Crystal Structure and Spectroscopic Properties of <Emphasis Type="Italic">trans</Emphasis>-Dibromobis(1,2-ethanediamine)chromium(III) Perchlorate

Abstract  

The crystal structure of trans-[Cr(en)₂Br₂]ClO₄ (en = 1,2-ethanediamine) has been determined by a single-crystal X-ray diffraction study at 150 K. The complex crystallizes in the space group P[`1] P\overline{1} of the triclinic system with two mononuclear formula units in a cell of dimensions a = 6.853(4), b = 8.109(5), c = 12.475(8) ?, α = 81.006(10)°, β = 77.005(10)° and γ = 74.981(10)°. The Cr atom is in a slightly distorted octahedral environment, coordinated by four nitrogen atoms of two en ligands and two bromine atoms in trans axial positions. The mean Cr–N(en) and Cr–Br bond lengths are 2.079(3) and 2.4743(10)?, respectively. The five-membered rings are in stable gauche conformations with N1–Cr1–N2 and N3–Cr2–N4 angles of 82.81(11)° and 83.67(11)°, respectively. The crystal packing is stabilized by a network of N–H···O and N–H···Br hydrogen bonds. The infrared and electronic absorption spectra are consistent with the results of X-ray crystallography.     

Crystal Structure of [2,13-Dibenzyl-5,16-dimethyl-2,6,13,17-tetraazatricyclo(14,4,0<Superscript>1.18</Superscript>,0<Superscript>7.12</Superscript>)docosane]copper(II) Diperchlorate

Abstract  

In the title compound, [Cu(C₃₄H₅₂N₄)](ClO₄)₂, the Cu(II) ion has a square-planar coordination somewhat distorted towards tetrahedral geometry. The macrocyclic ligand adopts a less stable trans-I (RSRS) configuration. The two benzyl groups and two secondary amine H atoms are oriented towards the same side of the macrocyclic plane. The two six-membered rings are in slightly distorted chair and unsymmetrical twist-boat forms while both five-membered chelate rings are in the gauche conformation. The longer distances (2.050(4) and 2.035(4) Å) of Cu–N(tertiary) compared to 2.017(4) and 1.990(4) Å for Cu–N(secondary) may be due to the steric effects of the attached two benzyl groups on the tertiary N atoms. The crystal structure is stabilized by hydrogen bonds between secondary NH groups and O atoms of perchlorate counter-ions.     

X—射线荧光光谱法分析保护渣中元素

保护渣元素的定量分析一般采用传统的湿法化学分析 ,化学分析虽然准确度好 ,但难以做到快速且劳动量大。利用 X-射线荧光光谱法分析保护渣中各元素含量是一种快速、准确的分析方法 ,在国外已得到广泛应用。本文从现场分析的实际出发 ,选择融样条件、最佳仪器参数 ,用基准物质合成标准样品 ,绘制标准工作曲线 ,曲线线性良好 ,用化学分析法对荧光分析值进行验证 ,结果符合化学允许差。1　试验部分1 .1　仪器设备、试剂及工作条件MXF2 1 0 0 - X-射线荧光光谱仪TR- AUTO- BEAD- 1 0 0 0 S/W熔融炉混合熔剂 :4g四硼酸钠 +4g四硼酸锂 +0 .…     

Laser-induced fluorescence of seeded nitric oxide as a flame thermometer

Received: 10 June 1997/Revised version: 25 November 1997     

宽波段多步激发K_2-系统产生的钾原子高位态辐射

本文首次报道以690.0～715.0nm宽波段范围内任何波长的脉冲染料激光激发K_2—K系统,由高位钾分子与钾原子碰撞以及分子-原子的混合激发等过程而产生钾原子404.4,404.7和470.05～590.0nm波段内高位态辐射的实验结果,并对激发机制进行了探讨.     

Invariants de Maslov équivariants

We construct two cohomological invariants associated to pairs of Lagrangian sub-bundles of a symplectic bundle on a compact manifold upon which a compact Lie group is acting. The first invariant, which we call the classical equivariant Maslov H-invariant, provides an obstruction to Lagrangian transversality and lives in the Borel cohomology. The second invariant, which we call the equivariant Maslov U-invariant, generalises the author's results in K-Theory 13 (1998), 347–361 to the equivariant context and provides a necessary and sufficient condition for equivariant Lagrangian transversality, up to homotopic stability, and lives in the U-theory (intermediate between the real complex K-theories). As an application, we show that two Lagrangian sub-bundles of a symplectic bundle on a homogeneous space are always stably transverse.     

A Hyland-Bernstein approach to the digital control of Pritchard-Salamon systems

In this paper we consider the fixed finite-order digital linear-quadraticcontrol of Pritchard-Salamon infinite-dimensional systems withunbounded input and output operators under gaussian disturbances.A set of necessary conditions is given in terms of the solvabilityof a discrete-time Hyland-Bernstein system of equations (twomodified Riccati equations and two modified Lyapunov equationscoupled by an projection operator).     

Radiation and scattering from bodies of revolution

The problem of electromagnetic radiation and scattering from perfectly conducting bodies of revolution of arbitrary shape is considered. The mathematical formulation is an integro-differential equation, obtained from the potential integrals plus boundary conditions at the body. A solution is effected by the method of moments, and the results are expressed in terms of generalized network parameters. The expansion functions chosen for the solution are harmonic in ø (azimuth angle) and subsectional in t (contour length variable). Because of rotational symmetry, the solution becomes a Fourier series in ø, each term of which is uncoupled to every other term.Illustrative computations are given for radiation from apertures and plane wave scattering from bodies of revolution. The impedance elements, currents, radiation patterns, and scattering patterns for a conducting sphere are computed both from the general solution and from the classical eigenfunction solution. The agreement obtained serves to check the general solution. Similar computations for a cone-sphere illustrate the application of the general solution to problems not solvable by classical methods.     

Radiation and scattering from loaded bodies of revolution

The problem of electromagnetic radiation and scattering from loaded bodies of revolution of arbitrary shape is considered. The analysis assumes the existence of an impedance function relating the tangential electric field to the surface current on the body. A solution is obtained by the method of moments applied to the potential integral formulation of the problem. The results are expressed in terms of generalized network parameters, using formulas previously obtained for unloaded bodies. Representative computations are given for plane-wave scattering and radiation from apertures in loaded cylinders and hemispheres. A general computer program for arbitrary bodies of revolution is available.