Untersuchung der Flächen dritten Grades, welche bei der Abbildung nach dem Prinzip der reziproken Radienvektoren wieder in sich selbst zurückkehren.

"Wissenschaftliche Beilage zum Jahresbericht des Falk-Realgymnasiums zu Berlin, 1902-03."

Degree of strata of singular cubic surfaces

Determinación de los grados de algunos estratos de una clasificación de superficies cúbicas singulares, que son subvariedades del espacio proyectivo de dimensión 19 de las que se conoce su dimensión y que son irreducibles.

Deformation mechanisms of face-centered-cubic metal nanowires with twin boundaries

This letter addresses the issue of deformation mechanisms and mechanical tensile behavior of the twinned metal nanowires using atomistic simulations. Free surfaces are always the preferential dislocation nucleation sites in the initial inelastic deformation stage, while with further plastic deformation, twin boundary interfaces will act as sources of dislocations with the assistance of the newly formed defects. The smaller the twin boundary spacing, the higher the yielding stresses of the twinned nanowires. Twin boundaries, which serve both as obstacles to dislocation motion and dislocation sources, can lead to hardening effects and contribute to the tensile ductility. This work illustrates that the mechanical properties of metal nanowires could be controlled by tailoring internal growth twin structures. (c) 2007 American Institute of Physics.

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free-energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behavior above the transition temperature.

The chemistry of intrinsically chiral surfaces

Intrinsically chiral metal and mineral surfaces show enantioselective behaviour without modifiers. Examples are artificial high-Miller-index surfaces of metal single crystals with cubic bulk lattice symmetry, which have no mirror planes and are therefore chiral, or surfaces of naturally occurring crystallites of some common minerals, such as alpha-quartz or calcite. Recent findings with regards to the surface geometry, reactivity and thermal stability of intrinsically chiral surfaces are discussed. A number of enantioselective effects have been reported in connection with the adsorption of small chiral molecules (e.g. alanine, cysteine) on intrinsically chiral surfaces under well-defined conditions. From a combination of experimental surface science techniques and theoretical ab initio model calculations it emerges that these effects are due to a combination of attractive and repulsive adsorbate-substrate and inter-adsorbate interactions.

A DFT study of the structures, stabilities and redox behaviour of the major surfaces of magnetite Fe3O4

The renewed interest in magnetite (Fe3O4) as a major phase in different types of catalysts has led us to study the oxidation–reduction behaviour of its most prominent surfaces. We have employed computer modelling techniques based on the density functional theory to calculate the geometries and surface free energies of a number of surfaces at different compositions, including the stoichiometric plane, and those with a deficiency or excess of oxygen atoms. The most stable surfaces are the (001) and (111), leading to a cubic Fe3O4 crystal morphology with truncated corners under equilibrium conditions. The scanning tunnelling microscopy images of the different terminations of the (001) and (111) stoichiometric surfaces were calculated and compared with previous reports. Under reducing conditions, the creation of oxygen vacancies in the surface leads to the formation of reduced Fe species in the surface in the vicinity of the vacant oxygen. The (001) surface is slightly more prone to reduction than the (111), due to the higher stabilisation upon relaxation of the atoms around the oxygen vacancy, but molecular oxygen adsorbs preferentially at the (111) surface. In both oxidized surfaces, the oxygen atoms are located on bridge positions between two surface iron atoms, from which they attract electron density. The oxidised state is thermodynamically favourable with respect to the stoichiometric surfaces under ambient conditions, although not under the conditions when bulk Fe3O4 is thermodynamically stable with respect to Fe2O3. This finding is important in the interpretation of the catalytic properties of Fe3O4 due to the presence of oxidised species under experimental conditions.

The atomic structure of low-index surfaces of the intermetallic compound InPd

The intermetallic compound InPd (CsCl type of crystal structure with a broad compositional range) is considered as a candidate catalyst for the steam reforming of methanol. Single crystals of this phase have been grown to study the structure of its three low-index surfaces under ultra-high vacuum conditions, using low energy electron diffraction (LEED), X-ray photoemission spectroscopy (XPS), and scanning tunneling microscopy (STM). During surface preparation, preferential sputtering leads to a depletion of In within the top few layers for all three surfaces. The near-surface regions remain slightly Pd-rich until annealing to ∼580 K. A transition occurs between 580 and 660 K where In segregates towards the surface and the near-surface regions become slightly In-rich above ∼660 K. This transition is accompanied by a sharpening of LEED patterns and formation of flat step-terrace morphology, as observed by STM. Several superstructures have been identified for the different surfaces associated with this process. Annealing to higher temperatures (≥750 K) leads to faceting via thermal etching as shown for the (110) surface, with a bulk In composition close to the In-rich limit of the existence domain of the cubic phase. The Pd-rich InPd(111) is found to be consistent with a Pd-terminated bulk truncation model as shown by dynamical LEED analysis while, after annealing at higher temperature, the In-rich InPd(111) is consistent with an In-terminated bulk truncation, in agreement with density functional theory (DFT) calculations of the relative surface energies. More complex surface structures are observed for the (100) surface. Additionally, individual grains of a polycrystalline sample are characterized by micro-spot XPS and LEED as well as low-energy electron microscopy. Results from both individual grains and “global” measurements are interpreted based on comparison to our single crystals findings, DFT calculations and previous literature.

Functionalized surfaces and surface functionalization of nanomaterials

Nature leads, we follow. But nanotechnologists are in hot pursuit, in designing controllable structures that can mimic naturally occurring and artificially synthesized materials on a common platform. The supramolecular chemistry concerns the investigation of nature principles to produce fascinating complexed and functional molecular assemblies, as well as the utilization of these principles to generate novel devices and materials, potentially useful for sensing, catalysis, transport and other applications in medical or engineering science. The work presented in this thesis is a compilation of different synthetic methods to achieve inorganic-organic hybrid nanomaterials. Silicatein, a protein enzyme, which acts both as a catalyst and template for the formation of silica needles in marine sponges, has been used for the biosynthesis of semiconductor metal oxides on surfaces. Silicatein was immobilized on gold (111) surfaces using alkane thiol, as well as on a novel self-assembly of NTA on top of a “cushion” of reactive ester polymer has been successfully employed to make functionalised surfaces. The immobilization of silicatein on surfaces was monitored by surface plasmon spectroscopy, atomic force microscopy and confocal laser scanning microscopy. Surface bound silicatein retains its biocatalytic activity, which was demonstrated by monitoring its hydrocatalytic activity to catalyse the synthesis of biosilica, biotitania, and biozirconia. The synthesis of semiconductor metal oxides was characterized using scanning electron microscopy. This hydrolytic biocatalyst is used to synthesize the gold nanoparticles. The gold nanoparticles are formed by reduction of tetrachloroaurate, AuCl4-, by the action of sulfhydryl groups hidden below the surface groups of the protein. The resulting gold nanoparticles which are stabilized by surface bound silicatein further aggregate to form Au nanocrystals. The shape of the nanocrystals obtained by using recombinant silicatein is controlled through chiral induction by the protein during the nucleation of the nanocrystals. As an extension of this work, TiO2 nanowires were functionalized using polymeric ligand which incorporates the nitrilotriacetic acid (NTA) linker in the back bone to immobilize His-tagged silicatein onto the TiO2 nanowires. The surface bound protein not only retains its original hydrolytic properties, but also acts as a reductant for AuCl4- in the synthesis of hybrid TiO2/silicatein/Au nanocomposites. Functionalized, monocrystalline rutile TiO2 nanorods were prepared from TiCl4 in aqueous solution in the presence of dopamine. The surface bound organic ligand controls the morphology as well as the crystallinity and the phase selection of TiO2. The surface amine groups can be tailored further with functional molecules such as dyes. As an example, this surface functionality is used for the covalent binding of a fluorescent dye,4-chloro-7- nitrobenzylurazene (NBD) to the TiO2 nanorods. The polymeric ligands have been used successfully for the in-situ and post-functionalization of TiO2 nanoparticles. Besides to chelating dopamine anchor group the multifunctional ligand system presented here incorporates a modifier molecule which allows the binding of functional molecules (here the dyes pyrene, NBD, and Texas Red) as well as additional entities which allow tailoring the solubility of inorganic nanocrystals in different solvents. A novel method for the surface functionalization of fullerene-type MoS2 nanoparticles and subsequently binding these nanoparticles onto TiO2 nanowires has been reported using polymeric ligands. The procedure involves the complexation of IF-MoS2 with a combination of Ni2+ via an umbrella-type nitrilotriacetic acid (NTA) and anchoring them to the sidewalls of TiO2 nanowires utilizing the hydroxyl groups of dopamine present in the main contents of polymeric ligand. A convenient method for the synthesis of Au/CdS nanocomposites has been presented, which were achieved through the novel method of thiol functionalization of gold colloids. The thermodynamically most stable phase of ZrO2 (cubic) has been obtained at much lower temperature (180°C). These nanoparticles are highly blue fluorescent, with a high surface area.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

Yield functions for porous materials with cubic symmetry using different definitions of yield

Plastic yield criteria for porous ductile materials are explored numerically using the finite-element technique. The cases of spherical voids arranged in simple cubic, body-centred cubic and face-centred cubic arrays are investigated with void volume fractions ranging from 2 % through to the percolation limit (over 90 %). Arbitrary triaxial macroscopic stress states and two definitions of yield are explored. The numerical data demonstrates that the yield criteria depend linearly on the determinant of the macroscopic stress tensor for the case of simple-cubic and body-centred cubic arrays - in contrast to the famous Gurson-Tvergaard-Needleman (GTN) formula - while there is no such dependence for face-centred cubic arrays within the accuracy of the finite-element discretisation. The data are well fit by a simple extension of the GTN formula which is valid for all void volume fractions, with yield-function convexity constraining the form of the extension in terms of parameters in the original formula. Simple cubic structures are more resistant to shear, while body-centred and face-centred structures are more resistant to hydrostatic pressure. The two yield surfaces corresponding to the two definitions of yield are not related by a simple scaling.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.