Neutron diffraction

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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 the different scattering properties of neutrons versus x-rays complementary information can be obtained.

Description

Principle

Neutrons are particles found in the atomic nucleus of almost all atoms, but they are bound. The technique requires free neutrons and these normally do not occur in nature, because they have limited life-time. In a nuclear reactor, however, neutrons can be set free through nuclear decay particularly when fission occurs. All quantum particles can exhibit wave phenomena we typically associate with light or sound. Diffraction is one of these phenomena; it occurs when waves encounter obstacles whose size is comparable with the wavelength. If the wavelength of a quantum particle is short enough, atoms or their nuclei can serve as diffraction obstacles. When a beam of neutrons emanating from a reactor is slowed down and selected properly by their speed, their wavelength lies near one angstrom (0.1 nanometer), the typical separation between atoms in a solid material. Such a beam can then be used to perform a diffraction experiment. Impinging on a crystalline sample it will scatter under a limited number of well-defined angles according to the same Bragg's law that describes X-ray diffraction.

Instrumental requirements

A neutron diffraction measurement requires a neutron source (e.g. a nuclear reactor or spallation source), a sample (the material to be studied), and a detector. Samples sizes are large compared to those used in X-ray diffraction. The technique is therefore mostly performed as powder diffraction. At a research reactor other components such as crystal monochromators or filters may be needed to select the desired neutron wavelength. Some parts of the setup may also be movable. At a spallation source the time of flight technique is used to sort the energies of the incident neutrons (Higher energy neutrons are faster), so no monochromator is needed, but rather a series of aperture elements synchronized to filter neutron pulses with the desired wavelength.

Nuclear scattering

Neutrons interact with matter differently than x-rays. X-rays interact primarily with the electron cloud surrounding each atom. The contribution to the diffracted x-ray intensity is therefore larger for atoms with a large atomic number (Z) than it is for atoms with a small Z. On the other hand, neutrons interact directly with the nucleus of the atom, and the contribution to the diffracted intensity is different for each isotope; for example, regular hydrogen and deuterium contribute differently. It is also often the case that light (low Z) atoms contribute strongly to the diffracted intensity even in the presence of large Z atoms. The scattering length varies from isotope to isotope rather than linearly with the atomic number. An element like vanadium is a strong scatterer of X-rays, but its nuclei hardly scatter neutrons, which is why it often used as a container material. Non-magnetic neutron diffraction is directly sensitive to the positions of the nuclei of the atoms.

A major difference with X-rays is that the scattering is mostly due to the tiny nuclei of the atoms. That means that there is no need for an atomic form factor to describe the shape of the electron cloud of the atom and the scattering power of an atom does not fall off with the scattering angle as it does for X-rays. Diffractograms therefore can show strong well defined diffraction peaks even at high angles, particularly if the experiment is done at low temperatures. Many neutron sources are equipped with liquid helium cooling systems that allow to collect data at temperatures down to 4.2 K. The superb high angle (i.e. high resolution) information means that the data can give very precise values for the atomic positions in the structure. On the other hand, Fourier maps (and to a lesser extent difference Fourier maps) derived from neutron data suffer from series termination errors, sometimes so much that the results are meaningless.

Magnetic scattering

Although neutrons are uncharged, they carry a spin, and therefore interact with magnetic moments, including those arising from the electron cloud around an atom. Neutron diffraction can therefore reveal the microscopic magnetic structure of a material.^[1]

Magnetic scattering does require an atomic form factor as it is caused by the much larger electron cloud around the tiny nucleus. The intensity of the magnetic contribution to the diffraction peaks will therefore dwindle towards higher angles.

History

The first neutron diffraction experiments were carried out in 1945 by Ernest O. Wollan using the Graphite Reactor at Oak Ridge. He was joined shortly thereafter (June 1946)^[2] by Clifford Shull, and together they established the basic principles of the technique, and applied it successfully to many different materials, addressing problems like the structure of ice and the microscopic arrangements of magnetic moments in materials. For this achievement Shull was awarded one half of the 1994 Nobel Prize in Physics. Wollan had died in the 1990s. (The other half of the 1994 Nobel Prize for Physics went to Bert Brockhouse for development of the inelastic scattering technique at the Chalk River facility of AECL. This also involved the invention of the triple axis spectrometer). Brockhouse and Shull jointly take the somewhat dubious distinction of the longest gap between the work being done (1946) and the Nobel Prize being awarded (1994).

Uses

Neutron diffraction can be used to determine the static structure factor of gases, liquids or amorphous solids. Most experiments, however, aim at the structure of crystalline solids, making neutron diffraction an important tool of crystallography.

Neutron diffraction is closely related to X-ray powder diffraction.^[3] In fact the single crystal version of the technique is less commonly used because currently available neutron sources require relatively large samples and large single crystals are hard or impossible to come by for most materials. Future developments, however, may well change this picture. Because the data is typically a 1D powder diffractogram they are usually processed using Rietveld refinement. In fact the latter found its origin in neutron diffraction (at Petten in the Netherlands) and was later extended for use in X-ray diffraction.

One practical application of elastic neutron scattering/diffraction is that the lattice constant of metals and other crystalline materials can be very accurately measured. Together with an accurately aligned micropositioner a map of the lattice constant through the metal can be derived. This can easily be converted to the stress field experienced by the material. This has been used to analyse stresses in aerospace and automotive components to give just two examples. This technique has led to the development of dedicated stress diffractometers, such as the ENGIN-X instrument at the ISIS neutron source.

Neutron Diffraction can also be employed to give insight into the 3D structure of novel molecules such as Nanoparticles, Nanorods, Nanotubes, Fullerenes ^[4] .^[5]

Hydrogen, null-scattering and contrast variation

Neutron diffraction can be used to establish the structure of low atomic number materials like proteins and surfactants much more easily with lower flux than at a synchrotron radiation source. This is because some low atomic number materials have a higher cross section for neutron interaction than higher atomic weight materials.

One major advantage of neutron diffraction over X-ray diffraction is that the latter is rather insensitive to the presence of hydrogen (H) in a structure, whereas the nuclei ¹H and ²H (i.e. Deuterium, D) are strong scatterers for neutrons. This means that the position of hydrogen in a crystal structure and its thermal motions can be determined far more precisely with neutrons. In addition the neutron scattering lengths b_H = -3.7406(11) fm ^[6] and b_D = 6.671(4) fm,^[6] for H and D respectively, have opposite sign allowing for contrast variation. In fact there is a particular isotope ratio for which the contribution of the element would cancel, this is called null-scattering. In practice however it is not desirable to work with the relatively high concentration of H in such a sample. The scattering intensity by H-nuclei has a large inelastic component and this creates a large continuous background that is more or less independent of scattering angle. The elastic pattern typically consists of sharp Bragg reflections if the sample is crystalline. They tend to drown in the inelastic background. This is even more serious when the technique is used for the study of liquid structure. Nevertheless, by preparing samples with different isotope ratios it is possible to vary the scattering contrast enough to highlight one element in an otherwise complicated structure. The variation of other elements is possible but usually rather expensive. Hydrogen is inexpensive and particularly interesting because it plays an exceptionally large role in biochemical structures and is difficult to study structurally in other ways.

Further reading

• Lovesey, S. W. (1984). Theory of Neutron Scattering from Condensed Matter; Volume 1: Neutron Scattering. Oxford: Clarendon Press. ISBN 0-19-852015-8. 
• Lovesey, S. W. (1984). Theory of Neutron Scattering from Condensed Matter; Volume 2: Condensed Matter. Oxford: Clarendon Press. ISBN 0-19-852017-4. 
• Squires, G.L. (1996). Introduction to the Theory of Thermal Neutron Scattering (2nd ed.). Mineola, New York: Dover Publications Inc. ISBN 0-486-69447-X. 

Applied Computational Powder Diffraction Data Analysis

• Young, R.A., ed (1993). The Rietveld Method. Oxford: Oxford University Press & International Union of Crystallography. ISBN 0-19-855577-6. 

See also

• Crystallography
• Crystallographic database
• Electron diffraction
• Neutron crystallography

References

1. ^ Neutron diffraction of magnetic materials / Yu. A. Izyumov, V.E. Naish, and R.P. Ozerov ; translated from Russian by Joachim Büchner. New York : Consultants Bureau, c1991.ISBN 0-306-11030-X
2. ^ Clifford Shull: Early development of neutron scattering. Rev. Mod. Phys. 67 (1995) 753–757
3. ^ Neutron powder diffraction by Richard M. Ibberson and William I.F. David, Chapter 5 of Structure determination form powder diffraction data IUCr monographphs on crystallography, Oxford scientific publications 2002, ISBN 0-19-850091-2
4. ^ Ojeda-May, P., Terrones, M., Terrones, H., Hoffman, D., Proffen, T., Cheetham, A. (2007), "Determination of chiralities of single-walled carbon nanotubes by neutron powder diffraction technique", Diamond and Related Materials 16: 473–476 
5. ^ Page, K., Proffen, T., Niederberger, M., Seshadri, R. (2010), "Probing Local Dipoles and Ligand Structure in BaTiO3 Nanoparticles", Chemistry of Materials 22: 4386–4391 
6. ^ ^{a b} Sears, V. F. (1992), "Neutron scattering lengths and cross sections", Neutron News 3: 26–37 

External links

• National Institute of Standards and Technology Center for Neutron Research
• Stress determination in crystalline materials