The Silicides M4Si4 with M = Na,K, Rb,Cs, and Ba2Si4 – NMR Spectroscopy and Quantum Mechanical Calculations

The Zintl phases M₄Si₄ with M = Na, K, Rb, Cs, and Ba₂Si₄ feature a common structural unit, the Si₄^4– anion. The coordination of the anions by the cations varies significantly. This allows a systematic investigation of the bonding situation of the anions by ²⁹Si NMR spectroscopy. The compounds were characterized by powder X‐ray diffraction, differential thermal analysis, magnetic susceptibility measurements, ²³Na, ²⁹Si, ⁸⁷Rb, ¹³³Cs NMR spectroscopy, and quantum mechanical calculation of the NMR coupling parameter. The chemical bonding was investigated by quantum mechanical calculations of the electron localizability indicator (ELI). Synthesis of the compounds results for all of them in single phase material. A systematic increase of the isotropic ²⁹Si NMR signal shift with increasing atomic number of the cations is observed by NMR experiments and quantum mechanical calculation of the NMR coupling parameter. The agreement of experimental and theoretical results is very good allowing an unambiguous assignment of the NMR signals to the atomic sites. Quantum mechanical modelling of the NMR shift parameter indicates a dominant influence of the cations on the isotropic ²⁹Si NMR signal shift. In contrast to this a negligible influence of the geometry of the anions on the NMR signal shift is obtained by these model calculations. The origin of the systematic variation of the isotropic NMR signal shift is not yet clear although an influence of the charge transfer estimated by calculation using the QTAIM approach is indicated.     

Natural convection-radiation interaction on boundary layer flow along a thin vertical cylinder

A free convertion flow of an optically dense viscous incompressible fluid along a vertical thin circular cylinder has been studied with effect of radiation when the surface temperature is uniform. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations. Solutions of the governing equations are obtained employing the implicit finite difference methods together with Keller box scheme as well the local nonsimilarity method with second order truncation for all ξ (nondimensional transverse curvature parameter) in the interval [0,10] and are expressed in terms of local Nusselt number for a range of values of the pertinent parameters. Effects of pertinent parameters, such as, the radiation parameter, R _d , the surface temperature parameter, θ _w , taking Prandtl number, Pr, equals 0.7 on the velocity and temperature field are also presented graphically. From the solution it is seen that increase of R _d , or θ _w leads to increase in the local rate of heat transfer coefficients. Results obtained by both the methods are obtained in excellent agreement between each other upto ξ = 10.     

Optimising key performance indicator adherence with application to emergency department congestion

Many operational queueing systems must adhere to systems of Key Performance Indicators (KPIs), each comprising a waiting time limit and a level of compliance specifying the minimal fraction of customers that must meet the standard. KPIs are frequently employed as measures of system performance in health care settings. The primary flaw with KPIs is that they represent a system of constraints with no objective function. KPIs say nothing about customers who exceed their limit, so long as such occurrences are sufficiently rare, when in fact customers who miss their time limit in a health care setting are of greater importance, not lesser. We address this flaw by minimising the mean number of customers present who have exceeded their respective limits; we consider also weighted averages of the numbers in excess for each class. We then show that one logical service discipline to achieve this goal is the Accumulating Priority Queueing (APQ) discipline. We carry out numerical examples to investigate the utility of our method. We then apply the optimisation approach to the case of an Emergency Department in Southern Ontario, Canada.     

In-Cage Interactions in the Clathrate Superconductor Sr8Si46

The clathrate I superconductor Sr₈Si₄₆ is obtained under high-pressure high-temperature conditions, at 5 GPa and temperatures in the range of 1273 to 1373 K. At ambient pressure, the compound decomposes upon heating at T=796(5) K into Si and SrSi₂. The crystal structure of the clathrate is isotypic to that of Na₈Si₄₆. Chemical bonding analysis reveals conventional covalent bonding within the silicon network as well as additional multi-atomic interactions between Sr and Si within the framework cages. Physical measurements indicate a bulk BCS type II superconducting state below T_c=3.8(3) K.     

Theoretical prediction and experimental validation of the angle-of-arrival probability density of a laser beam in a strong plane-flame turbulence

The propagation of a laser beam through a plane turbulent flame is studied using geometrical optics approximation. The random fluctuations of the refractive index caused by a strong thermal turbulence in the flame create random perturbations of the laser beam direction. From the Markovian process model applied along the whole random path of the beam, the theoretical probability density of the laser beam angle-of-arrival is derived from the analytical solution of the Einstein-Fokker-Kolmogorov equation, which we have determined in terms of a series expansion of spherical harmonics. An experimental setup and a method for measuring this probability density are described. The experimental results obtained are shown to agree with the theoretical predictions.     

The Inhomogeneous Quantum Invariance Group of The Two Parameter Deformed Boson Algebra

We consider two parameter deformed boson algebra and investigate the inhomogeneous invariance quantum group of this system. We find the R-matrix which collects all information about the non-commuting structure of the quantum group. We extend our study to the d-dimensional case.     

Interplay of Atomic Interactions in the Intermetallic Semiconductor Be5Pt

Semiconducting substances form one of the most important families of functional materials. However, semiconductors containing only metals are very rare. The chemical mechanisms behind their ground‐state properties are only partially understood. Our investigations have rather unexpectedly revealed the semiconducting behaviour (band gap of 190 meV) for the intermetallic compound Be₅Pt formed at a very low valence‐electron count. Quantum‐chemical analysis shows strong charge transfer from Be to Pt and reveals a three‐dimensional entity of vertex‐condensed empty Be₄ tetrahedrons with multi‐atomic cluster bonds interpenetrated by the framework of Pt‐filled vertex‐condensed Be₄ tetrahedrons with two‐atomic polar Be?Pt bonds. The combination of strong Coulomb interactions with relativistic effects results in a band gap.     

Research on the electrochemistry of oxygen ion conductors in the former Soviet Union. I. ZrO2-based ceramic materials

Developments of solid electrolytes and mixed conductors based on stabilized zirconia in the former Soviet Union are reviewed. Primary attention is given to experimental data on high-conducting electrolytes, mixed conductors obtained by doping zirconia with transition metal oxides, oxygen exchange and oxygen permeation processes, as well as properties of metal electrodes in contact with the stabilized zirconia. Received: 26 March 1998 / Accepted: 4 June 1998     

Ultrashort self-similar periodic waves and similaritons in an inhomogeneous optical medium with an external source and modulated coefficients

Nonlinear Dynamics - In this paper, we use the similarity transformation to reduce the generalized higher-order nonlinear Schrödinger equation with space- and time-modulated coefficients...     

Graphene‐mesoporous anatase TiO2 nanocomposite: A highly efficient and recyclable heterogeneous catalyst for one‐pot multicomponent synthesis of benzodiazepine derivatives

The potential to bias chemical reaction pathways is a significant goal for physicists and material researchers to design revolutionary materials. Recently, two‐dimensional materials have appeared as a promising candidate for exploring novel catalyst activity in organic reaction. In this context, herein we report an easy and efficient synthesis of substituted benzodiazepines in high yields through the graphene‐based mesoporous TiO₂ nanocomposite (Gr@TiO₂ NCs) catalyst. To validate the merits of the Gr@TiO₂ NCs as a catalyst, we have also designed TiO₂ nanoparticle (NPs) under similar conditions. Successful comprehension realization of Gr@TiO₂ NCs and TiO₂ NPs were concluded from the XRD, SEM, HR‐TEM, EDS elemental mapping, FT‐IR, Raman, UV–Vis and TGA analysis. Gr@TiO₂ NCs has the propitious catalyst performance (~98%) over the TiO₂ NPs (~77%), which could be scrutinized in terms of graphene support toward the TiO₂ NPs and enable the large contact area between graphene and TiO₂ NPs. Incorporated graphene maintaining TiO₂ as a catalytically active and attracting electron to site isolation, as well as protecting TiO₂ from oxidative degradation during the reaction. Moreover, the role of graphene is suggested to prolonged reaction duration, yield and unaltered throughout the reaction because of the π‐π interaction between graphene and TiO₂ NPs. Additionally, the catalyst is recycled by filtration and reprocessed six times without having a significant loss in its catalytic activity.