Local tetragonal distortions of the (CrF6)3− and (FeF6)3− octahedral clusters in Cr3+- and Fe3+-doped tetragonal Rb2KGaF6 crystals

The local tetragonal distortions (α???α₀) (where α is the angle defined as tgα?=?R_⊥/R_//, R_⊥ and R_// are the metal–ligand distances parallel with and normal to the C₄ axis, α₀?=?45° is the same angle in cubic symmetry) of (CrF₆)^3? and (FeF₆)^3? octahedral clusters in the tetragonal Rb₂KGaF₆ crystals are estimated by analyzing their electron paramagnetic resonance (EPR) zero-field splittings D. The results indicate that the two impurity octahedra and hence the host (GaF₆)^3? octahedra are tetragonally elongated. The distortion (α???α₀) in magnitude differs from impurity to impurity because of the different sizes and natures of these impurities. These results are analogous to those in ABX₃ and doped ABX₃ perovskite crystals where the cubic-to-tetragonal phase transition is due to the rotation of BX₆ octahedra associated with the release or elongation of B–X bond along the C₄ rotational axis.     

Structure of two-loop evolution kernels and evolution of the pion wave function in ϕ(6)3 and QCD

The general structure of the two-loop nonforward evolution kernels is investigated in the ϕ₍₆₎³ model and QCD. The solution of the two-loop evolution equations is constructed in both models. In QCD, the contribution of the two-loop corrections to the wave function evolution is estimated numerically.     

6×6 matrix formalism of optical elements for modeling and analyzing 3D optical systems

Although conventional 2×2 ray matrices, i.e. ABCD matrices, provide a convenient means of obtaining initial estimates of the performance of an optical system during the early stages of the design process, they are suitable only for optical systems with the axisymmetric property. Accordingly, this study utilizes the 6×6 matrix formalism, which was proposed by our group, for optical boundary surfaces to develop a new approach for modeling and analyzing 3D optical systems comprising multiple lenses and/or mirrors and clarifying many of the system’s basic properties, e.g. the effective focal length, primary aberration and cardinal points, and so forth. To reduce the complexity of the modeling process, general matrix formalisms of sub-systems in a 3D optical system are presented. The validity of the proposed approach is evaluated by modeling and analyzing a simple 3D optical system and comparing the results with those obtained from the skew ray-tracing computer program and commercial optical design software. The results confirm that the proposed methodology provides a convenient means of obtaining initial insights into a variety of 3D optical systems with non-coplanar axes.     

Three-alpha force and the 3-α model of12C

We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0⁺ and 2⁺ states of¹²C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 ₂ ⁺ state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.     

Structural and electronic properties of Fe-doped BaTiO3 and SrTiO3

We have performed first principles calculations of Fe-doped BaTiO3 and SrTiO3. Dopant formation energy, structure distortion, band structure and density of states have been computed. The dopant formation energy is found to be 6.8eV and 6.5eV for Fe-doped BaTiO3 and SrTiO3 respectively. The distances between Fe impurity and its nearest O atoms and between Fe atom and Ba or Sr atoms are smaller than those of the corresponding undoped bulk systems. The Fe defect energy band is obtained, which mainly originates from Fe 3d electrons. The band gap is still an indirect one after Fe doping for both BaTiO3 and SrWiO3, but the gap changes from Γ-R point to Γ-X point.     

Spectral energy characteristics of 6,γ- and 7,γ-dimethyl ethers of chlorine 6 in water-alcohol solutions

Absorption spectra and dispersion of optical rotation (DOR) are measured for monomers of 6,γ- and,7,γ-dimethyl ethers of chlorin e₆ (Ch-6,γ-DME and Ch-7,γ-DME) in 96% ethanol and for associates of them that are polymers and colloidal particles. The optical activity of Ch-6,γ-DME monomers is higher than that of Ch-7,γ-DME monomers, which is linked with more pronounced distortion of the molecular macrocycle for Ch-6,γ-DME in the γ-C₆ local region. The structural and energy parameters of dimeric unit cells of Ch-6,γ-DME and Ch-7,γ-DME polymers are discussed from the standpoint of the Davydov-Tinoko exciton theories. Longwave absorption spectra and DOR are resolved into individual components with the aid of a modified Alentsev-Fock method. Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, 68, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 3, pp. 331–337, May–June, 1999.     

Study of intermolecular interactions in binary mixtures of 2′-chloro-4-methoxy-3-nitro benzil in various solvents and at different concentrations by the measurement of acoustic properties

Density (ρ), ultrasonic velocity (u), adiabatic compressibility (β), apparent molar volume (Ø), acoustic impedance (Z), intermolecular free length (L_f), relative association (RA) of binary mixtures of 2′-chloro-4-methoxy-3-nitro benzil (abbreviated as 2CBe) in ethanol, acetonitrile, chloroform, dioxane and benzene were measured at different concentrations at 298 K. Several useful parameters such as excess density, excess ultrasonic velocity, excess adiabatic compressibility, excess apparent molar volume, excess acoustic impedance and excess intermolecular free length have been calculated. These parameters are used to explain the nature of intermolecular interactions taking place in the binary mixture. The above study is useful in understanding the solute – solvent interactions occurring in different concentrations at room temperature.     

Structures of superconducting Ba2YCu3O7-ϖ and semiconducting Ba2YCu3O6 between 25°C and 750°C

The structure and copper valence states of the 100K superconductor, Ba₂YCu₃O₇ have recently been determined by neutron powder diffraction between 5K and 300K¹, and at room temperature². This ′oxygen deficient orthorhombic perovskite structure′, now independently confirmed^3,4, is well ordered and stochiometric, and contains one Cu⁺⁺⁺ and two Cu⁺⁺ atoms distributed over two square planar oxygen co-ordinated sites. In the a-b plane CuO₄ squares are linked by their oxygen corners to form infinite sheets, while along the b-axis CuO₄ squares form infinite chains on the second Cu-site. In this paper we show that when Ba₂YCu₃O₇ is heated above room temperature, it progressively loses all oxygen from the O4 sites on the b-axis chains, while the remaining oxygen sites remain fully occupied. Near 700°C it becomes tetragonal⁵, with the P4/mmm Ba₂YCu₃O₆ structure obtained by X-ray diffraction at room temperature⁶. This material is well ordered, stochiometric and stable when cooled under vacuum. The valence of Cu2 in the a-b sheets remains close to 2, while that of Cu1 in the b-axis chains falls to near 1. The valence of copper in these chains can perhaps fluctuate, since the vibration of O4 out of the chain, which we observed even at 5K¹, implies a reduction of the valence charge on this copper site. We have observed similar large amplitude oxygen vibration at low temperature in La₂CuO₄.     

Defect chemistry and electrical properties of La1-xSrxCoO3-δ

This paper considers defect chemistry models of La_1−xSr_xCoO_3−δ, such as random defect model and the cluster defect model. These models are considered in terms of defect equilibria with respect to (i) the formation of oxygen vacancies, (ii) intrinsic electronic ionisation and (iii) the formation of defect clusters. The defect models are derived using the available data of nonstoichiometry for the LSC materials.     

Spectrophotometric Determination of Trace Amounts of Cobalt and Copper with 3- (2′-Thiazolylazo)- 2,6- Diaminopyridine

Abstract

Sensitive methods for the determination of trace amounts of cobalt and copper by complexation with 3-(2′-Thiazolylazo)-2,6- diaminopyridine (2,6-TADAP) are described. Copper forms a 1:2 violet complex with the reagent having a molar absorptivity of 1.00 × 10⁴ L mol^?1cm^?1, Baer's law is obeyed over the range 0 ?50.84 μg in the total volume of 10ml. Cobalt also forms a 1:1 green complex with a molar absorptivity of 1.07 × 10⁴L mol^?1cm^?1 and obeying Beer's law over the range 0 –23.57 μg in the total volume of 10 ml. The procedure is simple and rapid without any tedious extraction steps for copper and without oxidation of cobalt (II) to cobalt (III).     

Structural and superconducting behaviour of Mg- and Zn-substituted YBa2Cu3O7-δ

Effects of doping YBa₂Cu₃O_7-δ with Mg and Zn on its crystallographic structure and superconducting behaviour have been investigated. Orthorhombic structure is retained upto Mg/Cu ratio of 0.12 (the highest investigated here), but T_c decreases rapidly with the level of Mg-doping. The effects produced by Mg-doping are very similar to those due to Zn-doping investigated by the present authors as well as by others. Neutron diffraction measurements have been carried out on two substituted materials: YBa₂Cu_2.82Mg_0.18O_7-δ and YBa₂Cu_2.82Zn_0.18O_7-δ. Both Mg- and Zn-dopants show strong tendency of occupying Cu(II)-sites in the unit cell. In the case of Mg-doping, however, a strikingly different feature is the concomitant depletion of oxygen at the O₃-sites by an amount nearly equal to the Mg-concentration.     

The ν6 and 2ν3 bands of CH2DI: Infrared and nuclear quadrupole spectra

Pure quadrupole transitions of the iodine nucleus in CH₂DI have been measured by laser-radio frequency double resonance, and analyzed to yield quadrupole coupling constants in the ground, v₆ = 1 and v₃ = 2 states. The corresponding infrared spectra, which were required in order to make assignments, have also been analyzed using Fourier transform data at a resolution of about 0.05 cm⁻¹.     

Magneto-optical trapping of bosonic and fermionic neon isotopes and their mixtures: isotope shift of the 3P2 ↔ 3D3 transition and hyperfine constants of the 3D3 state of 21Ne

We have magneto-optically trapped all three stable neon isotopes, including the rare ²¹Ne, and all two-isotope combinations. The atoms are prepared in the metastable ³P₂ state and manipulated via laser interaction on the ³P₂ ? ³D₃ transition at 640.2?nm. These cold (T ≈ 1?mK) and environmentally decoupled atom samples present ideal objects for precision measurements and the investigation of interactions between cold and ultracold metastable atoms. In this work, we present accurate measurements of the isotope shift of the ³P₂ ? ³D₃ transition and the hyperfine interaction constants of the ³D₃ state of ²¹Ne. The determined isotope shifts are (1625.9 ± 0.15)?MHz for ²⁰Ne ? ²²Ne, (855.7 ± 1.0)?MHz for ²⁰Ne ? ²¹Ne, and (770.3 ± 1.0)?MHz for ²¹Ne ? ²²Ne. The obtained magnetic dipole and electric quadrupole hyperfine interaction constants are A(³D₃) = (?142.4 ± 0.2)?MHz and B(³D₃) = (?107.7 ± 1.1)?MHz, respectively. All measurements give a reduction of uncertainty by about one order of magnitude over previous measurements.     

Mixing and decays of ρ- and ω-mesons

Isospin-violating mixing of ρ- and ω-mesons is reconsidered in terms of propagators. Its influence on various pairs of (ρ,ω)-decays to the same final states is demonstrated. Some of them, (ρ,ω)↦π⁺π^- and (ρ,ω)↦πγ, have been earlier discussed in the literature, others (e.g., (ρ,ω)↦ηγ and (ρ,ω)↦e ⁺ e ^-) are new in this context. Changes in partial widths for all the decay pairs are shown to be correlated. The set of present experimental data, though yet inconclusive, provides some limits for the direct (ρω)-coupling and indirectly supports enhancement of ρ↦πγ in comparison with ρ^±↦π^±γ, though not so large as in some previous estimates. Received: 16 September 2002 / Accepted: 23 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: azimov@pa1400.spb.edu Communicated by V.V. Anisovich     

Stability of the scalar potential and symmetry breaking in the economical 3-3-1 model

A detailed study of the criteria for stability of the scalar potential and the proper electroweak symmetry breaking pattern in the economical 3-3-1 model, is presented. For the analysis we use and improve a method previously developed to study the scalar potential in the two-Higgs-doublet extension of the standard model. A new theorem related to the stability of the potential is stated. As a consequence of this study, the consistency of the economical 3-3-1 model emerges.