On the electron energy spectrum in heavily doped non-parabolic semiconductors

An attempt is made to present a simple theoretical analysis of the energy-wave vector dispersion relation of the conduction electrons in heavily doped non-parabolic semiconductors forming band tails. We observe that the complex energy spectrum in doped small-gap materials whose unperturbed conduction band is described by the three band model of Kane is due to the interaction of the impurity atoms in the tail with the spin-orbit splitting constant of the valence band (Δ), For band-gap (E_g)<Δ the imaginary part predominates which tails in to the conduction band. For the opposite inequality the real part comes in to play which tails in to the split-off band. In the absence of the band tailing effect, the imaginary part of the complex energy spectrum vanishes and the same is also true for doped two-band Kane-type and parabolic energy bands respectively. The present formulation helps us in investigating the Boltzmann transport equation dependent transport properties of degenerate semiconductors and are expected to agree better with experiments. The well-known results of unperturbed three and two band models of Kane together with wide-gap parabolic energy bands have been obtained as special cases of our generalized analysis under certain limiting conditions.     

Multifunctional ToF-SIMS: combinatorial mapping of gradient energy substrates

We present a simple method for chemical modification of chlorosilane self-assembled monolayers (SAMs) on Si surfaces by exposure to a gradient of UV-ozone radiation to create stable substrates with a range of contact angles (θ_H2O≈5–95°) and surface energies on a single substrate. These gradient energy substrates are developed to potentially generate libraries for combinatorial studies of thin film phenomenology, where a systematic variation of interfacial surface energy represents one of the significant parameters along one axis. The graded oxidation process presents a systematic variation of surface chemical composition. We have utilized contact angle measurements and time-of-flight secondary ion mass spectrometry (ToF-SIMS) to investigate this variation for a series of ions, among which are SiCH₃⁺, SiOH⁺ and COOH⁻. We show that the macroscopic measurements of surface free energy/contact angle correlate with the detailed analysis of surface chemistry (as assessed by ToF-SIMS) on these test substrates.     

Breathers in ferrimagnetic systems

Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

Diff (S 1) and the Teichmüller spaces

Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations, , carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These areN=Diff(S ¹)/Rot(S ¹) andM=Diff(S ¹)/Möb(S ¹). Note thatN is a holomorphic disc fiber space overM. Now,M can be naturally considered as embedded in the classical universal Teichmüller spaceT(1), simply by noting that a diffeomorphism ofS ¹ is a quasisymmetric homeomorphism.T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion ofM inT(1) iscomplex analytic.In the latter portion of this paper it is shown that theunique homogeneous Kähler metric carried byM = Diff (S ¹/SL(2, ) induces preciselythe Weil-Petersson metric on the Teichmüller space. This is via our identification ofM as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller spaceT(G) of finite or infinite dimension is contained canonically and holomorphically withinT(1). Our computations allow us also to prove that everyT(G), G any infinite Fuchsian group, projects out ofM transversely. This last assertion is related to the fractal nature ofG-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach.     

Oxidation of cyclohexane with molecular oxygen using a Schiff base cobalt complex bonded to carbamate-modified silica gel

The Schiff base [1,2-bis(salicylidene amino)phenylene]cobalt(II) complex, chemically bonded to a carbamate-modified silica gel catalyst, has been prepared by a four step procedure. The oxidation of cyclohexane was studied in the presence of this catalyst under relatively mild conditions (150–200 °C, 15–20 atm) using molecular oxygen. The catalyst was found to be very selective for the production of cyclohexanol, with cyclohexanone formed in only a small amount (45:1). This is in contrast to the commercially available processes in which cyclohexanol and cyclohexanone are both formed in appreciable amounts. The t.g.a. analysis shows the catalyst to be stable up to 211 °C and atomic absorption spectroscopy indicated negligible metal loss during 50 h use of the catalyst up to 180 °C.     

Synthesis and characterization of cobalt(II), nickel(II), copper(II), palladium(II) and dioxouranium(VI) complexes of the antipyrine Schiff base of 3-formylsalicylic acid

A new Schiff base has been synthesized from 4-aminoantipyrine and 3-formylsalicylic acid. The ligand has a dianionic tetradentate compartmental OONO donor system. The cobalt(II), nickel(II), copper(II) and dioxouranium(VI) complexes exist in phenolato-bridged dinuclear species, while palladium(II) gives a mononuclear complex with free –COOH groups. The complexes have been characterized by elemental analyses, i.r., u.v.-vis, thermal and magnetic measurements.     

An efficient route to regioselective opening of N-tosylaziridines with zinc(II) halides

An efficient route for the regio- and stereoselective ring opening of N-tosylaziridines with zinc dihalides (ZnX₂, X = Cl, Br, I) is described. Depending on the solvent and Zn(II) halide, β-halo amines or imidazolines are obtained selectively in good to excellent yields.     

Cu-nanoparticles: a chemoselective catalyst for the aza-Michael reactions of N-alkyl- and N-arylpiperazines with acrylonitrile

A novel method for effecting the aza-Michael reactions of N-alkyl- and N-arylpiperazines with acrylonitrile using Cu-nanoparticles is described. The method features the use of 10 mol % Cu (14-17 nm) nanoparticles under mild reaction conditions to afford the addition products in good to excellent yields. The Cu-nanoparticles selectively catalysed the aza-Michael reaction of N-alkyl- and N-arylpiperazines in the presence of aromatic amino or aliphatic hydroxy groups.