Real‐space modeling for complex structures based on small‐angle X‐ray scattering.

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. [ABSTRACT FROM AUTHOR]