A study of diquark and meson condensation in the Nambu–Jona-Lasinio model and Fermi momentum

Using a three- and four-dimensional Pauli–Villars regularization scheme, we investigate quark–antiquark and diquark condensation in the framework of the Nambu–Jona-Lasinio model. Using the particle Fermi momentum as a cutoff parameter, we study the energy gap width and coherence length for the meson condensate 〈\(q\bar q\)〉. We also study the energy gap width and critical coherence length (the distance over which there would be no diquark condensation) for the diquark 〈qq〉 and the dependence on the Fermi momentum. We obtain an estimate of the Fermi momentum value for meson and diquark condensates with an energy gap width of the order of 100 MeV.     

Correlation of size and oxygen bonding at the interface of Si nanocrystal in Si–SiO2 nanocomposite: A Raman mapping study

Raman spectroscopy/mapping is used to investigate the variation of Si phonon wavenumbers, i.e., lower wavenumber (LW ~ 495–510 cm⁻¹) and higher wavenumber (HW ~ 515–519 cm⁻¹) phonons, observed in Si–SiO₂ multilayer nanocomposite (NCp) grown using pulsed laser deposition. Sensitivity of Raman spectroscopy as a local probe to surface/interface is effectively used to show that LW and HW phonons originate at surface (Si–SiO₂ interface) and core of Si nanocrystals, respectively. The consistent picture of this understanding is developed using Raman spectroscopy monitored laser heating/annealing and cooling experiment at the site of the desired wavenumber, chosen with the help of Raman mapping. Raman spectra calculations for Si₄₁ cluster with oxygen and hydrogen termination show strong mode at 512 cm⁻¹ for oxygen terminated cluster corresponding to the vibration of surface Si atoms. This supports our attribution of LW phonons to be originating at the Si–SiO₂ surface/interface. These results along with XPS show that nature of interface (oxygen bonding) in turn depends on the size of nanocrystals and LW phonons originate at the surface of smaller Si nanocrystals. The understanding developed can conclude the ongoing debate on large variation in Si phonon wavenumbers of Si–SiO₂ NCps in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Cooling of a composite slab

A mixed boundary value problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite parallel-sided composite slab, is solved completely by using the Wiener-Hopf technique. An analytical expression is derived for the sputtering temperature at the quench front being created by a cold fluid moving on the upper surface of the slab at a constant speed v. The dependence of the various configurational parameters of the problem under consideration, on the sputtering temperature, is rather complicated and representative tables of numerical values of this important physical quantity are prepared for certain typical values of these parameters. Asymptotic results in their most simplified forms are also obtained when (i) the ratio of the thicknesses of the two materials comprising the slab is very much smaller than unity, and (ii) the quench-front speed v is very large, keeping the other parameters fixed, in both the cases.     

Scalar field collapse with an exponential potential

An analogue of the Oppenheimer–Synder collapsing model is treated analytically, where the matter source is a scalar field with an exponential potential. An exact solution is derived followed by matching to a suitable exterior geometry, and an analysis of the visibility of the singularity. In some situations, the collapse indeed leads to a finite time curvature singularity, which is always hidden from the exterior by an apparent horizon.     

Effects of various competing ligands on the kinetics of trace metal complexes of Laurentian Fulvic Acid in model solutions and natural waters

The objective of this work was to study the effects of the following Ligands: Chelex-100, Dowex MAC-3 and Dowex 50WX-8 using Competing Ligand Exchange Method. This objective was achieved by investigating complex dissociation kinetics of trace metals: Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Mn(II) and Pb(II) of a well-characterized Laurentian Fulvic Acid (LFA) in model solutions and in a natural waters of Lake Heva (Québec, Canada). The effects of variation in the competing ligands (including their quantities) on the complex dissociation kinetics were quantitatively characterized by their first-order dissociation rate coefficients. The kinetic lability of the metal complexes varied with the metal-to-LFA ratio, as expected from the theory of metal complexes of the chemically and physically heterogeneous complexants, LFA. The general trend in the metal-binding by the above competing ligands was: Dowex 50WX-8 > Chelex-100 > Dowex MAC-3. However, no difference was found between the Dowex 50WX-8 and Chelex-100 for Cd(II), Zn(II), and Co(II). The results revealed the importance of the quantity of Chelex-100 as a competing ligand in the metal(II)-LFA complexation, on the dissociation kinetics of these complexes in model solutions. By developing Competing Ligand Exchange Method as an analytical technique, for studying the relative affinities of the above competing ligands for metals complexation in natural waters this work has made a substantial contribution to analytical chemistry.     

Sol-gel derived nanoparticles of Zn substituted lithium ferrite (Li0.32Zn0.36Fe2.32O4): magnetic and Mössbauer effect measurements and their theoretical analysis

Nanoparticles of Zn substituted lithium ferrite (Li_0.32Zn_0.36Fe_2.32O₄) have been prepared by a sol-gel method where the ultra-sonication technique has been adopted to reduce the agglomeration effect among the nanoparticles. The samples were heat-treated at three different temperatures and the formation of the nanocrystalline phase was confirmed by X-ray diffractograms (XRD). The average particle size of each sample has been estimated from the (311) peak of the XRD pattern using the Debye-Scherrer formula and the average sizes are in the range of 10-21 nm. The average particle size, crystallographic phase, etc. of some selected samples obtained from the high-resolution transmission electron microscopy are in agreement with those estimated from the XRD patterns. Static magnetic measurements viz., hysteresis loops, field cooled and zero field cooled magnetization versus temperature curves of some samples carried out by SQUID in the temperature range of 300 to 5 K clearly indicate the presence of superparamagnetic (SPM) relaxation of the nanoparticles in the samples. The maximum magnetization of the SPM sample annealed at 500 °C is quite high (68 Am²/Kg) and the hysteresis loops are almost square shaped with very low value of coercive field at room temperature (827.8 A/m). The particle size, magneto-crystalline anisotropy, etc. have been estimated from the detailed theoretical analysis of the static magnetic data. The dynamic magnetic behavior of the samples was also investigated by observing the ac hysteresis loops and magnetization versus field curves with different time windows at room temperatures. The different soft magnetic quantities viz., coercive field, magnetization, remanance, hysteresis losses, etc. were extracted from dynamic measurements. Dynamic measurements confirmed that the samples are in their mixed state of SPM and ordered ferrimagnetic particles, which is in good agreement with the results of static magnetic measurements. Mössbauer spectra of the samples recorded at room temperature (300 K) and at different temperatures down to 20 K confirmed the presence of the SPM relaxation of the nanoparticles of the samples.     

Chemical reactions in the atomization of molybdenum in graphite furnace atomic absorption spectrometry

Summary Chemical reactions in the atomization of molybdenum in graphite furnace atomic absorption spectrometry have been studied using graphite platforms for atomization along with X-ray diffraction analysis. When Mo [as an aqueous solution of (NH₄)₂MoO₄] is heated in a graphite furnace, three molybdenum oxides: [MoO_2(s), MoO_3(s) and Mo₄O_11(s)], are formed at relatively low temperatures (<1,500 K). When Mo is atomized from a pyrolytic graphite surface, the charring curve of Mo shows a dip in absorbance in the temperature range 1,200–1,800 K. Hence, a charring temperature <1,200 K should be used for quantitative determination of Mo when a pyrolytically coated tube or a platform made of pyrolytic graphite is used. Mo_(s), MoC_(s) and Mo₂C_(s) have been found on both the pyrolytic and the regular graphite surface after the charring step is completed. Formation of Mo_(g) by direct sublimation of Mo_(s) and by dissociation of MoC_(g) are all thermodynamically favourable reactions at the temperature considered.

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Chemische Reaktionen bei der Atomisierung von Molybdän in der Graphitofen-AAS

Zusammenfassung Die chemischen Reaktionen bei der Atomisierung von Molybdän wurden mit Hilfe von GraphitPlattformen zusammen mit der Röntgen-Diffraktionsanalyse untersucht. Bei der Erhitzung von Molybdän [als wäßrige (NH₄)₂MoO₄-Lösung] im Graphitofen werden drei Molybdänoxide (MoO_2(s), MoO_3(s) und Mo₄O_11(s)) bei relativ niedrigen Temperaturen (<1 500 K) gebildet. Wenn Molybdän von einer pyrolytischen Graphitoberfiäche atomisiert wird, zeigt die Veraschungskurve eine Absenkung der Extinktion im Bereich von 1200 bis 1800 K. Deshalb sollte bei Verwendung eines mit pyrolytischem Graphit überzogenen Rohres oder einer entsprechenden Plattform für quantitative Molybdänbestimmungen eine Veraschungstemperatur von <1 200 K benutzt werden. Nach der Veraschungsstufe wurden sowohl auf der pyrolytischen als auch auf der normalen Graphitoberfläche Mo_(s), MoC_(s) und Mo₂C_(s) gefunden. Bildung von Mo_(g) durch direkte Sublimation von Mo_(s) und durch Dissoziation von MoC_(g) sind thermodynamisch günstige Reaktionen bei der betreffenden Temperatur.