The Glauber dynamics for a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions

We present a study, within a mean-field approximation, of the dynamics of a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions in the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the set of mean-field dynamic equations. Then, we study the time variation of the average order parameters to find the phases in the system. We also investigate the thermal behavior of dynamic order parameters to characterize the nature (first- or second-order) of the dynamic transitions. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different the planes. The phase diagrams contain a disordered and ordered phases, and four different mixed phases that strongly depend on interaction parameters. Phase diagrams also display one or two dynamic tricritical points, a dynamic double critical end and dynamic quadruple points. A comparison is made with the results of the other metamagnetic Ising systems.     

The influence of nitridation time on the structural properties of GaN grown on Si (111) substrate

In the present paper, the effect of in-situ substrate nitridation time on crystalline quality of GaN films grown on Si (111) substrates by metal organic chemical vapor deposition (MOCVD) were investigated. A thin buffer layer of silicon nitride (SiN _x ) with various thicknesses was achieved through the nitridation of substrate at different nitiridation times ranging from 0 to 660 s. The structural characteristics, such as dislocation densities, correlation lengths of columnar crystallites, the tilt and twist of the mosaic structure, and the angles of rotational disorder, were all studied in detail by using a planar and cross-sectional view of high resolution transmission electron microscopy (HRTEM) and X-ray diffraction (HRXRD) performed at different scattering geometries. It was found that the dislocation densities, lateral coherence lengths, vertical coherence lengths, and the tilt and twist of mosaic blocks in GaN films monotonically varies with the nitridation time. The experimental findings showed that the nitridation times had more influence on edge dislocation densities than the screw type.     

The morphology and structural properties of InP thin films deposited by spray pyrolysis method

InP film samples were prepared by spray pyrolysis technique using aqueous solutions of InCl₃ and Na₂HPO₄, which were atomized with compressed air as carrier gas onto glass substrates at 500 °C with different thicknesses of the films. The structural properties of the samples have been determined by using X-ray diffraction (XRD). It was found that the crystal structure of the InP films is polycrystalline hexagonal. The orientations for all the obtained films are along the c-axis perpendicular to the substrate. It is observed that the crystallite sizes of the films increase with the thickness of the film up to 616 nm. The changes observed in the morphology and structural phases related to the film thickness have been discussed in detail.     

Synthesis and characterization of bis(diphenylphosphinomethyl)amino ligands and their Ni(II), Pd(II) complexes: Application to hydrogenation of styrene

Transition metal complexes of Ni(II) and Pd(II) with ditertiary bis(diphenylphosphinomethyl)amino ligands, (Ph₂PCH₂)₂NC(CH₃)₃ ( 1 ) and [(Ph₂PCH₂)Nm‐PhSO₃]Na ( 2 ) (Ph = phenyl), have been synthesized in good yields under nitrogen atmosphere by Schlenk technique. All complexes have been characterized using elemental analyses and spectroscopic techniques such as atomic absorption, FT‐IR, and NMR (¹H, ³¹P). Atomic absorption spectroscopic analysis showed that the reactions of ligands 1 and 2 with NiCl₂ ⋅ 6H₂O and [PdCl₂(COD)] occurred in 1:1 molar ratio. The metal complexes [NiCl₂(Ph₂PCH₂)₂Nm‐PhSO₃Na] ( 4 ) and [PdCl₂(Ph₂PCH₂)₂Nm‐PhSO₃Na] ( 6 ) were found to be soluble in ethanolic and aqueous solutions, as well as slightly soluble in water. Electrochemical behaviors of complexes were investigated by cyclic voltammetry. Catalytic effects of Pd(II) complexes were tested throughout the hydrogenation of styrene to ethylbenzene. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:113–118, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20384     

Facile synthesis of model 1,4‐dihydro‐1H‐1,3,4‐benzotriazepin‐5‐ones

2‐Aminobenzoic acid reacts readily, in the presence of triethylamine, with hydrazonoyl chlorides ( 5a‐c ) (precursors of the reactive nitrile imine 1,3‐dipolar species) to afford high yields of the corresponding acyclic amidrazone adducts ( 6a‐c ). The latter adducts undergo, in THF in presence of 1,1‐carbonyldiimida‐zole, smooth intramolecular cyclization involving the activated carboxyl and the NH‐ termini to deliver unequivocally the respective dihydro‐1,3,4‐benzotriazepin‐5‐ones ( 7a‐c ).     

A new method for tieline calculations in binary fluid systems

We describe a method to determine tielines for a mixture with a given volume V_t and a given mole fraction x_t at fixed temperature, which is based on the orientation of the tangent plane to the Helmholtz free energy surface. The method works equally well for gas-liquid separation as for liquid-liquid separation. The method is based on a rotation in coordinate space followed by a rotation in function space which establishes the correct direction and the end points of the tieline. The mathematics is described and the general outline of a computer program to implement the method is given. This is followed by an application to a special form of the van der Waals equation, which describes the influence of chain-molecules as proposed by Tompa. The example given shows a three phase separation and the influence of the chain-length thereupon.     

On polyhedral extension of some LP theorems

McLinden (Mathematical Programming 24 (1982) 162–176) has extended theorems of Tucker (1956) and Williams (1970) on the complementarity behaviour of feasible and optimal solutions to a pair of canonical linear programs to proper convex polyhedral functions. He achieved this by heavily using the well-developed machinery of convex analysis. In this note, we prove most of his results mainly using linear programming theory.     

Reactions with heterocyclic diazonium salts. Synthesis of several new azolylhydrazones

Several new stable azolylhydrazones could be synthesized via coupling of diazotised cycliuc amidines with active methylene reagents. The obtained compounds were utilised for synthesis of several, otherwise not readily accessible fused azoles.     

A Note on Shadow Prices in Linear Programming

Using convex analysis and a characterization of the entire family of optimal solutions to an L.P., we show that in order to obtain shadow prices, one has to solve a much smaller L.P. derived from any optimal tableau. We then show that positive as well as negative shadow prices for any constraint or for any combination of constraints can easily be computed by parametric linear programming. Some examples exhibiting the method are also included.     

Distribution of eigenvalues for the discontinuous boundary-value problem with functional-manypoint conditions

In this study, we investigate the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also a point of discontinuity, a finite number of internal points and abstract linear functionals. So our problem is not a pure boundary-value one. We single out a class of linear functionals and find simple algebraic conditions on the coefficients which guarantee the existence of an infinite number of eigenvalues. Also, the asymptotic formulas for the eigenvalues are found. The results obtained in this paper are new, even in the case of boundary conditions either without internal points or without linear functionals.