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

Abstract

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 twodimensional (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.