Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

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.

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.

Development of Asymmetric Protonation Reactions for the Synthesis of Indoline Alkaloids

Nitrogen-containing heterocycles, such as indolines and pyrroloindolines, are prevalent in a variety of diverse natural products, many of which exhibit remarkable biological activities. These frameworks have inspired innovative research aimed at discovering novel methods for their stereoselective preparation.

We have developed an enantioselective synthesis of pyrroloindolines based on a formal (3 + 2) cycloaddition of indoles and 2-amidoacrylates. This reaction is promoted by (R)-BINOL•SnCl₄; this complex is a Lewis acid-assisted Brønsted acid that effects a highly face-selective catalyst-controlled protonation of an enolate. Mechanistic studies also determined that the initial product of this reaction is an indolinium ion, which upon aqueous workup undergoes cyclization to the pyrroloindoline.

Based on this result, we investigated alternative nucleophiles to trap the indolinium ion. First, addition of sodium borohydride to the optimized reaction conditions yields indoline-containing amino acid derivatives.

Next, carbon nucleophiles were explored. Indole substrates incorporating a tethered alkene were exposed to the conditions for the formal (3 + 2) cycloaddition, resulting in a conjugate addition/asymmetric protonation/Prins cyclization cascade. In this transformation, the indolinium ion is attacked by the olefin, and the resulting carbocation is quenched by a chloride ion. Zirconium tetrachloride was found to be the optimal Lewis acid. Stoichiometric proton and chloride sources were also found to be crucial for reactivity.

Observations of nitrogen and oxygen isotopes in the low energy cosmic rays

The isotopic composition of the enhanced low energy nitrogen and oxygen cosmic rays can provide information regarding the source of these particles. Using the Caltech Electron/Isotope Spectrometer aboard the IMP-7 satellite, a measurement of this isotopic composition was made. To determine the isotope response of the instrument, a calibration was performed, and it was determined that the standard range-energy tables were inadequate to calculate the isotope response. From the calibration, corrections to the standard range-energy tables were obtained which can be used to calculate the isotope response of this and similar instruments.

The low energy nitrogen and oxygen cosmic rays were determined to be primarily ^(14)N and ^(16)O. Upper limits were obtained for the abundances of the other stable nitrogen and oxygen isotopes. To the 84% confidence level the isotopic abundances are: ^(15)N/N ≤ 0.26 (5.6- 12.7 MeV/nucleon), ^(17)0/0 ≤ 0.13 (7.0- 11.8 MeV/nucleon), (18)0/0 ≤ 0.12 (7.0 - 11.2 MeV/nucleon). The nitrogen composition differs from higher energy measurements which indicate that ^(15)N, which is thought to be secondary, is the dominant isotope. This implies that the low energy enhanced cosmic rays are not part of the same population as the higher energy cosmic rays and that they have not passed through enough material to produce a large fraction of ^(15)N. The isotopic composition of the low energy enhanced nitrogen and oxygen is consistent with the local acceleration theory of Fisk, Kozlovsky, and Ramaty, in which interstellar material is accelerated to several MeV/nucleon. If, on the other hand, the low energy nitrogen and oxygen result from nucleosynthesis in a galactic source, then the nucleosynthesis processes which produce an enhancement of nitrogen and oxygen and a depletion of carbon are restricted to producing predominantly ^(14)N and ^(16)O.

A balloon measurement of the isotopic composition of galactic cosmic ray boron, carbon, and nitrogen

The isotopic compositions of galactic cosmic ray boron, carbon, and nitrogen have been measured at energies near 300 MeV amu^-1, using a balloon-borne instrument at an atmospheric depth of ~5 g cm^-2. The calibrations of the detectors comprising the instrument are described. The saturation properties of the cesium iodide scintilla tors used for measurement of particle energy are studied in the context of analyzing the data for mass. The achieved rms mass resolution varies from ~ 0.3 amu at boron to ~ 0.5 amu at nitrogen, consistent with a theoretical analysis of the contributing factors. Corrected for detector interactions and the effects of the residual atmosphere, the results are ^(10)B/B = 0.33^(+0.17)_(-0.11), ^(13)C/C = 0.06^(+0.13)_(-0.01), and ^(15)N/N = 0.42 (+0.19)_(-0.17). A model of galactic propagation and solar modulation is described. Assuming a cosmic ray source composition of solar-like isotopic abundances, the model predicts abundances near earth consistent with the measurements.

Nitrogen and phosphorus forms in water and the food requirements of algae. [Translation from: Wiadomosci Ekologiczne 19 238-244, 1973. ]

When dissolved in water, compounds of nitrogen and phosphorus ought to contain the basic assimilated food requirements for autotrophic plants and therefore autotrophic algae. This article summarises the occurrence of nitrogen in water, how species of algae utilize nitrogen and phosphorus forms for growth and the capacities of algae to adapt to environments of different nutrient wealth. This topic has unquestionable importance not only for the purpose of survival of a species but also in deciding indirectly about the stability of ecosystems.

I. The rate and mechanism of the vapor-phase reaction between water and parts-per-million concentrations of nitrogen dioxide. II. The rate and mechanism of the air oxidation of parts-per-million concentrations of nitric oxide in the presence of water vapor.

Part I

A study of the thermal reaction of water vapor and parts-per-million concentrations of nitrogen dioxide was carried out at ambient temperature and at atmospheric pressure. Nitric oxide and nitric acid vapor were the principal products. The initial rate of disappearance of nitrogen dioxide was first order with respect to water vapor and second order with respect to nitrogen dioxide. An initial third-order rate constant of 5.5 (± 0.29) x 10⁴ liter² mole^-2 sec^-1 was found at 25˚C. The rate of reaction decreased with increasing temperature. In the temperature range of 25˚C to 50˚C, an activation energy of -978 (± 20) calories was found.

The reaction did not go to completion. From measurements as the reaction approached equilibrium, the free energy of nitric acid vapor was calculated. This value was -18.58 (± 0.04) kilocalories at 25˚C.

The initial rate of reaction was unaffected by the presence of oxygen and was retarded by the presence of nitric oxide. There were no appreciable effects due to the surface of the reactor. Nitric oxide and nitrogen dioxide were monitored by gas chromatography during the reaction.

Part II

The air oxidation of nitric oxide, and the oxidation of nitric oxide in the presence of water vapor, were studied in a glass reactor at ambient temperatures and at atmospheric pressure. The concentration of nitric oxide was less than 100 parts-per-million. The concentration of nitrogen dioxide was monitored by gas chromatography during the reaction.

For the dry oxidation, the third-order rate constant was 1.46 (± 0.03) x 10⁴ liter² mole^-2 sec^-1 at 25˚C. The activation energy, obtained from measurements between 25˚C and 50˚C, was -1.197 (±0.02) kilocalories.

The presence of water vapor during the oxidation caused the formation of nitrous acid vapor when nitric oxide, nitrogen dioxide and water vapor combined. By measuring the difference between the concentrations of nitrogen dioxide during the wet and dry oxidations, the rate of formation of nitrous acid vapor was found. The third-order rate constant for the formation of nitrous acid vapor was equal to 1.5 (± 0.5) x 10⁵ liter² mole^-2 sec^-1 at 40˚C. The reaction rate did not change measurably when the temperature was increased to 50˚C. The formation of nitric acid vapor was prevented by keeping the concentration of nitrogen dioxide low.

Surface effects were appreciable for the wet tests. Below 35˚C, the rate of appearance of nitrogen dioxide increased with increasing surface. Above 40˚C, the effect of surface was small.

Conversão do metanol em olefinas catalisada por zeólitas com diferentes características ácidas e estruturais

A reação de transformação de metanol em olefinas leves foi investigada sobre as peneiras moleculares HZSM-5, HFER, SAPO-34 e HMCM-22. A caracterização físico-química das amostras foi realizada através das técnicas de FRX, DRX, fisissorção de nitrogênio, MEV, espectrometria no IV com adsorção de piridina e TPD de NH3. O desempenho catalítico das mesmas foi comparado em condições de isoconversão inicial de 755%. Verificou-se que as características ácidas e estruturais exerceram forte influência sobre o desempenho catalítico quanto à atividade, estabilidade e seletividade aos produtos da reação. A amostra mais estável foi a HZSM-5 que apresentou maior densidade de sítios fortes e uma estrutura porosa que permite uma circulação tridimensional das moléculas. Já a menos estável, SAPO-34, apresentou a menor concentração de sítios ácidos fortes dentre os materiais estudados e uma estrutura com cavidades com aberturas estreitas (4Å) que oferecem restrições ao acesso dos reagentes aos sítios ácidos do catalisador. Quanto à seletividade a olefinas, a primeira foi mais seletiva a propeno e a segunda, a eteno. A ferrierita não se mostrou seletiva às olefinas leves tendo apresentado, no entanto, comportamento promissor quanto a formação de DME a partir do metanol. Já a HMCM-22 foi seletiva às olefinas leves e aos hidrocarbonetos com 4, 5 e 6 ou mais átomos de carbono. A influência da temperatura no desempenho catalítico foi investigada variando-se a temperatura de reação (300, 400 e 500C). Verificou-se que para a HZSM-5 e HMCM-22, perda da atividade catalítica foi intensificada a partir de 400C. Quanto à seletividade a olefinas leves, apenas a SAPO-34 não se mostrou sensível a variações na temperatura, efeito este que foi nitidamente observado nos outros três catalisadores: um aumento na temperatura promoveu um aumento na seletividade a olefinas leves no caso da HZSM-5 e da HMCM-22 e queda nesse valor para a HFER

Ratio of natural isotopes of nitrogen. I. Primary results: soils of Dombes [Translation from: Revue d'Ecologie et de Biologie du Sol 14, 279-287, 1977]

Utilization of the heavy isotope of nitrogen as a tracer has found numerous applications in soil biology. It allows better definition of different stages of the nitrogen cycle, in particular the immobilization-mineralization cycle. In this work, the authors report the results of calculations of natural isotope ratios of nitrogen in samples of water, soil and vegetation prevailing in Dombes and discuss the possibilities of errors and coefficients of fractionation.

A generalized treatment of the order-disorder transformation in alloys and its effects on their magnetic properties

A theory of the order-disorder transformation is developed in complete generality. The general theory is used to calculate long range order parameters, short range order parameters, energy, and phase diagrams for a face centered cubic binary alloy. The theoretical results are compared to the experimental determination of the copper-gold system, Values for the two adjustable parameters are obtained.

An explanation for the behavior of magnetic alloys is developed, Curie temperatures and magnetic moments of the first transition series elements and their alloys in both the ordered and disordered states are predicted. Experimental agreement is excellent in most cases. It is predicted that the state of order can effect the magnetic properties of an alloy to a considerable extent in alloys such as Ni₃Mn. The values of the adjustable parameter used to fix the level of the Curie temperature, and the adjustable parameter that expresses the effect of ordering on the Curie temperature are obtained.

The effect of oxygen concentration in water on the growth and nitrogen metabolism in the fry of rainbow trout [Translation from: Rybnoe Khoziaistvo,V.33, 74-75, 1957]

To ascertain the effect of various concentrations of oxygen in water on the fry of rainbow trout experiments were made with aquaria at various concentrations of oxygen. The food supplied was chironomid larvae (Chironomus plumosus). A surplus of food was supplied to the fry. Indices are given of the reaction of the fry to different temperatures.

The rate and mechanism of the partial oxidation of acetaldehyde by PPM concentrations of nitrogen dioxide

The thermal reaction between nitrogen dioxide and acetaldehyde in the gas phase was investigated at room temperature and atmospheric pressure. The initial rate of disappearance of nitrogen dioxide was 1.00 ± 0.03 order with respect to nitrogen dioxide and 1.00 ± 0.07 order with respect to acetaldehyde. An initial second order rate constant of (8.596 ± 0.189) x 10^-3 1.mole^-1 sec^-1 was obtained at 22.0 ± 0.1 °C and a total pressure of one atmosphere. The activation energy of the reaction was 12,900 cal/mole in the temperature range between 22°C and 122°C.

The products of the reaction were nitric oxide, carbon dioxide, methyl nitrite, nitromethane and a trace amount of trans-dimeric nitrosomethane. The addition of nitric oxide increased the rate of formation of nitromethane and decreased the rate of formation of methyl nitrite. There were no measurable surface effects due to the addition of glass wool or glass beads to the reactor.

Reactants and products were analyzed by gas chromatography. A mechanism was proposed incorporating the principal features of the reaction.

The Design and Synthesis of Transition Metal Complexes Supported by Non-innocent Ligand Scaffolds for Small Molecule Activation

This dissertation focuses on the incorporation of non-innocent or multifunctional moieties into different ligand scaffolds to support one or multiple metal centers in close proximity. Chapter 2 focuses on the initial efforts to synthesize hetero- or homometallic tri- or dinuclear metal carbonyl complexes supported by para-terphenyl diphosphine ligands. A series of [M₂M’(CO)₄]-type clusters (M = Ni, Pd; M’ = Fe, Co) could be accessed and used to relate the metal composition to the properties of the complexes. During these studies it was also found that non-innocent behavior was observed in dinuclear Fe complexes that result from changes in oxidation state of the cluster. These studies led to efforts to rationally incorporate central arene moieties capable managing both protons and electrons during small molecule activation.

Chapter 3 discusses the synthesis of metal complexes supported by a novel para-terphenyl diphosphine ligand containing a non-innocent 1,4-hydroquinone moiety as the central arene. A Pd⁰-hydroquinone complex was found to mediate the activation of a variety of small molecules to form the corresponding Pd⁰-quinone complexes in a formal two proton ⁄ two electron transformation. Mechanistic investigations of dioxygen activation revealed a metal-first activation process followed by subsequent proton and electron transfer from the ligand. These studies revealed the capacity of the central arene substituent to serve as a reservoir for a formal equivalent of dihydrogen, although the stability of the M-quinone compounds prevented access to the PdII-quinone oxidation state, thus hindering of small molecule transformations requiring more than two electrons per equivalent of metal complex.

Chapter 4 discusses the synthesis of metal complexes supported by a ligand containing a 3,5-substituted pyridine moiety as the linker separating the phenylene phosphine donors. Nickel and palladium complexes supported by this ligand were found to tolerate a wide variety of pyridine nitrogen-coordinated electrophiles which were found to alter central pyridine electronics, and therefore metal-pyridine π-system interactions, substantially. Furthermore, nickel complexes supported by this ligand were found to activate H-B and H-Si bonds and formally hydroborate and hydrosilylate the central pyridine ring. These systems highlight the potential use of pyridine π-system-coordinated metal complexes to reversibly store reducing equivalents within the ligand framework in a manner akin to the previously discussed 1,4-hydroquinone diphosphine ligand scaffold.

Chapter 5 departs from the phosphine-based chemistry and instead focuses on the incorporation of hydrogen bonding networks into the secondary coordination sphere of [Fe₄(μ₄-O)]-type clusters supported by various pyrazolate ligands. The aim of this project is to stabilize reactive oxygenic species, such as oxos, to study their spectroscopy and reactivity in the context of complicated multimetallic clusters. Herein is reported this synthesis and electrochemical and Mössbauer characterization of a series of chloride clusters have been synthesized using parent pyrazolate and a 3-aminophenyl substituted pyrazolate ligand. Efforts to rationally access hydroxo and oxo clusters from these chloride precursors represents ongoing work that will continue in the group.

Appendix A discusses attempts to access [Fe₃Ni]-type clusters as models of the enzymatic active site of [NiFe] carbon monoxide dehydrogenase. Efforts to construct tetranuclear clusters with an interstitial sulfide proved unsuccessful, although a (μ₃-S) ligand could be installed through non-oxidative routes into triiron clusters. While [Fe₃Ni(μ₄-O)]-type clusters could be assembled, accessing an open heterobimetallic edge site proved challenging, thus prohibiting efforts to study chemical transformations, such as hydroxide attack onto carbon monoxide or carbon dioxide coordination, relevant to the native enzyme. Appendix B discusses the attempts to synthesize models of the full H-cluster of [FeFe]-hydrogenase using a bioinorganic approach. A synthetic peptide containing three cysteine donors was successfully synthesized and found to chelate a preformed synthetic [Fe₄S₄] cluster. However, efforts to incorporate the diiron subsite model complex proved challenging as the planned thioester exchange reaction was found to non-selectively acetylate the peptide backbone, thus preventing the construction of the full six-iron cluster.