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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.
Most industrial nanoparticles have non-spherical shapes and also possess polydisperse size distributions, and due to their agglomeration/ aggregation state are difficult (or even impossible) to be addressed individually. Further, driven by regulatory purposes related to the identification of a material as a nanomaterial, the accurate measurement of the smallest dimension of a (nano)particulate material makes the analysis even more complex.
In the first phase of the EU Project nPSize - Improved traceability chain of nanoparticle size measurements (https://www.bam.de/Content/DE/Projekte/laufend/nPSize/npsize.html), the efforts are focused on synthesis of nanoparticles of well-defined, non-spherical shape. Following candidates of reference materials (CRM) with certifiable particle size (distribution) are under characterization with respect to their homogeneity and stability: (i) titania nanoplatelets (10-15 nm thickness x 50-60 nm lateral), (ii) titania bipyramides (~60 nm length x 40 nm width), (iii) titania acicular particles (100 nm length x 15-20 nm width; aspect ratio 5.5/6), (iv) gold nanorods (~10 nm width x 30 nm length), and (v) gold nanocubes (~55 nm x 55 nm x 55 nm).