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A round-robin study has been carried out to estimate the impact of the human element in small-angle scattering data analysis. Four corrected datasets were provided to participants ready for analysis. All datasets were measured on samples containing spherical scatterers, with two datasets in dilute dispersions and two from powders. Most of the 46 participants correctly identified the number of populations in the dilute dispersions, with half of the population mean entries within 1.5% and half of the population width entries within 40%. Due to the added complexity of the structure factor, far fewer people submitted answers on the powder datasets. For those that did, half of the entries for the means and widths were within 44 and 86%, respectively. This round-robin experiment highlights several causes for the discrepancies, for which solutions are proposed.
The study described in this paper was conducted in the framework of the European nPSize project (EMPIR program) with the main objective of proposing new reference certified nanomaterials for the market in order to improve the reliability and traceability of nanoparticle size measurements. For this purpose, bimodal populations as well as complexly shaped nanoparticles (bipyramids, cubes, and rods) were synthesized. An inter-laboratory comparison was organized for comparing the size measurements of the selected nanoparticle samples performed with electron microscopy (TEM, SEM, and TSEM), scanning probe microscopy (AFM), or small-angle X-ray scattering (SAXS). The results demonstrate good consistency of the measured size by the different techniques in cases where special care was taken for sample preparation, instrument calibration, and the clear definition of the measurand. For each characterization method, the calibration process is described and a semi-quantitative table grouping the main error sources is proposed for estimating the uncertainties associated with the measurements. Regarding microscopy-based techniques applied to complexly shaped nanoparticles, data dispersion can be observed when the size measurements are affected by the orientation of the nanoparticles on the substrate. For the most complex materials, hybrid approaches combining several complementary techniques were tested, with the outcome being that the reliability of the size results was improved.
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.
A case study on the TEM analysis of the size and shape distribution of TiO2 bipyramidal nanoparticles prepared on TEM grids was included in the recently published ISO standard ISO 21363. It was agreed to organize at a later stage a second inter-lab comparison with the nanoparticles distributed to the participants as a liquid suspension. Protocols for uniform nanoparticle deposition on suited supports developed and optimized within the EMPIR nPSize project are also prepared to be distributed. For this, we have chosen the VAMAS platform (www.vamas.org) which offers an excellent international infrastructure of laboratories with high competence in nanoparticle measurement. The VAMAS technical working area dedicated to nanoparticle measurement is TWA 34 ‘Nanoparticle populations’. For this type of nanoparticles, the size and shape distributions are the primary parameters to be reported. Due to the good deposition protocols developed, an automated image analysis is enabled (in contrast to the manual analysis of irregular TiO2 nanoparticles.
In parallel with the TiO2 nanoparticle exercise, two spherical SiO2 nanoparticle samples with bi-modal size distributions (nominal relative number concentrations of 1:1 and 10:1) are prepared for a second VAMAS inter-lab comparison. Here, the nanoparticle concentration is the primary parameter to be measured. For the imaging methods it is targeted to measure the relative nanoparticle concentrations of the two modes. For the absolute nanoparticle concentration to be measured by imaging methods it is necessary to control the volume of the liquid suspension deposited on the substrate and to obtain such a homogeneous nanoparticle deposition on the substrate which allows to count (or extrapolate) all the deposited particles.