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.     

A simplified green chemistry approach to the Biginelli reaction using ‘Grindstone Chemistry’

Grindstone Chemistry--a greatly evolved version of Toda’s method of grinding solids together for solvent-free chemical reactions--has been described and its usefulness illustrated by the successful application of this technique to a simplified process for conducting the multi-component Biginelli reaction for the synthesis of physiologically active tetrahydropyrimidinones.     

Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

Magnetic behaviour of TbMnFe

Neutron diffraction and M?ssbauer measurements have been carried out on the cubic Laves phase intermetallic TbMnFe. The magnetic moment on the transition metal atom is found to be low, 0.2μ _B, at room temperature. This moment is temperature independent down to 10 K. Magnetic moment on the rare earth atom varies from 2.5μ _B at 296 K to 7.27μ _B at 10 K. M?ssbauer spectra recorded at 298 K and 78 K have magnetic character but there is a large distribution of hyperfine field values. Both these features arise due to magnetic frustration created in the sample due to the competing ferro and antiferromagnetic interactions between the transition metal atoms.     

Structural study and electrical properties of Zr-doped Nd<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript> pyrochlore compounds

Nd₂Sn₂O₇ pyrochlores with the substitution of Zr⁴⁺ were prepared by conventional ceramic double sintering technique. The single-phase formation was confirmed by X-ray diffraction and neutron diffraction techniques. Relative intensity calculations for X-ray diffraction analysis were performed for oxygen positional parametersx = 0.331 and 0.375, while Rietveld refinements were employed for neutron diffraction data. The neutron diffraction study revealed that there are only two anion sites with 48f and 8b positions. This indicates that the 8a site, i.e. O(3) sublattice, is completely vacant and the structure is a perfect cubic pyrochlore with space group Fd3m (O _h ⁷ ). From the conductivity measurements, it is observed that the electronic conductivity dominates from room temperature up to about 525 K and forT > 525 K, the oxygen ion conduction dominates the charge transport in these compositions. Complex impedance spectroscopy indicates the existence of grain and grain boundary as two separate elements.     

57Fe Mössbauer spectroscopic study of (25−x)MnO–xZnO–15Fe2O3–60B2O3 glasses

The ⁵⁷Fe Mössbauer technique has been used to investigate the effect of zinc oxide substitution in (25???x)MnO–xZnO–15Fe₂O₃–60B₂O₃ glass system (x?=?0, 5, 10, 15 and 20 mol% of ZnO ). Mössbauer absorption spectra for all the samples recorded at room temperature suggest the existence of the two paramagnetic quadrupole doublets. The observed variations in hyperfine parameters have been explained on the basis of cations distribution and exchange interaction at the lattice sites and it is concluded that B–B interaction increases while the metal–metal interaction decreases due to replacement of manganese oxide by zinc oxide. These results suggest that the present glass system exhibits a paramagnetic behaviour that changes towards the weak paramagnetic when manganese oxide was replaced with zinc oxide.     

Direct synthesis of Cbz-protected β-amino ketones by iodine-catalyzed three-component condensation of aldehydes, ketones and benzyl carbamate

Iodine has been found to be very effective catalyst for a Mannich reaction between an aryl aldehyde, an aryl ketone and benzyl carbamate, even though this is a less reactive amine, to produce Cbz-protected β-aryl β-amino carbonyl compounds in high yields.