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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.
We investigated the growth of β-phase NaYF4:Yb3+,Er3+ upconversion nanoparticles synthesized by the thermal decomposition method using a combination of in situ and offline analytical methods for determining the application-relevant optical properties, size, crystal phase, and chemical composition. This included in situ steady state luminescence in combination with offline time-resolved luminescence spectroscopy as well as small-angle X-ray scattering (SAXS) transmission electron microscopy (TEM), X-ray diffraction analysis (XRD), and inductively coupled Plasma optical emission spectrometry (ICP-OES). For assessing the suitability of our optical monitoring approach, the in situ-collected spectroscopic data, which reveal the luminescence evolution during nanocrystal synthesis, were compared to measurements done after cooling of the reaction mixture of the as-synthesized particles. The excellent correlation of the in situ and time-resolved upconversion luminescence with the nanoparticle sizes determined during the course of the reaction provides important insights into the various stages of nanoparticle growth. This study highlights the capability of in situ luminescence monitoring to control the efficiency of UCNP synthesis, particularly the reaction times at elevated temperatures and the particle quality in terms of size, shape, and crystal structure, as well as luminescence lifetime and upconversion quantum yield.