The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Effect of the Vulcanization Time and Storage on the Stability and Physical Properties of Sulfur-Prevulcanized Natural Rubber Latex

Prevulcanized natural rubber latex was prepared by the heating of the latex compound at 55°C for different periods of time (2, 4, 6, 8, and 10 h). The changes in the colloidal stability and physical properties were evaluated during the course of prevulcanization. The prevulcanized latex compounds were stored for 300 days, and the properties were monitored at different storage intervals (0, 20, 40, 60, 120, 180, 240, and 300 days). During prevulcanization, the mechanical stability time increased, and the viscosity remained almost constant. The tensile strength increased during storage for a period of 20 days. The degree of crosslinking, modulus, elongation at break, and chloroform number were varied with the time of storage.

Magnetic, Dielectric and Physicomechanical Properties of Rubber Ferrite Nanocomposites

In the present study the preparation and characterisation of rubber ferrite composites containing nickel ferrite and gamma ferric oxide have been dealt with.Synthetic rubbers viz. ethylene propylene diene rubber and neoprene rubber were used for the incorporation of nickel ferrite and gamma ferric oxide for the synthesis of RFCs. Incorporation of ferrites were carried out according to a specific recipe for various loadings of the magnetic fillers. The ferrites used for the preparation of RFCs were synthesised using sol-gel method and structural characterisation was carried out. Experimental techniques like X-ray diffraction, Transmission electron microscopy and other analytical techniques were used for this. Precharaterised ferrites were then incorporated at different loading into rubber according to conventional mixing methods. The cure characteristics, mechanical, dielectric, magnetic and microwave properties of these composites were evaluated. The effect of carbon black on these properties of RFCs were carried out.

Studies on the structural, electrical and magnetic properties of composites based on spinel ferrites

This thesis mainly deals with the preparation and studies on magnetic composites based on spinel ferrites prepared both chemically and mechanically. Rubber ferrite composites (RFC) are chosen because of their mouldability and flexibility and the ease with which the dielectric and magnetic properties can be manipulated to make them as useful devices. Natural rubber is chosen as the Matrix because of its local availability and possible value addition. Moreover, NR represents a typical unsaturated nonpolar matrix. The work can be thought of as two parts. Part l concentrates on the preparation and characterization of nanocomposites based on y-Fe203. Part 2 deals with the preparation and characterization of RFCs containing Nickel zinc ferrit In the present study magnetic nanocomposites have been prepared by ionexchange method and the preparation conditions have been optimized. The insitu incorporation of the magnetic component is carried out chemically. This method is selected as it is the easiest and simplest method for preparation of nanocomposite. Nanocomposite samples thus prepared were studied using VSM, Mossbauer spectroscopy, Iron content estimation, and ESR spectroscopy. For the preparation of RFCs, the filler material namely nickel zinc ferrite having the general formula Ni)_xZnxFez04, where x varies from 0 to 1 in steps of 0.2 have been prepared by the conventional ceramic techniques. The system of Nil_xZn"Fe204 is chosen because of their excellent high frequency characteristics. After characterization they are incorporated into the polymer matrix of natural rubber by mechanical method. The incorporation is done according to a specific recipe and for various Loadings of magnetic fillers and also for all compositions. The cure characteristics, magnetic properties and dielectric properties of these composites are evaluated. The ac electrical conductivity of both ceramic nickel zinc ferrites and rubber ferrite composites are also calculated using a simple relation. The results are correlated.

On structural, optical and dielectric properties of zinc aluminate nanoparticles

Zinc aluminate nanoparticles with average particle size of 40 nm were synthesized using a sol–gel combustion method. X-ray diffractometry result was analysed by Rietveld refinement method to establish the phase purity of the material. Different stages of phase formation of the material during the synthesis were investigated using differential scanning calorimetry and differential thermogravimetric analysis. Particle size was determined with transmission electron microscopy and the optical bandgap of the nanoparticles was determined by absorption spectroscopy in the ultraviolet-visible range. Dielectric permittivity and a.c. conductivity of the material were measured for frequencies from 100 kHz to 8 MHz in the temperature range of 30–120◦C. The presence of Maxwell– Wagner type interfacial polarization was found to exist in the material and hopping of electron by means of quantum mechanical tunneling is attributed as the reason for the observed a.c. conductivity

The Effect of Antimony Substitution on the Magnetic and Structural Properties of Fe0.75–xSi0.25Sbx Alloys

The results of the investigation of the magnetic and structural properties of the alloy system Fe0.75–xSi0.25Sbx, where x = 0, 0.05, 0.1, 0.15, 0.2, and 0.25 synthesized by mechanical alloying followed by heat treatment are described. The x-ray diffraction reveals that all samples crystallize in the DO3-type cubic phase structure. Substituting Fe by Sb led to a de-crease in the lattice constant and the unit cell volume. The magnetic properties are investigated by vibrating sample magnetometer and show that all the samples are ferromagnetically ordered at room temperature. The Curie temperature is found to decrease linearly from (850 ± 5) K for the parent alloy to (620 ± 5) K for the alloyith x = 0.25. The satura-tion magnetizations at room temperature and at 100 K are found to decrease with increasing the antimony concentration. The above results indicate that Sb dissolves in the cubic structure of this alloy system.

Tailoring Magnetic Properties of Co-Fe Thin Films by Topographical Modifications Using Thermal Annealing and Swift Heavy Ion Irradiation and Fabrication of Magnetoelectric Multilayers for Device Applications

Magnetism and magnetic materials have been playing a lead role in improving the quality of life. They are increasingly being used in a wide variety of applications ranging from compasses to modern technological devices. Metallic glasses occupy an important position among magnetic materials. They assume importance both from a scientific and an application point of view since they represent an amorphous form of condensed matter with significant deviation from thermodynamic equilibrium. Metallic glasses having good soft magnetic properties are widely used in tape recorder heads, cores of high-power transformers and metallic shields. Superconducting metallic glasses are being used to produce high magnetic fields and magnetic levitation effect. Upon heat treatment, they undergo structural relaxation leading to subtle rearrangements of constituent atoms. This leads to densification of amorphous phase and subsequent nanocrystallisation. The short-range structural relaxation phenomenon gives rise to significant variations in physical, mechanical and magnetic properties. Magnetic amorphous alloys of Co-Fe exhibit excellent soft magnetic properties which make them promising candidates for applications as transformer cores, sensors, and actuators. With the advent of microminiaturization and nanotechnology, thin film forms of these alloys are sought after for soft under layers for perpendicular recording media. The thin film forms of these alloys can also be used for fabrication of magnetic micro electro mechanical systems (magnetic MEMS). In bulk, they are drawn in the form of ribbons, often by melt spinning. The main constituents of these alloys are Co, Fe, Ni, Si, Mo and B. Mo acts as the grain growth inhibitor and Si and B facilitate the amorphous nature in the alloy structure. The ferromagnetic phases such as Co-Fe and Fe-Ni in the alloy composition determine the soft magnetic properties. The grain correlation length, a measure of the grain size, often determines the soft magnetic properties of these alloys. Amorphous alloys could be restructured in to their nanocrystalline counterparts by different techniques. The structure of nanocrystalline material consists of nanosized ferromagnetic crystallites embedded in an amorphous matrix. When the amorphous phase is ferromagnetic, they facilitate exchange coupling between nanocrystallites. This exchange coupling results in the vanishing of magnetocrystalline anisotropy which improves the soft magnetic properties. From a fundamental perspective, exchange correlation length and grain size are the deciding factors that determine the magnetic properties of these nanocrystalline materials. In thin films, surfaces and interfaces predominantly decides the bulk property and hence tailoring the surface roughness and morphology of the film could result in modified magnetic properties. Surface modifications can be achieved by thermal annealing at various temperatures. Ion irradiation is an alternative tool to modify the surface/structural properties. The surface evolution of a thin film under swift heavy ion (SHI) irradiation is an outcome of different competing mechanism. It could be sputtering induced by SHI followed by surface roughening process and the material transport induced smoothening process. The impingement of ions with different fluence on the alloy is bound to produce systematic microstructural changes and this could effectively be used for tailoring magnetic parameters namely coercivity, saturation magnetization, magnetic permeability and remanence of these materials. Swift heavy ion irradiation is a novel and an ingenious tool for surface modification which eventually will lead to changes in the bulk as well as surface magnetic property. SHI has been widely used as a method for the creation of latent tracks in thin films. The bombardment of SHI modifies the surfaces or interfaces or creates defects, which induces strain in the film. These changes will have profound influence on the magnetic anisotropy and the magnetisation of the specimen. Thus inducing structural and morphological changes by thermal annealing and swift heavy ion irradiation, which in turn induce changes in the magnetic properties of these alloys, is one of the motivation of this study. Multiferroic and magneto-electrics is a class of functional materials with wide application potential and are of great interest to material scientists and engineers. Magnetoelectric materials combine both magnetic as well as ferroelectric properties in a single specimen. The dielectric properties of such materials can be controlled by the application of an external magnetic field and the magnetic properties by an electric field. Composites with magnetic and piezo/ferroelectric individual phases are found to have strong magnetoelectric (ME) response at room temperature and hence are preferred to single phasic multiferroic materials. Currently research in this class of materials is towards optimization of the ME coupling by tailoring the piezoelectric and magnetostrictive properties of the two individual components of ME composites. The magnetoelectric coupling constant (MECC) (_ ME) is the parameter that decides the extent of interdependence of magnetic and electric response of the composite structure. Extensive investigates have been carried out in bulk composites possessing on giant ME coupling. These materials are fabricated by either gluing the individual components to each other or mixing the magnetic material to a piezoelectric matrix. The most extensively investigated material combinations are Lead Zirconate Titanate (PZT) or Lead Magnesium Niobate-Lead Titanate (PMNPT) as the piezoelectric, and Terfenol-D as the magnetostrictive phase and the coupling is measured in different configurations like transverse, longitudinal and inplane longitudinal. Fabrication of a lead free multiferroic composite with a strong ME response is the need of the hour from a device application point of view. The multilayer structure is expected to be far superior to bulk composites in terms of ME coupling since the piezoelectric (PE) layer can easily be poled electrically to enhance the piezoelectricity and hence the ME effect. The giant magnetostriction reported in the Co-Fe thin films makes it an ideal candidate for the ferromagnetic component and BaTiO3 which is a well known ferroelectric material with improved piezoelectric properties as the ferroelectric component. The multilayer structure of BaTiO3- CoFe- BaTiO3 is an ideal system to understand the underlying fundamental physics behind the ME coupling mechanism. Giant magnetoelectric coupling coefficient is anticipated for these multilayer structures of BaTiO3-CoFe-BaTiO3. This makes it an ideal candidate for cantilever applications in magnetic MEMS/NEMS devices. SrTiO3 is an incipient ferroelectric material which is paraelectric up to 0K in its pure unstressed form. Recently few studies showed that ferroelectricity can be induced by application of stress or by chemical / isotopic substitution. The search for room temperature magnetoelectric coupling in SrTiO3-CoFe-SrTiO3 multilayer structures is of fundamental interest. Yet another motivation of the present work is to fabricate multilayer structures consisting of CoFe/ BaTiO3 and CoFe/ SrTiO3 for possible giant ME coupling coefficient (MECC) values. These are lead free and hence promising candidates for MEMS applications. The elucidation of mechanism for the giant MECC also will be the part of the objective of this investigation.

Ni-Zn-Sm nanopowder ferrites: Morphological aspects and magnetic properties

Ni-Zn ferrites have been widely used in components for high-frequency range applications due to their high electrical resistivity, mechanical strength and chemical stability. Ni-Zn ferrite nanopowders doped with samarium with a nominal composition of Ni0.5Zn0.5Fe2-xSmxO4 (x = 0.0, 0.05, and 0.1 mol) were obtained by combustion synthesis using nitrates and urea as fuel. The morphological aspects of Ni-Zn-Sm ferrite nanopowders were investigated by X-ray diffraction, nitrogen adsorption by BET, sedimentation, scanning electron microscopy and magnetic properties. The results indicated that the Ni-Zn-Sm ferrite nanopowders were composed of soft agglomerates of nanoparticles with a high surface area (55.8-64.8 m(2)/g), smaller particles (18-20 nm) and nanocrystallite size particles. The addition of samarium resulted in a reduction of all the magnetic parameters evaluated, namely saturation magnetization (24-40 emu/g), remanent magnetization (2.2-3.5 emu/g) and coercive force (99.3-83.3 Oe). (c) 2007 Elsevier B. V. All rights reserved.

Theoretical investigation of electronic and optical properties of andalusite within density functional theory

The electronic and optical properties of andalusite were studied by using quantum-mechanical calculations based on the density functional theory (DFT). The electronic structure shows that andalusite has a direct band gap of 5.01 eV. The complex dielectric function and optical constants, such as extinction coefficient, refractive index, reflectivity and energy-loss spectrum, are calculated. The optical properties of andalusite are discussed based on the band structure calculations. It is shown that the O-2p states and Al-3s states play a major role in optical transitions as initial and final states, respectively. (C) 2010 Elsevier Ltd. All rights reserved.

Electronic structure and optical properties of BaMoO(4) powders

Barium molybdate (BaMoO(4)) powders were synthesized by the co-precipitation method and processed in microwave-hydrothermal at 140 degrees C for different times. These powders were characterized by X-ray diffraction (XRD), Fourier transform Raman (FT-Raman), Fourier transform infrared (FT-IR), ultraviolet-visible (UV-vis) absorption spectroscopies and photoluminescence (PL) measurements. XRD patterns and FT-Raman spectra showed that these powders present a scheelite-type tetragonal structure without the presence of deleterious phases. FT-IR spectra exhibited a large absorption band situated at around 850.4 cm(-1), which is associated to the Mo-O antisymmetric stretching vibrations into the [MoO(4)] clusters. UV-vis absorption spectra indicated a reduction in the intermediary energy levels within band gap with the processing time evolution. First-principles quantum mechanical calculations based on the density functional theory were employed in order to understand the electronic structure (band structure and density of states) of this material. The powders when excited with different wavelengths (350 nm and 488 nm) presented variations. This phenomenon was explained through a model based in the presence of intermediary energy levels (deep and shallow holes) within the band gap. (C) 2009 Elsevier B.V. All rights reserved.

Structural and Electronic Properties of Dipyridamole and Derivatives

Quantum mechanical calculations at the B3LYP theory level, together with the 6-31G* basis set, were employed to obtain the energy, ionization potential, and polarizabilites for dipyridamole and derivatives, which are compared with their biological activity. Density functional calculations of the spin densities were performed for radical formed by electron abstraction of dipyridamole and derivatives. The unpaired electron remains in dipyridamole is localized on the nitrogen atoms in the substituent positions 1, 3, 5, 7, 11, 12, 13, 14, with participation of the 9 and 10 carbons in the pyrimido-pyrimidine ring. The antioxidant activity is related with ionization potential, polarizability and Log P.

Synthesis and physical properties of lipid-based poly(ester-urethane)s, I: Effect of varying polyester segment length

Four aliphatic thermoplastic poly(ester-urethane)s (PEUs) with similar molecular weights but varying polyesters molecular weight (534-1488 g/mol) were prepared from polyester diols, obtained by melt condensation of Azelaic acid and 1,9-Nonanediol, and 1,7-heptamethylene di-isocyanate (HPMDI) all sourced from vegetable oil feedstock. The thermal, and mechanical properties, and crystal structure of PEUs were investigated using DSC, TGA, DMA, tensile analysis and WAXD. For sufficiently long polyester chain, WAXD data indicated no hydrogen bonds polyethylene (PE)-like crystalline packing and for short polyester chains, small crystal domains with significant H-bonded polyamide (PA)-like packing. Crystallinity decreased with decreasing polyester molecular weights. The polymorphism of PEUs and consequently their melting characteristics were found to be largely controlled by polyester segment length. TGA of the PEUs indicated improved thermal stability with decreasing polyester chain length, suggesting a stabilization effect by urethane groups. Mechanical properties investigated by DMA and tensile analysis were found to scale predictably with the overall crystallinity of PEUs. (C) 2012 Elsevier Ltd. All rights reserved.

Structure and Physical Properties of EVA/Starch Precursor Materials for Foaming Applications

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

Semisolid systems containing propolis for the treatment of periodontal disease: In vitro release kinetics, syringeability, rheological, textural, and mucoadhesive properties

Formulations containing poloxamer 407 (P407), carbopol 934P (C934P), and propolis extract (PE) were designed for the treatment of periodontal disease. Gelation temperature, in vitro drug release, rheology, hardness, compressibility, adhesiveness, mucoadhesion, and syringeability of formulations were determined. Propolis release from formulations was controlled by the phenomenon of relaxation of polymer chains. Formulations exhibited pseudoplastic flow and low degrees of thixotropy or rheopexy. In most samples, increasing the concentration of C934P content significantly increased storage modulus (G'), loss modulus (G ''), and dynamic viscosity (n') at 5 degrees C, G '' exceeded G'. At 25 and 37 degrees C, n' of each formulation depended on the oscillatory frequency. Formulations showed thermoresponsive behavior, existing as a liquid at room temperature and gel at 34-37 degrees C. Increasing the C934P content or temperature significantly increased formulation hardness, compressibility, and adhesiveness. The greatest mucoadhesion was noted in the formulation containing 15% P407 (w/w) and 0.25% C934P (w/w). The work of syringeability values of all formulations were similar and very desirable with regard to ease of administration. The data obtained in these formulations indicate a potentially useful role in the treatment of periodontitis and suggest they are worthy of clinical evaluation. (c) 2007 Wiley-Liss, Inc.