TiO2-Cu photocatalysts: A study on the long- and short-range chemical environment of the dopant

In this study, the short- and long-range chemical environments of Cu dopant in TiO2 photocatalyst have been investigated. The Cu-doped and undoped TiO2 specimens were prepared by the sol-gel approach employing CuSO4·5H2O and Ti(O-iPr)4 precursors and subjecting the dried gels to thermal treatment at 400 and 500 C. The photocatalytic activity, investigated by methylene blue degradation under sunlight irradiation, showed a significantly higher efficiency of Cu-doped samples than that of pure TiO2. The X-ray diffraction results showed the presence of anatase phase for samples prepared at 400 and 500 C. No crystalline CuSO4 phase was detected below 500 C. It was also found that doping decreases the crystallite size in the (004) and (101) directions. Infrared spectroscopy results indicated that the chemical environment of sulfate changes as a function of thermal treatment, and UV-vis spectra showed that the band gap decreases with thermal treatment and Cu doping, showing the lowest value for the 400 C sample. X-ray absorption fine structure measurements and analysis refinements revealed that even after thermal treatment and photocatalytic assays, the Cu2+ local order is similar to that of CuSO4, containing, however, oxygen vacancies. X-ray photoelectron spectroscopy data, limited to the near surface region of the catalyst, evidenced, besides CuSO4, the presence of Cu1+ and CuO phases, indicating the active role of Cu in the TiO2 lattice. © 2013 Springer Science+Business Media New York.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Laplace transform approach to the quantum harmonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Long-range and short-range structures of cube-like shape SrTiO3 powders: microwave-assisted hydrothermal synthesis and photocatalytic activity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fingerprints of short-range and long-range structure in BaZr1-xHfxO3 solid solutions: an experimental and theoretical study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

Search for a spin-dependent short-range force between nucleons with a 3 He, 129 Xe clock-comparison experiment

Light pseudoscalar bosons, such as the axion that was originally proposed as a solution of the strong CP problem, would cause a new spin-dependent short-range interaction. In this thesis, an experiment is presented to search for axion mediated short-range interaction between a nucleon and the spin of a polarized bound neutron. This interaction cause a shift in the precession frequency of nuclear spin-polarized gases in the presence of an unpolarized mass. To get rid of magnetic field drifts co-located, nuclear spin polarized 3He and 129Xe atoms were used. The free nuclear spin precession frequencies were measured in a homogeneous magnetic guiding field of about 350nT using LTc SQUID detectors. The whole setup was housed in a magnetically shielded room at the Physikalisch Technische Bundesanstalt (PTB) in Berlin. With this setup long nuclear spin-coherence times, respectively, transverse relaxation times of 5h for 129Xe and 53h for 3He could be achieved. The results of the last run in September 2010 are presented which give new upper limits on the scalar-pseudoscalar coupling of axion-like particles in the axion-mass window from 10^(-2) eV to 10^(-6) eV. The laboratory upper bounds were improved by up to 4 orders of magnitude.

Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls

We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.

Hyalotekite, (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2)(Si,B)(2)O28F, a Tectosilicate Related to Scapolite: New Structure Refinement, Phase Transitions and a Short-Range Ordered 3B Superstructure

Hyalotekite, a framework silicate of composition (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2) (Si,B)(2)O28F, is found in relatively high-temperature(greater than or equal to 500 degrees C) Mn skarns at Langban, Sweden, and peralkaline pegmatites at Dara-i-Pioz, Tajikistan. A new paragenesis at Dara-i-Pioz is pegmatite consisting of the Ba borosilicates leucosphenite and tienshanite, as well as caesium kupletskite, aegirine, pyrochlore, microcline and quartz. Hyalotekite has been partially replaced by barylite and danburite. This hyalotekite contains 1.29-1.78 wt.% Y2O3, equivalent to 0.172-0.238 Y pfu or 8-11% Y on the Ca site; its Pb/(Pb+Ba) ratio ranges 0.36-0.44. Electron microprobe F contents of Langban and Dara-i-Pioz hyalotekite range 1.04-1.45 wt.%, consistent with full occupancy of the F site. A new refinement of the structure factor data used in the original structural determination of a Langban hyalotekite resulted in a structural formula, (Pb1.96Ba1.86K0.18)Ca-2(B1.76Be0.24)(Si1.56B0.44)Si8O28F, consistent with chemical data and all cations with positive-definite thermal parameters, although with a slight excess of positive charge (+57.14 as opposed to the ideal +57.00). An unusual feature of the hyalotekite framework is that 4 of 28 oxygens are non-bridging; by merging these 4 oxygens into two, the framework topology of scapolite is obtained. The triclinic symmetry of hyalotekite observed at room temperature is obtained from a hypothetical tetragonal parent structure via a sequence of displacive phase transitions. Some of these transitions are associated with cation ordering, either Pb-Ba ordering in the large cation sites, or B-Be and Si-B ordering on tetrahedral sites. Others are largely displacive but affect the coordination of the large cations (Pb, Ba, K, Ca). High-resolution electron microscopy suggests that the undulatory extinction characteristic of hyalotekite is due to a fine mosaic microstructure. This suggests that at least one of these transitions occurs in nature during cooling, and that it is first order with a large volume change. A diffuse superstructure observed by electron diffraction implies the existence of a further stage of short-range cation ordering which probably involves both (Pb,K)-Ba and (BeSi,BB)-BSi.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Guessing Harmonic Oscillator Wavefunctions Using Maple

The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.

The Harmonic Oscillator's Frobenius Solution

The Frobenius solution to the differential equations associated with the harmonic oscillator (QM) is carried out in detail.

The Driven Harmonic Oscillator in Chemistry

The molecular dynamical simulation of the normal vibrational mode of water which involves H-O-H angle deformation, when driven by an external force, can be used to see how a driven harmonic oscillator, classically, is associated with the infra-red spectrum of water (and the absorption for this particular normal mode).