Ferromagnetic Resonance Force Microscopy

A new approach to magnetic resonance was introduced in 1992 based upon detection of spin-induced forces by J. Sidles [1]. This technique, now called magnetic resonance force microscopy (MRFM), was first demonstrated that same year via electron paramagnetic resonance (EPR) by D. Rugar et al. [2]. This new method combines principles of magnetic resonance with those of scanned probe technology to detect spin resonance through mechanical, rather than inductive, means. In this thesis the development and use of ferromagnetic resonance force microscopy (FMRFM) is described. This variant of MRFM, which allows investigation of ferromagnetic samples, was first demonstrated in 1996 by Z. Zhang et al. [3]. FMRFM enables characterization of (a) the dynamic magnetic properties of microscale magnetic devices, and (b) the spatial dependence of ferromagnetic resonance within a sample. Both are impossible with conventional ferromagnetic resonance techniques.

Ferromagnetically coupled systems, however, pose unique challenges for force detection. In this thesis the attainable spatial resolution - and the underlying physical mechanisms that determine it - are established. We analyze the dependence of the magnetostatic modes upon sample dimensions using a series of microscale yttrium iron garnet (YIG) samples. Mapping of mode amplitudes within these sample is attained with an unprecedented spatial resolution of 15μm. The modes, never before analyzed on this scale, fit simple models developed in this thesis for samples of micron dimensions. The application of stronger gradient fields induces localized perturbation of the ferromagnetic resonance modes. The first demonstrations of this effect are presented in this study, and a simple theoretical model is developed to explain our observations. The results indicate that the characteristics of the locally-detected ferromagnetic modes are still largely determined by the external fields and dimensions of the entire sample, rather than by the localized interaction volume (i.e., the locale most strongly affected by the local gradient field). Establishing this is a crucial first step toward understanding FMRFM in the high gradient field limit where the dispersion relations become locally determined. In this high gradient field regime, FMRFM imaging becomes analogous with that of EPR MRFM.

FMRFM has also been employed to characterize magnetic multilayers, similar to those utilized in giant magnetoresistance (GMR) devices, on a lateral scale 40 x 40μm. This is orders of magnitude smaller than possible via conventional methods. Anisotropy energies, thickness, and interface qualities of individual layers have been resolved.

This initial work clearly demonstrates the immense and unique potential that FMRFM offers for characterizing advanced magnetic nanostructures and magnetic devices.

Electronic structure and phonon thermodynamics of iron alloys

Inelastic neutron scattering (INS) and nuclear-resonant inelastic x-ray scattering (NRIXS) were used to measure phonon spectra of FeV as a B2- ordered compound and as a bcc solid solution. Contrary to the behavior of ordering alloys studied to date, the phonons in the B2-ordered phase are softer than in the solid solution. Ordering increases the vibrational entropy, which stabilizes the ordered phase to higher temperatures. Ab initio calculations show that the number of electronic states at the Fermi level increases upon ordering, enhancing the screening between ions, and reducing the interatomic force constants. The effect of screening is larger at the V atomic sites than at the Fe atomic sites.

The phonon spectra of Au-rich alloys of fcc Au-Fe were also measured. The main effect on the vibrational entropy of alloying comes from a stiffening of the Au partial phonon density of states (DOS) with Fe concentration that increases the miscibility gap temperature. The magnitude of the effect is non- linear and it is reduced at higher Fe concentrations. Force constants were calculated for several compositions and show a local stiffening of Au–Au bonds close to Fe atoms, but Au–Au bonds that are farther away do not show this effect. Phonon DOS curves calculated from the force constants reproduced the experimental trends. The Au–Fe bond is soft and favors ordering, but a charge transfer from the Fe to the Au atoms stiffens the Au–Au bonds enough to favor unmixing. The stiffening is attributed to two main effects comparable in magnitude: an increase in electron density in the free-electron-like states, and stronger sd-hybridization.

INS and NRIXS measurements were performed at elevated temperatures on B2-ordered FeTi and NRIXS measurements were performed at high pressures. The high-pressure behavior is quasi- harmonic. The softening of the phonon DOS curves with temperature is strongly nonharmonic. Calculations of the force constants and Born-von Karman fits to the experimental data show that the bonds between second nearest neighbors (2nn) are much stiffer than those between 1nn, but fits to the high temperature data show that the former softens at a faster rate with temperature. The Fe–Fe bond softens more than the Ti–Ti bond. The unusual stiffness of the 2nn bond is explained by the calculated charge distribution, which is highly aspherical and localized preferentially in the t2g orbitals. Ab initio molecular dynamics (AIMD) simulations show a charge transfer from the t2g orbitals to the eg orbitals at elevated temperatures. The asphericity decreases linearly with temperature and is more severe at the Fe sites.

Sound velocities and equation of state of iron-rich (Mg,Fe)O

Ultralow-velocity zones (ULVZs) are small structures at the base of the mantle characterized by sound velocities up to 30% lower than those of surrounding mantle. In this thesis, we propose that iron-rich (Mg,Fe)O plays a key role in the observed sound velocities, and argue that chemically distinct, iron-enriched structures are consistent with both the low sound velocities and the measured shapes of ULVZs.

Catalytic conversion of nitrogen to ammonia by an iron model complex

Threefold symmetric Fe phosphine complexes have been used to model the structural and functional aspects of biological N₂ fixation by nitrogenases. Low-valent bridging Fe-S-Fe complexes in the formal oxidation states Fe(II)Fe(II), Fe(II)/Fe(I), and Fe(I)/Fe(I) have been synthesized which display rich spectroscopic and magnetic behavior. A series of cationic tris-phosphine borane (TPB) ligated Fe complexes have been synthesized and been shown to bind a variety of nitrogenous ligands including N₂H₄, NH₃, and NH₂-. These complexes are all high spin S = 3/2 and display EPR and magnetic characteristics typical of this spin state. Furthermore, a sequential protonation and reduction sequence of a terminal amide results in loss of NH₃ and uptake of N₂. These stoichiometric transformations represent the final steps in potential N₂ fixation schemes.

Treatment of an anionic FeN₂ complex with excess acid also results in the formation of some NH₃, suggesting the possibility of a catalytic cycle for the conversion of N₂ to NH₃ mediated by Fe. Indeed, use of excess acid and reductant results in the formation of seven equivalents of NH₃ per Fe center, demonstrating Fe mediated catalytic N₂ fixation with acids and protons for the first time. Numerous control experiments indicate that this catalysis is likely being mediated by a molecular species.

A number of other phosphine ligated Fe complexes have also been tested for catalysis and suggest that a hemi-labile Fe-B interaction may be critical for catalysis. Additionally, various conditions for the catalysis have been investigated. These studies further support the assignment of a molecular species and delineate some of the conditions required for catalysis.

Finally, combined spectroscopic studies have been performed on a putative intermediate for catalysis. These studies converge on an assignment of this new species as a hydrazido(2-) complex. Such species have been known on group 6 metals for some time, but this represents the first characterization of this ligand on Fe. Further spectroscopic studies suggest that this species is present in catalytic mixtures, which suggests that the first steps of a distal mechanism for N₂ fixation are feasible in this system.

A Study on iron-based amorphous alloys : alloy development, thermodynamics and soft magnetism

Metallic glass has since its debut been of great research interest due to its profound scientific significance. Magnetic metallic glasses are of special interest because of their promising technological applications. In this thesis, we introduced a novel series of Fe-based alloys and offer a holistic review of the physics and properties of these alloys. A systematic alloy development and optimization method was introduced, with experimental implementation on transition metal based alloying system. A deep understanding on the influencing factors of glass forming ability was brought up and discussed, based on classical nucleation theory. Experimental data of the new Fe-based amorphous alloys were interpreted to further analyze those influencing factors, including reduced glass transition temperature, fragility, and liquid-crystal interface free energy. Various treatments (fluxing, overheating, etc.) were discussed for their impacts on the alloying systems' thermodynamics and glass forming ability. Multiple experimental characterization methods were discussed to measure the alloys' soft magnetic properties. In addition to theoretical and experimental investigation, we also gave a detailed numerical analysis on the rapid-discharge-heating-and-forming platform. It is a novel experimental system which offers extremely fast heating rate for calorimetric characterization and alloy deformation.

Metasomatism and magmatic assimilation at a gabbro-limestone contact, Christmas Mountains, Big Bend region, Texas

A composite stock of alkaline gabbro and syenite is intrusive into limestone of the Del Carmen, Sue Peake and Santa Elena Formations at the northwest end of the Christmas Mountains. There is abundant evidence of solution of wallrock by magma but nowhere are gabbro and limestone in direct contact. The sequence of lithologies developed across the intrusive contact and across xenoliths is gabbro, pyroxenite, calc-silicate skarn, marble. Pyroxenite is made up of euhedral crystals of titanaugite and sphene in a leucocratic matrix of nepheline, Wollastonite and alkali feldspar. The uneven modal distribution of phases in pyroxenite and the occurrence' of nepheline syenite dikes, intrusive into pyroxenite and skarn, suggest that pyroxenite represents an accumulation of clinopyroxene "cemented" together by late-solidifying residual magma of nepheline syenite composition. Assimilation of limestone by gabbroic magma involves reactions between calcite and magma and/or crystals in equilibrium with magma and crystallization of phases in which the magma is saturated, to supply energy for the solution reaction. Gabbroic magma was saturated with plagioclase and clinopyroxene at the time of emplacement. The textural and mineralogic features of pyroxenite can be produced by the reaction 2( 1-X) CALCITE + AN_XAB_l-X = (1-X) NEPHELINE+ 2(1-X) WOLLASTONITE+ X ANORTHITE+ 2(1-X) CO₂. Plagioclase in pyroxenite has corroded margins and is rimmed by nepheline, suggestive of resorption by magma. Anorthite and wollastonite enter solid solution in titanaugite. For each mole of calcite dissolved, approximately one mole of clinopyroxene was crystallized. Thus the amount of limestone that may be assimilated is limited by the concentration of potential clinopyroxene in the magma. Wollastonite appears as a phase when magma has been depleted in iron and magnesium by crystallization of titanaugite. The predominance of mafic and ultramafic compositions among contaminated rocks and their restriction to a narrow zone along the intrusive contact provides little evidence for the generation of a significant volume of desilicated magma as a result of limestone assimilation.

Within 60 m of the intrusive contact with the gabbro, nodular chert in the Santa Elena Limestone reacted with the enveloping marble to form spherical nodules of high-temperature calc-silicate minerals. The phases wollastonite, rankinite, spurrite, tilleyite and calcite, form a series of sharply-bounded, concentric monomineralic and two-phase shells which record a step-wise decrease in silica content from the core of a nodule to its rim. Mineral zones in the nodules vary 'with distance from the gabbro as follows:

0-5 m CALCITE + SPURRITE + RANKINITE + WOLLASTONITE
5-16 m CALCITE + TILLEYITE ± SPURRITE + RANKINITE + WOLLASTONITE
16-31 m CALCITE + TILLEYITE + WOLLASTONITE
31-60 m CALCITE + WOLLASTONITE
60-plus CALCITE + QUARTZ

The mineral of a one-phase zone is compatible with the phases bounding it on either side but these phases are incompatible in the same volume of P-T-X_CO2.

Growth of a monomineralio zone is initiated by reaction between minerals of adjacent one-phase zones which become unstable with rising temperature to form a thin layer of a new single phase that separates the reactants and is compatible with both of them. Because the mineral of the new zone is in equilibrium with the phases at both of its contacts, gradients in the chemical potentials of the exchangeable components are established across it. Although zone boundaries mark discontinuities in the gradients of bulk composition, two-phase equilibria at the contacts demonstrate that the chemical potentials are continuous. Hence, Ca, Si and CO₂ were redistributed in the growing nodule by diffusion. A monomineralic zone grows at the expense of an adjacent zone by reaction between diffusing components and the mineral of the adjacent zone. Equilibria between two phases at zone boundaries buffers the chemical potentials of the diffusing species. Thus, within a monomineralic zone, the chemical potentials of the diffusing components are controlled external to the local assemblage by the two-phase equilibria at the zone boundaries.

Mineralogically zoned calc-silicate skarn occurs as a narrow band that separates pyroxenite and marble along the intrusive contact and forms a rim on marble xenoliths in gabbro. Skarn consists of melilite or idocrase pseudomorphs of melili te, one or two . stoichiometric calcsilicate phases and accessory Ti-Zr garnet, perovskite and magnetite. The sequence of mineral zones from pyroxenite to marble, defined by a characteristic calc-silicate, is wollastonite, rankinite, spurrite, calcite. Mineral assemblages of adjacent skarn zones are compatible and the set of zones in a skarn band defines a facies type, indicating that the different mineral assemblages represent different bulk compositions recrystallized under identical conditions. The number of phases in each zone is less than the number that might be expected to result from metamorphism of a general bulk composition under conditions of equilibrium, trivariant in P, T and u_CO2. The "special" bulk composition of each zone is controlled by reaction between phases of the zones bounding it on either side. The continuity of the gradients of composition of melilite and garnet solid solutions across the skarn is consistent with the local equilibrium hypothesis and verifies that diffusion was the mechanism of mass transport. The formula proportions of Ti and Zr in garnet from skarn vary antithetically with that of Si Which systematically decreases from pyroxenite to marble. The chemical potential of Si in each skarn zone was controlled by the coexisting stoichiometric calc-silicate phases in the assemblage. Thus the formula proportion of Si in garnet is a direct measure of the chemical potential of Si from point to point in skarn. Reaction between gabbroic magma saturated with plagioclase and clinopyroxene produced nepheline pyroxenite and melilite-wollastonite skarn. The calcsilicate zones result from reaction between calcite and wollastonite to form spurrite and rankinite.

Fundamental Studies of Carbon Oxygen Bond Activation in Nickel Diphosphine Ether Complexes. And, Metallomacrocycles as Ligands: Synthesis and Characterization of Aluminum-Bridged Bisglyoximato Complexes of Iron and Cobalt

In order to develop better catalysts for the cleavage of aryl-X bonds fundamental studies of the mechanism and individual steps of the mechanism have been investigated in detail. As the described studies are difficult at best in catalytic systems, model systems are frequently used. To study aryl-oxygen bond activation, a terphenyl diphosphine scaffold containing an ether moiety in the central arene was designed. The first three chapters of this dissertation focus on the studies of the nickel complexes supported by this diphosphine backbone and the research efforts in regards to aryl-oxygen bond activation.

Chapter 2 outlines the synthesis of a variety of diphosphine terphenyl ether ligand scaffolds. The metallation of these scaffolds with nickel is described. The reactivity of these nickel(0) systems is also outlined. The systems were found to typically undergo a reductive cleavage of the aryl oxygen bond. The mechanism was found to be a subsequent oxidative addition, β-H elimination, reductive elimination and (or) decarbonylation.

Chapter 3 presents kinetic studies of the aryl oxygen bond in the systems outlined in Chapter 2. Using a series of nickel(0) diphosphine terphenyl ether complexes the kinetics of aryl oxygen bond activation was studied. The activation parameters of oxidative addition for the model systems were determined. Little variation was observed in the rate and activation parameters of oxidative addition with varying electronics in the model system. The cause of the lack of variation is due to the ground state and oxidative addition transition state being affected similarly. Attempts were made to extend this study to catalytic systems.

Chapter 4 investigates aryl oxygen bond activation in the presence of additives. It was found that the addition of certain metal alkyls to the nickel(0) model system lead to an increase in the rate of aryl oxygen bond activation. The addition of excess Grignard reagent led to an order of magnitude increase in the rate of aryl oxygen bond activation. Similarly the addition of AlMe3 led to a three order of magnitude rate increase. Addition of AlMe₃ at -80 °C led to the formation of an intermediate which was identified by NOESY correlations as a system in which the AlMe3 is coordinated to the ether moiety of the backbone. The rates and activation parameters of aryl oxygen bond activation in the presence of AlMe3 were investigated.

The last two chapters involve the study of metalla-macrocycles as ligands. Chapter 5 details the synthesis of a variety of glyoxime backbones and diphenol precursors and their metallation with aluminum. The coordination chemistry of iron on the aluminum scaffolds was investigated. Varying the electronics of the aluminum macrocycle was found to affect the observed electrochemistry of the iron center.

Chapter 6 extends the studies of chapter 5 to cobalt complexes. The synthesis of cobalt dialuminum glyoxime metal complexes is described. The electrochemistry of the cobalt complexes was investigated. The electrochemistry was compared to the observed electrochemistry of a zinc analog to identify the redox activity of the ligand. In the presence of acid the cobalt complexes were found to electrochemically reduce protons to dihydrogen. The electronics of the ancillary aluminum ligands were found to affect the potential of proton reduction in the cobalt complexes. These potentials were compared to other diglyoximate complexes.

Magnetic behavior of basic iron(III) compounds. I. Magnetic behavior of the basic iron sulphates and basic iron chromate. II. Magnetic behavior of delta ferric oxide hydroxide

I. The thermomagnetic behavior and infrared spectroscopic features of KFe₃(SO₄)₂(OH)₆ (jarosite), (H₃O)Fe₃(SO₄)₂ (OH)₆ (hydronium jarosite), KFe₃(CrO₄)₂ (OH)₆, Fe(OH)SO₄ (basic iron sulfate), and Fe(OH)CrO₄ (basic iron chromate) are reported. Fe(OH)CrO₄ and KFe₃(CrO₄)₂ (OH)₆ are shown to be weak ferro magnets with Curie temperatures of 73 and 71 °K, respectively. This unusual magnetic behavior is rationalized in terms of the ionic spin configurations of the phases. Exchange coupling through chromate bridging groups is shown to be weak.

II. The magnetic behavior and the influence of preparative history on the magnetic behavior of δFeO(OH) is reported. δFeO(OH) is shown to be a fine-particulate, uniaxial, magnetic species. Magnetization data for this species are shown to be consistent with the existence of magnetically inactive layers surrounding magnetic particles.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Absolute oscillator strengths for iron, copper, cadmium and gold measured by the atomic beam method

Absolute f-values for 7 transitions in the first spectra of 4 elements have been measured using the atomic beam absorption technique. The equivalent widths of the absorption lines are measured with a photoelectric scanner and the atomic beam density is determined by continuously weighing a part of it with a sensitive automatic microbalance. The complete theory is presented and corrections are calculated to cope with gas absorption by the deposit on the microbalance pan and atoms which do not stick to the pan. An additional correction for the failure of the assumption of effusive flow in the formation of the atomic beam at large densities has been measured experimentally.

The following f-values were measured:

Fe: f_λ3720 = 0.0430 ± 8%

Cu: f_λ3247 = 0.427 ± 4.5%, f_λ3274 = 0.206 ± 4.7%, f_λ2492 = 0.0037 ± 9%

Cd: f_λ3261 = 0.00190 ± 7%, f_λ2288 = 1.38 ± 12%

Au: f_λ2428 = 0.283 ± 5.3%

Comparison with other accurately measured f-values, where they exist, shows agreement within experimental errors.

Design, Synthesis, and Study of Novel Platforms for Iron-N2 Chemistry and Photoinduced, Copper-mediated C-N Bond Formation

Several new ligand platforms designed to support iron dinitrogen chemistry have been developed. First, we report Fe complexes of a tris(phosphino)alkyl (CP^iPr₃) ligand featuring an axial carbon donor intended to conceptually model the interstitial carbide atom of the nitrogenase iron-molybdenum cofactor (FeMoco). It is established that in this scaffold, the iron center binds dinitrogen trans to the C_alkyl anchor in three structurally characterized oxidation states. Fe-C_alkyl lengthening is observed upon reduction, reflective of significant ionic character in the Fe-C_alkyl interaction. The anionic (CP^iPr₃)FeN₂^- species can be functionalized by a silyl electrophile to generate (CP^iPr₃)Fe-N₂SiR₃. This species also functions as a modest catalyst for the reduction of N₂ to NH₃. Next, we introduce a new binucleating ligand scaffold that supports an Fe(μ-SAr)Fe diiron subunit that coordinates dinitrogen (N₂-Fe(μ-SAr)Fe-N₂) across at least three oxidation states (Fe^IIFe^II, Fe^IIFe^I, and Fe^IFe^I). Despite the sulfur-rich coordination environment of iron in FeMoco, synthetic examples of transition metal model complexes that bind N₂ and also feature sulfur donor ligands remain scarce; these complexes thus represent an unusual series of low-valent diiron complexes featuring thiolate and dinitrogen ligands. The (N₂-Fe(μ-SAr)Fe-N₂) system undergoes reduction of the bound N₂ to produce NH₃ (~50% yield) and can efficiently catalyze the disproportionation of N₂H₄ to NH₃ and N₂. The present scaffold also supports dinitrogen binding concomitant with hydride as a co-ligand. Next, inspired by the importance of secondary-sphere interactions in many metalloenzymes, we present complexes of iron in two new ligand scaffolds ([SiP^NMe₃] and [SiP^iPr₂P^NMe]) that incorporate hydrogen-bond acceptors (tertiary amines) which engage in interactions with nitrogenous substrates bound to the iron center (NH₃ and N₂H₄). Cation binding is also facilitated in anionic Fe(0)-N₂ complexes. While Fe-N₂ complexes of a related ligand ([SiP^iPr₃]) lacking hydrogen-bond acceptors produce a substantial amount of ammonia when treated with acid and reductant, the presence of the pendant amines instead facilitates the formation of metal hydride species.

Additionally, we present the development and mechanistic study of copper-mediated and copper-catalyzed photoinduced C-N bond forming reactions. Irradiation of a copper-amido complex, ((m-tol)₃P)₂Cu(carbazolide), in the presence of aryl halides furnishes N-phenylcarbazole under mild conditions. The mechanism likely proceeds via single-electron transfer from an excited state of the copper complex to the aryl halide, generating an aryl radical. An array of experimental data are consistent with a radical intermediate, including a cyclization/stereochemical investigation and a reactivity study, providing the first substantial experimental support for the viability of a radical pathway for Ullmann C-N bond formation. The copper complex can also be used as a precatalyst for Ullmann C-N couplings. We also disclose further study of catalytic C_alkyl-N couplings using a CuI precatalyst, and discuss the likely role of [Cu(carbazolide)₂]^- and [Cu(carbazolide)₃]^- species as intermediates in these reactions.

Finally, we report a series of four-coordinate, pseudotetrahedral P₃Fe^II-X complexes supported by tris(phosphine)borate ([PhBP₃Fe^R]^-) and phosphiniminato X-type ligands (-N=PR'₃) that in combination tune the spin-crossover behavior of the system. Low-coordinate transition metal complexes such as these that undergo reversible spin-crossover remain rare, and the spin equilibria of these systems have been studied in detail by a suite of spectroscopic techniques.