Chemical and mineralogical characterization of micro-inclusions in diamonds

Secondary-ion mass spectrometry (SIMS), electron probe analysis (EPMA), analytical scanning electron microscopy (SEM) and infrared (IR) spectroscopy were used to determine the chemical composition and the mineralogy of sub-micrometer inclusions in cubic diamonds and in overgrowths (coats) on octahedral diamonds from Zaire, Botswana, and some unknown localities.

The inclusions are sub-micrometer in size. The typical diameter encountered during transmission electron microscope (TEM) examination was 0.1-0.5 µm. The micro-inclusions are sub-rounded and their shape is crystallographically controlled by the diamond. Normally they are not associated with cracks or dislocations and appear to be well isolated within the diamond matrix. The number density of inclusions is highly variable on any scale and may reach 10^(11) inclusions/cm^3 in the most densely populated zones. The total concentration of metal oxides in the diamonds varies between 20 and 1270 ppm (by weight).

SIMS analysis yields the average composition of about 100 inclusions contained in the sputtered volume. Comparison of analyses of different volumes of an individual diamond show roughly uniform composition (typically ±10% relative). The variation among the average compositions of different diamonds is somewhat greater (typically ±30%). Nevertheless, all diamonds exhibit similar characteristics, being rich in water, carbonate, SiO_2, and K_2O, and depleted in MgO. The composition of micro-inclusions in most diamonds vary within the following ranges: SiO_2, 30-53%; K_2O, 12-30%; CaO, 8-19%; FeO, 6-11%; Al_2O_3, 3-6%; MgO, 2-6%; TiO_2, 2-4%; Na_2O, 1-5%; P_2O_5, 1-4%; and Cl, 1-3%. In addition, BaO, 1-4%; SrO, 0.7-1.5%; La_2O_3, 0.1-0.3%; Ce_2O_3, 0.3-0.5%; smaller amounts of other rare-earth elements (REE), as well as Mn, Th, and U were also detected by instrumental neutron activation analysis (INAA). Mg/(Fe+Mg), 0.40-0.62 is low compared with other mantle derived phases; K/ AI ratios of 2-7 are very high, and the chondrite-normalized Ce/Eu ratios of 10-21 are also high, indicating extremely fractionated REE patterns.

SEM analyses indicate that individual inclusions within a single diamond are roughly of similar composition. The average composition of individual inclusions as measured with the SEM is similar to that measured by SIMS. Compositional variations revealed by the SEM are larger than those detected by SIMS and indicate a small variability in the composition of individual inclusions. No compositions of individual inclusions were determined that might correspond to mono-mineralic inclusions.

IR spectra of inclusion- bearing zones exhibit characteristic absorption due to: (1) pure diamonds, (2) nitrogen and hydrogen in the diamond matrix; and (3) mineral phases in the micro-inclusions. Nitrogen concentrations of 500-1100 ppm, typical of the micro-inclusion-bearing zones, are higher than the average nitrogen content of diamonds. Only type IaA centers were detected by IR. A yellow coloration may indicate small concentration of type IB centers.

The absorption due to the micro-inclusions in all diamonds produces similar spectra and indicates the presence of hydrated sheet silicates (most likely, Fe-rich clay minerals), carbonates (most likely calcite), and apatite. Small quantities of molecular CO_2 are also present in most diamonds. Water is probably associated with the silicates but the possibility of its presence as a fluid phase cannot be excluded. Characteristic lines of olivine, pyroxene and garnet were not detected and these phases cannot be significant components of the inclusions. Preliminary quantification of the IR data suggests that water and carbonate account for, on average, 20-40 wt% of the micro-inclusions.

The composition and mineralogy of the micro-inclusions are completely different from those of the more common, larger inclusions of the peridotitic or eclogitic assemblages. Their bulk composition resembles that of potassic magmas, such as kimberlites and lamproites, but is enriched in H_2O, CO_3, K_2O, and incompatible elements, and depleted in MgO.

It is suggested that the composition of the micro-inclusions represents a volatile-rich fluid or a melt trapped by the diamond during its growth. The high content of K, Na, P, and incompatible elements suggests that the trapped material found in the micro-inclusions may represent an effective metasomatizing agent. It may also be possible that fluids of similar composition are responsible for the extreme enrichment of incompatible elements documented in garnet and pyroxene inclusions in diamonds.

The origin of the fluid trapped in the micro-inclusions is still uncertain. It may have been formed by incipient melting of a highly metasomatized mantle rocks. More likely, it is the result of fractional crystallization of a potassic parental magma at depth. In either case, the micro-inclusions document the presence of highly potassic fluids or melts at depths corresponding to the diamond stability field in the upper mantle. The phases presently identified in the inclusions are believed to be the result of closed system reactions at lower pressures.

Infared observations of H II regions

Spectral data are presented, giving intensities of the Brackett ɤ (B₇) line at six positions in M 42 and of the Brackett ten through fourteen (B₁₀-B₁₄) lines plus the He 4d³D-3p³p⁰ line at three positions in M 42. Observations of the Brackett ɤ line are also given for the planetary nebulae NGC 7027 and IC 418. Brackett gamma is shown to exhibit an anomalous satellite line in NGC 7027. Broadband data are presented, giving intensities at effective wavelengths of 1.25 μ, 1.65 μ, 2.2 μ, 3.5 μ and 4.8 μ for three positions in M 42.

Comparisons with visual and radio data as well as 12 micron and 20 micron data are used to derive reddening, electron temperatures, and electron densities for M 42 and the two planetaries, as well as a helium abundance for M 42. A representative electron temperature of 8400°K ± 1000°K, an electron density of 1.5 ±0.1 x 10³ cm^-3 and a He/H number density ratio of 0.10 +0.10/-0.05 are derived for the central region of M 42. The electron temperature is found to increase slightly with distance from the Trapezium.

M 42 is shown to emit in excess of the predicted recombination radiation throughout the entire infrared spectrum. The variations in the excess with wavelength and with position are analyzed to determine which of several physical processes may be operating. The longer wavelength infrared excess is shown to be dominated by dust emission, while the shorter wavelength infrared excess is caused by dust scattering. The dust is shown to be larger than the average interstellar particle. A new feature of the Orion red star ORS-1 is found in that it appears to have a reflection nebula around it.

Deep near-infrared spectroscopy of high-redshift galaxies: the physical growth of passive systems

The assembly history of massive galaxies is one of the most important aspects of galaxy formation and evolution. Although we have a broad idea of what physical processes govern the early phases of galaxy evolution, there are still many open questions. In this thesis I demonstrate the crucial role that spectroscopy can play in a physical understanding of galaxy evolution. I present deep near-infrared spectroscopy for a sample of high-redshift galaxies, from which I derive important physical properties and their evolution with cosmic time. I take advantage of the recent arrival of efficient near-infrared detectors to target the rest-frame optical spectra of z > 1 galaxies, from which many physical quantities can be derived. After illustrating the applications of near-infrared deep spectroscopy with a study of star-forming galaxies, I focus on the evolution of massive quiescent systems.

Most of this thesis is based on two samples collected at the W. M. Keck Observatory that represent a significant step forward in the spectroscopic study of z > 1 quiescent galaxies. All previous spectroscopic samples at this redshift were either limited to a few objects, or much shallower in terms of depth. Our first sample is composed of 56 quiescent galaxies at 1 < z < 1.6 collected using the upgraded red arm of the Low Resolution Imaging Spectrometer (LRIS). The second consists of 24 deep spectra of 1.5 < z < 2.5 quiescent objects observed with the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE). Together, these spectra span the critical epoch 1 < z < 2.5, where most of the red sequence is formed, and where the sizes of quiescent systems are observed to increase significantly.

We measure stellar velocity dispersions and dynamical masses for the largest number of z > 1 quiescent galaxies to date. By assuming that the velocity dispersion of a massive galaxy does not change throughout its lifetime, as suggested by theoretical studies, we match galaxies in the local universe with their high-redshift progenitors. This allows us to derive the physical growth in mass and size experienced by individual systems, which represents a substantial advance over photometric inferences based on the overall galaxy population. We find a significant physical growth among quiescent galaxies over 0 < z < 2.5 and, by comparing the slope of growth in the mass-size plane dlogR_e/dlogM_∗ with the results of numerical simulations, we can constrain the physical process responsible for the evolution. Our results show that the slope of growth becomes steeper at higher redshifts, yet is broadly consistent with minor mergers being the main process by which individual objects evolve in mass and size.

By fitting stellar population models to the observed spectroscopy and photometry we derive reliable ages and other stellar population properties. We show that the addition of the spectroscopic data helps break the degeneracy between age and dust extinction, and yields significantly more robust results compared to fitting models to the photometry alone. We detect a clear relation between size and age, where larger galaxies are younger. Therefore, over time the average size of the quiescent population will increase because of the contribution of large galaxies recently arrived to the red sequence. This effect, called progenitor bias, is different from the physical size growth discussed above, but represents another contribution to the observed difference between the typical sizes of low- and high-redshift quiescent galaxies. By reconstructing the evolution of the red sequence starting at z ∼ 1.25 and using our stellar population histories to infer the past behavior to z ∼ 2, we demonstrate that progenitor bias accounts for only half of the observed growth of the population. The remaining size evolution must be due to physical growth of individual systems, in agreement with our dynamical study.

Finally, we use the stellar population properties to explore the earliest periods which led to the formation of massive quiescent galaxies. We find tentative evidence for two channels of star formation quenching, which suggests the existence of two independent physical mechanisms. We also detect a mass downsizing, where more massive galaxies form at higher redshift, and then evolve passively. By analyzing in depth the star formation history of the brightest object at z > 2 in our sample, we are able to put constraints on the quenching timescale and on the properties of its progenitor.

A consistent picture emerges from our analyses: massive galaxies form at very early epochs, are quenched on short timescales, and then evolve passively. The evolution is passive in the sense that no new stars are formed, but significant mass and size growth is achieved by accreting smaller, gas-poor systems. At the same time the population of quiescent galaxies grows in number due to the quenching of larger star-forming galaxies. This picture is in agreement with other observational studies, such as measurements of the merger rate and analyses of galaxy evolution at fixed number density.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.

A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method

The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

I. The structure and properties of closed circular duplex DNA. II. Chemically interacting systems at equilibrium in a buoyant density gradient

I. The binding of the intercalating dye ethidium bromide to closed circular SV 40 DNA causes an unwinding of the duplex structure and a simultaneous and quantitatively equivalent unwinding of the superhelices. The buoyant densities and sedimentation velocities of both intact (I) and singly nicked (II) SV 40 DNAs were measured as a function of free dye concentration. The buoyant density data were used to determine the binding isotherms over a dye concentration range extending from 0 to 600 µg/m1 in 5.8 M CsCl. At high dye concentrations all of the binding sites in II, but not in I, are saturated. At free dye concentrations less than 5.4 µg/ml, I has a greater affinity for dye than II. At a critical amount of dye bound I and II have equal affinities, and at higher dye concentration I has a lower affinity than II. The number of superhelical turns, τ, present in I is calculated at each dye concentration using Fuller and Waring's (1964) estimate of the angle of duplex unwinding per intercalation. The results reveal that SV 40 DNA I contains about -13 superhelical turns in concentrated salt solutions.

The free energy of superhelix formation is calculated as a function of τ from a consideration of the effect of the superhelical turns upon the binding isotherm of ethidium bromide to SV 40 DNA I. The value of the free energy is about 100 kcal/mole DNA in the native molecule. The free energy estimates are used to calculate the pitch and radius of the superhelix as a function of the number of superhelical turns. The pitch and radius of the native I superhelix are 430 Å and 135 Å, respectively.

A buoyant density method for the isolation and detection of closed circular DNA is described. The method is based upon the reduced binding of the intercalating dye, ethidium bromide, by closed circular DNA. In an application of this method it is found that HeLa cells contain in addition to closed circular mitochondrial DNA of mean length 4.81 microns, a heterogeneous group of smaller DNA molecules which vary in size from 0.2 to 3.5 microns and a paucidisperse group of multiples of the mitochondrial length.

II. The general theory is presented for the sedimentation equilibrium of a macromolecule in a concentrated binary solvent in the presence of an additional reacting small molecule. Equations are derived for the calculation of the buoyant density of the complex and for the determination of the binding isotherm of the reagent to the macrospecies. The standard buoyant density, a thermodynamic function, is defined and the density gradients which characterize the four component system are derived. The theory is applied to the specific cases of the binding of ethidium bromide to SV 40 DNA and of the binding of mercury and silver to DNA.