A decade ago, a statistics-based method was introduced to count the number of atoms from annular dark-field scanning transmission electron microscopy (ADF STEM) images. In the past years, this method was successfully applied to nanocrystals of arbitrary shape, size, and composition (and its high accuracy and precision has been demonstrated). However, the counting results obtained from this statistical framework are so far presented without a visualization of the actual uncertainty about this estimate. In this paper, we present three approaches that can be used to represent counting results together with their statistical error, and discuss which approach is most suited for further use based on simulations and an experimental ADF STEM image.

We introduce a novel method to improve the computational efficiency for (S)TEM image simulation by employing matrix diagonalization of the mixed envelope function (MEF). The MEF is derived by taking the finite size and the energy spread of the effective electron source into account, and is a component of the transmission cross-coefficient that accounts for the correlation between partially coherent waves. Since the MEF is a four-dimensional array and its application in image calculations is time-consuming, we reduce the computation time by using its eigenvectors. By incorporating the aperture function into the matrix diagonalization, only a small number of eigenvectors are required to approximate the original matrix with high accuracy. The diagonalization enables for each eigenvector the calculation of the corresponding image by employing the coherent model. The individual images are weighted by the corresponding eigenvalues and then summed up, resulting in the total partially coherent image.

In this study, the spin-dependent nonlinear contrast transfer in transmission electron microscopy is derived from the eikonal expansion of the Dirac equation. The transmission cross-coefficient of the standard imaging theory is amended by a spin-dependent factor, whose effect is investigated for single scattering in the object by an electrical field under polarized and unpolarized illumination, and it is illustrated with numerical results and plots for a kinetic energy of 80 keV. The resulting image displacement and image convolution increase with decreasing kinetic energy but are always smaller than a wavelength. General features of the cross-coefficient are discussed to identify favorable conditions for the measurement of the small spin effects, possibly in an unmodified instrument.

We report on the automatic alignment of a transmission electron microscope equipped with an orbital angular momentum sorter using a convolutional neural network. The neural network is able to control all relevant parameters of both the electron-optical setup of the microscope and the external voltage source of the sorter without input from the user. It can compensate for mechanical and optical misalignments of the sorter, in order to optimize its spectral resolution. The alignment is completed over a few frames and can be kept stable by making use of the fast fitting time of the neural network.

The solubility limit of carbon in α-Al2O3 (alumina) equilibrated at 1,600°C under He in a graphite furnace was measured by wavelength-dispersive spectroscopy. Undoped alumina and alumina containing carbon at a concentration resulting in the precipitation of a second phase were prepared and equilibrated at 1,600°C. The undoped alumina was used to quantify the amount of carbon deposited on the surface of samples because of hydrocarbon contamination in the electron microscope, and this background level was removed from the signal measured from carbon-doped samples. The solubility limit of carbon in alumina was found to be 5,300 ± 390 at. ppm, and it is believed that carbon substitutes oxygen as an anion and is charge-compensated by oxygen vacancies. Doping alumina with carbon at concentrations below the solubility limit does not impede densification and reduces grain growth. Doping above the solubility limit hinders densification during sintering.

Current progress in programmable electrostatic phase plates raises questions about their usefulness for specific applications. Here, we explore different designs for such phase plates with the specific goal of correcting spherical aberration in the transmission electron microscope (TEM). We numerically investigate whether a phase plate could provide down to 1 Ångström spatial resolution on a conventional uncorrected TEM. Different design aspects (fill factor, pixel pattern, symmetry) were evaluated to understand their effect on the electron probe size and current density. Some proposed designs show a probe size ($d_{50}$) down to 0.66 Å, proving that it should be possible to correct spherical aberration well past the 1 Å limit using a programmable phase plate consisting of an array of electrostatic phase-shifting elements.

Refractory high-entropy alloys (RHEAs) are promising candidates for next-generation high-temperature materials. RHEAs containing Al, often exhibit a checkered pattern microstructure comprising a combination of disordered BCC and ordered B2 phases. Since the ordered B2 phase is based on the BCC parent matrix, distinguishing these two phases can be rather challenging. Advanced characterization techniques are necessary for a reliable qualitative and quantitative analysis of BCC and B2 phases in RHEAs. Additionally, there is a tendency for transformation of the ordered B2 phase into more complex ordered-omega type phases that are usually deleterious to mechanical properties. The current study focuses on the phase stability of a candidate RHEA, Al0.5Mo0.5NbTa0.5TiZr. Correlative transmission electron microscopy (TEM) and atom probe tomography (APT) have been employed to investigate the phase stability and transformation pathway of this RHEA when isothermally annealed at 800°C. The results show that a metastable two-phase BCC + B2 microstructure formed at the early stages of decomposition, eventually transforming into a three-phase BCC + B2 + hP18 microstructure. The hP18 phase is an ordered omega derivative of the ordered B2 phase. The correlative microscopy techniques (TEM and APT) reveal a very interesting interplay of compositional partitioning between the different phases and their respective stability.

Aberration correction in the analytical transmission electron microscope is most closely associated with improvements in high-resolution imaging. In this paper, the combination of that technology with new system designs, which optimize both electron optics and x-ray detection, is shown to provide more than a tenfold increase in performance over the last 25 years.