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.     

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.     

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.     

Accumulation of radiocesium by <Emphasis Type="Italic">Pleurotus citrinopileatus</Emphasis> species of edible mushroom

Pleurotus citrinopileatus, a species of edible mushrooms, is widely accepted food component, especially in Indian subcontinent. The accumulating susceptibility of this edible mushroom species towards long-lived radioisotopes of cesium was studied in controlled laboratory condition using the ¹³⁴Cs (T _1/2 = 2.06 y) radioisotope. It was observed that the experimental mushroom species accumulated ¹³⁴Cs and maximum accumulation took place in the cap portion. The pileus (cap)/stipes (stem) ratio of each ¹³⁴Cs accumulated mushroom sample was determined and found 2.22±0.74. The protein and fat fractions of the experimental mushroom species were extracted separately after accumulation of radiocesium and it was found that most of the radiocesium accumulation occurred in the protein fraction of the mushroom. The mushroom Pleurotus citrinopileatus which is white in color, turned completely black after radiocesium accumulation. The black mushroom so obtained was produced upto fourth generation by tissue culture method without using any radiocesium further. All the successors were found to be black indicating a permanent mutation of the mushroom species.     

Synthesis,Crystal Structure and Thermal Behavior of Gadolinium Dicyanamide Dihydrate Gd[N(CN)2]3 · 2 H2O

Gadolinium dicyanamide dihydrate Gd[N(CN)₂]₃ · 2 H₂O was prepared by ion exchange in aqueous solution followed by evaporation of the solvent at room temperature. Gd[N(CN)₂]₃ · 2 H₂O was characterized by single‐crystal structure analysis, FTIR spectroscopy and DSC analysis. In the crystal there are three crystallographically independent [N(CN)₂]^? ions and Gd³⁺ which are coordinated by six N atoms from six different [N(CN)₂]^? ions and two O atoms from two water molecules forming an irregular quadratic antiprism. Four H bonds have been identified in the structure of Gd[N(CN)₂]₃ · 2 H₂O, two of them running to terminal N atoms and two to the bridging N atoms of dicyanamide ions (Gd[N(CN)₂]₃ · 2 H₂O: P2₁/n (no. 14), a = 7.4845(15) Å, b = 11.529(2) Å, c = 13.941(3) Å, β = 93.98(3)°, Z = 4, 1948 reflections, 175 parameters, R1 = 0.0493). The DSC analysis indicates that Gd[N(CN)₂]₃ · 2 H₂O looses the crystal water at temperatures around 130 – 140 °C forming anhydrous Gd[N(CN)₂]₃, the structure of which has been refined by the Rietveld method based on X‐ray powder diffraction data. Gd[N(CN)₂]₃ was found to be isotypic with Ln[N(CN)₂]₃ (Ln = La, Ce, Pr, Nd, Sm and Eu) which previously have been described in the literature.     

Schiffer variation of complex structure and coordinates for Teichmüller spaces

Schiffer variation of complex structure on a Riemann surfaceX ₀ is achieved by punching out a parametric disc \(\bar D\) fromX ₀ and replacing it by another Jordan domain whose boundary curve is a holomorphic image of \(\partial \bar D\) . This change of structure depends on a complex parameter ε which determines the holomorphic mapping function around \(\partial \bar D\) . It is very natural to look for conditions under which these ε-parameters provide local coordinates for Teichmüller spaceT(X ₀), (or reduced Teichmüller spaceT ^#(X₀)). For compactX ₀ this problem was first solved by Patt [8] using a complicated analysis of periods and Ahlfors' [2] τ-coordinates. Using Gardiner's [6], [7] technique, (independently discovered by the present author), of interpreting Schiffer variation as a quasi conformal deformation of structure, we greatly simplify and generalize Patt's result. Theorems 1 and 2 below take care of all the finitedimensional Teichmüller spaces. In Theorem 3 we are able to analyse the situation for infinite dimensionalT(X ₀) also. Variational formulae for the dependence of classical moduli parameters on the ε's follow painlessly.     

Model Compounds for Iron Proteins. Structures and Magnetic, Spectroscopic, and Redox Properties of Fe(III)M(II) and [Co(III)Fe(III)](2)O Complexes with (&mgr;-Carboxylato)bis(&mgr;-phenoxo)dimetalate and (&mgr;-Oxo)diiron(III) Cores

A series of heterobimetallic complexes of the type [Fe(III)M(II)L(&mgr;-OAc)(OAc)(H(2)O)](ClO(4)).nH(2)O (2-5) and [{Fe(III)Co(III)L(&mgr;-OAc)(OAc)}(2)(&mgr;-O)](ClO(4))(2).3H(2)O (6) where H(2)L is a tetraaminodiphenol macrocyclic ligand and M(II) = Zn(2), Ni(3), Co(4), and Mn(5) have been synthesized and characterized. The (1)H NMR spectrum of 6 exhibits all the resonances between 1 and 12 ppm. The IR and UV-vis spectra of 2-5 indicate that in all the cases the metal ions have similar coordination environments. A disordered crystal structure determined for 3 reveals the presence of a (&mgr;-acetate)bis(&mgr;-phenoxide)-Ni(II)Fe(III) core, in which the two metal ions have 6-fold coordination geometry and each have two amino nitrogens and two phenolate oxygens as the in-plane donors; aside from the axial bridging acetate, the sixth coordination site of nickel(II) is occupied by the unidentate acetate and that of iron(III) by a water molecule. The crystal structure determination of 6 shows that the two heterobinuclear Co(III)Fe(III) units are bound by an Fe-O-Fe linkage. 6 crystallizes in the orthorhombic space group Ibca with a = 17.577(4) ?, b = 27.282(7) ?, c = 28.647(6) ?, and Z = 8. The two iron(III) centers in 6 are strongly antiferromagnetically coupled, J = -100 cm(-1) (H = -2JS(1).S(2)), whereas the other two S(1) = S(2) = (5)/(2) systems, viz. [Fe(2)(III)(HL)(2)(&mgr;-OH)(2)](ClO(4))(2) (1) and the Fe(III)Mn(II) complex (5), exhibit weak antiferromagnetic exchange coupling with J = -4.5 cm(-1) (1) and -1.8 cm(-1) (5). The Fe(III)Ni(II) (3) and Fe(III)Co(II) (4) systems, however, exhibit weak ferromagnetic behavior with J = 1.7 cm(-1) (3) and 4.2 cm(-1) (4). The iron(III) center in 2-5 exhibits quasi-reversible redox behavior between -0.44 and -0.48 V vs Ag/AgCl associated with reduction to iron(II). The oxidation of cobalt(II) in 4 occurs quasi-reversibly at 0.74 V, while both nickel(II) and manganese(II) in 3 and 5 undergo irreversible oxidation at 0.85 V. The electrochemical reduction of 6 leads to the generation of 4.     

Electrical conductivity and phase transitions of the solid electrolyte system (Cs1−yRby)Cu4Cl3(I2−xClx)

Results of electrical conductivity measurements, thermal analysis, and X-ray diffraction studies indicate the existence of four phases, between 295 K and the melting points, in the system (Cs_1?yRb_y)Cu₄Cl₃I₂. These phases are designated α, á β, γ in order of decreasing temperature. The α phase is isostructural with α-RbAg₄I₅; the á phase is also cubic and very likely belongs to space groupP2₁3, a subgroup ofP4₁32 andP4₃32 to which the α phase belongs. There is a high probability that the á → α transition is continuous. The á → α transition is not discernible in the conductivity measurements or thermal analysis; therefore the line of á-α transitions is presently unknown. The β phase transforms to the á and the γ phase transforms to the β phase wheny ≤ 0.36; the γ phase transforms to the α phase wheny ≥ 0.36. That is, there is a triple point aty = 0.36, T = 399K. The γ-β, β-α′, and γ-α transitions are all hysteretic and are therefore first order. The conductivities of the β phases are relatively low and the enthalpies of activation relatively high. The conductivity of the β phase decreases with increasingy. The β phase probably belongs to space groupR3, in which the Cu⁺ ions can be ordered. The α and á phases are the true solid electrolytes; the conductivities are high, >0.73 Ω^?1cm^?1 at 419 K, and the enthalpies of activation of motion of the Cu⁺ ions low, 0.11 eV.In the system CsCu₄Cl₃(I_2?xCl_x), 0 ≤ x ≤ 0.25, the Cl^? for I^? substitutions affect the transitions to only a small extent relative to the stoichiometric compound. The β phase occurs for allx and transforms to á.