A Low-Energy Ion Scattering (LEIS) Study of the Influence of the Vanadium Concentration on the Activity of Vanadium-Niobium Oxide Catalysts for the Oxidative Dehydrogenation of Propane

A series of vanadium-niobium oxide catalysts in which the vanadia content varies between 0.3 and 18mol%was prepared by coprecipitation. These catalysts were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), low-energy ion scattering (LEIS), and by catalytic testing in the oxidative dehydrogenation reaction of propane. The results of the surface analysis by XPS and LEIS are compared. It is concluded that the active site on the catalyst surface contains 2.0 ± 0.3 vanadium atoms on average. This can be understood byassuming the existenceof two or three different sites:isolated vanadium atoms, pairs of vanadium atoms, or ensembles of three vanadium atoms. At higher vanadium concentration more vanadium clusters with a higher activity are at the surface.LEIS revealed that as the vanadium concentration in the catalyst increases, vanadium replaces niobium at the surface. At vanadium concentrations above 8 mol%, new phases such as P-(Nb, V)20S which are less active because vanadium is present in isolated sites are formed, while the vanadium surface concentration shows a slight decrease

Rice husk ash – A valuable reinforcement for high density polyethylene

This paper presents the results of a study on the use of rice husk ash (RHA) for property modification of high density polyethylene (HDPE). Rice husk is a waste product of the rice processing industry. It is used widely as a fuel which results in large quantities of RHA. Here, the characterization of RHA has been done with the help of X-ray diffraction (XRD), Inductively Coupled Plasma Atomic Emission Spectroscopy (ICPAES), light scattering based particle size analysis, Fourier transform infrared spectroscopy (FTIR) and Scanning Electron Microscope (SEM). Most reports suggest that RHA when blended directly with polymers without polar groups does not improve the properties of the polymer substantially. In this study RHA is blended with HDPE in the presence of a compatibilizer. The compatibilized HDPE-RHA blend has a tensile strength about 18% higher than that of virgin HDPE. The elongation-at-break is also higher for the compatibilized blend. TGA studies reveal that uncompatibilized as well as compatibilized HDPERHA composites have excellent thermal stability. The results prove that RHA is a valuable reinforcing material for HDPE and the environmental pollution arising from RHA can be eliminated in a profitable way by this technique.

HDPE-Ash Nanocomposites

Ash-based polymer composites are assuming increasing importance because of the pollutant potential, fine particle size, and low price of ash. Fly ash and rice husk ash are two prominent ash materials on which some investigations have already been done for potential use in polymer composites. This article highlights the results of a study on the use of wood ash in HDPE. Wood ash is mainly a mixture of various metallic compounds and some silica. Here, the characterization of wood ash has been done with the help of XRD, ICPAES, light scattering based particle size analysis, FTIR, and SEM. The results show that wood ash particle size has an average value of 293 nm, much lower than other categories of ash. When blended with HDPE in the presence of a compatibilizer, wood ash gives rise to vastly improved mechanical properties over that of the base polymer. The results prove that wood ash is a valuable reinforcing material for HDPE and the environmental pollution due to wood ash can be solved in a most profitable way by this technique.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

Studies on collective excitations of quasi-two-dimensional Bose-Einstein condensate

Theory Division Department of Physics

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

The Navier-Stokes Equations with Particle Methods

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0

X-Ray spectra of superheavy and quasi-superheavy elements

We discuss the possibility of identifying superheavy elements from the observation of their M-shell x-ray spectra, which might occur during the collision of a superheavy element with a heavy target. The same question is discussed for the possible observation of the x-rays from the quasimolecule (quasi-superheavy element) which is formed during such a heavy-ion collision. It is shown that it is very difficult, if not impossible, to determine any information about the interesting quantum electrodynamical effects from the M-shell x-ray spectra of these quasimolecules.

Influence of the electronic shell structure on the elastic scattering of heavy ions

The interatomic potential of the system I - I at intermediate and small distances is calculated from atomic DFS electron densities within a statistical model. Structures in the potential, due to the electronic shells, are investigated. Calculations of the elastic differential scattering cross section for small angles and several keV impact energies show a detailed peak pattern which can be correlated to individual electronic shell interaction.

Total differential scattering cross section of {Ar^+}-Ar at 15 to 400 keV

We report on the measurement of the total differential scattering cross section of {Ar^+}-Ar at laboratory energies between 15 and 400 keV. Using an ab initio relativistic molecular program which calculates the interatomic potential energy curve with high accuracy, we are able to reproduce the detailed structure found in the experiment.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Evidence for an additional coupling of the innermost shells in very heavy quasi-molecular ion-atom collisions

Due to the tremendous spin-orbit splitting of quasi-molecular levels in superheavy collision systems (Z = Z_1 + Z_2 {\ge\approx} 137) bombarding energy 0.5-6 MeV N{^-1}, unusual couplings may occur around Z \simeq 165. Experimental evidence for such a theoretically predicted coupling is discussed.

New calculations of P(b) curves for 1s_\sigma excitation in low-Z (Z\le10) ion-atom scattering

Ab initio fully relativistic SCF molecular calculations of energy eigenvalues as well as coupling-matrix elements are used to calculate the 1s_\sigma excitation differential cross section for Ne-Ne and Ne-O in ion-atom collisions. A relativistic perturbation treatment which allows a direct comparison with analogous non-relativistic calculations is also performed.

Multiple vacancy inclusive probabilities for the scattering system 16 MeV S{^16+} on Ar

To evaluate single and double K-shell inclusive charge transfer probabilities in ion-atom collisions we solve the time-dependent Dirac equation. By expanding the timedependent wavefunction in a set of molecular basis states the time-dependent equation reduces to a set of coupled-channel equations. The energy eigenvalues and matrix elements are taken from self-consistent relativistic molecular many-electron Dirac-Fock-Slater calculations. We present many-electron inclusive probabilities for different final configurations as a function of impact parameter for single and double K-shell vacancy production in collisions of bare S on Ar.