Small-Angle X-ray Scattering: Characterization of cubic Au nanoparticles using Debye's scattering formula

TL;DR

This paper introduces CDEF, a Python software package for efficiently calculating small-angle X-ray scattering profiles of arbitrarily shaped nanoparticles, demonstrated on gold nanocubes, with fast performance and verified accuracy.

Contribution

The paper presents CDEF, a versatile, fast, and accurate Python tool for modeling SAXS profiles of complex nanoparticle shapes, improving computational efficiency and flexibility.

Findings

CDEF accurately models SAXS profiles of gold nanocubes.

The software runs efficiently on a desktop computer, enabling quick model fitting.

Validation against analytical form factors and other implementations confirms reliability.

Abstract

We propose a versatile software package in the form of a Python extension, named CDEF (Computing Debye's scattering formula for Extraordinary Formfactors), to approximately calculate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS). CDEF generates a quasi-randomly distributed point cloud in the desired particle shape and then applies the open source software DEBYER for efficient evaluation of Debye's scattering formula to calculate the SAXS pattern. If self-correlation of the scattering signal is not omitted, the quasi-random distribution provides faster convergence compared to a true random distribution of the scatterers, especially at higher momentum transfer. The usage of the software is demonstrated for the evaluation of scattering data of Au nanocubes with rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. Our implementation is fast enough to run on a single desktop computer and perform model fits within minutes. The accuracy of the method was analyzed by comparison with analytically known form factors and verified with another implementation, the SPONGE, based on a similiar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows us to further retrieve information on the uncertainty of the size distribution using a Monte-Carlo uncertainty estimation algorithm.