Electron microscopy measurements of electron orbitals

Electron density evolution of the Co–O and O–O interactions. a Structural model of LiCoO₂ with the indexed ($ 01\stackrel{-}{4} $) plane near the [100] direction (top). CoO₄ ($ 01\stackrel{-}{4} $) plane of the CoO₆ octahedra (bottom). b–e Static deformation density maps of the ($ 01\stackrel{-}{4} $) CoO₄ plane and corresponding three-dimensional (3D) views of b LiCoO₂, c Li_0.6CoO₂, d Li_0.4CoO₂, and e Li_0.3CoO₂. The electron density is present in different colors with the color scale shown on the left. The red color region means the electron density accumulation, and the blue color region represents the electron density depletion. All of the maps use a contour interval of 0.1 e Å⁻³, with positive, negative, and zero contours drawn as solid black, dashed black, and solid olive-green lines, respectively. The inclined arrows show the [001] direction, and all of the 3D views use the same color scheme. All scale bars indicate 1 Å^[32]. Copyright 2022, Springer Nature.

Orbital strategy to control the Jahn–Teller effects (JTE). a Three common structure models (olivine, layered, spinel) of cathode materials for rechargeable Li-ion battery. b MnO₆ octahedra with different symmetries. Ligands with the same color are identical and vice versa. The left octahedron is JT active, while the right two octahedra are JT inactive. c The orbital strategy to maintain the degeneracy of e_g levels to suppress the JTE. d By combining convergent-beam electron diffraction and density functional theory (DFT) calculations, d-orbital occupancy can be quantified, and therefore the JTE can be detected ^[34]. Copyright 2024, Oxford University Press.

Real-space mapping of electronic orbitals in Rutile with STEM-EELS. a Ti L_2,3 edge extracted from a single pixel (dots), and averaged over all 14000 pixels (line) of the data set. The energy window used for the energy-filtered e_g maps is highlighted in yellow. Gaussian least squares fits representing the individual shapes of the e_g and t_2g contributions are depicted in blue and green. b Projected DOS above the Fermi energy E_F calculated by WIEN2k. c Dark field image acquired simultaneously with the spectrum image dataset. d Unit cell along the [0 0 1] direction used in the experiment with the summed three-dimensional charge density of the e_g Wannier functions. Also shown are the projected positions of Ti (blue) and O (orange) atoms as well as yellow ellipses indicating the nearest O neighbours of each Ti (due to the projection, only two of the four nearest neighbours are visible). e Charge density for the unoccupied e_g orbitals projected along the [0 0 1] crystallographic axis as calculated by WIEN2k. f Experimental energy-filtered map for the Ti L ionization edge for final states with e_g character after unit-cell averaging. g Same as f, but after Gaussian smoothing. h Simulated energy-filtered map using the multislice algorithm and the mixed dynamic form factor approach after Gaussian blurring. i Same as h with added noise to better mimic the experimental conditions. j Same as i after Gaussian smoothing. All maps are replicated in a 3 × 3 raster for better visibility. Overlays show the projected positions of Ti and O atoms as well as yellow ellipses indicating the nearest O neighbours of each Ti. All scale bars indicate 5 Å^[39]. Copyright 2017, Elsevier.

Optimizing experimental parameters for orbital mapping in a heterostructure with EELS. a-f Simulated STEM spectrum images of the interface between STO and LMO in the [100] zone axis for both materials, the indicated sample thickness and energy loss with an infinite electron dose. All scale bars indicate 1 nm. g-h Image difference maps of the STO-LMO spectrum images for the indicated energy losses. The incident dose is measured relative to the image dose of 10⁶ e⁻/nm² for the image of a 15.6 nm thick sample, marked by the red x. The reference image in all cases is calculated with infinite electron dose. The dark green and olive contour lines indicate an image difference of 0.18 and 0.3, respectively. i STO-LMO SIFT image difference as a function of sample thickness for an acceleration voltage of 300 kV and several convergence and collection semi-angles α and β. All image differences are relative to the orbital map for α = 30 mrad and β = 50 mrad^[46]. Copyright 2024, Elsevier.

Probing core-electron orbitals of Sr and Ti atoms in SrTiO₃ with STEM-EDX. a Individual Sr Kα and L EDX maps from the Sr column of STO viewed along the [001] crystallographic direction. b Individual Ti Kα and L EDX maps from the Ti/O column of STO viewed along the same direction. The less circular shape of the Ti L map is due to a much lower signal-to-noise ratio in the data, showing that the Ti L signal still needs to be improved. For direct comparison, maps are background subtracted and normalized to their central intensity. Azimuthally averaged radial profiles are presented at right for better comparison. These maps constitute the cross-correlated average of data from approximately 450 identical atomic columns and all obtained simultaneously in a single experiment. c-f Experimentally observed projected excitation potentials for 1s and 2p orbitals of Sr and Ti, including the effects of atomic thermal vibrations and excitation broadening^[48]. Copyright 2016, American Physical Society.

High-resolution molecular orbital imaging with STM. a Naphthalocyanine on NaCl (2 ML) on Cu (111) measured using a Cu tip, a CO tip in constant-current mode, and a CO tip in constant-height mode. The PIR (1st row) is measured at V=−1.65 V and the NIR (2nd row) at V=0.60 V. b Calculated images at z₀=5.0 Å of the HOMO (3rd row) and LUMO (4th row) with an s-wave tip, a p-wave tip, and a mixed tip. All images: 27 Å×27 Å^[51]. Copyright 2011, American Physical Society.

Visualization of charge transfer energy and orbital ordering with STM. a Schematic of the relevant orbitals in the CuO₂ plane depicting the crucial inter-oxygen-orbital Coulomb interaction V_pp. b Schematic of the charge-quadrupole two-level systems within the Ising-domain walls. The top panel shows the schematic of the charge distribution in the four intra-unit-cell oxygen sites consequent to the intra-unit-cell charge transfer symmetry breaking. The bottom panel shows a schematic of two orbitally ordered domains. The darker circles indicate oxygen sites with higher charge transfer energy ε. c Unit-cell-averaged structure of T(r) averaged over the regions where N_ε > +5 meV. d Unit-cell-averaged structure of T(r) averaged over the regions where N_ε < –5 meV. In both c and d, C₄ symmetry is preserved. e Unit-cell-averaged structure of δε(r) averaged over the regions same as c. The charge transfer energy strongly breaks C₄ symmetry about every Cu site (yellow dots), and consequently, there is an energy splitting of approximately 50 meV between the charge transfer energies at the two crystal-equivalent oxygen sites (indicated by the crosses). f Unit-cell-averaged structure of δε(r) averaged over the regions same as d. Virtually identical phenomena as in e, but rotated by 90°. The difference between e and f is the difference in the internal structure of the CuO₂ unit cell in the two distinct Ising domains of orbital order^[53]. Copyright 2024, Springer Nature.