Neutron scattering

Neutron scattering

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Neutron scattering,
the scattering of free neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

s by matter,
is a physical process
and an experimental technique using this process
for the investigation of materials.

Neutron scattering as a physical process is of primordial importance
in nuclear engineering
Nuclear engineering
Nuclear engineering is the branch of engineering concerned with the application of the breakdown as well as the fusion of atomic nuclei and/or the application of other sub-atomic physics, based on the principles of nuclear physics...


Neutron scattering as an experimental technique is
used in crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, physical chemistry
Physical chemistry
Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...

Biophysics is an interdisciplinary science that uses the methods of physical science to study biological systems. Studies included under the branches of biophysics span all levels of biological organization, from the molecular scale to whole organisms and ecosystems...

, and materials research.
It is practised at research reactor
Research reactor
Research reactors are nuclear reactors that serve primarily as a neutron source. They are also called non-power reactors, in contrast to power reactors that are used for electricity production, heat generation, or maritime propulsion.-Purpose:...

s and spallation
In general, spallation is a process in which fragments of material are ejected from a body due to impact or stress. In the context of impact mechanics it describes ejection or vaporization of material from a target during impact by a projectile...

 neutron sources
that provide neutron radiation
Neutron radiation
Neutron radiation is a kind of ionizing radiation which consists of free neutrons. A result of nuclear fission or nuclear fusion, it consists of the release of free neutrons from atoms, and these free neutrons react with nuclei of other atoms to form new isotopes, which, in turn, may produce...

 of sufficient intensity
Neutron flux
The neutron flux is a quantity used in reactor physics corresponding to the total length travelled by all neutrons per unit time and volume . The neutron fluence is defined as the neutron flux integrated over a certain time period....

Neutron diffraction
Neutron diffraction
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...

 (elastic scattering) is used for
determining structures;
Inelastic neutron scattering
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....

 is used for the study of
atomic vibration
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

s and other excitations
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....


Scattering of fast neutrons

Fast neutrons (see neutron temperature
Neutron temperature
The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term temperature is used, since hot, thermal and cold neutrons are moderated in a medium with a certain temperature. The neutron energy distribution is...

) have a kinetic energy far above 1 eV.
Their scattering by condensed matter
(with nuclei having kinetic energies far below 1 eV)
is in a good approximation an elastic collision
Elastic collision
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter...

 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.

Such neutron moderator
Neutron moderator
In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235....

s are used to produce thermal neutrons
that have kinetic energies below 1 eV.
Thermal neutrons are used to maintain a nuclear chain reaction in a nuclear reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...

and as a research tool in neutron science comprising scattering experiments and
other applications (see box: "Science with neutrons").

In the remainder of this article we will concentrate 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
Energy transfer
Energy transfer is the transfer of energy from one body to another.There are a few main ways that energy transfer occurs:*Radiant energy *Heat conduction*Convection*Electrical power transmission*Mechanical work...

 effects in scattering experiments.
Unlike an x-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

 with a similar wavelength,
which interacts with the electron cloud
surrounding the nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

neutrons interact with the nucleus itself.
The interaction is described by Fermi's pseudopotential.
Neutron scattering and absorption cross section
Neutron cross-section
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. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power...

vary 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.
Moreover, the nucleus provides a very short range,
isotropic potential varying randomly from isotope
Isotopes are variants of atoms of a particular chemical element, which have differing numbers of neutrons. Atoms of a particular element by definition must contain the same number of protons but may have a distinct number of neutrons which differs from atom to atom, without changing the designation...

 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
Debye-Waller factor
The Debye–Waller factor , named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x-ray scattering or coherent neutron scattering caused by thermal motion. It has also been called the B factor or the temperature factor...

 or the Mössbauer-Lamb factor.
Depending on the research question,
most measurements concentrate
on either the elastic or the inelastic scattering.

Magnetic scattering

The neutron has an additional advantage over the x-ray photon
in the study of condensed matter.
It readily interacts with internal magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s in the sample.
In fact, the strength of the magnetic scattering signal
is often very similar to that of the nuclear scattering signal
in many materials,
which allows the simultaneous exploration
of both nuclear and magnetic structure.
Because the neutron scattering amplitude can be measured in absolute units,
both the structural and magnetic properties as measured by neutrons
can be compared quantitatively
with the results of other characterisation techniques.

Neutron Scattering Instruments

  • Neutron diffraction
    Neutron diffraction
    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...

    • Crystallographic Instrumentation
    • Small angle neutron scattering
      Small angle neutron scattering
      Small angle neutron scattering is a laboratory technique, similar to the often complementary techniques of small angle X-ray scattering and light scattering, used for investigations of structure of various substances, with spatial sensitivity of about 1 - 1000 nm...

    • Neutron Reflectometry
      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...

  • Inelastic neutron scattering
    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....

    • Neutron triple-axis spectrometry
    • Neutron time-of-flight scattering
      Neutron time-of-flight scattering
      In Neutron time-of-flight scattering, a form of inelastic neutron scattering, the initial position and velocity of a pulse of neutrons is fixed, and their final position and the time after the pulse that the neutrons are detected are measured...

    • Neutron backscattering
      Neutron backscattering
      Neutron backscattering is one of several inelastic neutron scattering techniques. Backscattering from monochromator and analyzer crystals is used to achieve an energy resolution in the order of μeV...

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

    • Neutron resonance spin echo


First neutron-scattering instruments were installed at 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
Institut Laue-Langevin
The Institut Laue–Langevin, or ILL, is an internationally-financed scientific facility, situated in Grenoble, France. It is one of the world centres for research using neutrons...

 (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.

Performing a Neutron Scattering Experiment

Today, most neutron scattering experiments are performed by research scientists
who apply for beamtime at neutron sources through
a formal proposal procedure.
Proposals are assessed for feasibility and scientific interest.
Results of successful experiments are published in scientific journals.
Short reports on all performed experiments are collected
and published by the neutron sources.


Neutron scattering has been used to study various
vibration modes
Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies...


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