Small-angle X-ray scattering: characterization of cubic Au nanoparticles using Debye's scattering formula

Jérôme Deumer (1) , Brian R. Pauw (2) , Sylvie Marguet (3) , Dieter Skroblin (1) , Olivier Taché (4) , Michael Krumrey (1) , Christian Gollwitzer (1)

1 PTB - Physikalisch-Technische Bundesanstalt [Berlin]
2 BAM Federal Institute for Materials Research and Testing
3 LEDNA - Laboratoire Edifices Nanométriques
4 LIONS - Laboratoire Interdisciplinaire sur l'Organisation Nanométrique et Supramoléculaire

We propose a versatile, user-friendly approach, named (Computing Debye's scattering formula for Extraordinary Formfactors) (CDEF), to approximately calculate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS) using Debye's scattering formula, also known as the Debye equation. This equation generally allows to compute the scattering pattern of an ensemble of scatterers with a known form factor in the kinematic limit. The ensemble can hereby consist of atoms, atomic nuclei or larger shapes. In the method proposed in this paper, a quasi-randomly distributed point cloud in the desired particle shape is generated. Then, Debye's formula is applied to this ensemble of point scatterers to calculate the SAXS pattern of a single particle with random orientation. The quasi-random distribution ensures faster convergence compared to a true random distribution of scatterers, especially in the higher region of the momentum transfer q. In order to compute realistic SAXS curves of polydisperse nanoparticle ensembles with a given size distribution, the single particle master curve is rescaled and convolved with the size distribution. This allows us to fit measured data in reasonable time. We have used the method to evaluate scattering data of Au nanocubes with truncated or rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. Our implementation of this method 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 another implementation, the SPONGE, based on a similiar principle but with fewer assumptions. Additionally, the SPONGE coupled to McSAS3 allows us to further retrieve information on the uncertainty of the size distribution using a Monte-Carlo uncertainty estimation algorithm.

Mots clés: SAXS; Debye's scattering formula; non-spherical nanoparticles

Domaines: Matériaux

Jérôme Deumer, Brian R. Pauw, Sylvie Marguet, Dieter Skroblin, Olivier Taché, et al.. Small-angle X-ray scattering: characterization of cubic Au nanoparticles using Debye's scattering formula. 2021. ⟨cea-03741283v1⟩