Abstract text (incl. figure legends and references)

To understand the structure-property relationship in nanostructured materials, we need to probe their crystal structures and compositions at the atomic scale. Advanced materials usually consist of multiple elements in a complicated structure. Significant difficulties remain to disentangle the contributions of composition and thickness in STEM due to dynamic scattering, which needs to be taken into account by detailed simulations. However, the combination of the computational cost of the multislice calculation and the enormous ordering possibilities for a given composition makes the quantification of mixed columns almost impossible. To address these challenges, we here report the development of an incoherent non-linear method for the fast prediction of ADF-EDX scattering cross-sections of mixed columns under channelling conditions.

Due to electron channelling, ADF and EDX have a non-linear relationship against thickness and composition, particularly at the atomic scale in zone axis orientation. However, preliminary experiments indicate a linear dependence between EDX and ADF scattering cross-sections, which are defined as the integration of signal intensities for each atomic column. We performed frozen phonon multislice calculations for a pure Au crystal and investigated the linear dependence of the ADF-EDX scattering cross-sections using the coefficient of determinantion R2 for different ADF inner and outer collection angles. Since EDX can be considered as a perfect incoherent reference, an R2 value equal to 1 suggests perfect longitudinal incoherence of the ADF, which is the case for high angles.

Because of the incoherent signal mode, we can treat dynamical scattering as a superposition of individual atoms focussing the incident electrons. Here we expanded the so-called atomic lensing model [1] (developed previously for ADF) to spectroscopy to enable fast generation of EDX scattering cross-sections with the ordering of elements taken into account under the channelling condition. As shown in Fig. 1 for a core-shell Au-Pt nanorod, scattering cross-sections extracted from the multislice calculations agree reasonably well with the atomic lensing model predictions but are very different from those of the linear model where the signal is assumed to scale linearly with the number of atoms for each type. To deploy the atomic lensing model to experimental results, we can incorporate the experimentally measured EDX partial cross-section [2], that bypasses the difficult characterisation of the EDX detector. We can also make use of the linear dependence between the signal modes as a constraint for simultaneous ADF-EDX atom counting. This method allows us to explore the enormous ordering possibilities of heterogeneous materials with multiple elements.

[1] K.H.W. van den Bos, A. De Backer, G.T. Martinez, N. Winckelmans, S. Bals, P.D. Nellist, S. Van Aert, Physical Review Letters 116 (2016) p. 246101.

[2] A. Varambhia, L. Jones, A. London, D. Ozkaya, P.D. Nellist, & S. Lozano-Perez, Micron 113 (2018) p. 69-82.

[3] The authors acknowledge financial support from the Research Foundation Flanders (FWO) through Project No. G.0502.18N and a post-doctoral grant to ADB. This project has received funding from the European Research Council (ERC) under the European Union"s Horizon 2020 research and innovation programme No. 770887 PICOMETRICS and No. 823717 ESTEEM3

Fig.1 Comparing the simulated and predicted scattering cross-sections (SCS) of ADF and EDX for an Au-Pt core-shell nanorod.