Real-space Modeling for Complex Structures Based on Small-angle X-ray Scattering Kazuhiko Omote and Tomoyuki Iwata*
X-ray Research Laboratory, Rigaku Corporation, 3-9-12 Mastubara-cho, Akishima, Tokyo 196-8666, Japan. *Correspondence e-mail: t-iwata@rigaku.co.jp
A three-dimensional real-space model has been created for hierarchical materials by matching observed and simulated small-angle X-ray scattering patterns. The simulation is performed by arranging the positions of small primary particles and constructing an aggregate structure in a finite-sized cell. In order to avoid the effect of the finite size of the cell, the cell size is extended to infinity by introducing an asymptotic form of the long-range correlations among the primary particles. As a result, simulations for small-angle X-ray scattering patterns can be performed correctly in the low-wavenumber regime (<0.1 nm-1), allowing the model to handle hundred-nanometre-scale structures composed of primary particles of a few nanometres in size. An aerogel structure was determined using this model, resulting in an excellent match with the experimental scattering pattern. The resultant three-dimensional model can generate cross-sectional images similar to those obtained by transmission electron microscopy, and the calculated pore-size distribution is in accord with that derived from the gas adsorption method. J. Appl. Cryst. (2021). 54, 1290–1297 Click here to read the paper. | 
