Functoroids and ptykoids

Summary A type of first-order analogues of ptykes, namely ‘ptykoids’, are introduced, and bounds are found for the ptykoids of level 1 and 2 which can be proved to be ptykoids in Peano arithmetic. This gives rise toΠ ₃ ⁰ andΠ ₄ ⁰ independence results.     

Strategies for modelling of catalysts

Summary and conclusions The strategy summarised above in which modelling calculations are combined with QM cluster calculations is a viable procedure for the study of catalysis. Our discussion has emphasised studies of zeolite catalysts but the same approach could be used in modelling reactions catalysed on metal and metal oxide surfaces. Moreover, the techniques and potentials are available for these methods to have a wide range of applications.     

Dielectric relaxation and computer simulation studies of rutile-structured MnF2 crystals

The fluorides of the rutile structure are relatively simple ionic materials with tetragonal symmetry for which the dominant intrinsic defect has not been established. The present experiments involve low-temperature dielectric relaxation measurements on Er³⁺-and Y³⁺-doped MnF₂ single crystals. Unexpectedly, dielectric loss peaks were observed at cryogenic temperatures, involving very low activation energies,E. For both dopants a prominent peak is observed for samples oriented parallel to thec-axis withE 6 meV and in perpendicular orientations withE=37 meV for Er³⁺ and 46 meV for Y³⁺ doping. Such lowE-values are probably too small to be controlled by lattice migration of a defect. Rather, we expect that they are due to a very low symmetry configuration created when the ions near the defect move off symmetry to a more stable configuration. Computer simulation calculations have been carried out which are much improved over early studies of this system in terms of the code used and the F-F interatomic potentials. The results show that the energy per defect for the anion Frenkel (1.53 eV) is lower than that of the Schottky (1.99 eV). It was also shown that the fluorine interstitial, F_i, adopts a split-interstitial form. This defect associates strongly with trivalent dopants Er and Y to produce a low symmetry dipolar structure with the necessary off-symmetry configuration to explain the experimental findings. Since there is no alternative way to explain these low temperature relaxations in terms of impurities associated with Mn vacancies, as would be required by the Schottky model, we conclude that these experiments serve to establish the nature of the intrinsic defect in MnF₂ as anion Frenkel.     

Adsorption of organosilanes at a Zn-terminated ZnO (0001) surface: molecular dynamics study

Four different organosilanes (octyltrihydroxysilane, butyltrihydroxysilane, aminopropyltrihydroxysilane, and thiolpropyltrihydroxysilane) adsorbed at a reconstructed Zn-terminated polar ZnO (0001) surface are studied via constant temperature (298 K) molecular dynamics simulations. Both single adsorbed silane molecules as well as adsorbed silane layers are modeled, and the energy, distance, orientation, and alignment of these adsorbates are analyzed. The adsorbed silane molecules exhibit behavior depending on the chemical nature of their tail (nonpolar or polar) as well as on the silane concentration at the solid surface (single adsorption or silane layer). In contrast to the O-terminated ZnO surface studied previously, now adsorption can only occur at the vacancies of this reconstructed crystal surface, thus leading to an arched structure of the liquid phase near the crystal surface. Nevertheless, both nonpolar and polar single adsorbed silanes show a similar orientation and alignment at the surface (orthogonal in the former, parallel in the latter case) as for the O-terminated ZnO surface, although the interaction energy with the surface is considerably increased for nonpolar silanes while it is nearly unaffected for the polar ones. For adsorbed silanes within silane layers, the difference to single adsorbed silanes depends on the polarity of the tail: nonpolar silanes again show an orthogonal alignment, while polar silanes exhibit two different orientations at the solid surface-a head and a tail down configuration. This leads to two completely different but nevertheless stable orientations of these silanes at the Zn-terminated ZnO surface.     

Structure and properties of ZnS nanoclusters

Earlier studies have shown that the most stable structures for (ZnS)n clusters with n = 10-47 are hollow polyhedral clusters ("bubbles"). We report a detailed study of larger clusters, where n = 50, 60, 70, and 80, for which onionlike or "double bubble" structures are predicted. We report calculations of the vibrational spectra and the electronic structure of bubble and double bubble clusters, which may assist in their experimental identification.