The concept of electronic orbitals has enabled the understanding of a wide range of physical and chemical properties of solids through the definition of, for example, chemical bonding between atoms. In the transmission electron microscope, which is one of the most used and powerful analytical tools for high-spatial-resolution analysis of solids, the accessible quantity is the local distribution of electronic states. However, the interpretation of electronic state maps at atomic resolution in terms of electronic orbitals is far from obvious, not always possible, and often remains a major hurdle preventing a better understanding of the properties of the system of interest. In this review, the current state of the art of the experimental aspects for electronic state mapping and its interpretation as electronic orbitals is presented, considering approaches that rely on elastic and inelastic scattering, in real and reciprocal spaces. This work goes beyond resolving spectral variations between adjacent atomic columns, as it aims at providing deeper information about, for example, the spatial or momentum distributions of the states involved. The advantages and disadvantages of existing experimental approaches are discussed, while the challenges to overcome and future perspectives are explored in an effort to establish the current state of knowledge in this field. The aims of this review are also to foster the interest of the scientific community and to trigger a global effort to further enhance the current analytical capabilities of transmission electron microscopy for chemical bonding and electronic structure analysis.

Knowledge of atomic-level details of structure, chemistry, and electronic states is paramount for a comprehensive understanding of emergent properties at oxide interfaces. We utilise a novel methodology based on atomic-scale electron energy loss spectroscopy (EELS) to spatially map the electronic states tied to the formation of a two-dimensional electron gas (2DEG) at the prototypical non-polar/polar $TiO_2$/$LaAlO_3$ interface. Combined with differential phase contrast analysis we directly visualise the microscopic locations of ions and charge and find that 2DEG states and $Ti^{3+}$ defect states exhibit different spatial distributions. Supported by density functional theory (DFT) and inelastic scattering simulations we examine the role of oxygen vacancies in 2DEG formation. Our work presents a general pathway to directly image emergent phenomena at interfaces using this unique combination of arising microscopy techniques with machine learning assisted data analysis procedures.

A new material characterization technique is emerging for the transmission electron microscope (TEM). Using electron energy-loss spectroscopy, real space mappings of the underlying electronic transitions in the sample, so called orbital maps, can be produced. Thus, unprecedented insight into the electronic orbitals responsible for most of the electrical, magnetic and optical properties of bulk materials can be gained. However, the incredibly demanding requirements on spatial as well as spectral resolution paired with the low signal-to-noise ratio severely limits the day-to-day use of this new technique. With the use of simulations, we strive to alleviate these challenges as much as possible by identifying optimal experimental parameters. In this manner, we investigate representative examples of a transition metal oxide, a material consisting entirely of light elements, and an interface between two different materials to find and compare acceptable ranges for sample thickness, acceleration voltage and electron dose for a scanning probe as well as for parallel illumination.

Journal Article 4D Energy-Filtered STEM: A New Approach for Mapping Orbital Transitions Get access Stefan Löffler, Stefan Löffler University Service Centre for Transmission Electron Microscopy, TU Wien, Vienna, Austria Corresponding author: stefan.loeffler@tuwien.ac.at Search for other works by this author on: Oxford Academic Google Scholar Manuel Ederer Manuel Ederer University Service Centre for Transmission Electron Microscopy, TU Wien, Vienna, Austria Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 29, Issue Supplement_1, 1 August 2023, Page 376, https://doi.org/10.1093/micmic/ozad067.176 Published: 22 July 2023

The spatial distributions of antibonding π^{*} and σ^{*} states in epitaxial graphene multilayers are mapped using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic channeling simulations validate the interpretation of the spatially resolved signals in terms of electronic orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to resolve the distribution of unoccupied states. This work illustrates the current potential of core-level electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of materials, of huge interest to better understand chemical bonding among many other properties at interfaces and defects in solids.

Digital image comparison and matching brings many advantages over the traditional subjective human comparison, including speed and reproducibility. Despite the existence of an abundance of image difference metrics, most of them are not suited for high-resolution transmission electron microscopy (HRTEM) images. In this work we adopt two image difference metrics not widely used for TEM images. We compare them to subjective evaluation and to the mean squared error in regards to their behaviour regarding image noise pollution. Finally, the methods are applied to and tested by the task of determining precipitate sizes of a model material.

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