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Traceable particle size measurements of non-spherical nanoparticles


Image: Calculated scattering curve of the cubic point cloud (colored points) where the particle volume is indicated by the colored background. The electron micrograph on the bottom left confirms the cubic shape of the particles.

Small-angle X-ray scattering (SAXS) is ideally suited for the traceable determination of the size or size distribution of nanoparticles. At PTB, monochromatized X-rays from the four-crystal monochromator beamline in the PTB laboratory at BESSY II are used for this purpose. SAXS was also used in the recently successfully completed European research project "Improved traceability chain of nanoparticle size measurements" (EMPIR 17NRM04, nPSize). At PTB, two working groups were involved in this project, which dealt, among other things, with the production and size distribution determination of non-spherical nanoparticles:

In the working group 5.24 "Electron Microscopy" traceable measurements were performed in the transmission mode of a scanning electron microscope (TSEM). A prerequisite for such highly accurate measurements is the understanding of the image formation. The Monte Carlo simulations used for this purpose were substantially further developed within the framework of the project and, among other things, supplemented by a detailed treatment of inelastic scattering.

For an efficient SAXS data analysis, the evaluation software "Computing Debye's scattering formula for Extraordinary Formfactors" (CDEF) was developed in the working group 7.21 "X-ray radiometry". CDEF allows the approximate numerical calculation of SAXS scattering curves of arbitrarily shaped and isotropically oriented nanoparticles, so that the necessity of complicated analytical expressions for the respective form factor can be circumvented. For this purpose, a 3D cloud of virtual point scatterers in the shape of the desired particle is generated and then the corresponding scattering curve is calculated using the Debye formula. In general, the scattering curve describes the intensity of the scattered X-rays as a function of the momentum transfer q of the photons (proportional to the scattering angle). The scattering curve of an individual particle is largely determined by its shape, so using the "correct" particle model is essential for accurate data analysis. With CDEF, the desired point cloud can be generated in a user-friendly manner by loading an appropriate STL file that can be imported from CAD programs and other sources. The CDEF software has been made freely available as an open source library in the Python programming language through the PyPI library index (https://pypi.org/project/CDEF/).

The results were published in two joint publications with the project partners of the nPSize project, in which the method was applied to the characterization of cubic gold nanoparticles with rounded edges and to bipyramids of TiO2 with cut-off tips. For this work, PhD student Jérôme Deumer (PTB AG 7.21) received a prize for the best presentation at this year's Nordic Workshop on Scattering from Soft Matter (NSSM 2022).

Within the framework of the nPSize project, PTB has also participated in a YouTube video series showing the practical application of the measurement methods: https://www.youtube.com/channel/UC6kdn4epvHF4OZM7T-mLXJ


L. Crouzier et al., 2021. Correlative Analysis of the Dimensional Properties of Bipyramidal Titania Nanoparticles by Complementing Electron Microscopy with Other Methods, Nanomaterials 11(12), 3359.

DOI: https://doi.org/10.3390/nano11123359

J. Deumer et al., 2022 Small-Angle X-ray Scattering: Characterization of cubic Au nanoparticles using Debye’s scattering formula, Journal of Applied Crystallography, in press


C. Gollwitzer, 7.21, E-Mail: Opens local program for sending emailChristian.Gollwitzer(at)ptb.de

T. Klein, 5.24, E-Mail: Opens local program for sending emailTobias.Klein(at)ptb.de