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 Mesoscopic physics is a subdiscipline of condensed matter physics that deals with materials of an intermediate size. These materials range in size between the nanoscale for a quantity of atoms (such as a molecule) and of materials measuring mic ...

of about 1–100 nm. Small angle neutron scattering is in many respects very similar to

small-angle X-ray scattering Small-angle X-ray scattering (SAXS) is a small-angle scattering technique by which nanoscale density differences in a sample can be quantified. This means that it can determine nanoparticle size distributions, resolve the size and shape of (monodi ...

(SAXS); both techniques are jointly referred to as

small-angle scattering Small-angle scattering (SAS) is a scattering technique based on deflection of collimated radiation away from the straight trajectory after it interacts with structures that are much larger than the wavelength of the radiation. The deflection is sma ...

(SAS). Advantages of SANS over SAXS are its sensitivity to light elements, the possibility of isotope labelling, and the strong scattering by magnetic moments.

Technique

During a SANS experiment a beam of neutrons is directed at a sample, which can be an

aqueous An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be rep ...

solution, a solid, a

powder A powder is a dry, bulk solid composed of many very fine particles that may flow freely when shaken or tilted. Powders are a special sub-class of granular materials, although the terms ''powder'' and ''granular'' are sometimes used to distin ...

, or a

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

. The neutrons are elastically scattered by nuclear interaction with the nuclei or interaction with magnetic momentum of unpaired electrons. In X-ray scattering, photons interact with the electronic cloud so the bigger the element, the bigger the effect is. In neutron scattering, neutrons interact with nuclei and the interaction depends on the isotope; some light elements like deuterium show similar scattering cross section as heavy elements like Pb. In zero order

dynamical theory of diffraction The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice are atomic crystal structures or nanometer-scale multi ...

the

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...

is directly related to the

scattering length density Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

and is a measure of the strength of the interaction of a neutron wave with a given nucleus. The following table shows the

neutron scattering length A neutron may pass by a nucleus with a probability determined by the nuclear interaction distance, or be absorbed, or undergo scattering that may be either coherent or incoherent. The interference effects in coherent scattering can be computed via t ...

for a few chemical elements (in 10⁻¹² cm). Note that the relative scale of the scattering lengths is the same. Another important point is that the scattering from hydrogen is distinct from that of

deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...

. Also, hydrogen is one of the few elements that has a negative scattering length, which means that neutrons deflected from hydrogen are 180° out of phase relative to those deflected by the other elements. These features are important for the technique of contrast variation (see below).

Related techniques

SANS usually uses collimation of the neutron beam to determine the scattering angle of a neutron, which results in an ever lower signal-to-noise ratio for data that contains information on the properties of a sample at relatively long length scales, beyond ~1 μm. The traditional solution is to increase the brightness of the source, as in Ultra Small Angle Neutron Scattering (USANS). As an alternative Spin-echo Small-angle Neutron Scattering (SESANS) was introduced, using

neutron spin echo 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 Walte ...

to track the scattering angle, and expanding the range of length scales which can be studied by neutron scattering to well beyond 10 μm.

Grazing-incidence small-angle scattering Grazing-incidence small-angle scattering (GISAS) is a scattering technique used to study nanostructured surfaces and thin films. The scattered probe is either photons (grazing-incidence small-angle X-ray scattering, GISAXS) or neutrons (grazing-inci ...

(GISANS) combines ideas of SANS and of

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 var ...

In biology

A crucial feature of SANS that makes it particularly useful for the biological sciences is the special behavior of hydrogen, especially compared to deuterium. In biological systems hydrogen can be exchanged with deuterium which usually has minimal effect on the sample but has dramatic effects on the scattering. The technique of contrast variation (or contrast matching) relies on the differential scatter of hydrogen vs. deuterium. Figure 1 shows the scattering length density for

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...

and various biological macromolecules as a function of the deuterium concentration. (Adapted from.) Biological samples are usually dissolved in water, so their hydrogens are able to

exchange Exchange may refer to: Physics *Gas exchange is the movement of oxygen and carbon dioxide molecules from a region of higher concentration to a region of lower concentration. Places United States * Exchange, Indiana, an unincorporated community * ...

with any deuteriums in the

solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...

. Since the overall scatter of a molecule depends on the scatter of all its components, this will depend on the ratio of hydrogen to deuterium in the molecule. At certain ratios of H₂O to D₂O, called match points, the scatter from the molecule will equal that of the solvent, and thus be eliminated when the scatter from the buffer is subtracted from the data. For instance the match point for proteins is typically around 40–45% D₂O, and at that concentration the scatter from the protein will be indistinguishable from that of the buffer. To use contrast variation, different components of a system must scatter differently. This can be based on inherent scattering differences, e.g. DNA vs. protein, or arise from differentially labeled components, e.g. having one protein in a complex deuterated while the rest are protonated. In terms of modelling, small-angle X-ray and neutron scattering data can be combined with the program MONSA. An example in which SAXS, SANS and EM data has been used to build an atomic model of a large multi-subunit enzyme has recently been published. For some examples of this method see. For the study of large scales of matter (e.g. Soft matter) and slow dynamics, very cold neutrons (VCN) should be used. However, because of the weak neutron flux and lack of optical components in this range, most scientists use neutrons of shorter wavelengths. Efforts are being made to remedy this lack.

Instruments

There are numerous SANS instruments available worldwide at neutron facilities such as

research reactor Research reactors are nuclear fission-based 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 maritim ...

s or spallation sources.

References

Textbooks

* Fejgin, Lev A.: ''Structure analysis by small-angle X-ray and neutron scattering.'' New York: Plenum (1987). * Higgins, Julia S.; Benoît, Henri: ''Polymers and neutron scattering.'' Oxford: Clarendon Press (1994?).

External links

The Small-Angle Scattering portal
link collection, with elaborate software list
World directory of SANS instruments
* B. Hammouda
Probing Nanoscale Structures – The SANS Toolbox
(690 pages)
Small Angle Scattering at ISIS Neutron and Muon Source
{{DEFAULTSORT:Small-Angle Neutron Scattering Small-angle scattering Neutron scattering