Small-angle scattering analysis has never been easy for those working with oriented nanostructures (e.g. fibres, processed polymers, rolled metal alloys), whose structure may lead to anisotropic small-angle scattering. Upon the collection of such 2D scattering patterns, one can integrate thin pie-slices of the data to obtain 1D curves and analyse them in the same way as “normal”, isotropic scattering patterns. This way, however, important cross-correlation information is lost. Alternative full-pattern fitting methods have been developed (amongst others during my Ph.D. studies), but they are complicated to tune to the system at hand and can be quite unstable in least-squares optimisations.
One alternative is to analyse the scattering pattern by using Norbert Stribeck‘s 2D inversion method to obtain a two-dimensional pair-correlation function. Unfortunately, correlation functions are not always the easiest for the researcher to understand. Recently, I presented a 1D Monte Carlo method for obtaining form-free particle size distributions from isotropic scattering patterns, which —as it turns out— can be adapted to analyse anisotropic scattering patterns as well. The first results of this two-dimensional Monte Carlo analysis was presented at the SAS2012 conference, at which it was shown that it can obtain three distributions: the width and length distribution and an orientation distribution.
These initial results were written down for the conference proceedings, which have been submitted recently. The pre-submission manuscript is available (as before) on ArXiv here. Now is the time to try to apply this method to a variety of samples, so if you are working with oriented structures (and their scattering) and you are interested, please drop me a line!