Computational Reverse Engineering Analysis of the Scattering Experiment Method for Interpretation of 2D Small-Angle Scattering Profiles (CREASE-2D).

Small-angle scattering (SAS) is a widely used characterization technique that provides structural information in soft materials at varying length scales (nanometers to microns). The output of an SAS measurement is the scattered intensity I ( q ) as a function of q , the scattered wavevector with respect to the incident wave; the latter is represented by its magnitude |q| ≡ q (in inverse distance units) and azimuthal angle θ . While isotropic structural arrangement can be interpreted by analysis of the azimuthally averaged one-dimensional (1D) scattering profile, to understand anisotropic arrangements, one has to interpret the two-dimensional (2D) scattering profile, I ( q , θ). Manual interpretation of such 2D profiles usually involves fitting of approximate analytical models to azimuthally averaged sections of the 2D profile. In this paper, we present a new method called CREASE-2D that interprets, without any azimuthal averaging, the entire 2D scattering profile, I ( q , θ), and outputs the relevant structural features. CREASE-2D is an extension of the "computational reverse engineering analysis for scattering experiments" (CREASE) method that has been used successfully to analyze 1D SAS profiles for a variety of soft materials. CREASE-2D goes beyond CREASE by enabling analysis of 2D scattering profiles, which is far more challenging to interpret than the azimuthally averaged 1D profiles. The CREASE-2D workflow identifies the structural features whose computed I ( q , θ) profiles, calculated using a surrogate XGBoost machine learning model, match the input experimental I ( q , θ). We expect that this CREASE-2D method will be a valuable tool for materials' researchers who need direct interpretation of the 2D scattering profiles in contrast to analyzing azimuthally averaged 1D I ( q ) vs q profiles that can lose important information related to structural anisotropy.