Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

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.

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.

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.

Luminescence properties of electron-hole-droplets in pure and doped germanium

This work contains 4 topics dealing with the properties of the luminescence from Ge.

The temperature, pump-power and time dependences of the photoluminescence spectra of Li-, As-, Ga-, and Sb-doped Ge crystals were studied. For impurity concentrations less than about 10¹⁵cm^-3, emissions due to electron-hole droplets can clearly be identified. For impurity concentrations on the order of 10¹⁶cm^-3, the broad lines in the spectra, which have previously been attributed to the emission from the electron-hole-droplet, were found to possess pump-power and time dependent line shape. These properties show that these broad lines cannot be due to emission of electron-hole-droplets alone. We interpret these lines to be due to a combination of emissions from (1) electron-hole- droplets, (2) broadened multiexciton complexes, (3) broadened bound-exciton, and (4) plasma of electrons and holes. The properties of the electron-hole-droplet in As-doped Ge were shown to agree with theoretical predictions.

The time dependences of the luminescence intensities of the electron-hole-droplet in pure and doped Ge were investigated at 2 and 4.2°K. The decay of the electron-hole-droplet in pure Ge at 4.2°K was found to be pump-power dependent and too slow to be explained by the widely accepted model due to Pokrovskii and Hensel et al. Detailed study of the decay of the electron-hole-droplets in doped Ge were carried out for the first time, and we find no evidence of evaporation of excitons by electron-hole-droplets at 4.2°K. This doped Ge result is unexplained by the model of Pokrovskii and Hensel et al. It is shown that a model based on a cloud of electron-hole-droplets generated in the crystal and incorporating (1) exciton flow among electron-hole-droplets in the cloud and (2) exciton diffusion away from the cloud is capable of explaining the observed results.

It is shown that impurities, introduced during device fabrication, can lead to the previously reported differences of the spectra of laser-excited high-purity Ge and electrically excited Ge double injection devices. By properly choosing the device geometry so as to minimize this Li contamination, it is shown that the Li concentration in double injection devices may be reduced to less than about 10¹⁵cm^-3 and electrically excited luminescence spectra similar to the photoluminescence spectra of pure Ge may be produced. This proves conclusively that electron-hole-droplets may be created in double injection devices by electrical excitation.

The ratio of the LA- to TO-phonon-assisted luminescence intensities of the electron-hole-droplet is demonstrated to be equal to the high temperature limit of the same ratio of the exciton for Ge. This result gives one confidence to determine similar ratios for the electron-hole-droplet from the corresponding exciton ratio in semiconductors in which the ratio for the electron-hole-droplet cannot be determined (e.g., Si and GaP). Knowing the value of this ratio for the electron-hole-droplet, one can obtain accurate values of many parameters of the electron-hole-droplet in these semiconductors spectroscopically.

An experimental study of the mobility of edge dislocations in pure copper single crystals

The velocity of selectively-introduced edge dislocations in 99.999 percent pure copper crystals has been measured as a function of stress at temperatures from 66°K to 373°K by means of a torsion technique. The range of resolved shear stress was 0 to 15 megadynes/ cm^2 for seven temperatures (66°K, 74°K, 83°K, 123°K, 173°K, 296°K, 296°K, 373°K.

Dislocation mobility is characterized by two distinct features; (a) relatively high velocity at low stress (maximum velocities of about 9000 em/sec were realized at low temperatures), and (b) increasing velocity with decreasing temperature at constant stress.

The relation between dislocation velocity and resolved shear stress is:

v = v_o(τ_r/τ_o)^n

where v is the dislocation velocity at resolved shear stress τ_r, v_o is a constant velocity chosen equal to 2000 cm/ sec, τ_o is the resolved shear stress required to maintain velocity v_o, and n is the mobility coefficient. The experimental results indicate that τ_o decreases from 16.3 x 10^6 to 3.3 x 10^6 dynes/cm^2 and n increases from about 0.9 to 1.1 as the temperature is lowered from 296°K to 66°K.

The experimental dislocation behavior is consistent with an interpretation on the basis of phonon drag. However, the complete temperature dependence of dislocation mobility could not be closely approximated by the predictions of one or a combination of mechanisms.

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.

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.

Spin wave resonance in ferromagnetic films

The objective of this investigation has been a theoretical and experimental understanding of ferromagnetic resonance phenomena in ferromagnetic thin films, and a consequent understanding of several important physical properties of these films. Significant results have been obtained by ferromagnetic resonance, hysteresis, torque magnetometer, He ion backscattering, and X-ray fluorescence measurements for nickel-iron alloy films.

Taking into account all relevant magnetic fields, including the applied, demagnetizing, effective anisotropy and exchange fields, the spin wave resonance condition applicable to the thin film geometry is presented. On the basis of the simple exchange interaction model it is concluded that the normal resonance modes of an ideal film are expected to be unpinned. The possibility of nonideality near the surface of a real film was considered by means of surface anisotropy field, inhomogeneity in demagnetizing field and inhomogeneity of magnetization models. Numerical results obtained for reasonable parameters in all cases show that they negligibly perturb the resonance fields and the higher order mode shapes from those of the unpinned modes of ideal films for thicknesses greater than 1000 Å. On the other hand for films thinner than 1000 Å the resonance field deviations can be significant even though the modes are very nearly unpinned. A previously unnoticed but important feature of all three models is that the interpretation of the first resonance mode as the uniform mode of an ideal film allows an accurate measurement of the average effective demagnetizing field over the film volume. Furthermore, it is demonstrated that it is possible to choose parameters which give indistinguishable predictions for all three models, making it difficult to uniquely ascertain the source of spin pinning in real films from resonance measurements alone.

Spin wave resonance measurements of 81% Ni-19% Fe coevaporated films 30 to 9000 Å thick, at frequencies from 1 to 8 GHz, at room temperature, and with the static magnetic field parallel and perpendicular to the film plane have been performed. A self-consistent analysis of the results for films thicker than 1000 Å, in which multiple excitations can be observed, shows for the first time that a unique value of exchange constant A can only be obtained by the use of unpinned mode assignments. This evidence and the resonance behavior of films thinner than 1000 Å strongly imply that the magnetization at the surfaces of permalloy films is very weakly pinned. However, resonance measurements alone cannot determine whether this pinning is due to a surface anisotropy, an inhomogeneous demagnetizing field or an inhomogeneous magnetization. The above analysis yields a value of 4πM=10,100 Oe and A = (1.03 ± .05) x 10^-6 erg/cm for this alloy. The ability to obtain a unique value of A suggests that spin wave resonance can be used to accurately characterize the exchange interaction in a ferromagnet.

In an effort to resolve the ambiguity of the source of pinning of the magnetization, a correlation of the ratio of magnetic moment and X-ray film thickness with the value of effective demagnetizing field 4πNM as determined from resonance, for films 45 to 300 Å has been performed. The remarkable agreement of both quantities and a comparison with the predictions of five distinct models, strongly imply that the thickness dependence of both quantities is related to a thickness dependent average saturation magnetization, which is far below 10,100 Oe for very thin films. However, a series of complementary experiments shows that this large decrease of average saturation magnetization cannot be simply explained by either oxidation or interdiffusion processes. It can only be satisfactorily explained by an intrinsic decrease of the average saturation magnetization for very thin films, an effect which cannot be justified by any simple physical considerations.

Recognizing that this decrease of average saturation magnetization could be due to an oxidation process, a correlation of resonance measurements, He ion backscattering, X-ray fluorescence and torque magnetometer measurements, for films 40 to 3500 Å thick has been performed. On basis of these measurements it is unambiguously established that the oxide layer on the surface of purposefully oxidized 81% Ni-19% Fe evaporated films is predominantly Fe-oxide, and that in the oxidation process Fe atoms are removed from the bulk of the film to depths of thousands of angstroms. Extrapolation of results for pure Fe films indicates that the oxide is most likely α-Fe₂O₃. These conclusions are in agreement with results from old metallurgical studies of high temperature oxidation of bulk Fe and Ni-Fe alloys. However, X-ray fluorescence results for films oxidized at room temperature, show that although the preferential oxidation of Fe also takes place in these films, the extent of this process is by far too small to explain the large variation of their average saturation magnetization with film thickness.