A reverse Monte Carlo algorithm to simulate two-dimensional small-angle scattering intensities

Small-angle scattering (SAS) experiments are a powerful method for studying self-assembly phenomena in nanoscopic materials because of the sensitivity of the technique to structures formed by interactions on the nanoscale. Numerous out-of-the-box options exist for analysing structures measured by SAS but many of these are underpinned by assumptions about the underlying interactions that are not always relevant for a given system. Here, a numerical algorithm based on reverse Monte Carlo simulations is described to model the intensity observed on a SAS detector as a function of the scattering vector. The model simulates a two-dimensional detector image, accounting for magnetic scattering, instrument resolution, particle polydispersity and particle collisions, while making no further assumptions about the underlying particle interactions. By simulating a two-dimensional image that can be potentially anisotropic, the algorithm is particularly useful for studying systems driven by anisotropic interactions. The final output of the algorithm is a relative particle distribution, allowing visualization of particle structures that form over long-range length scales (i.e. several hundred nanometres), along with an orientational distribution of magnetic moments. The effectiveness of the algorithm is shown by modelling a SAS experimental data set studying finite-length chains consisting of magnetic nanoparticles, which assembled in the presence of a strong magnetic field due to dipole interactions.