Small‐angle X‐ray scattering: characterization of cubic Au nanoparticles using Debye's scattering formula

A versatile software package in the form of a Python extension, named CDEF (computing Debye's scattering formula for extraordinary form factors), is proposed to calculate approximate 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 (https://github.com/j‐from‐b/CDEF). If self‐correlation of the scattering signal is not omitted, the quasi‐random distribution provides faster convergence compared with 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. The 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 similar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows one to retrieve information on the uncertainty of the size distribution using a Monte Carlo uncertainty estimation algorithm. The Python extension CDEF is a suitable evaluation tool for experimentalists to calculate single‐particle small‐angle X‐ray scattering profiles with satisfactory accuracy, as shown by comparison with common well‐known analytical form factors. Using different complex cubic models, a direct comparison between CDEF and the already established SPONGE with respect to the size distribution of imperfect Au nanocubes showed a clear agreement of the results.