Electrochemical and alkali metal reduction studies of silicon,germanium, and tin derivatives of cyclooctatetraene : Properties conferred by cyclooctatetraenide dianions by group IV substituents

The electrochemical behavior of trimethylsilyl-, trimethylgermyl-, trimethylstannyl- and t-butylcyclooctatetraenes has been examined by the techniques of polarography and cyclic voltammetry in THF and hexamethylphosphoramide (vastly preferred) solutions. Chemical reduction by means of potassium in ND₃ has also been studied. Evidence is presented that all four compounds undergo reduction to their respective dianions. However, the energetics of (Me₃)MCOT^? and (Me₃)MCOT^2? formation vary widely, as do the rates and mechanism of dianion disappearance under the conditions of electrochemical measurement. The available kinetic data suggest, for example, that destruction of the t-Bu and trimethylgermyl substituted dianions proceeds via protonation and/or disproportionation pathways. In contrast, the silyl and stannyl examples experience metal-ring carbon cleavage reactions at yet faster rates. Interestingly, the E¹_{$\text{1}\text{2}$} values give evidence of being quite well correlated by σ_p. Furthermore, when the magnitude of the E¹_{$\text{1}\text{2}$}-E²_{$\text{1}\text{2}$} gap are plotted vs the covalent radii of the M atoms, a straight line is obtained for the Si, Ge and Sn examples; C deviates widely. This effect is believed to have its origin in resonance of the M←C_π type involving the d orbitals of M which, of course, is not possible in the carbon case. The significance of these results as well as the other observations made in the course of this work is discussed.     

Deoxygenation of Pyridones Via Their Tetrazolyl Ethers

A mild process for the conversion of pyridones to the corresponding pyridines by palladium catalyzed ammonium formate hydrogenolysis of their (1-phenyltetrazol-2-yl) ethers is described.     

Hardness and elastic modulus of zircon as a function of heavy-particle irradiation dose: I. In situ α-decay event damage

Abstract

For a natural single crystal of zircon, ZrSiO₄, from Sri Lanka, exhibiting zonation in U and Th contents, the hardness and elastic modulus have been determined as a function of α-decay dose using a mechanical properties microprobe (MPM). The zones vary in thickness from one to hundreds of micrometers, and have uranium and thorium concentrations such that the α-decay dose varies between 2 × 10¹⁵ and 1 × 10¹⁶ α-decay events/mg (0.15 to 0.65 dpa, displacement per atom). The transition from the crystalline to the aperiodic metamict state occurs over this dose range. For a traverse of 75 indent pairs across layers sampling a large portion of the crystalline-to-metamict transition (3.7 × 10¹⁵ to 9.7 × 10¹⁵ α-decay events/mg) both the hardness and elastic modulus decrease linearly with increasing α-decay dose. The radiation-induced softening follows a behavior similar to other radiation-induced changes, that is with the expansion of the unit cell parameters there is a decrease in density, birefringence, hardness and bulk modulus.     

The analysis of multigrid algorithms for cell centered finite difference methods

In this paper, we examine multigrid algorithms for cell centered finite difference approximations of second order elliptic boundary value problems. The cell centered application gives rise to one of the simplest non-variational multigrid algorithms. We shall provide an analysis which guarantees that the W-cycle and variable V-cycle multigrid algorithms converge with a rate of iterative convergence which can be bounded independently of the number of multilevel spaces. In contrast, the natural variational multigrid algorithm converges much more slowly.     

Parent Beliefs about Technology and Innovative Mathematics Instruction

Parent beliefs about roles of education, teachers, computers, and innovative mathematics instruction were examined through factor analysis. Strong relationships between parent beliefs regarding teacher and computer roles were found. The beliefs of parents about the similar roles of teachers and computers in education may impact the implementation of innovations in mathematics education and the uses of computers in education. Reciprocally, the ways computers are implemented in education may impact the beliefs parents have about the purposes of education.     

Simulation of multiphase flows in porous media

The ability to numerically simulate single phase and multiphase flow of fluids in porous media is extremely important in developing an understanding of the complex phenomena governing the flow. The flow is complicated by the presence of heterogeneities in the reservoir and by phenomena such as diffusion, dispersion, and viscous fingering. These effects must be modeled by terms in coupled systems of nonlinear partial differential equations which form the basis of the simulator. The simulator must be able to handle both single and multiphase flows and the transition regimes between the two. A discussion of some of the aspects of modeling dispersion and viscous fingering is presented along with directions for future work.The partial differential equation models are convection-dominated and contain important local effects. An operator-splitting technique is used to address these different effects accurately. Convection is treated by time stepping along the characteristics of the associated pure convection problem, and diffusion is modeled via a Galerkin method for single phase flow and a Petrov-Galerkin technique for multiphase regimes. ELLAM (Eulerian-Lagrangian Localized Adjoint Methods) are discussed to effectively treat the advection-dominated processes. Accurate approximations of the fluid velocities needed in the Eulerian-Lagrangian time-stepping procedure are obtained by mixed finite element methods. Adaptive local grid refinement techniques are then indicated to resolve important local phenomena around wells and large heterogeneities or to resolve the moving internal boundary layers which often govern the mass transfer between phases.     

Self-chemical ionization of diethylzinc

The self-chemical ionization of diethylzinc is examined by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and semiempirical molecular orbital calculations. Electron impact of diethylzinc neutral produces the radical cation, C(4)H(15)Zn(+) (m/z x 122), which reacts further with the neutral (C(2)H(5))(2)Zn to give the following product ions: Zn(+) (m/z x 64), C(2)H(5)Zn(+) (m/z x 93), C(4)H(9)Zn(+) (m/z x 121), C(4)H(11)Zn(2)(+) (m/z x 187), and C(6)H(15)Zn(2)(+) (m/z x 215). To determine the structure and pathways for production of these ions, monoisotopic (12)C(4)H(15)(64)Zn(+), (64)Zn(+) and (12)C(2)H(5)(64)Zn(+) were individually isolated and reacted with the neutral background. We also performed semiempirical molecular orbital calculations (ZINDO/1). The molecular orbital calculations and experimental data are consistent in predicting that the ethyl group on the diethylzinc cation carries the positive charge. Copyright 1999 John Wiley & Sons, Ltd.     

A modular model of the crystal structure of the pyrochlore-murataite polysomatic series

This paper reports on the results of a structural investigation of an important group of synthetic compounds with derivative structures of the mineral murataite, a potential matrix for immobilization of radioactive wastes. A model describing the structure of the entire group of compounds is proposed on the basis of analyzing the results obtained using chemical (electron microprobe) analysis methods, high-resolution transmission electron microscopy (high-resolution electron images and microdiffraction patterns), and X-ray diffractometry of a large array of artificial murataite ceramics. In essence, the proposed structural model is as follows: in the structure, layers of two (pyrochlore and murataite) packing types alternate along the [111] direction of the cubic supercell, so that the resulting structures can undergo substitutional and displacive modulations. Experiments on irradiation of different murataite modifications with heavy ions demonstrate that these modifications have close values of the radiation resistance, which is higher than that of the pyrochlore coexisting with them.     

Eulerian–Lagrangian localized adjoint methods for reactive transport with biodegradation

The microbial degradation of organic contaminants in the subsurface holds significant potential as a mechanism for in-situ remediation strategies. The mathematical models that describe contaminant transport with biodegradation involve a set of advective–diffusive–reactive transport equations. These equations are coupled through the nonlinear reaction terms, which may involve reactions with all of the species and are themselves coupled to growth equations for the subsurface bacterial populations. In this article, we develop Eulerian–Lagrangian localized adjoint methods (ELLAM) to solve these transport equations. ELLAM are formulated to systematically adapt to the changing features of governing partial differential equations. The relative importance of retardation, advection, diffusion, and reaction is directly incorporated into the numerical method by judicious choice of the test functions that appear in the weak form of the governing equation. Different ELLAM schemes for linear variable–coefficient advective–diffusive–reactive transport equations are developed based on different operator splittings. Specific linearization techniques are discussed and are combined with the ELLAM schemes to solve the nonlinear, multispecies transport equations. © 1995 John Wiley & Sons, Inc.