Abstract:
Nano-holes, etched under an electron beam at room temperature in singlelayer graphene sheets as a result of their interaction with metalimpurities, are shown to heal spontaneously by filling up with either non-hexagon, graphene-like, or perfect hexagon 2D structures. Scanning transmission electron microscopy was employed to capture the healing process and study atom-by-atom the re-grown structure. A combination of these nano-scale etching and re-knitting processes could lead to new graphene tailoring approaches.

Abstract:
Recent dramatic progress in studying various two-dimensional (2D) atomic crystals and their heterostructures calls for better and more detailed understanding of their crystallography, reconstruction, stacking order, etc. For this, direct imaging and identification of each and every atom is essential. Transmission Electron Microscopy (TEM) and Scanning Transmission Electron Microscopy (STEM) are ideal, and perhaps the only tools for such studies. However, the electron beam can in some cases induce dramatic structure changes and radiation damage becomes an obstacle in obtaining the desired information in imaging and chemical analysis in the (S)TEM. This is the case of 2D materials such as molybdenum disulfide MoS2, but also of many biological specimens, molecules and proteins. Thus, minimizing damage to the specimen is essential for optimum microscopic analysis. In this letter we demonstrate, on the example of MoS2, that encapsulation of such crystals between two layers of graphene allows for a dramatic improvement in stability of the studied 2D crystal, and permits careful control over the defect nature and formation in it. We present STEM data collected from single layer MoS2 samples prepared for observation in the microscope through three distinct procedures. The fabricated single layer MoS2 samples were either left bare (pristine), placed atop a single-layer of graphene or finally encapsulated between single graphene layers. Their behaviour under the electron beam is carefully compared and we show that the MoS2 sample 'sandwiched' between the graphene layers has the highest durability and lowest defect formation rate compared to the other two samples, for very similar experimental conditions.

Abstract:
Atomic resolution high angle annular dark field imaging of suspended, single-layer graphene, onto which the metals Cr, Ti, Pd, Ni, Al and Au atoms had been deposited was carried out in an aberration corrected scanning transmission electron microscope. In combination with electron energy loss spectroscopy, employed to identify individual impurity atoms, it was shown that nano-scale holes were etched into graphene, initiated at sites where single atoms of all the metal species except for gold come into close contact with the graphene. The e-beam scanning process is instrumental in promoting metal atoms from clusters formed during the original metal deposition process onto the clean graphene surface, where they initiate the hole-forming process. Our observations are discussed in the light of calculations in the literature, predicting a much lowered vacancy formation in graphene when metal ad-atoms are present. The requirement and importance of oxygen atoms in this process, although not predicted by such previous calculations, is also discussed, following our observations of hole formation in pristine graphene in the presence of Si-impurity atoms, supported by new calculations which predict a dramatic decrease of the vacancy formation energy, when SiOx molecules are present.

Abstract:
One of the most desirable goals of graphene research is to produce ordered 2D chemical derivatives of suitable quality for monolayer device fabrication. Here we reveal, by focal series exit wave reconstruction, that C2F chair is a stable graphene derivative and demonstrates pristine long-range order limited only by the size of a functionalized domain. Focal series of images of graphene and C2F chair formed by reaction with XeF2 were obtained at 80 kV in an aberration-corrected transmission electron microscope. EWR images reveal that single carbon atoms and carbon-fluorine pairs in C2F chair alternate strictly over domain sizes of at least 150 nm^2 with electron diffraction indicating ordered domains >/= 0.16 square micrometer. Our results also indicate that, within an ordered domain, functionalization occurs on one side only as theory predicts. Additionally we show that electron diffraction provides a quick and easy method for distinguishing between graphene, C2F chair and fully fluorinated stoichiometric CF 2D phases.

Abstract:
We demonstrate that 60 keV electron irradiation drives the diffusion of threefold coordinated Si dopants in graphene by one lattice site at a time. First principles simulations reveal that each step is caused by an electron impact on a C atom next to the dopant. Although the atomic motion happens below our experimental time resolution, stochastic analysis of 38 such lattice jumps reveals a probability for their occurrence in a good agreement with the simulations. Conversions from three- to fourfold coordinated dopant structures and the subsequent reverse process are significantly less likely than the direct bond inversion. Our results thus provide a model of non-destructive and atomically precise structural modification and detection for two-dimensional materials.

Abstract:
Die Hessische Landesregierung hat mit JAMBA“ (Junge allein erziehende Mütter in der Berufsausbildung) ein Modell entwickelt und erprobt, um allein erziehenden jungen Müttern ohne Berufsausbildung eine Lehre im dualen System zu erm glichen. An dem Modellversuch haben hundert junge Frauen an zehn Standorten in Hessen teilgenommen. Ziel des Projekts war es, den Personenkreis der jungen allein erziehenden Mütter zu ermutigen und zu unterstützen, eine betriebliche Ausbildung zu absolvieren. Gleichzeitig sollten Betriebe darin best rkt werden, allein erziehende Frauen auszubilden. Prof. Dr. Angela Paul-Kohlhoff und Dr. Uta Zybell u. a. haben dieses Modellprojekt über vier Jahre wissenschaftlich begleitet. Das zweib ndige Werk pr sentiert die Ergebnisse des Modellprojektes und die Konsequenzen für die praktische Politik. Es zeigt Wege auf, Benachteiligungen junger Mütter nicht nur zu beseitigen, sondern aus den Erfahrungen mit der Ausbildung junger Mütter generelle Reformoptionen für die berufliche Ausbildung in Deutschland zu begründen. Flexibilisierung und Individualisierung ohne Abstriche an der Qualit t der beruflichen Ausbildung stehen damit – nicht nur für die in den vorliegenden Ver ffentlichungen untersuchten Zielgruppe junge allein erziehende Mütter“ – auf der Tagesordnung der Reformagenda. The Hessian state government has developed and tested a model (JAMSA—young single mothers in career training) to give young single mothers without career training an apprenticeship in Germany’s dual system of vocational education. Hundreds of young women took part in the test model at ten different locations in the state of Hessen. The project’s goal was to encourage and support young single mothers in their completion of a company-based traineeship. Concurrently, the intention was to support those companies that trained young single mothers. Prof. Dr. Angela Paul-Kohlhoff and Dr. Uta Zybell, among others, followed the project model for four years. The two-volume work presents the results of the model and the consequences for practical politics. It not only sketches ways in which disadvantages for young single mothers can be eradicated, but also establishes general options for reforming career education in Germany based on experiences in training young mothers. Thus, at the top of the agenda for reform in career education is flexibility and individuality without the reduction of quality—and this applies not only to the book’s target group “young single mothers.”

Abstract:
We present a new optimal systolic inequality for a closed Riemannian manifold X, which generalizes a number of earlier inequalities, including that of C. Loewner. We characterize the boundary case of equality in terms of the geometry of the Abel-Jacobi map, A_X, of X. For an extremal metric, the map A_X turns out to be a Riemannian submersion with minimal fibers, onto a flat torus. We characterize the base of J_X in terms of an extremal problem for Euclidean lattices, studied by A.-M. Berg\'e and J. Martinet. Given a closed manifold X that admits a submersion F to its Jacobi torus T^{b_1(X)}, we construct all metrics on X that realize equality in our inequality. While one can choose arbitrary metrics of fixed volume on the fibers of F, the horizontal space is chosen using a multi-parameter version of J. Moser's method of constructing volume-preserving flows.

Abstract:
In this paper, we prove that for every Finsler metric on the 2-dimensional sphere there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem posed by D. V. Anosov in 1974.

Abstract:
For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small singular set. There is the natural question if a similar result is true for submanifolds of higher codimension. Specifically, B.White asked if the non-existence of an isoperimetric inequality for k-varifolds implies the existence of a nonzero, stationary, integral k-varifold. We present examples showing that this is not true in codimension greater than two. The key step is the construction of a Riemannian metric on the closed four-dimensional ball B with the following properties: (1) B has strictly convex boundary. (2) There exists a complete nonconstant geodesic. (3) There does not exist a closed geodesic in B.

Abstract:
What are appropriate geometric conditions ensuring that a complete Riemannian 2-cylinder without conjugate points is flat? Examples with nonpositive curvature show that one has to assume that the ends of the cylinder open sublinearly. We show that sublinear growth of the ends is indeed sufficient if it is measured by the length of horocycles. This is used to extend results by K. Burns and G. Knieper [9], and by H. Koehler [18], where the opening of the ends is measured in terms of shortest noncontractible loops.