Neutron scattering

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Neutron scattering, the scattering of free neutrons by matter, can refer to either the physical process or the experimental technique which uses this process for the investigation of materials. Neutron scattering as a physical process is of primordial importance in nuclear engineering. Neutron scattering as an experimental technique is used in crystallography, physics, physical chemistry, biophysics, and materials research. It is practiced at research reactors and spallation neutron sources that provide neutron radiation of sufficient intensity. Neutron diffraction (elastic scattering) is used for determining structures; Inelastic neutron scattering is used for the study of atomic vibrations and other excitations.

Scattering of fast neutrons

"Fast neutrons" (see neutron temperature) have a kinetic energy above 1 MeV. Their scattering by condensed matter (with nuclei having kinetic energies far below 1 eV) is in a good approximation an elastic collision with a particle at rest. At each collision the fast neutron transfers a significant part of its kinetic energy to the scattering nucleus; the more so the lighter the nucleus. In this way the neutron is slowed down until it reaches thermal equilibrium with the material in which it is scattered.

Neutron moderators are used to produce "thermal neutrons" that 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 science comprising scattering experiments and other applications (see below). The remainder of this article concentrates on the scattering of thermal neutrons.

Neutron-matter interaction

Since neutrons are electrically neutral, they penetrate matter more deeply than electrically charged particles of comparable kinetic energy; therefore they are valuable probes of bulk properties.

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

Also depending on isotope, the scattering can be incoherent or coherent. Among all isotopes, hydrogen has the highest neutron scattering cross section. Also, important elements like carbon and oxygen are well visible in neutron scattering. This is marked contrast to X-ray scattering where cross sections systematically increase with atomic number. Thus neutrons can be used to analyse materials with low atomic numbers like 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, isotropic potential varying randomly from isotope to isotope, making it possible to tune the nuclear scattering contrast to suit the experiment.

The scattering almost always has an elastic and an inelastic component. The fraction of elastic scattering is given by the Debye-Waller factor or the Mössbauer-Lamb factor. Depending on the research question, most measurements concentrate on either the elastic or the inelastic scattering.

Achieving a precise velocity, i.e. a precise energy & de Broglie wavelength, of the neutron beam is important. Such single-energy beams are termed 'monochromatic'. Monochromaticity is achieved either with a crystal monochromator or a time of flight spectrometer. In the time-of-flight technique, neutrons are sent through a sequence of two rotating slits, so that only neutrons of a particular velocity are selected. Recently there has been the development of spallation sources which can create a rapid pulse of neutrons. In this method, the pulse contains neutrons of many different velocities / de Broglie wavelengths. However, the 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]

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 to get good data. Proposals are assessed for feasibility and scientific interest.