I have written some small, simple bits of Matlab software that can generate scattering patterns in the range you request for polydisperse, dilute spheres or ellipsoids. While nothing new per se, this implementation is guaranteed to produce correct scattering patterns irrespective of the width of the distribution. Allow me to quickly explain.

The normal way of calculating these patterns in fitting functions and the likes, is to choose an upper size limit (perhaps related to the width and mean of the distribution), and divide the size range between zero and this upper limit into perhaps 100 different sizes. Then the scattering pattern of each of these contributions is calculated, multiplied with their probability (obtained from the probability (or size) distribution function), multiplied with the square of the particle volume for that size, and then summed. In all, then, this is a numeric integration over the volume-square weighted size distribution.

The problem lies in the determination of the upper limit and the number of divisions required. In the past, I have tried using the cumulative distribution function to select “smart” divisions, or adjusting the width and mean to compensate for the volume-square weighting, but this often resulted in the appearance of oscillatory behaviour in the scattering patterns. An alternative solution was therefore required.

These functions are not necessarily fast enough for fitting purposes, but they can be used for checking the applicability of your fitting procedures. You should get out of your fitting functions what you put into these simulated patterns.

These functions work by random generation of a number of spheres or ellipsoids. A scattering pattern is calculated from an initial number of spheres or ellipsoids. Then, the scattering pattern is calculated of the original block with the addition of a new set of shapes. This is repeated until the effect of adding a new block on the scattering pattern no longer exceeds a certain threshold.

Included are the programs for generating scattering patterns using polydisperse distributions of spheres or ellipsoids. All distributions supported by the “statistics library”’s RANDOM function are available. For ellipsoids, an additional distribution can be used for the aspect ratio. If the use is not clear, let me know and I will write some more extensive documentation.

The programs are: perfectpattern_spheres and perfectpattern_ellipsoids. Have fun!

We teach. Every one of us. If we have a classroom of students, it is obvious, but also when we talk to colleagues, we sometimes try to teach them something (even if it is only our point of view).

I spoke last time about the teaching horrors that modern textbooks have. Well, this video by Dan Meyer explains why the textbooks are absolutely not helping to teach by asking the questions wrong, and he proposes an alternative way to pose the questions. He also, by the way, has a nice blog full of examples of how to get a class of students to actually think.

This gets me thinking. How can we apply this to our presentations? Are we really engaging our audience by starting with a “talk outline”, or should we pose the final question as simple as possible and work from there? I will be experimenting with this and I will let you know how it goes!

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 analysing it?

On another note, I want to point you towards the horror of textbooks. How fitting then, that the next special issue of the J. of Appl. Cryst. is about teaching! As you may have read on Slashdot a few weeks ago, textbooks are still very expensive, even for topics as stagnant as elementary mathematics. prof. Feynman also had a few words to say on the topic of textbooks. And there are now some alternatives popping up allowing your students an alternative to ridiculous and expensive textbooks: Free textbooks.

http://www.curriki.org/xwiki/bin/view/Main/WebHome

http://about.ck12.org/

http://www.lightandmatter.com/

http://www.wikibooks.org/

If you know more, let me know and I will add them to the list!

There is a scathing review coming out on the topic of academia (particularly the US one). While the general tone of the dissertation is negative, they do indicate a strong need, or rather duty, of scientists to communicate our findings as clear and understandibly as possible. Personally, I completely agree with this. Clear communication sometimes hinges on explaining everything in cool graphics, be it in posters or in presentations. So how do we learn how to create cool graphics? Well, one avenue is comics! They have supplied us with concise stories, be it comical or educational, applying graphics to provide a visual narrative.

One of my favourite online comics is Dresden Codak. Witty, beautifully drawn and often requiring quite some thought to understand the story, it is everything I seek in a comic. The author/artist also provides us with excellent tools to learn about visualisations, as he keeps a superb weblog analysing various forms of visual narration. This post is my favourite, as it indicates very clearly how we can use space intelligently in our graphics to tell a story, and what pitfalls to avoid. I hope it will provide us all with good inspiration for our next talks! Good luck!

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 completely read it yet. Looks interesting, though.

Also, it is not everyday you see a new geometry diffractometer being suggested. I wish these guys good luck in the further development of their diffractometer and I hope they publish some fantastic results when they get to it.

At the moment, I am trying to do a literature research (something I should have done much, much earlier) on in-situ particle growth studies using SAXS. I have come up with quite some references by now, but if you know an excellent study, do drop me a line at brian at stack dot nl, and I will be eternally grateful. If you are, on the other hand, interested in co-authoring a small review paper on the topic, I am always open to collaborate!

Dear all, the reason I have been silent for a few weeks was that I was waiting for this:

Herewith (with a little bit of pride), I would like to present the first paper published as a result of my Ph.D. research. This groundbreaking paper is naturally essential reading for all working in the fields of small-angle scattering, fibres, world politics and astrology. The paper is published at:
Journal of Applied Crystallography, 2010, Volume 43, pages 837-849

And is also available for download from here.

Abstract: After consideration of the applicability of classical methods, a novel analysis method for the characterization of fibre void structures is presented, capable of fitting the entire anisotropic two-dimensional scattering pattern to a model of perfectly aligned, polydisperse ellipsoids. It is tested for validity against the computed scattering pattern for a simulated nanostructure, after which it is used to fit the scattering from the void structure of commercially available heat-treated poly(p-phenylene terephtalamide) fibre and its as-spun precursor fibre. The application shows a reasonable fit and results in size distributions for both the lengths and the widths of the ellipsoidal voids. Improvements to the analysis methods are compared, consisting of the introduction of an orientation distribution for the nano-ellipsoids, and the addition of large scatterers to account for the effect of fibrillar scattering on the scattering pattern. The fit to the scattering pattern of as-spun aramid fibre is improved by the introduction of the large scatterers, while the fit to the scattering pattern obtained from the heat-treated fibre improves when an orientation distribution is taken into account. It is concluded that, as a result of the heat treatment, the average width and length of the scatterers increase.

Thank you all for your interest! I will be posting again in a few weeks.

I have a new movie made, which may be a bit more suited for those of you working with isotropic samples. Instead of a bundle of filaments it now displays a box of isotropic scatterers at the sample position. Please feel free to download and use this one in your presentations. You can also contact me for a larger version.

2Dsaxs_new_w

Hi all,

I am not abandoning you, I am merely in the middle of a string of four experiments divided over three beamtimes in an almost consecutive span of 10 days, which required preparation and lots of catch-up sleep in between. I have something useful coming up soon, and a publication in print as well, which I’ll be happy to share with you once it is out (August).

Yours sincerely,

Brian.

Just a quick heads up before I start on the ellipsoid form factor alternative: I spoke last post of the efforts for data archiving for possible open-access purposes. Shortly after that post, this news appeared. It seems we may be heading (more rapidly than I thought) towards an age where we have to make data public, which means archiving with metadata and storing in an archival format. I do hope (Matlab) writing and reading functions for NeXus format files become available soon.

Regarding the ellipsoid form factor, I have mainly been using the ellipsoid adaptation to the Rayleigh sphere scattering function. However, this function requires integration over all orientations (see f.ex. equation 3.46 in the SASfit manual). This becomes very time-consuming for use as a fitting function if you furthermore would like to integrate over minor- and main-axis size distributions.

An alternative form factor appears to have been published in a light-scattering paper in 1969 [1] by Beattie and Tisinger. Although this procedure requires an iterative approach, it may prove to be faster to use than the aforementioned method. Efforts are underway to implement this method. Assistance, as always, is highly appreciated.

[1] Beattie and Tisinger. Light Scattering Functions and Particle-Scattering Factors for Ellipsoids of Revolution. Journal of the Optical Society of America (1969) vol. 59 pp. 818

At the 3-way meeting last week, there was some discussion into general file formats for beamlines. The argument for them is that when beamlines and scientific institutes will be asked to open their research data to the general public (perhaps after a certain period has expired, just like the astronomy community apparently has to), it should be published in a readable format with enough metadata attached to uniquely identify the experiment and conditions.

While it sounds like a lot of extra work (and there is a barrier to extra work, as we have enough to do as it is), the idea of using such a format as an archival and interchange format is one that appeals to me. The Astronomy community could agree on a format, but X-ray and neutron scattering communities have discussed plenty and reached (let’s be honest) not much yet. Whether that is because there is as yet no need for such a universal file format or whether it needs to be more flexible than it can ever support is not known. All I know is that a file format I made for my experiments, containing the calibrated and corrected data, has saved me a lot of time.

At the 3-way meeting, there was consensus that the file format should be gently forced by the management upon the beamlines. However, it was also agreed that money needs to be spent hiring full-time employees to set up, maintain and support the file format. Finally, it was agreed that the NeXus file format is the format to go for.

With that in mind, I contacted the community to ask whether I can write NeXus files from Matlab (the only language I know). In short, the file format can be read, but writing tools are not yet implemented. This will involve the inclusion of Java classes into the Matlab environment, a method I am unfortunately unfamiliar with. As the effort continues, I will let you know once more is available.