Abstract text (incl. figure legends and references)

In 4D STEM, the Center of Mass (COM) signal is commonly used to measure electromagnetic fields. Its direct interpretation relies on the use of Ehrenfest's theorem and on the Phase Object Approximation (POA)[1]. One challenging aspect to quantify in such measurements is the signal arising at interfaces with different mean inner potentials (MIP). This component of the COM is therefore dependent on the shape of the investigated specimen. Nonetheless, in general, the direct interpretation of this contrast is not as straightforward as previously described. This is due to atomic electric fields, which makes it necessary to take the effects of propagation and multiple scattering into account [2].

In this work, we studied to which extent dedicated conditions can suppress the influence of high spatial frequency components, and where the specimen can be described with a continuous model (CM), with the inclusion of propagation and scattering effects at interfaces via multislice (MS) calculations. There, the specimen-beam interaction simplifies to a refraction-like behaviour.

This model is tested through MIP measurements of large (∼100 nm) amorphous latex spheres. The projected potential is retrieved via integration in Fourier space of the electric fields, calculated from the COM data, and the polar average around the center of the sphere is fitted via linear least squares. Our extracted result of 5.92 V from the experimental curve in figure 1 shows deviations from previous measurements [3]. The curve also shows a mismatch in shape, which can be explained by including charging heuristically with the help of MS simulations within the CM approach.

We then employ this model on facetted gold nanoparticles (≤30 nm) [4] in an attempt to deduce their projected shape. Our findings show that this type of model is only applicable under certain conditions and can then only be used to understand qualitative features as those visible in figure 2. Quantitative agreement is hindered by thickness and orientation dependency of the effective MIP acting on the electron travelling through a crystalline specimen.

Funding from the Initative and Network Fund of the Helmholtz Association under contracts VH-NG-1317 and ZT-I-0025 are gratefully acknowledged

Figure 1: a) Measurement of an experimentally retrieved projected potential of a latex sphere next to a simulated one in figure 1 b). The simulated one is only half the size as in the experiment, but includes additional heuristic charging potentials to fit better to the experimental data. c) Normalized profile curves from from spheres in a) and b), with the addition of a simulated uncharged sphere. The filled blue region marks the curve of a perfect sphere. The curves from a) and b) deviate from the perfect sphere but show good qualitative agreement between each other.

Figure 2: Comparison between experimental (left) and simulated (right) COM. The COM is depicted in color wheel representation. The simulation shows good qualitative agreement with the experimental data within the marked region of interest (white doted square). The model used for the MS is visible in the bottom right corner.

References:

[1] Knut Mu ̈ller et al. In: Nat. Com. 5.1 (2014), p. 5653.

[2] Christoph Mahr et al. In: Ultram. 236 (2022), p. 113503.

[3] Frederick Allars et al. In: Ultram. 231 (2021), p. 113257.

[4] Felizitas Kirner et al. In: J. Mater. Chem. C 8 (31 2020), pp. 10844–10851.