The needle in the hundred square degree haystack: The hunt for binary neutron star mergers with LIGO and Palomar Transient Factory

The Advanced LIGO and Virgo experiments are poised to detect gravitational waves (GWs) directly for the first time this decade. The ultimate prize will be joint observation of a compact binary merger in both gravitational and electromagnetic channels. However, GW sky locations that are uncertain by hundreds of square degrees will pose a challenge. I describe a real-time detection pipeline and a rapid Bayesian parameter estimation code that will make it possible to search promptly for optical counterparts in Advanced LIGO. Having analyzed a comprehensive population of simulated GW sources, we describe the sky localization accuracy that the GW detector network will achieve as each detector comes online and progresses toward design sensitivity. Next, in preparation for the optical search with the intermediate Palomar Transient Factory (iPTF), we have developed a unique capability to detect optical afterglows of gamma-ray bursts (GRBs) detected by the Fermi Gamma-ray Burst Monitor (GBM). Its comparable error regions offer a close parallel to the Advanced LIGO problem, but Fermi's unique access to MeV-GeV photons and its near all-sky coverage may allow us to look at optical afterglows in a relatively unexplored part of the GRB parameter space. We present the discovery and broadband follow-up observations (X-ray, UV, optical, millimeter, and radio) of eight GBM-IPTF afterglows. Two of the bursts (GRB 130702A / iPTF13bxl and GRB 140606B / iPTF14bfu) are at low redshift (z=0.145 and z = 0.384, respectively), are sub-luminous with respect to "standard" cosmological bursts, and have spectroscopically confirmed broad-line type Ic supernovae. These two bursts are possibly consistent with mildly relativistic shocks breaking out from the progenitor envelopes rather than the standard mechanism of internal shocks within an ultra-relativistic jet. On a technical level, the GBM--IPTF effort is a prototype for locating and observing optical counterparts of GW events in Advanced LIGO with the Zwicky Transient Facility.

Superionic Noble Metal Chalcogenide Thermoelectrics

Measurements and modeling of Cu₂Se, Ag₂Se, and Cu₂S show that superionic conductors have great potential as thermoelectric materials. Cu₂Se and Ag₂Se are predicted to reach a zT of 1.2 at room temperature if their carrier concentrations can be reduced, and Cu-vacancy doped Cu₂S reaches a maximum zT of 1.7 at 1000 K. Te-doped Ag₂Se achieves a zT of 1.2 at 520 K, and could reach a zT of 1.7 if its carrier concentration could be reduced. However, superionic conductors tend to have high carrier concentrations due to the presence of metal defects. The carrier concentration has been found to be difficult to reduce by altering the defect concentration, therefore materials that are underdoped relative to the optimum carrier concentration are easier to optimize. The results of Te-doping of Ag₂Se show that reducing the carrier concentration is possible by reducing the maximum Fermi level in the material.

Two new methods for analyzing thermoelectric transport data were developed. The first involves scaling the temperature-dependent transport data according to the temperature dependences expected of a single parabolic band model and using all of the scaled data to perform a single parabolic band analysis, instead of being restricted to using one data point per sample at a fixed temperature. This allows for a more efficient use of the transport data. The second involves scaling only the Seebeck coefficient and electrical conductivity. This allows for an estimate of the quality factor (and therefore the maximum zT in the material) without using Hall effect data, which are not always available due to time and budget constraints and are difficult to obtain in high-resistivity materials. Methods for solving the coherent potential approximation effective medium equations were developed in conjunction with measurements of the resistivity tensor elements of composite materials. This allows the electrical conductivity and mobility of each phase in the composite to be determined from measurements of the bulk. This points out a new method for measuring the pure-phase electrical properties in impure materials, for measuring the electrical properties of unknown phases in composites, and for quantifying the effects of quantum interactions in composites.

I. Electronic states of heavily-doped molecular crystals--naphthalene. I. Theoretical. II. Experimental. II. Lowest singlet and triplet excited states of pyrazine

PART I

The energy spectrum of heavily-doped molecular crystals was treated in the Green’s function formulation. The mixed crystal Green’s function was obtained by averaging over all possible impurity distributions. The resulting Green’s function, which takes the form of an infinite perturbation expansion, was further approximated by a closed form suitable for numerical calculations. The density-of-states functions and optical spectra for binary mixtures of normal naphthalene and deuterated naphthalene were calculated using the pure crystal density-of-state functions. The results showed that when the trap depth is large, two separate energy bands persist, but when the trap depth is small only a single band exists. Furthermore, in the former case it was found that the intensities of the outer Davydov bands are enhanced whereas the inner bands are weakened. Comparisons with previous theoretical calculations and experimental results are also made.

PART II

The energy states and optical spectra of heavily-doped mixed crystals are investigated. Studies are made for the following binary systems: (1) naphthalene-h₈ and d₈, (2) naphthalene--h₈ and αd₄, and (3) naphthalene--h₈ and βd₁, corresponding to strong, medium and weak perturbations. In addition to ordinary absorption spectra at 4˚K, band-to-band transitions at both 4˚K and 77˚K are also analyzed with emphasis on their relations to cooperative excitation and overall density-of-states functions for mixed crystals. It is found that the theoretical calculations presented in a previous paper agree generally with experiments except for cluster states observed in system (1) at lower guest concentrations. These features are discussed semi-quantitatively. As to the intermolecular interaction parameters, it is found that experimental results compare favorably with calculations based on experimental density-of-states functions but not with those based on octopole interactions or charge-transfer interactions. Previous experimental results of Sheka and the theoretical model of Broude and Rashba are also compared with present investigations.

PART III

The phosphorescence, fluorescence and absorption spectra of pyrazine-h₄ and d₄ have been obtained at 4˚K in a benzene matrix. For comparison, those of the isotopically mixed crystal pyrazine-h₄ in d₄ were also taken. All these spectra show extremely sharp and well-resolved lines and reveal detailed vibronic structure.

The analysis of the weak fluorescence spectrum resolves the long-disputed question of whether one or two transitions are involved in the near-ultraviolet absorption of pyrazine. The “mirror-image relationship” between absorption and emission shows that the lowest singlet state is an allowed transition, properly designated as ¹B_3u ← ¹A_1g. The forbidden component ¹B_2g, predicted by both “exciton” and MO theories to be below the allowed component, must lie higher. Its exact location still remains uncertain.

The phosphorescence spectrum when compared with the excitation phosphorescence spectra, indicates that the lowest triplet state is also symmetry allowed, showing a strong 0-0 band and a “mirror-image relationship” between absorption and emission. In accordance with previous work, the triplet state is designated as ³B_3u.

The vibronic structure of the phosphorescence spectrum is very complicated. Previous work on the analysis of this spectrum all concluded that a long progression of v_6a exists. Under the high resolution attainable in our work, the supposed v_6a progression proves to have a composite triplet structure, starting from the second member of the progression. Not only is the v_9a hydrogen-bending mode present as shown by the appearance of the C-D bending mode in the d₄ spectrum, but a band of 1207 cm^-1 in the pyrazine in benzene system and 1231 cm^-1 in the mixed crystal system is also observed. This band is assigned as 2v_6b and of a_1g symmetry. Its anonymously strong intensity in the phosphorescence spectrum is interpreted as due to the Fermi resonance with the 2v_6a and v_9a band.

To help resolve the present controversy over the crystal phosphorescence spectrum of pyrazine, detailed vibrational analyses of the emission spectra were made. The fluorescence spectrum has essentially the same vibronic structure as the phosphorescence spectrum.

Photoelectrochemistry of GaAs and Si liquid junctions

A quantitative study has been performed on the stability of GaAs surfaces in a 0.10 M K₂Se-0.01 M K₂Se₂ aqueous solution. In this electrolyte, n-type GaAs electrodes displayed significant photocorrosion in competition with faradaic charge transfer to Se^2-. Chemisorption of group VIIIB metal ions onto the GaAs surfaces yielded improved current-voltage behavior of the GaAs photoanodes, and also resulted in a significant reduction in photocorrosion. This behavior implies that the chemisorbed metal ions act to increase the rate of hole transfer to the Se^2- species. Related experiments on n-GaAs, pGaAs, and Sn-doped In₂O₃ electrodes in Te^2-/- aqueous solutions have also been performed.

The majority carrier (electrons) transfer rate constant at a highly doped n⁺-Si/Co(Cp)₂Cl-methanol junction has been measured directly using the chronoamperometry electrochemical technique. The reduction reaction rate of Co(Cp)₂+ was 0.03 cm-s^-1 at the Si electrode, and was more than 100 times slower than at a hanging mercury electrode. The slower rate was attributed to the smaller optical and static dielectric constants, and the lower density of electrons of the semiconductor. The experimental results were compared to the Marcus theory of charge transfer.

The unique properties of high purity Si/liquid junctions have been investigated under illumination conditions in which the photogenerated carrier concentration exceeds the dopant concentration. Under these high injection conditions, negligible electric fields exist at the semiconductor/liquid interface, and carrier motion is driven by diffusion. Studies of the current-voltage properties of the Si in methanol solutions containing various redox couples suggested that high efficiency photoelectrochemical cells could be established through selective collection of carriers at the semiconductor/liquid junction. The quasi-Fermi levels of electrons and holes were measured directly against the solution potential. Steady-state and transient photovoltage measurements, and theoretical modeliug of the carrier transport, generation, and recombination dynamics indicated that the quasi-Fermi levels were flat across the semiconductor sample. The recombination velocities at the Si/liquid junctions have also been measured, and were shown to vary with the solution potential following the Shockley-Read-Hall theory on recombination.

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.

Carbon-13 magnetic resonance spectroscopy

High-resolution, natural-abundance ¹³C spectra have been obtained from a wide variety of organic compounds; ¹³C chemical shifts and coupling constants have been correlated with other molecular properties.

Geminal and vicinal, carbon-proton couplings in benzene and the five- and six-membered aromatic heterocycles have been related to the corresponding proton-proton couplings in substituted ethylenes. The carbon-proton coupling constants in benzene are J_CCH = + 1.0, J_CCCH = +7.4 and J_CCCH = -1.1 Hz. Extended Hückel wavefunctions are uniformly poor in explaining the long-range, carbon-proton couplings in aromatic systems.

Couplings between carbon and elements other than hydrogen have been observed in proton decoupled ¹³C spectra. All of the carbons in fluorobenzene and 1-fluoronaphthalene, but only six of the carbons in 2-fluoronaphthalene are coupled to the fluorine. One-bond, carbon-phosphorus coupling in trialkylphosphines is negative, while one-bond, carbon-phosphorus coupling in tetra-alkylphosphonium ions is positive. Atoms which do not use hybrid orbitals to form bonds to carbon (F, P(III), Se, Te) may have negative, one-bond coupling constants because of the failure of the average energy approximation. One-bond couplings between carbon and carbon, silicon, tin, lead and mercury appear to be explainable in terms of an effective nuclear charge and the s-bond order of the metal. Couplings between carbon and nitrogen and phosphorus (IV) have significant negative contributions to the Fermi contact coupling expression, though, within one series, correlations with s-bond order may be valid. Carbon-carbon coupling in cyclopropane derivatives (10-15 Hz) is consistent with a high degree of p character in the interior orbitals. Some two- and three-bond carbon-carbon coupling constants have also been observed.

Substituent effects of hydroxyl groups on the ¹³C chemical shifts of continuous-chain alkanes depend both on steric and electronic factors. The hydroxyl substituent effects in the long-chain, primary alcohols are α = -48.3, β = -10.2, and γ = +6.0 ppm. The upfield γ effect is attributed to steric crowding in the gauche conformations. Additivity of the hydroxyl and carbonyl and alkyl substituent effects in alkyl-substituted cyclohexanols and cyclohexanones has been demonstrated.

Chemical and Electrochemical Behavior of Graphene-Covered Silicon Photoanodes

This dissertation describes efforts over the last five years to develop protective layers for semiconductor photoelectrodes based on monolayer or few-layer graphene sheets. Graphene is an attractive candidate for a protective layer because of its known chemical inertness, transparency, ease of deposition, and limited number of electronic states. Monolayer graphene was found to effectively inhibit loss of photocurrent over 1000 seconds at n-Si/aqueous electrolyte interfaces that exhibit total loss over photocurrent over 100 seconds. Further, the presence of graphene was found to effect only partial Fermi level pinning at the Si/graphene interface with respect to a range of nonaqueous electrolytes. Fluorination of graphene was found to extend the stability imparted on n-Si by the monolayer sheet in aqueous Fe(CN)₆^3-/4- electrolyte to over 100,000 seconds. It was demonstrated that the stability of the photocurrent of n-Si/fluorinated graphene/aqueous electrolyte interfaces relative to n-Si/aqueous electrolyte interfaces is likely attributable to the inhibition of oxidation of the silicon surface.

This dissertation also relates efforts to describe and define terminology relevant to the field of photoelectrochemistry and solar fuels production. Terminology describing varying interfaces employed in electrochemical solar fuels devices are defined, and the research challenges associated with each are discussed. Methods for determining the efficiency of varying photoelectrochemical and solar-fuel-producing cells from the current-voltage behavior of the individual components of such a device without requiring the device be constructed are described, and a range of commonly employed performance metrics are explored.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.