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Generalised oscillator strength for core-shell electron excitation by fast electrons based on Dirac solutions

Authors: Zezhong Zhang; Ivan Lobato; Hamish Brown; Lamoen, Dirk; Daen Jannis; Johan Verbeeck; Sandra Van Aert; +1 Authors

Generalised oscillator strength for core-shell electron excitation by fast electrons based on Dirac solutions

Abstract

The rich information of electron energy-loss spectroscopy (EELS) comes from the complex inelastic scattering process whereby fast electrons transfer energy and momentum to atoms, exciting bound electrons from their ground states to higher unoccupied states. To quantify EELS, the common practice is to compare the cross-sections integrated within an energy window or fit the observed spectrum with theoretical differential cross-sections calculated from a generalized oscillator strength (GOS) database with experimental parameters [1]. The previous Hartree-Fock-based [2] or DFT-based [3] GOS was calculated from Schrödinger's solution of atomic orbitals, which does not include the full relativistic effects. Here, we attempt to go beyond the limitations of the Schrödinger solution in the GOS tabulation by including the full relativistic effects using the Dirac equation within the local density approximation using FAC [4], which is particularly important for core-shell electrons of heavy elements with strong spin-orbit coupling. This has been done for all elements in the periodic table (up to Z = 118) for all possible excitation edges using modern computing capabilities and parallelization algorithms. The relativistic effects of fast incoming electrons were included to calculate cross-sections that are specific to the acceleration voltage. We make these tabulated GOS available under an open-source license to the benefit of both academic users as well as allowing integration into commercial solutions. If you wish to be notfied by the database updates, please register here. For details, you can find the paper on arxiv. Database Details: Covers all elements (Z: 1-108) and all edges Large energy range: 0.01 - 4000 eV Large momentum range: from minimum momentum transfer to double Bethe ridge for each edge. Adaptive momentum sampling is developed in such a manner to maximize the physical information for a given finite number of sampling points. For example, for C edge this range is 0.14 -67 Å-1 Fine log sampling: 128 points for energy and 256 points for momentum Data format: GOSH [3] Calculation Details: Single atoms only; solid-state effects are not considered Unoccupied states before continuum states of ionization are not considered; no fine structure Plane Wave Born Approximation Frozen Core Approximation is employed; electrostatic potential remains unchanged for orthogonal states when a core-shell electron is excited Self-consistent Dirac–Fock–Slater iteration is used for Dirac calculations; A modified local density approximation is used for the correct asymptotic behavior of the exchange energy; continuum states are normalized against asymptotic form at large distances Both large and small component contributions of Dirac solutions are included in GOS Final state contributions are included until the contribution of the last states falls below 0.1%. A convergence log is provided for reference. Version 1.7 release note: Add white lines GOS database of neautral atoms, which is calculated based on interband transitions (ground states to discrete unoccupied state). Version 1.6.5 release note: Add a compact version of the database which uses (a) single precesion, (b) 80x80 sampling in the energy and momentum space (c) 'gzip' to compress the gos data array. This helps for user with limited bandwidth for downloading. Version 1.6.1 release note: Add missing metadata Version 1.6 release note: Improved convergence for M and N edges for some elements Version 1.5 release note: Adaptive sampling for momentum space (previously it is fixed at 0.05 -50 Å-1, now adaptive for each edge) Improved convergence Version 1.2 release note: Add “File Type / File version” information Version 1.1 release note: Update to be consistent with GOSH data format [3] All the edges are now within a single hdf5 file. A notable change in particular, the sampling in momentum is in 1/m, instead of previously in 1/Å. Great thanks to Gulio Guzzinati for his suggestions and sending conversion script for GOSH format. [1] Verbeeck, J., and S. Van Aert. Ultramicroscopy 101.2-4 (2004): 207-224. [2] Leapman, R. D., P. Rez, and D. F. Mayers. The Journal of Chemical Physics 72.2 (1980): 1232-1243. [3] Segger, L, Guzzinati, G, & Kohl, H. Zenodo (2023). doi:10.5281/zenodo.7645765 [4] Gu, M. F. Canadian Journal of Physics 86(5) (2008): 675-689.

The authors acknowledge financial support from the Research Foundation Flanders (FWO, Belgium) through Project No.G.0502.18N. This project has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 770887 PICOMETRICS and No. 823717 ESTEEM3).

Country
Belgium
Related Organizations
Keywords

Chemistry, EELS, electron energy loss spectroscopy, Physics, GOS, transmission electron microscopy, TEM

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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