Computation of the atomic inner-shell excitation cross-sections for fast electrons in crystals

Detection of isolated protein-bound metal ions by single-particle cryo-STEM

Metal ions play essential roles in many aspects of biological chemistry. Detecting their presence and location in proteins and cells is important for understanding biological function. Conventional structural methods such as X-ray crystallography and cryo-transmission electron microscopy can identify metal atoms on protein only if the protein structure is solved to atomic resolution. We demonstrate here the detection of isolated atoms of Zn and Fe on ferritin, using cryogenic annular dark-field scanning transmission electron microscopy (cryo-STEM) coupled with single-particle 3D reconstructions. Zn atoms are found in a pattern that matches precisely their location at the ferroxidase sites determined earlier by X-ray crystallography. By contrast, the Fe distribution is smeared along an arc corresponding to the proposed path from the ferroxidase sites to the mineral nucleation sites along the twofold axes. In this case the single-particle reconstruction is interpreted as a probability distribution function based on the average of individual locations. These results establish conditions for detection of isolated metal atoms in the broader context of electron cryo-microscopy and tomography.

Modified automatic term selection v2: A faster algorithm to calculate inelastic scattering cross-sections

We present a new algorithm for calculating inelastic scattering cross-section for fast electrons. Compared to the previous Modified Automatic Term Selection (mats) algorithm (Rusz et al. [18]), it has far better convergence properties in zone axis calculations and it allows to identify contributions of individual atoms. One can think of it as a blend of mats algorithm and a method described by Weickenmeier and Kohl [10].

The role of symmetry in the theory of inelastic high-energy electron scattering and its application to atomic-resolution core-loss imaging

The inelastic scattering of a high-energy electron in a solid constitutes a bipartite quantum system with an intrinsically large number of excitations, posing a considerable challenge for theorists. It is demonstrated how and why the utilization of symmetries, or approximate symmetries, can lead to significant improvements in both the description of the scattering physics and the efficiency of numerical computations. These ideas are explored thoroughly for the case of core-loss excitations, where it is shown that the coupled angular momentum basis leads to dramatic improvements over the bases employed in previous work. The resulting gains in efficiency are demonstrated explicitly for K-, L- and M-shell excitations, including such excitations in the context of atomic-resolution imaging in the scanning transmission electron microscope. The utilization of other symmetries is also discussed.

Calculation of inelastic scattering processes of relativistic electrons in oriented crystals

The inelastic scattering of electrons in oriented crystals has been used to determine the positions of atoms within a crystal, to obtain site-dependent electron energy loss spectra and, more recently, to obtain an energy loss signal corresponding to the circular dichroism in X-ray absorption spectroscopy. The theoretical approaches currently used for the description of these processes are based on the nonrelativistic Schrödinger equation. Nowadays many experiments, however, are conducted with incident energies of 200 or 300 keV. Therefore it is indispensable to use a relativistic description for such processes based on the Dirac equation. Using the Coulomb gauge it is shown, that the fully relativistic cross sections for plane wave scattering are given by the modulus square of a sum of two terms: one describing the electrostatic interactions similar to the nonrelativistic theory plus one additional term describing the interaction of the specimen with the magnetic field produced by the incident electron. In crystals both terms can interfere leading to large deviations from nonrelativistic theory.

Energy loss by channeled electrons: a quantitative study on transition metal oxides

Electron energy-loss spectroscopy (EELS) attached to current transmission electron microscopes can probe not only element-selective chemical information, but also site-selective information that depends on the position that a specific element occupies in a crystal lattice. The latter information is exploited by utilizing the Bloch waves symmetry in the crystal, which changes with its orientation with respect to the incident electron wave (electron channeling). We demonstrate the orientation dependence of the cross-section of the electron energy-loss near-edge structure for particular crystalline sites of spinel ferrites, by quantitatively taking into account the dynamical diffraction effects with a large number of the diffracted beams. The theoretical results are consistent with a set of experiments in which the transition metal sites in spinel crystal structures are selectively excited. A new measurement scheme for site-selective EELS using a two-dimensional position-sensitive detector is proposed and validated by theoretical predictions and trial experiments.

Multislice theory of fast electron scattering incorporating atomic inner-shell ionization

It is demonstrated how atomic inner-shell ionization can be incorporated into a multislice theory of fast electron scattering. The resulting theory therefore accounts for both inelastic scattering due to inner-shell ionization and dynamical elastic scattering. The theory uses a description of the ionization process based on the angular momentum representation for both the initial and final states of the atomic electron. For energy losses near threshold, only a small number of independent states of the ejected atomic electron need to be considered, reducing demands on computing time, and eliminating the need for tabulated inelastic scattering factors. The theory is used to investigate the influence of the collection aperture size on the spatial origin of the silicon K-shell EELS signal generated by a STEM probe. The validity of a so-called local approximation is also considered.

The physical significance of the mixed dynamic form factor

We show that the mixed dynamic form factor for inelastic scattering of fast electrons in crystals is closely related to the density matrix of the probe electron and to that of the scatterer. With this insight it is possible to calculate both energy filtered diffraction patterns and energy spectroscopic high-resolution images. As an example we discuss the Si-K and -L edges.

Computation of contrasts in atomic resolution electron spectroscopic images of planar defects in crystalline specimens

The image obtained in a conventional transmission electron microscope contains contributions from elastically and from inelastically scattered electrons. The electron spectroscopic imaging mode of an energy-filtering transmission electron microscope allows us to separate these two different contributions by inserting an energy-selecting slit in the energy-dispersive plane of an imaging energy filter. Selecting a specific energy loss corresponding to the ionization of the inner shell of a particular element one can obtain information on the distribution of the element within the specimen. The contrast is then caused by inelastically scattered electrons. For crystalline specimens, however, the contrast will be influenced additionally by the elastic contrast. This elastic contrast arises from electron diffraction and increases with increasing crystal thickness. Therefore the intensity distribution in the image cannot directly be interpreted as an elemental map. For a reliable interpretation of contrast formation in elemental maps it is therefore necessary to compute theoretical energy-loss images for various crystal thicknesses and compare these images with the experimental images. As an example we discuss the influence of electron diffraction effects on energy-loss images of two crystals with planar defects. Linescans are computed for various thicknesses of these crystals. Our calculations are performed using first-order perturbation theory to describe the transitions between the Bloch-wave states of the incident electron. The computed linescans for various crystal thicknesses show clearly that the influence of the elastic contrast on an image increases when we investigate thicker specimens. Furthermore, the comparison between elastic and energy-loss images demonstrates the partial preservation of the elastic contrast as a function of thickness. We find that for specimens thicker than about one third of the extinction length (here approximately 80-100 A) it is impossible to interpret an energy-loss image directly as elemental map.