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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.
he main objective of the nPSize project is to improve the measurement capabilities for nanoparticle size based on both measurement methods traceable to SI units and new reference materials. Two basic approaches have been used in order to develop measurement procedures resulting in traceable results of the nanoparticle size distribution: physical modelling for the methods used in the project (TSEM, SEM, AFM and SAXS) and machine learning.
Physical modelling: In this part, the physical models associated with different shape measurements for the techniques TSEM, SEM, AFM and SAXS have been collected and further developed with the aim to simulate the resulting signal as measured by the individual methods. Uncertainties and traceability associated with each model were investigated and evaluated. In the following, the progress on these physical models is reported for each individual method.
Machine Learning modelling: The aim of this part is to use machine learning to enable automatic measurement of nanoparticle shape from expert a-priori information only. No physical model will be used as a-priori information in this task.
The accuracy and traceability of the size results obtained by each technique will be analyzed and compared with the physical modelling. A machine learning database will then be used to create automatic detection algorithms.
In this paper, the accurate determination of the size and size distribution of bipyramidal anatase nanoparticles (NPs) after deposition as single particles on a silicon substrate by correlative Scanning Electron Microscopy (SEM) with Atomic Force Microscopy (AFM) analysis is described as a new measurement procedure for metrological purposes. The knowledge of the exact orientation of the NPs is a crucial step in extracting the real 3D dimensions of the particles. Two approaches are proposed to determine the geometrical orientation of individual nano‐bipyramides: (i) AFM profiling along the long bipyramid axis and (ii) stage tilting followed by SEM imaging. Furthermore, a recently developed method, Transmission Kikuchi Diffraction (TKD), which needs preparation of the crystalline NPs on electron‐transparent substrates such as TEM grids, has been tested with respect to its capability of identifying the geometrical orientation of the individual NPs. With the NPs prepared homogeneously on a TEM grid, the transmission mode in a SEM, i.e., STEM‐in‐SEM (or T‐SEM), can be also applied to extract accurate projection dimensions of the nanoparticles from the same sample area as that analysed by SEM, TKD and possibly AFM. Finally, Small Angle X‐ray Scattering (SAXS) can be used as an ensemble technique able to measure the NPs in liquid suspension and, with ab‐initio knowledge of the NP shape from the descriptive imaging techniques, to provide traceable NP size distribution and particle concentration.