# Neutrons

Production of neutrons requires a large scale facility like a scientific nuclear reactor for fission production of neutrons, or a large particle accelerator with a metal target for spallation production of neutrons. In order to perform neutron experiments on condensed matter samples, scientists have to travel to one of the few large-scale science facilities.

Neutrons are subatomic particles and can be found in the nucleus of most atoms. The mass of a neutron is approximately the same as a proton mn = 1.675*10-27kg, but unlike protons, neutrons carry no electrical charge. If neutrons are expelled from the nucleus, as is done purposefully at spallation source facility, the neutrons will decay with a half time of τ = 886s – close to 15 minutes. The mass of a neutron is approximately the same as a proton, which equals 1.675 times 10 to the power of -27 kilograms, but unlike protons, neutrons carry no electrical charge. If neutrons are expelled from the nucleus, as is done purposefully at spallation source facility, the neutrons will decay with a half time of 886 second, which is close to 15 minutes. This is well above the time it takes a neutron to travel from the source to the instrument in a neutron experiment, which is usually less than a second.

Figure 1: a) Illustration of the atomic structure of an atom. b) the de Broglie equation. c) The kinetic energy of the neutrons.

Neutrons exist as both particles and waves, called the particle-wave duality which is the cornerstone of quantum mechanics. The relation between the velocity and the wavelength of the neutron is described by the de Broglie equation (see figure 1. b).

Here λ is the wavelength, mn is the mass of the neutron, v is the velocity, and h is the Planck constant. The product of mass and velocity is also called the momentum p = mnv. Since the mass is constant we can see that the wavelength and velocity are inversely proportional λ ≈ 1/v. The kinetic energy of the neutrons can be written as the equation in figure 1.c. Here lambda is the wavelength, mn is the mass of the neutron, v is the velocity, and h is the Planck constant. The product of mass and velocity is also called the momentum, p equals m n times velocity. Since the mass is constant we can see that the wavelength and velocity are inversely proportional, lambda is approximately 1 divided by v. The kinetic energy of the neutrons can be written as the equation in figure 1 c

We see that the energy, E, of a neutron is proportional to the velocity squared, v2 and inversely proportional to the wavelength squared, λ2. We see that the energy, E, of a neutron is proportional to the velocity squared, and inversely proportional to the wavelength squared . The important thing to notice that if we know one of the quantities we know them all. This is useful for instance when we deduce the energy of neutrons by recording the time it takes them to move a certain distance.

Bertram N. Brockhouse and Clifford G. Shull received the Nobel prize in 1994 for “pioneering contributions to the development of neutron scattering techniques for studies of condensed matter”. Since their work, neutron techniques have successfully been used in a variety of scientific fields like medical research, biochemistry, machine engineering, and more. The strength of the neutron techniques can be captured in the five points below

• Energy and wavelength: The wavelength of thermal neutrons matches the inter-atomic distances in solids, Ångstrøms or 10-10m, and the energies match the elementary excitations meV, 1.6×10−16 Angstroms or 10 to the power of -10 meters, and the energies match the elementary excitations in electronvolts, 1.6 times 10 to the power of -16 joules. This simultaneous match make neutrons a very useful probe for studying the structure and dynamics of atoms in solid samples. We could, for example, use neutron beams to study how lithium is bound in an atomic structure in a charged battery and how it moves by diffusion in a lithium-ion battery during discharge.
• Isotopes and light elements: In neutron experiments one can distinguish between different elements in a sample including light elements such as Hydrogen or Lithium which are almost invisible to, for example, X-rays. We can also distinguish between different isotopes of the same element in a sample, for instance between Hydrogen (1H) and Deuterium (2H) because the neutron cross-section depends on the composition of the nucleus of each atom in the sample. It is therefore possible to get the overall shape of the molecule and identify specific atoms position in the molecule. The large variation in the neutron cross-sections between element can for example be used to “highlight” a specific part of a molecule, where 1H is replaced by 2H hydrogen is replaced by deuterium or to track the movement of a particular light element in a chemical reaction, like the lithium movement in a lithium ion battery as it is discharged.
• Transparency: Most everyday objects are transparent to neutrons because the neutrons interact only weakly with matter. Thus the neutron beam can easily penetrate most large objects made from materials composed by heavy elements like a combustion engine which would be difficult with e.g. for example X-rays. It can therefore be used to investigate samples in a bulky sample environment or see the internal workings of an engine, or battery, in use. This is very useful since a measurement can be performed on the object as it is sample rather than having to disassemble it or cut it into pieces to study the different components.
• Quantitative experiments: Since neutrons interact only weakly with matter, it also makes it easier to compare theory to experimental data, even quantitatively. For example, you can make a simulation of the neutron experiment with a sample model based on theory and compare the simulated data directly to real measured data. Since neutrons can penetrate a large sample measurements can be performed at a bulk sample and not just the surface of it. So we can for example probe the effect of discharge in the entire battery during discharge.
• Magnetism: Neutrons have a magnetic moment, which means that they also can be used to investigate the magnetic structure and magnetic excitations of materials.