Small-angle scattering

Most of this information is taken [with permission from the PCCP Owner Societies] from my recent review: “Practical Applications of small-angle neutron scattering”, which was written with a broad audience in mind. I’m currently looking into the possibility of uploading that article onto this site.

Small-angle scattering (SAS) is a powerful analysis tool, capable of selectively resolving structures of the order 1 nm to over 100 nm. Because of this, it is commonly applied to a variety of scientific fields ranging from soft materials, (molecular self-assemblies, gels etc.) to hard, porous structures or even precipitates in steels. Probably the major advantage of the technique is the ability to measure a statistically significant bulk average particle size over a large sample volume. For SAS with neutrons (small-angle neutron scattering, SANS) this is typically in the region of 10-100 mm³. This allows a statistically significant number of scatterers to be measured in a single snap-shot. For example, over 10¹⁴ particles occupy a 10 mm³sample if their average diameter is 10 nm and concentration is 1 vol%. Imaging such a number using microscopy would be inconceivable, even with the aid of image analysis software.

A second advantage of scattering techniques is their ability to visualize the internal structure of materials in-situ, for example in solution in capillaries, at elevated temperatures, under pressure, applied load or in the presence of an external magnetic field (vide infra). The ability to do this removes the need for pre-treatment steps such as drying, freezing or sectioning that may otherwise perturb a sample. In this respect, neutrons have particular advantages over X-rays (SAXS), having a larger penetration depth and not suffering from issues of sample beam damage.

Finally, SANS affords the possibility of using contrast variation to selectively highlight different parts of a sample. This is one by isotopic labelling, typically by exchanging hydrogen (¹H) for deuterium (²D), which have very different scattering power. This is particularly useful for measuring SANS of hydrogen-rich organic or biological materials. As you might guess if you’ve looked at my “research” tab, I use this technique a lot in my work.

Unfortunately, all is not rosy when SANS is concerned. Arguably, its more widespread application has been limited by some pretty serious disadvantages. The first of these is a historical problem with access. While direct access schemes such as those run by ISIS, UK have addressed this issue, the simple fact is that you have to go to an external, usually government-run and funded “large scale facility” to perform SANS measurements. This can be a massively disadvantage if you have highly sensitive samples, although in my case doesn’t present too many problems.

The second issue is the low flux of neutron sources in comparison to even lab-scale X-ray sources. This means that SANS requires longer measurement times to obtain statistically reasonable data! 15-30 minutes minimum, usually, even for strongly scattering samples.

Finally, and perhaps most problematic of all, is a lack of familiarity outside the scattering community of the general abilities of small-angle scattering. This is compounded by the relative complexity of data analysis in comparison to more visual microscopy techniques. Because of this, academics and industrial researchers are often unaware of the power of SANS (or SAXS) and its potential to address some of their problems, or unwilling to try it! My goal is to attempt to break down some of these barriers….I’ll post here in the future on my successes in this respect.

Notes on data reduction and analysis:

***Any data modelling should always be carried out alongisde information from other techniques!***

Just because a fit looks good, it doesn’t mean that it is the correct solution. Often many solutions exist for the same data-set, especially given the error on the measured SAS intensity (>1%), which must be considered to generate goodness-of-fit values. The use of other techniques (e.g. microscopy) to, for example, confirm the shape of the scatterer (particle), is a powerful way to justify the use of one model over another. This allows the strengths of SAS – i.e. in situ measurement of a bulk average particle size/structure – to be exploited.

Obviously, to minimize error on the measured SAS intensity, the experiment must be carried out carefully, with corrections as appropriate. Currently, 1% error on the measured I(Q) for each data point is considered a minimum – and this is only obtainable for SAXS after many corrections, most of which are non-standard. So your data most likely has >>1% error on I(Q) – especially for SANS measurements. If it is less, then the error calculation is not taking everything into account! There’s a nice review of the state-of-the-art about data reduction (correction) here. To get useable data in absolute units (inverse centimeters by convention), that can be compared with data from other sources, the bare minimum of things that need to be considered are: (1) sample thickness, (2) measurement time (3) sample transmisson [absorption] (4) sample background, (5) detector-specific corrections, such as bad pixel marking, dark current etc and (6) the calibration factor determined by measuring the scattering pattern of a known sample. At many neutron and X-ray sources in Europe (but not, for example, at SPring8 in Japan) it seems to be becoming common for these corrections to be carried out at the beam-line with the help of the in-house scientists, meaning that the users take home data that can directly be analyzed. This practice is to be encouraged!

Analysis Software

There are many different ways to analyze SAS data, many of which tend to invoke quasi-religious devotion in their users. My preferred method (i.e. the one I’ve used so far in most of my publications that involve SAS techniques) is to model the data to an assumed shape (with justification – see above), although I appreciate that this method is not always appropriate. I should note that I’ve also been part of studies that have used the IFT method of Glatter and a bespoke, assumption-free Monte Carlo method (coming soon)! In my opinion, all methods are valid provided sufficient care is taken in their use.

SASfit (by Joachim Kohlbrecher and Ingo Bressler) is currently my favorite software for modelling SAS data, freely available here or here. It provides more models and combinations of models than probably will even be needed or justified (far, far more than the only recently released SASview, for example, which aims to replace FISH – the software I used during my PhD), the ability to chose the distribution type (e.g. Gaussian, Schultz-Zimm, LogNormal etc. – for polydisperse systems where justified). Documentation is excellent. However, as with pretty much any of the SAS software I’ve have had the pleasure (or misfortune) of attempting to use, the learning curve is quite steep at times – so be prepared to be frustrated and to turn to the manual from time to time! Not sure I’ve found many pieces of software that I haven’t had to do that with though, so this is hardly a criticism of what is really excellent work. I found using the software alongside “the SANS toolbox” (see link below) helped quite a bit. I should note that two (at least) powerful collections of software are available as plugins for IgorPro, developed by the folks at NIST (particularly S. Kline) or by Jan Ilavsky (IRENA). I haven’t used these much, mainly through not having purchased a copy of IgorPro, however I have heard them to be good, user friendly and rather comprehensive in terms of model availability, documentation etc.

A rather comprehensive list of many software packages available for SANS analysis etc. can be found here.

LINKS

Useful online resources:

“SAS Portal” – by the canSAS group – not had much time to check this out, but it looks like a good depository for useful links and information.

“The SANS toolbox” by B. Hammouda – a thoroughly recommended introduction to SANS, guide to performing experiments, reducing data and performing analyses.

“Looking at nothing” – Weblog by friend and collaborator Brian Pauw. Lots of interesting information on small-angle scattering, including (but not limited) to posts about instrument design and software development

Books or book chapters available online (not a comprehensive list – will be added to as and when new links are found):

“Small-angle X-ray Scattering” by O. Glatter and O. Kratky

“Structure analysis by Small-angle X-ray and Neutron Scattering” by L. A. Feigin and D. I. Svergun

“Introduction to Small-Angle Neutron Scattering and Neutron Reflectometry” by A. J. Jackson

Neutron beam-lines that I frequently use:

LOQ and SANS2D at ISIS, RAL, UK

D11 and D22 at ILL, France