Using Three-Dimensional 3D Grazing-Incidence Small-Angle X‑ray Scattering (GISAXS) Analysis To Probe Pore Deformation in Mesoporous Silica Films

In the past decade, remarkable progress has been made in studying nanoscale objects deposited on surfaces by grazing-incidence small-angle X-ray scattering (GISAXS). However, unravelling the structural properties of mesostructured thin films containing highly organized internal three-dimensional (3D) structures remains a challenging issue, because of the lack of efficient algorithms that allow prediction of the GISAXS intensity patterns. Previous attempts to calculate intensities have mostly been limited to cases of two-dimensional (2D) assemblies of nanoparticles at surfaces, or have been adapted to specific 3D cases. Here, we demonstrate that highly organized 3D mesoscale structures (for example, porous networks) can be modeled by the combined use of established crystallography formalism and the Distorted Wave Born Approximation (DWBA). Taking advantage of the near-zero intensity of symmetry-allowed Bragg reflections, the casual extinction or existence of certain reflections related to the anisotropy of the form factor of the pores can be used as a highly sensitive method to extract structural information. We employ this generic method to probe the slightly compressed anisotropic shape and orientation of pores in a mesoporous silica thin film having <i>P</i>6₃/<i>mmc</i> symmetry