### DXC review

The Denver X-ray conference was quite excellent, mostly becauase of the people to talk to during the coffee breaks and the dinners (as always, there should be more of these and longer!). Here’s my quick review of the [...]

The Denver X-ray conference was quite excellent, mostly becauase of the people to talk to during the coffee breaks and the dinners (as always, there should be more of these and longer!). Here’s my quick review of the [...]

One paper I managed to miss for my review paper on data corrections is a paper by M. H. J. Koch from Hamburg. The paper is written in a nice informal way, replete with good quotes, where he talks about his experiences in instrument development for SAXS and WAXS beamlines. In particular the paper details the development of delay line (wire) detectors, and may form a good introduction into this topic. It seems that wire detectors may still have their uses: their rapid response to incoming photons still puts them among the fastest 2D detectors out [...]

Following my previous work in progress detailing the data correction steps to obtain good data, I finally had the chance to write this down in a review article. This review article (open access) has been submitted on Monday. After it has been reviewed and (hopefully) published in the journal, I will ensure that that latest version is available as an open access paper (thanks to funds from NIMS/ICYS). Until then, please enjoy the pre-submission version and as always feel free to comment! [Sep. 22 edit: the ArXiv link has been replaced with a link to the journal, where the paper is available under an open-access [...]

After browsing through a recent Journal of Applied Crystallography, I came across a paper by Deschamps. It indicates to me that there is a slight lack of information communication in some aspects of SAXS. Firstly, it mentions in the introduction that the advanced (Fourier-transform-based) SAXS analysis methods cannot “extract simultaneously the precipitate form factor and the precipitate size distribution”. Indeed they cannot, but neither can the classical methods (see for example page 147 of [1]). It is only when we assume a shape of the scatterer in the classical methods, that the number of possible size distributions reduces to a single solution. Inversely, if we assume a size distribution, there is only one general form factor which will match. This leads to the erroneous conclusion that the classical methods can result in a simultaneous determination of size and polydispersity. My main point, however, is the research on the behaviour of the Guinier method in [...]

…well, his famous SAXS analysis method. This documentGuinier_short, copyright Brian Pauw gives a short description and review of the applicability of the Guinier method to polydisperse systems. It also shows, through analysis of simulated data, what q-range should be measured for the Guinier method to be valid. In short, the rule of qmax=1.3/Rg still holds, but Rg in polydisperse systems is the volume-squared weighted Rg of the distribution. This then implies that the Guinier method for polydisperse systems quickly becomes unusable as the required qmax cannot be reached with anything but USAXS systems for polydisperse samples. This text (the linked PDF) is released under copyright (copyright by Brian R. Pauw, 2011) as I may want to include some of this in a later publication. I hope you [...]

Catching up to current affairs, I stumbled across this beauty. Now, I find this paper starts a little bit chaotic, but very quickly we come across some very useful equations indeed, and a link between the used equation for their analysis of phase transitions in fluids, and various other equations such as the Ornstein-Zernike structure factor and the Debye-Bueche equation. The equations published in this paper appear ready to be applied to a wide variety of amorphous scattering patterns, capable of extracting quite a few physical parameters! There will likely be much more on this topic as I get to apply these. To top it all off, the data used in the paper has been “extracted” from published graphics by Ms. A. Höhle. I can see her sitting there now with a ruler and a paper, meticulously noting down her estimates for the q and S values for each datapoint…. Perhaps it would be a good starting point for publishing some of our best data online so others can have a go at [...]

Hi all, I found some interesting papers for you, and a talk. Let me start with the talk. It is a TED talk (naturally) concerning TED talks. This nice introspective talk is actually of interest for all of us as it gives a few pointers to the set-up of excellent (and terrible) talks, with a fascinating slide on the colours used to evoke certain responses from the audience. Funny and applicable to us to make our talks better (and we know we need it, right?). The talk is here. Then there are some papers, two of which I found to be closely related to what I did. One paper discusses the stretching of voids in tensile experiments, simulating the 2D patterns with cylinders (but unfortunately not using a 2D fit, but 1D slices to arrive at a solution). That paper is here (yes, you have probably already read it since it is in j.appl.cryst., but just in case you have been too busy like me to read the table of contents…). Another one is similar, but I must admit I have not managed to [...]

Although I cannot say I completely grasp the underlying theory, the Bayesian approach to the Inverse Fourier Transformation of (isotropic) small-angle scattering patterns certainly appeals to me. The idea is that the small-angle scattering pattern can be transformed (back) into real-space, resulting in either a distance distribution function p(r), a correlation function gamma(r) (=r^2 p(r) ), or through double derivation of the result, into a chord length distribution (CLD). The Bayesian approach removes the user-defined input requirements of the standard IFT. So what can you do with all this real-space information? Well, first of all, being in real space means that one’s intuition can once more be applied (because intuition does not work in reciprocal space). For example: a maximum probability at a certain radius really may indicate that this is a characteristic length scale in the system. Secondly, the real-space p(r) may be a lot easier to fit than the scattering pattern [...]

The determination of the particle size distribution from small-angle scattering curves is usually achieved by assuming a certain statistical size distribution model (f.ex. a Schultz distribution, a Gaussian distribution or a log-normal distribution), and fitting this to the data using a non-linear least-squares optimisation method. Fitting multimodal distributions then implies the addition of multiple contributions, each with their own set of parameters. This increase in the number of parameters may make the fitting function unstable and the results unreliable. Retrieval of distribution model-independent size information therefore would be of great benefit to the experimentalist. One problem with this is that the scattering intensity of particles scales with the volume of the particle squared (i.e. for spherical particles with the radius to the sixth power). This then causes information on the small particle sizes to be drowned out by the signal of the larger particles. A method to [...]

The famous question of the uninitiated in small-angle scattering is: “Do you have a bit of software which will give me an answer from my data?”. After a lengthy explanation (coloured with some anecdotes) about why small-angle scattering is not a uniquely defined problem with an often unique answer such as wide-angle diffraction might be, the new user is then left with a copy of Matlab or Fit2D and asked not to return until he has a more “sensible” question. I guess this is because there are not many alternative treatments for these users. These days, I may also give them a copy of the most recent SAXSGUI, but since this lacks quite some fitting functions, it is only really useful for users who already know what they are doing and can program their own 1D or 2D fitting functions. An all-in-one package that is not only good for beginning users but can also remain a useful tool for advanced users is not something which I’ve seen so far. Until now, that is. [...]

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