Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

A comparison of the effectiveness of TiO<sub>2sub> photocatalysis and UVA photolysis for the destruction of three pathogenic micro-organisms

TiO<sub>2sub> photocatalysis has demonstrated efficacy as a treatment process for water contaminated with chemical pollutants. When exposed to UVA light TiO<sub>2sub> also demonstrates an effective bactericidal activity. The mechanism of this process has been reported to involve attack by valence band generated hydroxyl radicals. In this study when three common bacterial pathogens, Escherichia coli, Salmonella enterica serovar Enteritidis and Pseudomonas aeruginosa, were exposed to TiO<sub>2sub> and UVA light a substantial decrease in bacterial numbers was observed. Control experiments in which all three pathogens were exposed to UVA light only resulted in a similar reduction in bacterial numbers. Moreover, exposure to UVA light alone resulted in the production of a smaller than average colony phenotype among the surviving bacteria, for all three pathogens examined, a finding which was not observed following treatment with UVA and TiO<sub>2sub>. Small slow growing colonies have been described for several pathogenic bacteria and are referred to as small colony variants. Several studies have demonstrated an association between small colony variants and persistent, recurrent and antibiotic resistant infections. We propose that the production of small colony variants of pathogenic bacteria following UVA treatment of drinking water may represent a health hazard. As these small colony variants were not observed with the UVA/TiO<sub>2sub> system this potential hazard is not a risk when using this technology. It would also appear that the bactericidal mechanism is different with the UVA/TiO<sub>2sub> process compared to when UVA light is used alone.

Measurements of particle emissions from nanotechnology processes, with assessment of measuring techniques and workplace controls

The overall aim of this project was to contribute to existing knowledge regarding methods for measuring characteristics of airborne nanoparticles and controlling occupational exposure to airborne nanoparticles, and to gather data on nanoparticle emission and transport in various workplaces. The scope of this study involved investigating the characteristics and behaviour of particles arising from the operation of six nanotechnology processes, subdivided into nine processes for measurement purposes. It did not include the toxicological evaluation of the aerosol and therefore, no direct conclusion was made regarding the health effects of exposure to these particles. Our research included real-time measurement of sub, and supermicrometre particle number and mass concentration, count median diameter, and alveolar deposited surface area using condensation particle counters, an optical particle counter, DustTrak photometer, scanning mobility particle sizer, and nanoparticle surface area monitor, respectively. Off-line particle analysis included scanning and transmission electron microscopy, energy-dispersive x-ray spectrometry, and thermal optical analysis of elemental carbon. Sources of fibrous and non-fibrous particles were included.

In situ SANS study of the surface and pore filling adsorption of subcritical and supercritical CO2 in porous silica as a function of pore size

We applied small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) to monitor evolution of the CO2 adsorption in porous silica as a function of CO2 pressure and temperature in pores of different sizes. The range of pressures (0 < P < 345 bar) and temperatures (T=18 OC, 35 OC and 60 OC) corresponded to subcritical, near critical and supercritical conditions of bulk fluid. We observed that the adsorption behavior of CO2 is fundamentally different in large and small pores with the sizes D > 100 Å and D < 30 Å, respectively. Scattering data from large pores indicate formation of a dense adsorbed film of CO2 on pore walls with the liquid-like density (ρCO2)ads≈0.8 g/cm3. The adsorbed film coexists with unadsorbed fluid in the inner pore volume. The density of unadsorbed fluid in large pores is temperature and pressure dependent: it is initially lower than (ρCO2)ads and gradually approaches it with pressure. In small pores compressed CO2 gas completely fills the pore volume. At the lowest pressures of the order of 10 bar and T=18 OC, the fluid density in smallest pores available in the matrix with D ~ 10 Å exceeds bulk fluid density by a factor of ~ 8. As pressure increases, progressively larger pores become filled with the condensed CO2. Fluid densification is only observed in pores with sizes less than ~ 25 – 30 Å. As the density of the invading fluid reaches (ρCO2)bulk~ 0.8 g/cm3, pores of all sizes become uniformly filled with CO2 and the confinement effects disappear. At higher densities the fluid in small pores appears to follow the equation of state of bulk CO2 although there is an indication that the fluid density in the inner volume of large pores may exceed the density of the adsorbed layer. The equivalent internal pressure (Pint) in the smallest pores exceeds the external pressure (Pext) by a factor of ~ 5 for both sub- and supercritical CO2. Pint gradually approaches Pext as D → 25 – 30 Å and is independent of temperature in the studied range of 18 OC ≤ T ≤ 60 OC. The obtained results demonstrate certain similarity as well as differences between adsorption of subcritical and supercritical CO2 in disordered porous silica. High pressure small angle scattering experiments open new opportunities for in situ studies of the fluid adsorption in porous media of interest to CO2 sequestration, energy storage, and heterogeneous catalysis.

Modeling and analysis of a novel variable-speed cage induction generator

This paper introduces a novel cage induction generator and presents a mathematical model, through which its behavior can be accurately predicted. The proposed generator system employs a three-phase cage induction machine and generates single-phase and constant-frequency electricity at varying rotor speeds without an intermediate inverter stage. The technique uses any one of the three stator phases of the machine as the excitation winding and the remaining two phases, which are connected in series, as the power winding. The two-series-connected-and-one-isolated (TSCAOI) phase winding configuration magnetically decouples the two sets of windings, enabling independent control. Electricity is generated through the power winding at both sub- and super-synchronous speeds with appropriate excitation to the isolated single winding at any frequency of generation. A dynamic mathematical model, which accurately predicts the behavior of the proposed generator, is also presented and implemented in MATLAB/Simulink. Experimental results of a 2-kW prototype generator under various operating conditions are presented, together with theoretical results, to demonstrate the viability of the TSCAOI power generation. The proposed generator is simple and capable of both storage and retrieval of energy through its excitation winding and is expected to be suitable for applications, such as small wind turbines and microhydro systems.

Photocatalytic activity of Ag-substituted and impregnated nano-TiO2

Ag-substituted (Ag sub) and Ag-impregnated (Ag imp), anatase phase nano-TiO2 have been synthesized by solution combustion technique and reduction technique, respectively. The catalysts were characterized extensively by powder XRD, TEM, XPS, FT-Raman, UV absorption, FT-IR, TGA, photoluminescence, BET surface area and isoelectric pH measurements. These catalysts were used for the photodegradation of dyes and for the selective photooxidation of cyclohexane to cyclohexanone. The photoactivities of the combustion-synthesized catalysts were compared with those of commercial Degussa P 25 (DP 25) TiO2, and Ag-impregnated DP 25 (Ag DP). For the photocatalytic degradation of dyes, unsubstituted combustion-synthesized TiO2 (CS TiO2) exhibited the highest activity, followed by 1% Ag imp and 1% Ag sub. For the photoconversion of cyclohexane, the total conversion of cyclohexane and the selectivity of cyclohexanone followed the order: 1% Ag sub > DP 25 > CS TiO2 > 1% Ag imp > 1% Ag DP. The kinetics of the photodegradation of dyes and of the photooxidation of cyclohexane were modeled using Langmuir–Hinshelwood rate equation and a free radical mechanism, respectively, and the rate coefficients were determined. The difference in activity values of the catalysts observed for these two reactions and the detailed characterization of these catalysts are described in this study.

Scanning tunneling spectroscopic studies on high-temperature superconductors and Dirac materials

This thesis details the investigations of the unconventional low-energy quasiparticle excitations in electron-type cuprate superconductors and electron-type ferrous superconductors as well as the electronic properties of Dirac fermions in graphene and three-dimensional strong topological insulators through experimental studies using spatially resolved scanning tunneling spectroscopy (STS) experiments.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type cuprate La<sub>0.1sub>Sr<sub>0.9sub>CuO<sub>2sub> (La-112) T<sub>Csub> = 43 K, are investigated experimentally. For temperature (T) less than the superconducting transition temperature (TC), and in zero field, the quasiparticle spectra of La-112 exhibits gapped behavior with two coherence peaks and no satellite features. For magnetic field measurements at T < TC, first ever observation of vortices in La-112 are reported. Moreover, pseudogap-like spectra are revealed inside the core of vortices, where superconductivity is suppressed. The intra-vortex pseudogap-like spectra are characterized by an energy gap of V<sub>PGsub> = 8.5 ± 0.6 meV, while the inter-vortex quasiparticle spectra shows larger peak-to-peak gap values characterized by Δ<sub>pk-pksub>(H) >V<sub>PGsub>, and Δ<sub>pk-pksub> (0)=12.2 ± 0.8 meV > Δ<sub>pk-pksub> (H > 0). The quasiparticle spectra are found to be gapped at all locations up to the highest magnetic field examined (H = 6T) and reveal an apparent low-energy cutoff at the V<sub>PGsub> energy scale.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type "122" iron-based Ba(Fe<sub>1-xsub>Co<sub>xsub>)<sub>2sub>A<sub>s2sub> are investigated for multiple doping levels (x = 0.06, 0.08, 0.12 with T<sub>Csub>= 14 K, 24 K, and 20 K). For all doping levels and the T < T<sub>Csub>, two-gap superconductivity is observed. Both superconducting gaps decrease monotonically in size with increasing temperature and disappear for temperatures above the superconducting transition temperature, T<sub>Csub>. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps have been identified in the tunneling quasiparticle spectra. Together with quasiparticle interference (QPI) analysis and magnetic field studies, this provides strong evidence for two-gap sign-changing s-wave superconductivity.

Additionally spatial scanning tunneling spectroscopic studies are performed on mechanically exfoliated graphene and chemical vapor deposition grown graphene. In all cases lattice strain exerts a strong influence on the electronic properties of the sample. In particular topological defects give rise to pseudomagnetic fields (B ~ 50 Tesla) and charging effects resulting in quantized conductance peaks associated with the integer and fractional Quantum Hall States.

Finally, spectroscopic studies on the 3D-STI, Bi<sub>2sub>Se<sub>3sub> found evidence of impurity resonance in the surface state. The impurities are in the unitary limit and the spectral resonances are localized spatially to within ~ 0.2 nm of the impurity. The spectral weight of the impurity resonance diverges as the Fermi energy approaches the Dirac point and the rapid recovery of the surface state suggests robust topological protection against perturbations that preserve time reversal symmetry.

Bis(thiophenolate)pyridine pincer ligands and trivalent zirconocene complexes relevant to early transition metal polymerization catalysts

Two major topics are covered: the first chapter is focused on the development of post-metallocene complexes for propylene polymerization. The second and third chapters investigate the consequences of diisobutylaluminum hydride (HAlⁱBu<sub>2sub>) additives in zirconocene based polymerization systems.

The synthesis, structure, and solution behavior of early metal complexes with a new tridentate LX<sub>2sub> type ligand, bis(thiophenolate)pyridine ((SNS) = (2-C<sub>6sub>H<sub>4sub>S)<sub>2sub>-2,6-C<sub>5sub>H<sub>3sub>N) are investigated. SNS complexes of Ti, Zr, and Ta having dialkylamido coligands were synthesized and structurally characterized. The zirconium complex, (SNS)Zr(NMe<sub>2sub>)<sub>2sub>, displays C<sub>2sub> symmetry in the solid state. Solid-state structures of tantalum complexes (SNS)Ta(NMe<sub>2sub>)<sub>3sub> and (SNS)TaCl(NEt<sub>2sub>)<sub>2sub> also display pronounced C<sub>2sub> twisting of the SNS ligand. 1D and 2D NMR experiments show that (SNS)Ta(NMe<sub>2sub>)<sub>3sub> is fluxional with rotation about the Ta N(amide) bonds occurring on the NMR timescale. The fluxional behavior of (SNS)TaCl(NEt<sub>2sub>)<sub>2sub> in solution was also studied by variable temperature ¹H NMR. Observation of separate signals for the diastereotopic protons of the methylene unit of the diethylamide indicates that the complex remains locked on the NMR timescale in one diastereomeric conformation at temperatures below -50 °C.

Reduction of Zr(IV) metallocenium cations with sodium amalgam (NaHg) produces EPR signals assignable to Zr(III) metallocene complexes. Thus, chloro-bridged heterobinuclear ansa-zirconocenium cation [((SBI))Zr(μ-Cl)<sub>2sub>AlMe<sub>2sub>]⁺B(C<sub>6sub>F<sub>5sub>)<sub>4¯sub> (SBI = rac-dimethylsilylbis(1-indenyl)), gives rise to an EPR signal assignable to the complex (SBI)Zr^III(μ-Cl)<sub>2sub>AlMe<sub>2sub>, while (SBI)Zr^III-Me and (SBI)Zr^III(-H)2AlⁱBu<sub>2sub> are formed by reduction of [(SBI)Zr(μ-Me)<sub>2sub>AlMe<sub>2sub>]⁺B(C<sub>6sub>F<sub>5sub>)<sub>4¯sub> and [(SBI)Zr(μ-H)<sub>3sub>(AlⁱBu<sub>2sub>)<sub>2sub>]⁺B(C<sub>6sub>F<sub>5sub>)4¯, respectively. These products are also formed, along with (SBI)Zr^III-ⁱBu and [(SBI)Zr^III]⁺ AlR4¯ when (SBI)ZrMe<sub>2sub> reacts with HAlⁱBu<sub>2sub>, eliminating isobutane en route to the Zr(III) complex. Studies concerning the interconversion reactions between these and other (SBI)Zr(III) complexes and reaction mechanisms involved in their formation are also reported.

The addition of HAlⁱBu<sub>2sub> to precatalyst [(SBI)Zr(µ-H)<sub>3sub>(AlⁱBu<sub>2sub>)<sub>2sub>]⁺ significantly slows the polymerization of propylene and changes the kinetics of polymerization from 1st to 2nd order with respect to propylene. This is likely due to competitive inhibition by HAlⁱBu<sub>2sub>. When the same reaction is investigated using [(ⁿBuCp)<sub>2sub>Zr(μ-H)<sub>3sub>(AlⁱBu<sub>2sub>)<sub>2sub>]⁺, hydroalumination between propylene and HAlⁱBu<sub>2sub> is observed instead of propylene polymerization.

Carbon-carbon bond forming reactions from bis(carbene)-platinum(II) complexes and olefin polymerization and oligomerization using group 4 post-metallocene complexes

A long-standing challenge in transition metal catalysis is selective C–C bond coupling of simple feedstocks, such as carbon monoxide, ethylene or propylene, to yield value-added products. This work describes efforts toward selective C–C bond formation using early- and late-transition metals, which may have important implications for the production of fuels and plastics, as well as many other commodity chemicals.

The industrial Fischer-Tropsch (F-T) process converts synthesis gas (syngas, a mixture of CO + H<sub>2sub>) into a complex mixture of hydrocarbons and oxygenates. Well-defined homogeneous catalysts for F-T may provide greater product selectivity for fuel-range liquid hydrocarbons compared to traditional heterogeneous catalysts. The first part of this work involved the preparation of late-transition metal complexes for use in syngas conversion. We investigated C–C bond forming reactions via carbene coupling using bis(carbene)platinum(II) compounds, which are models for putative metal–carbene intermediates in F-T chemistry. It was found that C–C bond formation could be induced by either (1) chemical reduction of or (2) exogenous phosphine coordination to the platinum(II) starting complexes. These two mild methods afforded different products, constitutional isomers, suggesting that at least two different mechanisms are possible for C–C bond formation from carbene intermediates. These results are encouraging for the development of a multicomponent homogeneous catalysis system for the generation of higher hydrocarbons.

A second avenue of research focused on the design and synthesis of post-metallocene catalysts for olefin polymerization. The polymerization chemistry of a new class of group 4 complexes supported by asymmetric anilide(pyridine)phenolate (NNO) pincer ligands was explored. Unlike typical early transition metal polymerization catalysts, NNO-ligated catalysts produce nearly regiorandom polypropylene, with as many as 30-40 mol % of insertions being 2,1-inserted (versus 1,2-inserted), compared to <1 mol % in most metallocene systems. A survey of model Ti polymerization catalysts suggests that catalyst modification pathways that could affect regioselectivity, such as C–H activation of the anilide ring, cleavage of the amine R-group, or monomer insertion into metal–ligand bonds are unlikely. A parallel investigation of a Ti–amido(pyridine)phenolate polymerization catalyst, which features a five- rather than a six-membered Ti–N chelate ring, but maintained a dianionic NNO motif, revealed that simply maintaining this motif was not enough to produce regioirregular polypropylene; in fact, these experiments seem to indicate that only an intact anilide(pyridine)phenolate ligated-complex will lead to regioirregular polypropylene. As yet, the underlying causes for the unique regioselectivity of anilide(pyridine)phenolate polymerization catalysts remains unknown. Further exploration of NNO-ligated polymerization catalysts could lead to the controlled synthesis of new types of polymer architectures.

Finally, we investigated the reactivity of a known Ti–phenoxy(imine) (Ti-FI) catalyst that has been shown to be very active for ethylene homotrimerization in an effort to upgrade simple feedstocks to liquid hydrocarbon fuels through co-oligomerization of heavy and light olefins. We demonstrated that the Ti-FI catalyst can homo-oligomerize 1-hexene to C<sub>12sub> and C<sub>18sub> alkenes through olefin dimerization and trimerization, respectively. Future work will include kinetic studies to determine monomer selectivity by investigating the relative rates of insertion of light olefins (e.g., ethylene) vs. higher α-olefins, as well as a more detailed mechanistic study of olefin trimerization. Our ultimate goal is to exploit this catalyst in a multi-catalyst system for conversion of simple alkenes into hydrocarbon fuels.

Vibrational pooling and constrained equilibration on surfaces

In this thesis, we provide a statistical theory for the vibrational pooling and fluorescence time dependence observed in infrared laser excitation of CO on an NaCl surface. The pooling is seen in experiment and in computer simulations. In the theory, we assume a rapid equilibration of the quanta in the substrate and minimize the free energy subject to the constraint at any time t of a fixed number of vibrational quanta N(t). At low incident intensity, the distribution is limited to one- quantum exchanges with the solid and so the Debye frequency of the solid plays a key role in limiting the range of this one-quantum domain. The resulting inverted vibrational equilibrium population depends only on fundamental parameters of the oscillator (ω<sub>esub> and ω<sub>esub>χ<sub>esub>) and the surface (ω<sub>Dsub> and T). Possible applications and relation to the Treanor gas phase treatment are discussed. Unlike the solid phase system, the gas phase system has no Debye-constraining maximum. We discuss the possible distributions for arbitrary N-conserving diatom-surface pairs, and include application to H:Si(111) as an example.

Computations are presented to describe and analyze the high levels of infrared laser-induced vibrational excitation of a monolayer of absorbed ¹³CO on a NaCl(100) surface. The calculations confirm that, for situations where the Debye frequency limited n domain restriction approximately holds, the vibrational state population deviates from a Boltzmann population linearly in n. Nonetheless, the full kinetic calculation is necessary to capture the result in detail.

We discuss the one-to-one relationship between N and γ and the examine the state space of the new distribution function for varied γ. We derive the Free Energy, F = NγkT − kTln(∑P<sub>nsub>), and effective chemical potential, μn ≈ γkT, for the vibrational pool. We also find the anti correlation of neighbor vibrations leads to an emergent correlation that appears to extend further than nearest neighbor.

Structure, chemistry, and energetics of organic and inorganic adsorbates on Ga-rich GaAs and GaP(001) surfaces

The work described in this dissertation includes fundamental investigations into three surface processes, namely inorganic film growth, water-induced oxidation, and organic functionalization/passivation, on the GaP and GaAs(001) surfaces. The techniques used to carry out this work include scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations. Atomic structure, electronic structure, reaction mechanisms, and energetics related to these surface processes are discussed at atomic or molecular levels.

First, we investigate epitaxial Zn<sub>3sub>P<sub>2sub> films grown on the Ga-rich GaAs(001)(6×6) surface. The film growth mechanism, electronic properties, and atomic structure of the Zn<sub>3sub>P<sub>2sub>/GaAs(001) system are discussed based on experimental and theoretical observations. We discover that a P-rich amorphous layer covers the crystalline Zn3P2 film during and after growth. We also propose more accurate picture of the GaP interfacial layer between Zn<sub>3sub>P<sub>2sub> and GaAs, based on the atomic structure, chemical bonding, band diagram, and P-replacement energetics, than was previously anticipated.

Second, DFT calculations are carried out in order to understand water-induced oxidation mechanisms on the Ga-rich GaP(001)(2×4) surface. Structural and energetic information of every step in the gaseous water-induced GaP oxidation reactions are elucidated at the atomic level in great detail. We explore all reasonable ground states involved in most of the possible adsorption and decomposition pathways. We also investigate structures and energies of the transition states in the first hydrogen dissociation of a water molecule on the (2×4) surface.

Finally, adsorption structures and thermal decomposition reactions of 1-propanethiol on the Ga-rich GaP(001)(2×4) surface are investigated using high resolution STM, XPS, and DFT simulations. We elucidate adsorption locations and their associated atomic structures of a single 1-propanethiol molecule on the (2×4) surface as a function of annealing temperature. DFT calculations are carried out to optimize ground state structures and search transition states. XPS is used to investigate variations of the chemical bonding nature and coverage of the adsorbate species.

Organotitanium and niobium chemistry. I. Structure and reactivity of a titanium ethylene complex. II. Reactivity of decamethyl niobocene derivatives

The synthesis and X-ray diffraction study of bis(pentamethylcyclopentadienyl) ethylene titanium (I) are reported. This complex represents the first example of an isolable ethylene adduct of a group IV metal, a key intermediate in Ziegler-Natta olefin polymerization schemes. While treatment of I with ethylene leads to only traces of polymer after months, I participates in a wide range of stoichiometric and catalytic reactions. These include the catalytic conversion of ethylene specifically to butadiene and ethane and the catalytic isomerization of alkenes. Detailed studies have been carried out on the stoichiometric reactions of I with nitriles and alkynes. At low temperatures, nitriles react to form metallacycloimine species which more slowly undergo a formal 1,3-hydrogen shift to generate metallacycloeneamines. The lowest energy pathway for this rearrangement is an intramolecular hydrogen shift which is sensitive to the steric bulk of the R substituent. The reactions of I with alkynes yield metallacyclopentene complexes with high regioisomer selectivity. Carbonylation of the metallacyclopentene (η-C<sub>5sub>Me<sub>5sub>5)<sub>2sub>TiC(CH<sub>3sub>)=C(CH<sub>3sub>)CH<sub>2sub> under relatively mild conditions cleanly produces the corresponding cyclopentenone and [C<sub>5sub>(CH<sub>3sub>)<sub>5sub>]<sub>2sub>Ti(CO)<sub>2sub>. Compounds derived from CO<sub>2sub> and acetaldehyde have also been isolated.

The synthesis and characterization of bis-(η-pentamethylcyclopentadienyl) niobium(III) tetrahydroborate (II) are described and a study of its temperature-dependent proton NMR spectroscopic behavior is reported. The complex is observed to undergo a rapid intramolecular averaging process at elevated temperatures. The free energy of activation, ΔG^≠ = 16.4 ± 0.4 kcal/mol, is calculated. The reinvestigation of a related compound, bis(η-cyclopentadienyl)niobium(III) tetrahydroborate, established ΔG^≠ = 14.6 ± 0.2 kcal/mol for the hydrogen exchange process. The tetrahydroborate complex, II reacts with pyridine and dihydrogen to yield (η-C<sub>5sub>Me<sub>5sub>5)<sub>2sub>NbH<sub>3sub> (III). The reactivity of III with CO and ethylene is reported.

Application of microwave diagnostics to copper chloride and carbon dioxide lasers

Part A

A problem restricting the development of the CuCl laser has been the decrease in output power with increases of tube temperature above 400°C. At that temperature the CuCl vapor pressure is about .1 torr. This is a small fraction of the buffer gas pressure (He at 10 torr).

The aim of the project was to measure the peak radiation temperature (assumed related to the mean energy of electrons) in the laser discharge as a function of the tube temperature. A 24 gHz gated microwave radiometer was used.

It was found that at the tube temperatures at which the output power began to deteriorate, the electron radiation temperature showed a sharp increase (compared with radiation temperature in pure buffer).

Using the above result, we have postulated that this sudden increase is a result of Penning ionization of the Cu atoms. As a consequence of this process the number of Cu atoms available for lasing decrease.

PART B

The aim of the project was to study the dissociation of CO<sub>2sub> in the glow discharge of flowing CO<sub>2sub> lasers.

A TM<sub>011sub> microwave (3 gHz) cavity was used to measure the radially averaged electron density n<sub>esub> and the electron-neutral collision frequency in the laser discharge. An estimate of the electric field is made from these two measurements. A gas chromatograph was used to measure the chemical composition of the gases after going through the discharge. This instrument was checked against a mass spectrometer for accuracy and sensitivity.

Several typical laser mixtures were .used: CO<sub>2sub>-N<sub>2sub>-He (1,3,16), (1,3,0), (1,0,16), (1,2,10), (1,2,0), (1,0,10), (2,3,15), (2,3,0), (2,0,15), (1,3,16)+ H<sub>2sub>O and pure CO<sub>2sub>. Results show that for the conditions studied the dissociation as a function of the electron density is uniquely determined by the STP partial flow rate of CO<sub>2sub>, regardless of the amount of N<sub>2sub> and/or He present. The presence of water vapor in the discharge decreased the degree of dissociation.

A simple theoretical model was developed using thermodynamic equilibrium. The electrons were replaced in the calculations by a distributed heat source.

The results are analyzed with a simple kinetic model.

Influence of composition on the structure and properties of Fe-Pd-P and Ni-Pd-P amorphous alloys

Ternary alloys of nickel-palladium-phosphorus and iron-palladium- phosphorus containing 20 atomic % phosphorus were rapidly quenched from the liquid state. The structure of the quenched alloys was investigated by X-ray diffraction. Broad maxima in the diffraction patterns, indicative of a glass-like structure, were obtained for 13 to 73 atomic % nickel and 13 to 44 atomic % iron, with palladium adding up to 80%.

Radial distribution functions were computed from the diffraction data and yielded average interatomic distances and coordination numbers. The structure of the amorphous alloys could be explained in terms of structural units analogous to those existing in the crystalline Pd<sub>3sub>P, Ni<sub>3sub>P and Fe<sub>3sub>P phases, with iron or nickel substituting for palladium. A linear relationship between interatomic distances and composition, similar to Vegard's law, was shown for these metallic glasses.

Electrical resistivity measurements showed that the quenched alloys were metallic. Measurements were performed from liquid helium temperatures (4.2°K) up to the vicinity of the melting points (900°K- 1000°K). The temperature coefficient in the glassy state was very low, of the order of 10^-4/°K. A resistivity minimum was found at low temperature, varying between 9°K and 14°K for Ni<sub>xsub>-Pd<sub>80-xsub> -P<sub>20sub> and between 17°K and 96°K for Fe<sub>xsub>-Pd<sub>80-xsub> -P<sub>20sub>, indicating the presence of a Kondo effect. Resistivity measurements, with a constant heating rate of about 1.5°C/min,showed progressive crystallization above approximately 600°K.

The magnetic moments of the amorphous Fe-Pd-P alloys were measured as a function of magnetic field and temperature. True ferromagnetism was found for the alloys Fe<sub>32sub>-Pd<sub>48sub>-P<sub>20sub> and Fe<sub>44sub>-Pd<sub>36sub>-P<sub>20sub> with Curie points at 165° K and 380° K respectively. Extrapolated values of the saturation magnetic moments to 0° K were 1.70 µ<sub>Bsub> and 2.10 µ<sub>Bsub> respectively. The amorphous alloy Fe<sub>23sub>-Pd<sub>57sub>-P<sub>20sub> was assumed to be superparamagnetic. The experimental data indicate that phosphorus contributes to the decrease of moments by electron transfer, whereas palladium atoms probably have a small magnetic moment. A preliminary investigation of the Ni-Pd-P amorphous alloys showed that these alloys are weakly paramagnetic.