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.

Structure-function studies of serine hydrolases: synthesis of a gene for ∝-lytic protease and the purification and characterization of a mutant β-lactamase

The author has constructed a synthetic gene for ∝-lytic protease. Since the DNA sequence of the protein is not known, the gene was designed by using the reverse translation of ∝-lytic protease's amino acid sequence. Unique restriction sites are carefully sought in the degenerate DNA sequence to aid in future mutagenesis studies. The unique restriction sites are designed approximately 50 base pairs apart and their appropriate codons used in the DNA sequence. The codons used to construct the DNA sequence of ∝-lytic protease are preferred codons in E-coli or used in the production of β-lactamase. Codon usage is also distributed evenly to ensure that one particular codon is not heavily used. The gene is essentially constructed from the outside in. The gene is built in a stepwise fashion using plasmids as the vehicles for the ∝-lytic oligomers. The use of plasmids allows the replication and isolation of large quantities of the intermediates during gene synthesis. The ∝-lytic DNA is a double-stranded oligomer that has sufficient overhang and sticky ends to anneal correctly in the vector. After six steps of incorporating ∝-lytic DNA, the gene is completed and sequenced to ensure that the correct DNA sequence is present and that no mutations occurred in the structural gene.

β-lactamase is the other serine hydrolase studied in this thesis. The author used the class A RTEM-1 β- lactamase encoded on the plasmid pBR322 to investigate the roll of the conserved threonine residue at position 71. Cassette mutagenesis was previously used to generate all possible amino acid substitutions at position 71. The work presented here describes the purification and kinetic characterization of a T71H mutant previously constructed by S. Schultz. The mutated gene was transferred into plasmid pJN for expression and induced with IPTG. The enzyme is purified by column chromatography and FPLC to homogeneity. Kinetic studies reveal that the mutant has lower k_(cat) values on benzylpenicillin, cephalothin and 6-aminopenicillanic acid but no changes in k_m except for cephalothin which is approximately 4 times higher. The mutant did not change siginificantly in its pH profile compared to the wild-type enzyme. Also, the mutant is more sensitive to thermal denaturation as compared to the wild-type enzyme. However, experimental evidence indicates that the probable generation of a positive charge at position 71 thermally stabilized the mutant.

Synthesis, structure, and photophysics of polypyridophenazine transition-metal complexes

The condensation of phenanthroline-5,6-dione (phendione) with polyamines is a versatile synthetic route to a wide variety of chelating ligands. Condensation with 2,3- napthalene diamine gives benzo[i]dipyrido[3,2-a:2',3'-c]phenazine (bdppz) a ligand containing weakly-coupled orbitals of benzophenazine (bpz) and 2,2' -bipyridinde(bpy) character. The bpy character gives Re and Ru complexes excited-state redox properties; intramolecular electron transfer (ET) takes place to the bpz portion of the ligand. The charge-separated state so produced has an extraordinarily-long 50 µs lifetime. The slow rate of charge recombination arises from a combination of extremely weak coupling between the metal center and the bpz acceptor orbital and Marcus "inverted region" behavior. Molecular orbital calculations show that only 3% the electron density in the lowest unoccupied molecular orbital lies on the bpy atoms of bdppz, effectively trapping the transferred electron on the bpz portion. The rate of charge recombination decreases with increasing driving force, showing that these rates lie in the inverted region. Comparison of forward and back ET rates shows that donor-acceptor coupling is four orders of magnitude greater for photoinduced electron transfer than it is for thermal charge recombination.

Condensation of phendione with itself or tetramines gives a series of binucleating tetrapyridophenazine ligands of incrementally-varying coordination-site separation. When a photoredox-active metal center is attached, excited-state energy and electron transfer to an acceptor metal center at the other coordination site can be studied as a function of distance. A variety of monometallic and homo- and heterodimetallic tetrapyridophenazine complexes has been synthesized. Electro- and magnetochemistry show that no ground-state interaction exists between the metals in bimetallic complexes. Excited-state energy and electron transfer, however, takes place at rates which are invariant with increasing donor-acceptor separation, indicating that a very efficient coupling mechanism is at work. Theory and experiment have suggested that such behavior might exist in extended π-systems like those presented by these ligands.

Condensation of three equivalents of 4,5-dimethyl-1,2-phenylenediamine with hexaketocyclohexane gives the trinucleating ligand hexaazahexamethyltrinapthalene (hhtn). Attaching two photredox-active metal centers and a third catalytic center to hhtn provides means by which multielectron photocatalyzed reactions might be carried out. The coordination properties of hhtn have been examined; X-ray crystallographic structure determination shows that the ligand's constricted coordination pocket leads to distorted geometries in its mono- and dimetallic derivatives.

Thin metastructures with engineered thermal expansion

The geometry and constituent materials of metastructures can be used to engineer the thermal expansion coefficient. In this thesis, we design, fabricate, and test thin thermally stable metastructures consisting of bi-metallic unit cells and show how the coefficient of thermal expansion (CTE) of these metastructures can be finely and coarsely tuned by varying the CTE of the constituent materials and the unit cell geometry. Planar and three-dimensional finite element method modeling is used to drive the design and inform experiments, and predict the response of these metastructures. We demonstrate computationally the significance of out-of-plane effects in the metastructure response. We develop an experimental setup using digital image correlation and an infrared camera to experimentally measure full displacement and temperature fields during testing and accurately measure the metastructures’ CTE. We experimentally demonstrate high aspect ratio metastructures of Ti/Al and Kovar/Al which exhibit near-zero and negative CTE, respectively. We demonstrate robust fabrication procedures for thermally stable samples with high aspect ratios in thin foil and thin film scales. We investigate the lattice structure and mechanical properties of thin films comprising a near-zero CTE metastructure. The mechanics developed in this work can be used to engineer metastructures of arbitrary CTE and can be extended to three dimensions.

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

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

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

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

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

Experimental and theoretical developments in extended x-ray absorption fine structure (EXAFS) spectroscopy

To obtain accurate information from a structural tool it is necessary to have an understanding of the physical principles which govern the interaction between the probe and the sample under investigation. In this thesis a detailed study of the physical basis for Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy is presented. A single scattering formalism of EXAFS is introduced which allows a rigorous treatment of the central atom potential. A final state interaction formalism of EXAFS is also discussed. Multiple scattering processes are shown to be significant for systems of certain geometries. The standard single scattering EXAFS analysis produces erroneous results if the data contain a large multiple scattering contribution. The effect of thermal vibrations on such multiple scattering paths is also discussed. From symmetry considerations it is shown that only certain normal modes contribute to the Debye-Waller factor for a particular scattering path. Furthermore, changes in the scattering angles induced by thermal vibrations produces additional EXAFS components called modification factors. These factors are shown to be small for most systems.

A study of the physical basis for the determination of structural information from EXAFS data is also presented. An objective method of determining the background absorption and the threshold energy is discussed and involves Gaussian functions. In addition, a scheme to determine the nature of the scattering atom in EXAFS experiments is introduced. This scheme is based on the fact that the phase intercept is a measure of the type of scattering atom. A method to determine bond distances is also discussed and does not require the use of model compounds or calculated phase shifts. The physical basis for this method is the absence of a linear term in the scattering phases. Therefore, it is possible to separate these phases from the linear term containing the distance information in the total phase.

Studies on the role of histones in the structure and function of chromatin

Studies on the dissociation of histones from chromatin by increasing concentrations of sodium deoxycholate (DOC) have shown that histrone II is removed at lowest concentrations of DOC, while slightly higher concentrations remove histones III and IV. Still higher concentrations remove histone I.

The complete separation of chromatin and ¹⁴C-DOC by sucrose sedimentation indicated that the binding of DOC to chromatin is readily and completely reversible.

The dissociation of histones from chromatin by increasing concentrations of related cholanic acids and some of their conjugated derivatives were studied. The results suggested that the driving force for the interaction between the cholanic acid anion and histones is the lowering of the activity coefficient of the cholanic acid anion which occurs when it is partially removed from solution by interaction with hydrophobic regions of the positively charged histones.

The role of histones in the structure of chromatin has been studied by comparing the effects of selective removal of histones from chromatin by increasing concentrations of DOC with those caused by NaCl (removes histone I at lowest concentrations, while higher concentrations remove histones II, III, and IV). Properties studied included thermal denaturation, sedimentation velocity, flow dichroism, relaxation times of molecules oriented in a flow field, and the irreversible disruption of a 130 S, cross-linked component of sheared chromatin. The data indicated that none of the structural or chemical parameters with which these properties are correlated show a dependence on the presence of one particular histone fraction.

The template activity (ability to prime a 0.2 M KC1 DNA-dependent RNA synthesis system catalyzed by E. coli RNA polymerase) increases from that of native chromatin (approximately 25 per cent of that pure DNA) to that of pure DNA in a fashion which shows a nearly linear relationship to the amount of histone coverage of the template. The precipitability of partially dehistonized chromatin samples in 0.15 M NaCl shows a large dependence on the presence of histone I.

I. The crystal structure of a new dimer of triphenylfluorocyclobutadiene. II. A low temperature refinement of the cyanuric triazide structure

I. THE CRYSTAL STRUCTURE OF A NEW DIMER OF TRIPHENYLFLUOROCYCLOBUTADIENE

The crystal structure of thermal isomer of the “head-to-head” dimer of triphenylfluorocyclobutadiene was determined by the direct method. The Σ₂ relationship involving the low angle reflections with the largest E’s were found and solved for the signs by the symbolic method of Zachariasen. The structure was seen in the electron density map and the E-map, and was refined antisotropically by the method of least squares. The residual R was 0.065.

The structure is a gem-difluorohexaphenyldihydropentalene. All of the phenyl groups are planar as it is the cyclopentadiene ring of the dihydropentalene skeleton. Overcrowding at the position of the flourines causes some deviations from the normal bond angles in the cyclopentene ring.

The list of observed and calculated structure factors on pages 32-34 will not be legible on the microfilm. Photographic copies may be obtained from the California Institute of Technology.

II. A LOW TEMPERATURE REFINEMENT OF THE CYANURIC TRIAZIDE STRUCTURE

The structure of cyanuric triazide was refined anisotropically by the method of least squares. Three-dimensional intensity data, which has been collected photographically with MoK_α radiation at -110˚C, were used in the refinement. The residual R was reduced to 0.081.

The structure is completely planar, and there is no significant bond alternation in the cyanuric ring. The packing of the molecules causes the azide groups to deviate from linearity by 8 degrees.