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.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

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

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

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.     

Effect of loading variables on the acoustic emissions of fatigue-crack growth

A series of experiments has been conducted to determine the effect of loading variables such as cyclic frequency, load ratio, and material on acoustic emission from fatigue-crack propagation. It is shown that the applied-stress intensity range (ΔK) is the controlling parameter for all materials studied while the other parameters have lesser effects. Two potential methods for engineering application of acoustic emission during fatigue loading are described.