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.
SAS techniques can give information about the size, shape and orientation of structures in a sample.
The most important feature of the SAS method is its potential for analyzing the inner structure of disordered systems, and frequently the application of this method is a unique way to obtain direct structural information on systems with random arrangement of density inhomogeneities in such large-scales.
Currently, the SAS technique, with its well-developed experimental and theoretical procedures and wide range of studied objects, is a self-contained branch of the structural analysis of matter.
Small-angle scattering is particularly useful because of the dramatic increase in forward scattering that occurs at phase transitions, known as critical opalescence, and because many materials, substances and biological systems possess interesting and complex features in their structure, which match the useful length scale ranges that these techniques probe.
The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, defects in materials, surfactants, colloids, ferromagnetic correlations in magnetism, alloy segregation, polymers, proteins, biological membranes, viruses, ribosome and macromolecules.
While analysis of the data can give information on size, shape, etc., without making any model assumptions a preliminary analysis of the data can only give information on the radius of gyration for a particle using Guinier's equation.
is the angle between the incident beam and the detector measuring the scattered intensity, and
One interpretation of the scattering vector is that it is the resolution or yardstick with which the sample is observed.
In the case of a two-phase sample, e.g. small particles in liquid suspension, the only contrast leading to scattering in the typical range of resolution of the SAS is simply Δρ, the difference in average scattering length density between the particle and the surrounding liquid, because variations in ρ due to the atomic structure only become visible at higher angles.
This means that the total integrated intensity of the SAS pattern (in 3D) is an invariant quantity proportional to the square Δρ2.
In 1-dimensional projection, as usually recorded for an isotropic pattern this invariant quantity becomes
It is also assumed that the density does not vary in the liquid or inside the particles, i.e. there is binary contrast.
At wave numbers that are relatively large on the scale of SAS, but still small when compared to wide-angle Bragg diffraction, local interface intercorrelations are probed, whereas correlations between opposite interface segments are averaged out.
A small-angle scattering pattern can be fitted with intensities calculated from different model shapes when the size distribution is known.
This is a necessary procedure that eliminates the concentration effect, which is a small shoulder that appears in the intensity patterns due to the proximity of neighbouring particles.
where When the intensities from low concentrations of particles are extrapolated to infinite dilution, the structure factor is equal to 1 and no longer disturbs the determination of the particle shape from the form factor
According to the Guinier approximation the intensity at small q depends on the radius of gyration of the particle.
[4] An important part of the particle shape determination is usually the distance distribution function
Small-angle scattering studies were initiated by André Guinier (1937).
[6] Subsequently, Peter Debye,[7] Otto Kratky,[8] Günther Porod,[9] R. Hosemann[10] and others developed the theoretical and experimental fundamentals of the method and they were established until around 1960.
As a 'low resolution' diffraction technique, the worldwide interests of the small-angle scattering community are promoted and coordinated by the Commission on Small-Angle Scattering of the International Union of Crystallography (IUCr/CSAS).
One such network, canSAS - the acronym stands for Collective Action for Nomadic Small-Angle Scatterers, emphasising the global nature of the technique, champions the development of instrumental calibration standards and data file formats.
There is a long history of international conferences on small-angle scattering.
The André Guinier Prize (in honor of André Guinier) is given for lifetime achievement, a major breakthrough, or an outstanding contribution to the field of small-angle scattering.
The prize jury is assembled by the conference organizers and staff of Anton Paar.
