Heterogeneity of porous structures is an important material property involved during the design of adsorbents, catalysts and molecular recognition materials. This review discusses the mathematical methods that can characterize adsorption site energies and surface heterogeneity from the adsorption isotherms.

MoS₂ is regarded as one of the most promising potassium-ion battery (PIB) anodes. Despite the great progress to enhance its electrochemical performance, understanding of the electrochemical mechanism to store K-ions in MoS₂ remains unclear. This work reports that the K storage process in MoS₂ follows a complex reaction pathway involving the conversion reactions of Mo and S, showing both cationic redox activity of Mo and anionic redox activity of S. The presence of dual redox activity, characterized in-depth through synchrotron X-ray absorption, X-ray photoelectron, Raman, and UV-vis spectroscopies, reveals that the irreversible Mo oxidation during the depotassiation process directs the reaction pathway toward S oxidation, which leads to the occurrence of K-S electrochemistry in the (de)potassiation process. Moreover, the dual reaction pathway can be adjusted by controlling the discharge depth at different cycling stages of MoS₂, realizing a long-term stable cycle life of MoS₂ as a PIB anode.

Black phosphorene quantum dots (BPQDs) are most commonly derived from high‐cost black phosphorus, while previous syntheses from the low‐cost red phosphorus (P_red) allotrope are highly oxidised. Herein, we present an intrinsically scalable method to produce high quality BPQDs, by first ball‐milling P_red to create nanocrystalline P_black and subsequent reductive etching using lithium electride solvated in liquid ammonia. The resultant ~25 nm BPQDs are crystalline with low oxygen content, and spontaneously soluble as individualized monolayers in tertiary amide solvents, as directly imaged by liquid‐phase transmission electron microscopy. This new method presents a scalable route to producing quantities of high quality BPQDs for academic and industrial applications.

During the last two decades, three-dimensional electron diffraction (3D ED) has undergone a renaissance, starting with the introduction of precession (Precession Electron Diffraction Tomography, PEDT) that led to variations on the idea of collecting as much of the diffraction space as possible in order to solve crystal structures from sub-micron sized crystals. The most popular of these acquisition methods is based on the continuous tilting/rotation of the crystal (so-called Microcrystal Electron Diffraction, MicroED) akin to the oscillating crystal method in X-ray crystallography, which was enabled by the increase of sensitivity and acquisition speed in electron detectors. While 3D ED data is more complex than the equivalent X-ray data due to the higher proportion of dynamical scattering, the same basic principles of what is required in terms of data quality and quantity in order to solve a crystal structure apply; high completeness, high data resolution and good signal-to-noise statistics on measured reflection intensities. However, it may not always be possible to collect data in these optimum conditions, the most common limitations being the tilt range of the goniometer stage, often due to a small pole piece gap or the use of a non-tomography holder, or the position of the sample on the TEM grid, which may be too close to a grid bar and then the specimen of interest becomes occluded during tilting. Other factors that can limit the quality of the acquired data include the limited dynamic range of the detector, which can result on truncated intensities, or the sensitivity of the crystal to the electron beam, whereby the crystallinity of the particle is changing under the illumination of the beam. This limits the quality and quantity of the measured intensities and makes structure analysis of such data challenging. Under these circumstances, traditional approaches may fail to elucidate crystal structures, and global optimization methods may be used here as an alternative powerful tool. In this context, this work presents a systematic study on the application of a global optimization method to crystal structure determination from 3D ED data. The results are compared with known structure models and crystal phases obtained from traditional ab initio structure solution methods demonstrating how this strategy can be reliably applied to the analysis of partially complete 3D ED data.

Characterisation of the electron beams trajectory in an electron microscope is possible in a few select commercial software packages, but these tools and their source code are not available in a free and accessible manner. This paper introduces the free and open-source software TEMGYM Advanced, which implements ray tracing methods that calculate the path of electrons through a magnetic or electrostatic lens and allow evaluation of the first-order properties and third-order geometric aberrations. Validation of the aberration coefficient calculations is performed by implementing two independent methods - the aberration integral and differential algebra (DA) methods and by comparing the results of each. This paper also demonstrates parallelised electron ray tracing through a series of magnetic components, which enables near real-time generation of a physically accurate beam-spot including aberrations and brings closer the realisation of a digital twin of an electron microscope. TEMGYM Advanced represents a valuable resource for the electron microscopy community, providing an accessible and open source means of characterising electron lenses. This software utilises the Python programming language to complement the growing ecosystem of free and open-source software within the electron microscopy community, and to facilitate the application of machine learning to an electron microscope digital twin for instrument automation. The software is available under GNU Public License number Three (GPL 3).

The high detection efficiencies of direct electron detectors facilitate the routine collection of low fluence electron micrographs and diffraction patterns. Low dose and low fluence electron microscopy experiments are the only practical way to acquire useful data from beam sensitive pharmaceutical and biological materials. Appropriate modeling of low fluence images acquired using direct electron detectors is, therefore, paramount for quantitative analysis of the experimental images. We have developed a new open-source Python package to accurately model any single layer direct electron detector for low and high fluence imaging conditions, including a means to validate against experimental data through computation of modulation transfer function and detective quantum efficiency.