Extraction of domain structure information from small-angle scattering patterns of bulk materials

A method is presented that permits the extraction and visualization of topological domain structure information contained in small-angle scattering (SAS) patterns without complex pretreatment. Multi-dimensional noisy raw data can be processed. Such data are, for instance, accumulated in the field of materials research from short-exposure-time in situ small-angle X-ray scattering (SAXS) experiments with synchrotron radiation. The result is a multi-dimensional intersect or chord distribution, which is defined as the Laplacian of the correlation function. Moreover, it is equivalent to the autocorrelation of the gradient of the electron density. The procedure is, in particular, adapted to the analysis of the nanoscale structure of samples with fibre symmetry, such as polymer fibres or strained elastomers. Multi-dimensional relations among morphological components become apparent in real space and help to elucidate the nature of the processes governing formation and change of structure on the nanometre scale. Utilizing digital signal processing tools, the algorithm is based on spatial frequency filtering of the raw data. The background to be subtracted from the small-angle scattering pattern is formed from its own low spatial frequencies. Noise may be removed by suppressing high spatial frequencies. In the frequency band between these low and high spatial frequencies, the domain structure information of the studied nanocomposite appears.