Probing the out-of-plane distortion of single point defects in atomically thin hexagonal boron nitride at the picometer scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride (h-BN) accompanied by first-principles calculations reveals a characteristic charge-induced pm symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer h-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the h-BN membrane.     

Varieties of wonder:: John Wilkins' mathematical magic and the perpetuity of invention

Akin to the mathematical recreations, John Wilkins' Mathematicall Magick ( 1648) elaborates the pleasant, useful and wondrous part of practical mathematics, dealing in particular with its material culture of machines and instruments. We contextualize the Mathematicall Magick by studying its institutional setting and its place within changing conceptions of art, nature, religion and mathematics. We devote special attention to the way Wilkins inscribes mechanical innovations within a discourse of wonder. Instead of treating ‘wonder’ as a monolithic category, we present a typology, showing that wonders were not only recreative, but were meant to inspire Wilkins' readers to new mathematical inventions.     

Largest bounding box,smallest diameter,and related problems on imprecise points

Imprecision of input data is one of the main obstacles that prevent geometric algorithms from being used in practice. We model an imprecise point by a region in which the point must lie. Given a set of imprecise points, we study computing the largest and smallest possible values of various basic geometric measures on point sets, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding box. We give efficient algorithms for most of these problems, and identify the hardness of others.     

Spectroscopy vs. Electrochemistry: Catalyst Layer Thickness Effects on Operando/In Situ Measurements

In recent years, operando/in situ X-ray absorption spectroscopy (XAS) has become an important tool in the electrocatalysis community. However, the high catalyst loadings often required to acquire XA-spectra with a satisfactory signal-to-noise ratio frequently imply the use of thick catalyst layers (CLs) with large ion- and mass-transport limitations. To shed light on the impact of this variable on the spectro-electrochemical results, in this study we investigate Pd-hydride formation in carbon-supported Pd-nanoparticles (Pd/C) and an unsupported Pd-aerogel with similar Pd surface areas but drastically different morphologies and electrode packing densities. Our in situ XAS and rotating disk electrode (RDE) measurements with different loadings unveil that the CL-thickness largely determines the hydride formation trends inferred from spectro-electrochemical experiments, therewith calling for the minimization of the CL-thickness in such experiments and the use of complementary thin-film control measurements.     

Bonding and redox properties of [Os(3)(CO)(9)(tmbp)(L)] (tmbp=4,4',5,5'-tetramethyl-2,2'-biphosphinine; L=CO, PPh(3)) clusters with an unprecedented electron-deficient metallic core and doubly bridging biphosphinine dianion

Herein we describe in detail the bonding properties and electrochemical behavior of the first known triosmium carbonyl clusters with a coordinated redox-active ligand 4,4',5,5'-tetramethyl-2,2'-biphosphinine (tmbp), the phosphorus derivative of 2,2'-bipyridine. The clusters investigated were [Os(3)(CO)(10)(tmbp)] (1) and its derivative [Os(3)(CO)(9)(PPh(3))(tmbp)] (2). The crystal structures of both clusters are compared with those of relevant compounds; they served as the basis for density functional theory (DFT and time-dependent DFT) calculations. The experimental and theoretical data reveal an unexpected and unprecedented bridging coordination mode of tmbp, with each P atom bridging two metal atoms. The tmbp ligand is formally reduced by transfer of two electrons from the triangular cluster core that consequently lacks one of the metal-metal bonds. Both 1 and 2 therefore represent 50e(-) clusters with a coordinated 8e(-) donor, [tmbp](2-). The HOMO and LUMO of 1 and 2 possess a predominant contribution from different pi*(tmbp) orbitals, implying that the lowest energy excited state possesses a significant intraligand character. This is in agreement with the photostability of these clusters. DFT calculations also predict the experimentally observed structure of 1 to be the most stable one in a series of several plausible structural isomers. Stepwise two-electron electrochemical reduction of 1 and 2 results in dissociation of CO and PPh(3), respectively, and formation of the [Os(3)(CO)(9)(tmbp)](2-) ion. The initially produced radical anions of the parent clusters, in which the odd electron is predominantly localized on the tmbp ligand, are sufficiently stable at low temperatures and can be observed with IR spectroelectrochemistry. The electron-deficiency of the cluster core in 1 permits facile electrocatalytic substitution of a CO ligand by tertiary phosphane and phosphite donors.     

Catalytic conversion of methane to methanol over Cu-mordenite

Methane can be converted to methanol over copper-exchanged mordenite at 200 °C. Methanol could be recovered at the end of the reactor. This multi-step reaction opens the possibility for methane to methanol conversion in a closed catalytic cyclic reaction system.     

Hydraulic Fracture Propagation with 3-D Leak-off

Hydraulic fracture models typically couple a fracture elasticity model with a geological reservoir model to forecast the rate of fluid leak-off from the propagating fracture. The most commonly used leak-off model is that originally specified by Carter, which involves the assumption that the fracture is embedded within an infinite homogenous porous medium where flow only occurs perpendicular to the fracture plane. The objectives of this paper are: (1) to show that assuming one-dimensional leak-off can lead to erroneous conclusions, (2) to present a robust numerical methodology for simulating three-dimensional leak-off from propagating hydraulic fractures, and (3) to present and compare a new analytical method based on assuming three-dimensional flow of an incompressible fluid through an incompressible porous formation from a circular planar fracture. Provided the fluid and formation compressibility can be ignored within the reservoir flow model, the three-dimensional leak-off from a circular planar fracture can be written in closed-form as a function, which depends linearly on fracture pressure and radial extent. This simple expression for leak-off can be easily coupled to a range of circular fracture elasticity models. As a comparison example, the Carter model, our new function and a three-dimensional numerical model of the full problem are coupled to the PK-radial fracture model. Comparison with the numerical model shows that our new function overestimates fracture growth during intermediate times but accurately predicts both the early and late-time asymptotic behavior. In contrast, the Carter model fails to replicate both the early and late-time asymptotic behavior. Our new function additionally improves on the Carter model by not requiring the evaluation of convolution integrals and allowing easy evaluation of both the spatial leakage flux distribution across the fracture face and the three-dimensional pressure distribution within the porous formation.