, and focuses solely on its nucleus. The method is based on neutron activation and therefore requires a source of neutrons. The sample is bombarded with neutrons, causing the elements to form radioactive isotopes. The radioactive emissions and radioactive decay paths for each element are well known. Using this information, it is possible to study spectra of the emissions of the radioactive sample, and determine the concentrations of the elements within it. A particular advantage of this technique is that it does not destroy the sample, and thus has been used for analysis of works of art and historical artifacts. NAA can also be used to determine the activity of a radioactive sample.

Small-angle neutron scattering

Small-angle neutron scattering (SANS) is an experimental technique that uses elastic neutron scattering at small scattering angles to investigate the structure of various substances at a mesoscopic scale of about 1–100 nm.

Neutron moderator Substance that slows down particles with no electric charge

In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, ideally without capturing any, leaving them as thermal neutrons with only minimal (thermal) kinetic energy. These thermal neutrons are immensely more susceptible than fast neutrons to propagate a nuclear chain reaction of uranium-235 or other fissile isotope by colliding with their atomic nucleus.

Neutron diffraction Application of neutron scattering to the determination of the atomic and/or magnetic structure of a material

Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.

Neutron radiation Ionizing radiation that presents as free neutrons

Neutron radiation is a form of ionizing radiation that presents as free neutrons. Typical phenomena are nuclear fission or nuclear fusion causing the release of free neutrons, which then react with nuclei of other atoms to form new isotopes—which, in turn, may trigger further neutron radiation. Free neutrons are unstable, decaying into a proton, an electron, plus an electron antineutrino with a mean lifetime of 887 seconds.

Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified. Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process in which the total kinetic energy of the system is conserved. During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place until the incident particle's energy and speed has been reduced to the same as its surroundings, at which point the particle is "stopped".

In chemistry, nuclear physics, and particle physics, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved. In an inelastic scattering process, some of the energy of the incident particle is lost or increased. Although the term is historically related to the concept of inelastic collision in dynamics, the two concepts are quite distinct; inelastic collision in dynamics refers to processes in which the total macroscopic kinetic energy is not conserved. In general, scattering due to inelastic collisions will be inelastic, but, since elastic collisions often transfer kinetic energy between particles, scattering due to elastic collisions can also be inelastic, as in Compton scattering.

The nuclear cross section of a nucleus is used to describe the probability that a nuclear reaction will occur. The concept of a nuclear cross section can be quantified physically in terms of "characteristic area" where a larger area means a larger probability of interaction. The standard unit for measuring a nuclear cross section is the barn, which is equal to 10−28 m², 10−24 cm² or 100 fm². Cross sections can be measured for all possible interaction processes together, in which case they are called total cross sections, or for specific processes, distinguishing elastic scattering and inelastic scattering; of the latter, amongst neutron cross sections the absorption cross sections are of particular interest.

Neutron cross section Effective area quantifying likelihood of interaction between an incident neutron and a target nucleus

In nuclear and particle physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. The neutron cross section σ can be defined as the area in cm2 for which the number of neutron-nuclei reactions taking place is equal to the product of the number of incident neutrons that would pass through the area and the number of target nuclei. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power of a nuclear power plant. The standard unit for measuring the cross section is the barn, which is equal to 10−28 m2 or 10−24 cm2. The larger the neutron cross section, the more likely a neutron will react with the nucleus.

Muon spin spectroscopy

Muon spin spectroscopy, also known as µSR, is an experimental technique based on the implantation of spin-polarized muons in matter and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The motion of the muon spin is due to the magnetic field experienced by the particle and may provide information on its local environment in a very similar way to other magnetic resonance techniques, such as electron spin resonance and, more closely, nuclear magnetic resonance (NMR).

A spin wave is a propagating disturbance in the ordering of a magnetic material. These low-lying collective excitations occur in magnetic lattices with continuous symmetry. From the equivalent quasiparticle point of view, spin waves are known as magnons, which are bosonic modes of the spin lattice that correspond roughly to the phonon excitations of the nuclear lattice. As temperature is increased, the thermal excitation of spin waves reduces a ferromagnet's spontaneous magnetization. The energies of spin waves are typically only μeV in keeping with typical Curie points at room temperature and below.

High Flux Isotope Reactor Nuclear research reactor in Oak Ridge, Tennessee

The High Flux Isotope Reactor (HFIR) is a nuclear research reactor at Oak Ridge National Laboratory (ORNL) in Oak Ridge, Tennessee, United States. Operating at 85 MW, HFIR is one of the highest flux reactor-based sources of neutrons for condensed matter physics research in the United States, and it has one of the highest steady-state neutron fluxes of any research reactor in the world. The thermal and cold neutrons produced by HFIR are used to study physics, chemistry, materials science, engineering, and biology. The intense neutron flux, constant power density, and constant-length fuel cycles are used by more than 500 researchers each year for neutron scattering research into the fundamental properties of condensed matter. HFIR has about 600 users each year for both scattering and in-core research.

Electron scattering Deviation of electrons from their original trajectories

Electron scattering occurs when electrons are deviated from their original trajectory. This is due to the electrostatic forces within matter interaction or, if an external magnetic field is present, the electron may be deflected by the Lorentz force. This scattering typically happens with solids such as metals, semiconductors and insulators; and is a limiting factor in integrated circuits and transistors.

Mainz Microtron

The Mainz Microtron, abbreviated MAMI, is a microtron which provides a continuous wave, high intensity, polarized electron beam with an energy up to 1.6 GeV. MAMI is the core of an experimental facility for particle, nuclear and X-ray radiation physics at the Johannes Gutenberg University in Mainz (Germany). It is one of the largest campus-based accelerator facilities for basic research in Europe. The experiments at MAMI are performed by about 200 physicists of many countries organized in international collaborations.

Neutron reflectometry

Neutron reflectometry is a neutron diffraction technique for measuring the structure of thin films, similar to the often complementary techniques of X-ray reflectivity and ellipsometry. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, polymer and surfactant adsorption, structure of thin film magnetic systems, biological membranes, etc.

Neutron spin echo Neutron scattering technique

Neutron spin echo spectroscopy is an inelastic neutron scattering technique invented by Ferenc Mezei in the 1970s, and developed in collaboration with John Hayter. In recognition of his work and in other areas, Mezei was awarded the first Walter Haelg Prize in 1999.

Atomic form factor

In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from real space to momentum space. For an object with spatial density distribution, , the form factor, , is defined as

Helium atom scattering (HAS) is a surface analysis technique used in materials science. HAS provides information about the surface structure and lattice dynamics of a material by measuring the diffracted atoms from a monochromatic helium beam incident on the sample.

Rutherford backscattering spectrometry (RBS) is an analytical technique used in materials science. Sometimes referred to as high-energy ion scattering (HEIS) spectrometry, RBS is used to determine the structure and composition of materials by measuring the backscattering of a beam of high energy ions impinging on a sample.

References

  1. 1 2 Lüth, Harald Ibach, Hans (2009). Solid-state physics : an introduction to principles of materials science (4th extensively updated and enlarged ed.). Berlin: Springer. ISBN   978-3-540-93803-3.
  2. Zaliznyak, Igor A.; Lee, Seung-Hun (2004), Magnetic Neutron Scattering
  3. G L Squires Introduction to the Theory of Thermal Neutron Scattering Dover 1997 (reprint?)
  4. Taylor, Andrew Dawson (1976). Inelastic Neutron Scattering by Chemical Rate Processes. ox.ac.uk (DPhil thesis). University of Oxford. OCLC   500576530. EThOS   uk.bl.ethos.474621.
  5. "How To Submit a Proposal". Neutron Sciences at ORNL. Oak Ridge National Laboratory. Retrieved May 12, 2022.