Advanced processing of differential phase contrast data: Distinction between different causes of electron phase shifts.

Differential phase contrast, in its high resolution modification also known as first moment microscopy or momentum resolved STEM [1-7] , basically measures the lateral momentum transfer to the electron probe due to the beam interaction with either electrostatic and/or magnetic fields, when the probe transmits the specimen. In other words, the result of the measurement is a vector field p→(x,y) which describes the lateral momentum transfer to the probe electrons. In the case of electric fields, this momentum transfer is easily converted to the electric field E→(x,y) causing the deflection, and from ϱ=ɛ0∇⋅E→ the local charge density can be calculated from the divergence of the electric field. However, from experimental data it is known that also the calculation of the vector field's curl ∇→×p→ in general yields non-zero results. In this paper, we use the Helmholtz decomposition (Wikipedia contributors, 2022), also known as the fundamental theorem of vector calculus, to split the measured vector fields into their curl-free and divergence-free components and to interpret the physical meaning of these components in detail. It will be shown, that non-zero curl components may be used to measure geometric phases occurring from irregularities in crystal structure such as a screw dislocation.

The differential phase contrast uncertainty relation: Connection between electron dose and field resolution.

Differential phase contrast (DPC) microscopy is a STEM imaging technique, which is used to measure magnetic and electric fields of mesoscopic and nanoscopic dimensions, i.e. interatomic distances (Chapman et al. 1978; Chapman et al. 1981; Chapman, 1984; Chapman et al. 1985; Chapman et al. 1997; Lohr et al. 2012; Shibata et al. 2015; Bauer et al. 2014; Carvalho et al. 2016; Lohr et al. 2016; Mueller-Caspary et al. 2019a,2019b; Mueller-Caspary et al. 2018; Mueller-Caspary et al. 2017; Mueller-Caspary et al. 2014; Winkler et al. 2020; Toyama et al. 2020). In this paper we will demonstrate that the electron dose per pixel deposited on the specimen is decisive to the precision and resolution of measurements of a field's local strength. Relations are given which connect a given electron dose per pixel to the fundamentally achievable precision to which the specimen's interaction with the electrons may be determined, taking into account quantum mechanical considerations. Vice versa, given a certain required precision, the required dose per pixel can be easily predicted for reliable measurements of a desired property. First, these relations are given for the case of a continuous, i.e. non-pixelated, detector followed by simulations which show that the same relations hold for pixelated detectors. Then, the achievable precision for detectors with different pixel counts in combination with different camera lengths is discussed and the maximum measurable field amplitude per set-up is determined. Finally, the effect of inhomogeneities within the diffraction disk is discussed and possible deviations from the derived relations are considered. We also demonstrate that Heisenberg's uncertainty relation determines the possible field resolution in differential phase contrast microscopy, and that the achievable local field resolution is a function of the applied electron dose per pixel.

Influence of combinatory effects of STEM setups on the sensitivity of differential phase contrast imaging.

Differential phase-contrast (DPC) imaging in the scanning transmission electron microscopy (STEM) mode has been suggested as a new method to visualize the nanoscale electromagnetic features of materials. However, the quality of the DPC image is very sensitive to the electron-beam alignment, microscope setup, and specimen conditions. Unlike normal STEM imaging, the microscope setup variables in the DPC mode are not independent; rather, they are correlated factors decisive for field sensitivity. Here, we systematically investigated the independent and combinatory effects of microscope setups on the sensitivity of the DPC image in a hard magnet, Nd2Fe14B alloy. To improve sensitivity, a smaller overlap of the electron beam with annular detectors and a greater camera length were required. However, these factors cannot be controlled independently in the two-condenser-lens system. In this linked system, the effect of the camera length on the DPC sensitivity was slightly more predominant than the overlap. Furthermore, the DPC signal was noisy and scattered at a small overlap of less than 11%. The electron-beam current does not evidently affect the sensitivity. In addition, the DPC sensitivity was examined with respect to the sample thickness, and the optimum thickness for high sensitivity was approximately 65 nm for the hard magnetic material Nd2Fe14B. This practical approach to the STEM setup and sample thickness may provide experimental guidelines for further application of the DPC analysis method.

Stereoselective Alkyne Hydrogenation by using a Simple Iron Catalyst.

The stereoselective hydrogenation of alkynes constitutes one of the key approaches for the construction of stereodefined alkenes. The majority of conventional methods utilize noble and toxic metal catalysts. This study concerns a simple catalyst comprised of the commercial chemicals iron(II) acetylacetonate and diisobutylaluminum hydride, which enables the Z-selective semihydrogenation of alkynes under near ambient conditions (1-3 bar H2 , 30 °C, 5 mol % [Fe]). Neither an elaborate catalyst preparation nor addition of ligands is required. Mechanistic studies (kinetic poisoning, X-ray absorption spectroscopy, TEM) strongly indicate the operation of small iron clusters and particle catalysts.

Introducing a non-pixelated and fast centre of mass detector for differential phase contrast microscopy.

With the advent of probe corrected STEM machines it became possible to probe specimens on a scale of less than 50 pm resolution. This opens completely new horizons for research, as it is e.g. possible to probe the electrostatic fields between individual rows of atoms, using differential phase contrast (DPC). However, in contrast to conventional DPC, where one deals with extended fields which can be assumed constant across the electron probe, this is not possible for sub-atomic probes in DPC. For the latter case it was shown [1,2], that the strongly inhomogeneous field distribution within the probe diameter, which usually is caused by the nuclear potentials of an atomic column, leads to a complicated intensity redistribution within the diffraction disk. The task is then to determine the intensity weighted centre of the diffraction disk pattern (frequently also called centre of mass, COM), which is proportional to the average lateral momentum gained by the average electron, transmitted through the probe diameter. In first reported measurements, the determination of this COM was achieved using a pixelated detector in combination with a software-based evaluation of the COM. This suffers from two disadvantages: first, the nowadays available pixelated detectors are still not very fast (approximately 1000 fps) and quite expensive, and second, the amount of data to be processed after acquisition is comparatively huge. In this paper we report on an alternative to a pixelated detector, which is able to directly deliver the COM of a diffraction disk's intensity distribution with frequencies up to 200 kHz. We present measurements on the sensitivity of this detector as well as first results from DPC imaging. From these results we expect the detector also to serve well in sub-atomic DPC field sensing, possibly replacing today's segmented or pixelated detectors.

Olefin-Stabilized Cobalt Nanoparticles for C=C, C=O, and C=N Hydrogenations.

The development of cobalt catalysts that combine easy accessibility and high selectivity constitutes a promising approach to the replacement of noble-metal catalysts in hydrogenation reactions. This report introduces a user-friendly protocol that avoids complex ligands, hazardous reductants, special reaction conditions, and the formation of highly unstable pre-catalysts. Reduction of CoBr2 with LiEt3 BH in the presence of alkenes led to the formation of hydrogenation catalysts that effected clean conversions of alkenes, carbonyls, imines, and heteroarenes at mild conditions (3 mol % cat., 2-10 bar H2 , 20-80 °C). Poisoning studies and nanoparticle characterization by TEM, EDX, and DLS supported the notion of a heterotopic catalysis mechanism.

On the achievable field sensitivity of a segmented annular detector for differential phase contrast measurements.

Differential phase contrast microscopy measures minute deflections of the electron probe due to electric and/or magnetic fields, using a position sensitive device. Although recently, pixelated detectors have become available which also serve as a position sensitive device, the most frequently used detector is a four-segmented annular semiconducting detector ring (or variations thereof), where the difference signals of opposing detector elements represent the components of the deflection vector. This deflection vector can be used directly to quantitatively determine the deflecting field, provided the specimen's thickness is known. While there exist many measurements of both electric and magnetic fields, even at an atomic level, until now the question of the smallest clearly resolvable field value for this detector has not yet been answered. This paper treats the problem theoretically first, leading to a calibration factor κ which depends solely on simple, experimentally accessible parameters and relates the deflecting field to the measured deflection vector. In a second step, the calibration factor for our combination of microscope and detector is determined experimentally for various combinations of camera length, condenser aperture and spot size to determine the optimum setup. From this optimized condition we determine the minimum change in field which leads to a clearly measurable signal change for both HMSTEM and LMSTEM operation. A strategy is described which allows the experimenter to choose the setup giving the highest field sensitivity. Quantification problems due to scattering processes in the specimen are addressed and ways are shown to choose a setup which is less sensitive to these artefacts.

On detector linearity and precision of beam shift detection for quantitative differential phase contrast applications.

Differential phase contrast is a STEM imaging mode where minute sideways deflections of the electron probe are monitored, usually by using a position sensitive device (Chapman, 1984 [1]; Lohr et al., 2012 [2]) or, alternatively in some cases, a fast camera (Müller et al., 2012 [3,4]; Yang et al., 2015 [5]; Pennycook et al., 2015 [6]) as a pixelated detector. While traditionally differential phase contrast electron microscopy was mainly focused on investigations of micro-magnetic domain structures and their specific features, such as domain wall widths, etc. (Chapman, 1984 [1]; Chapman et al., 1978, 1981, 1985 [7-9]; Sannomiya et al., 2004 [10]), its usage has recently been extended to mesoscopic (Lohr et al., 2012, 2016 [2,12]; Bauer et al., 2014 [11]; Shibata et al., 2015 [13]) and nano-scale electric fields (Shibata et al., 2012 [14]; Mueller et al., 2014 [15]). In this paper, the various interactions which can cause a beam deflection are reviewed and expanded by two so far undiscussed mechanisms which may be important for biological applications. As differential phase contrast microscopy strongly depends on the ability to detect minute beam deflections we first treat the linearity problem for an annular four quadrant detector and then determine the factors which limit the minimum measurable deflection angle, such as S/N ratio, current density, dwell time and detector geometry. Knowing these factors enables the experimenter to optimize the set-up for optimum performance of the microscope and to get a clear figure for the achievable field resolution error margins.