Deviation from standard inflationary cosmology and the problems in ekpyrosis

There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $\langle a_{lm}a_{l'm'}^*\rangle$ of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Control of wettability of carbon nanotube array by reversible dry oxidation for superhydrophobic coating and supercapacitor applications

In this thesis, dry chemical modification methods involving UV/ozone, oxygen plasma, and vacuum annealing treatments are explored to precisely control the wettability of CNT arrays. By varying the exposure time of these treatments the surface concentration of oxygenated groups adsorbed on the CNT arrays can be controlled. CNT arrays with very low amount of oxygenated groups exhibit a superhydrophobic behavior. In addition to their extremely high static contact angle, they cannot be dispersed in DI water and their impedance in aqueous electrolytes is extremely high. These arrays have an extreme water repellency capability such that a water droplet will bounce off of their surface upon impact and a thin film of air is formed on their surface as they are immersed in a deep pool of water. In contrast, CNT arrays with very high surface concentration of oxygenated functional groups exhibit an extreme hydrophilic behavior. In addition to their extremely low static contact angle, they can be dispersed easily in DI water and their impedance in aqueous electrolytes is tremendously low. Since the bulk structure of the CNT arrays are preserved during the UV/ozone, oxygen plasma, and vacuum annealing treatments, all CNT arrays can be repeatedly switched between superhydrophilic and superhydrophobic, as long as their O/C ratio is kept below 18%.

The effect of oxidation using UV/ozone and oxygen plasma treatments is highly reversible as long as the O/C ratio of the CNT arrays is kept below 18%. At O/C ratios higher than 18%, the effect of oxidation is no longer reversible. This irreversible oxidation is caused by irreversible changes to the CNT atomic structure during the oxidation process. During the oxidation process, CNT arrays undergo three different processes. For CNT arrays with O/C ratios lower than 40%, the oxidation process results in the functionalization of CNT outer walls by oxygenated groups. Although this functionalization process introduces defects, vacancies and micropores opening, the graphitic structure of the CNT is still largely intact. For CNT arrays with O/C ratios between 40% and 45%, the oxidation process results in the etching of CNT outer walls. This etching process introduces large scale defects and holes that can be obviously seen under TEM at high magnification. Most of these holes are found to be several layers deep and, in some cases, a large portion of the CNT side walls are cut open. For CNT arrays with O/C ratios higher than 45%, the oxidation process results in the exfoliation of the CNT walls and amorphization of the remaining CNT structure. This amorphization process can be implied from the disappearance of C-C sp2 peak in the XPS spectra associated with the pi-bond network.

The impact behavior of water droplet impinging on superhydrophobic CNT arrays in a low viscosity regime is investigated for the first time. Here, the experimental data are presented in the form of several important impact behavior characteristics including critical Weber number, volume ratio, restitution coefficient, and maximum spreading diameter. As observed experimentally, three different impact regimes are identified while another impact regime is proposed. These regimes are partitioned by three critical Weber numbers, two of which are experimentally observed. The volume ratio between the primary and the secondary droplets is found to decrease with the increase of Weber number in all impact regimes other than the first one. In the first impact regime, this is found to be independent of Weber number since the droplet remains intact during and subsequent to the impingement. Experimental data show that the coefficient of restitution decreases with the increase of Weber number in all impact regimes. The rate of decrease of the coefficient of restitution in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Experimental data also show that the maximum spreading factor increases with the increase of Weber number in all impact regimes. The rate of increase of the maximum spreading factor in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Phenomenological approximations and interpretations of the experimental data, as well as brief comparisons to the previously proposed scaling laws, are shown here.

Dry oxidation methods are used for the first time to characterize the influence of oxidation on the capacitive behavior of CNT array EDLCs. The capacitive behavior of CNT array EDLCs can be tailored by varying their oxygen content, represented by their O/C ratio. The specific capacitance of these CNT arrays increases with the increase of their oxygen content in both KOH and Et4NBF4/PC electrolytes. As a result, their gravimetric energy density increases with the increase of their oxygen content. However, their gravimetric power density decreases with the increase of their oxygen content. The optimally oxidized CNT arrays are able to withstand more than 35,000 charge/discharge cycles in Et4NBF4/PC at a current density of 5 A/g while only losing 10% of their original capacitance.

Sunyaev-Zel'dovich observations using large-format millimeter arrays

Galaxy clusters are the largest gravitationally bound objects in the observable universe, and they are formed from the largest perturbations of the primordial matter power spectrum. During initial cluster collapse, matter is accelerated to supersonic velocities, and the baryonic component is heated as it passes through accretion shocks. This process stabilizes when the pressure of the bound matter prevents further gravitational collapse. Galaxy clusters are useful cosmological probes, because their formation progressively freezes out at the epoch when dark energy begins to dominate the expansion and energy density of the universe. A diverse set of observables, from radio through X-ray wavelengths, are sourced from galaxy clusters, and this is useful for self-calibration. The distributions of these observables trace a cluster's dark matter halo, which represents more than 80% of the cluster's gravitational potential. One such observable is the Sunyaev-Zel'dovich effect (SZE), which results when the ionized intercluster medium blueshifts the cosmic microwave background via Compton scattering. Great technical advances in the last several decades have made regular observation of the SZE possible. Resolved SZE science, such as is explored in this analysis, has benefitted from the construction of large-format camera arrays consisting of highly sensitive millimeter-wave detectors, such as Bolocam. Bolocam is a submillimeter camera, sensitive to 140 GHz and 268 GHz radiation, located at one of the best observing sites in the world: the Caltech Submillimeter Observatory on Mauna Kea in Hawaii. Bolocam fielded 144 of the original spider web NTD bolometers used in an entire generation of ground-based, balloon-borne, and satellite-borne millimeter wave instrumention. Over approximately six years, our group at Caltech has developed a mature galaxy cluster observational program with Bolocam. This thesis describes the construction of the instrument's full cluster catalog: BOXSZ. Using this catalog, I have scaled the Bolocam SZE measurements with X-ray mass approximations in an effort to characterize the SZE signal as a viable mass probe for cosmology. This work has confirmed the SZE to be a low-scatter tracer of cluster mass. The analysis has also revealed how sensitive the SZE-mass scaling is to small biases in the adopted mass approximation. Future Bolocam analysis efforts are set on resolving these discrepancies by approximating cluster mass jointly with different observational probes.

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.

Magnetohydrodynamic turbulence

We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows.

1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves.

2) MHD turbulence is anisotropic with energy cascading more rapidly along k_⊥ than along k_∥, where k_⊥ and k_∥ refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_⊥ such that excited modes are confined inside a cone bounded by k_∥ ∝ k^γ_⊥ where γ less than 1. The opening angle of the cone, θ(k_⊥) ∝ k^-(1-γ)_⊥, defines the scale dependent anisotropy.

3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ² (k_⊥)≪1.

4) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/θ(k_⊥) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations.

6) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k by δ(t) correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance.

7) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up.

8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth by Goldreich and Sridhar (1995, 1997). Results from our simulations are also consistent with the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D power law spectra, E(k_⊥) ∝ k^-∝_⊥, determined from our simulations exhibit ∝ ≈ 3/2, whereas the GS model predicts ∝ = 5/3.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Nanostructured tungsten trioxide photoanodes for solar energy conversion

Nanostructured tungsten trioxide (WO₃) photoelectrodes are potential candidates for the anodic portion of an integrated solar water-splitting device that generates hydrogen fuel and oxygen from water. These nanostructured materials can potentially offer improved performance in photooxidation reactions compared to unstructured materials because of enhancements in light scattering, increases in surface area, and their decoupling of the directions of light absorption and carrier collection. To evaluate the presence of these effects and their contributions toward energy conversion efficiency, a variety of nanostructured WO₃ photoanodes were synthesized by electrodeposition within nanoporous templates and by anodization of tungsten foils. A robust fabrication process was developed for the creation of oriented WO₃ nanorod arrays, which allows for control nanorod diameter and length. Films of nanostructured WO₃ platelets were grown via anodization, the morphology of the films was controlled by the anodization conditions, and the current-voltage performance and spectral response properties of these films were studied. The observed photocurrents were consistent with the apparent morphologies of the nanostructured arrays. Measurements of electrochemically active surface area and other physical characteristics were correlated with observed differences in absorbance, external quantum yield, and photocurrent density for the anodized arrays. The capability to quantify these characteristics and relate them to photoanode performance metrics can allow for selection of appropriate structural parameters when designing photoanodes for solar energy conversion.

I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering

This dissertation consists of two parts. The first part presents an explicit procedure for applying multi-Regge theory to production processes. As an illustrative example, the case of three body final states is developed in detail, both with respect to kinematics and multi-Regge dynamics. Next, the experimental consistency of the multi-Regge hypothesis is tested in a specific high energy reaction; the hypothesis is shown to provide a good qualitative fit to the data. In addition, the results demonstrate a severe suppression of double Pomeranchon exchange, and show the coupling of two "Reggeons" to an external particle to be strongly damped as the particle's mass increases. Finally, with the use of two body Regge parameters, order of magnitude estimates of the multi-Regge cross section for various reactions are given.

The second part presents a diffraction model for high energy proton-proton scattering. This model developed by Chou and Yang assumes high energy elastic scattering results from absorption of the incident wave into the many available inelastic channels, with the absorption proportional to the amount of interpenetrating hadronic matter. The assumption that the hadronic matter distribution is proportional to the charge distribution relates the scattering amplitude for pp scattering to the proton form factor. The Chou-Yang model with the empirical proton form factor as input is then applied to calculate a high energy, fixed momentum transfer limit for the scattering cross section, This limiting cross section exhibits the same "dip" or "break" structure indicated in present experiments, but falls significantly below them in magnitude. Finally, possible spin dependence is introduced through a weak spin-orbit type term which gives rather good agreement with pp polarization data.

Density functional theory embedding for correlated wavefunctions

Methods that exploit the intrinsic locality of molecular interactions show significant promise in making tractable the electronic structure calculation of large-scale systems. In particular, embedded density functional theory (e-DFT) offers a formally exact approach to electronic structure calculations in which the interactions between subsystems are evaluated in terms of their electronic density. In the following dissertation, methodological advances of embedded density functional theory are described, numerically tested, and applied to real chemical systems.

First, we describe an e-DFT protocol in which the non-additive kinetic energy component of the embedding potential is treated exactly. Then, we present a general implementation of the exact calculation of the non-additive kinetic potential (NAKP) and apply it to molecular systems. We demonstrate that the implementation using the exact NAKP is in excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures.

Next, we introduce density-embedding techniques to enable the accurate and stable calculation of correlated wavefunction (CW) in complex environments. Embedding potentials calculated using e-DFT introduce the effect of the environment on a subsystem for CW calculations (WFT-in-DFT). We demonstrate that WFT-in-DFT calculations are in good agreement with CW calculations performed on the full complex.

We significantly improve the numerics of the algorithm by enforcing orthogonality between subsystems by introduction of a projection operator. Utilizing the projection-based embedding scheme, we rigorously analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using CWs, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We develop an algorithm which corrects this term and demonstrate the accuracy of this corrected embedding scheme.

Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

A model for energy and morphology of crystalline grain boundaries with arbitrary geometric character

It has been well-established that interfaces in crystalline materials are key players in the mechanics of a variety of mesoscopic processes such as solidification, recrystallization, grain boundary migration, and severe plastic deformation. In particular, interfaces with complex morphologies have been observed to play a crucial role in many micromechanical phenomena such as grain boundary migration, stability, and twinning. Interfaces are a unique type of material defect in that they demonstrate a breadth of behavior and characteristics eluding simplified descriptions. Indeed, modeling the complex and diverse behavior of interfaces is still an active area of research, and to the author's knowledge there are as yet no predictive models for the energy and morphology of interfaces with arbitrary character. The aim of this thesis is to develop a novel model for interface energy and morphology that i) provides accurate results (especially regarding "energy cusp" locations) for interfaces with arbitrary character, ii) depends on a small set of material parameters, and iii) is fast enough to incorporate into large scale simulations.

In the first half of the work, a model for planar, immiscible grain boundary is formulated. By building on the assumption that anisotropic grain boundary energetics are dominated by geometry and crystallography, a construction on lattice density functions (referred to as "covariance") is introduced that provides a geometric measure of the order of an interface. Covariance forms the basis for a fully general model of the energy of a planar interface, and it is demonstrated by comparison with a wide selection of molecular dynamics energy data for FCC and BCC tilt and twist boundaries that the model accurately reproduces the energy landscape using only three material parameters. It is observed that the planar constraint on the model is, in some cases, over-restrictive; this motivates an extension of the model.

In the second half of the work, the theory of faceting in interfaces is developed and applied to the planar interface model for grain boundaries. Building on previous work in mathematics and materials science, an algorithm is formulated that returns the minimal possible energy attainable by relaxation and the corresponding relaxed morphology for a given planar energy model. It is shown that the relaxation significantly improves the energy results of the planar covariance model for FCC and BCC tilt and twist boundaries. The ability of the model to accurately predict faceting patterns is demonstrated by comparison to molecular dynamics energy data and experimental morphological observation for asymmetric tilt grain boundaries. It is also demonstrated that by varying the temperature in the planar covariance model, it is possible to reproduce a priori the experimentally observed effects of temperature on facet formation.

Finally, the range and scope of the covariance and relaxation models, having been demonstrated by means of extensive MD and experimental comparison, future applications and implementations of the model are explored.

Nuclear reactions leading to energy levels of Ar37 and K37

In view of recent interest in the Cl³⁷ (ʋ solar’^e-)Ar³⁷ reaction cross section, information on some aspects of mass 37 nuclei has been obtained using the K³⁹ (d, ∝) Ar³⁷ and Cl³⁵ (He³, p) Ar³⁷ reactions. Ar³⁷ levels have been found at 0, 1.41, 1.62, 2.22, 2.50, 2.80, 3.17, 3.27, 3.53, 3.61, 3.71, (3.75), (3.90), 3.94, 4.02, (4.21), 4.28, 4.32, 4.40, 4.45, 4.58, 4.63, 4.74, 4.89, 4.98, 5.05, 5.10, 5.13, 5.21, 5.35, 5.41, 5.44, 5.54, 5.58, 5.67, 5.77, and 5.85 MeV (the underlined values correspond to previously tabulated levels). The nuclear temperature calculated from the Ar³⁷ level density is 1.4 MeV. Angular distributions of the lowest six levels with the K³⁹ (d, ∝) Ar³⁷ reaction at E_d = 10 MeV indicate a dominant direct interaction mechanism and the inapplicability of the 2I + 1 rule of the statistical model. Comparison of the spectra obtained with the K³⁹ (d, ∝) Ar³⁷ and Cl³⁵ (He³, p) Ar³⁷ reactions leads to the suggestion that the 5.13-MeV level is the T = 3/2 Cl³⁷ ground state analog. The ground state Q-value of the Ca⁴⁰ (p, ∝) K³⁷ reaction has been measured: -5179 ± 9 keV. This value implies a K³⁷ mass excess of -24804 ± 10 keV. Description of a NMR magnetometer and a sixteen-detector array used in conjunction with a 61-cm double-focusing magnetic spectrometer are included in appendices.

Energy loss of light ions channeling in silicon

Experimental measurements of rate of energy loss were made for protons of energy .5 to 1.6 MeV channeling through 1 μm thick silicon targets along the <110>, <111>, and <211> axial directions, and the {100}, {110}, {111}, and {211} planar directions. A .05% resolution automatically controlled magnetic spectrometer was used. The data are presented graphically along with an extensive summary of data in the literature. The data taken cover a wider range of channels than has previously been examined, and are in agreement with the data of F. Eisen, et al., Radd. Eff. 13, 93 (1972).

The theory in the literature for channeling energy loss due to interaction with local electrons, core electrons, and distant valence electrons of the crystal atoms is summarized. Straggling is analyzed, and a computer program which calculates energy loss and straggling using this theory and the Moliere approximation to the Thomas Fermi potential, V_TF, and the detailed silicon crystal structure is described. Values for the local electron density Z_loc in each of the channels listed above are extracted from the data by graphical matching of the experimental and computer results.

Zeroth and second order contributions to Z_loc as a function of distance from the center of the channel were computed from ∇²V_TF = 4πρ for various channels in silicon. For data taken in this work and data of F. Eisen, et al., Rad. Eff. 13, 93 (1972), the calculated zeroth order contribution to Z_loc lies between the experimentally extracted Z_loc values obtained by using the peak and the leading edge of the transmission spectra, suggesting that the observed straggling is due both to statistical fluctuations and to path variation.