Graduate Theses & Dissertations


Real-space renormalization group approach to the Anderson model
Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder. Author Keywords: disorder, localization, real-space renormalization, strong correlations
Supercritical Water Chemistry
Supercritical water (SCW) exhibits unique properties that differentiates it from its low temperature behaviour. Hydrogen bonding is dramatically reduced, there is no phase boundary between liquid and gaseous states, heat capacity increases, and there is a drastic reduction of the dielectric constant. Efforts are underway for researchers to harness these properties in the applications of power generation and hazardous waste destruction. However, the extreme environment created by the high temperatures, pressures and oxidizing capabilities pose unique challenges in terms of corrosion not present in subcritical water systems. Molecular Dynamics (MD) simulations have been used to obtain mass transport, hydration numbers and the influence on water structure of molecular oxygen, chloride, ammonia and iron (II) cations in corrosion crevices in an iron (II) hydroxide passivation layer. Solvation regimes marking the transitions of solvation based versus charge meditated processes were explored by locating the percolation thresholds of both physically and hydrogen bonded water clusters. A SCW flow through reactor was used to study hydrogen evolution rates over metal oxide surfaces, metal release rates and the kinetics for the oxidation of hydrogen gas by oxygen in SCW. Insights into corrosion phenomena are provided from the MD results as well as the experimental determination of flow reactor water and hydrogen chemistry. Author Keywords: Flow Studies, Molecular Dynamics, Supercritical Water
Role of Dielectric Screening in SrTiO3-Based Interfaces
We build a theoretical model for exploring the electronic properties of the two-dimensional (2D) electron gas that forms at the interface between insulating SrTiO3 (STO) and a number of perovskite materials including LaTiO3, LaAlO3, and GdTiO3. The model treats conduction electrons within a tight-binding approximation, and the dielectric polarization via a Landau-Devonshire free energy that incorporates STO's strongly nonlinear, nonlocal, field-, and temperature-dependent dielectric response. We consider three models for the dielectric polarization at the interface: an ideal-interface model in which the interface has the same permittivity as the bulk, a dielectric dead-layer model in which the interface has permittivity lower that the bulk, and an interfacial-strain model in which the strain effects are included. The ideal-interface model band structure comprises a mix of quantum 2D states that are tightly bound to the interface, and quasi-three-dimensional (3D) states that extend hundreds of unit cells into the STO substrate. We find that there is a substantial shift of electrons away from the interface into the 3D tails as temperature is lowered from 300 K to 10 K. We speculate that the quasi-3D tails form the low- density high-mobility component of the interfacial electron gas that is widely inferred from magnetoresistance measurements. Multiple experiments have observed a sharp Lifshitz transition in the band structure of STO interfaces as a function of applied gate voltage. To understand this transition, we first propose a dielectric dead-layer model. It successfully predicts the Lifshitz transition at a critical charge density close to the measured one, but does not give a complete description for the transition. Second, we use an interfacial-strain model in which we consider the electrostrictive and flexoelectric coupling between the strain and polarization. This coupling generates a thin polarized layer whose direction reverses at a critical density. The transition occurs concomitantly with the polarization reversal. In addition, we find that the model captures the two main features of the transition: the transition from one occupied band to multiple occupied bands, and the abrupt change in the slope of lowest energy band with doping. Author Keywords:
Modelling the Lanthanum Aluminate-Strontium Titanate Interface with a Modified Transverse Ising Model
In 2004 it was discovered that a two-dimensional electron gas (2DEG) forms at the interface between lanthanum aluminate (LAO) and strontium titanate (STO). This 2DEG exhibits a variety of electronic and magnetic phenomena, motivating intense research into its applicability to electronic devices. Over the years several models have been developed in theoretical exploration of this system. Here, the transverse Ising model is applied to the LAO/STO interface for the first time. It is shown that the model as it is traditionally formulated cannot accurately predict the structure of the electron density at the interface. I show that this can be fixed with a simple modification of the model, and discuss how this modification affects both the polarization distribution in ferroelectric thin films and the electron density at the LAO/STO interface. The importance of including the depolarizing field when modelling spatially inhomogeneous ferroelectric systems is also explored. Author Keywords: ferroelectric thin film, lanthanum aluminate, strontium titanate, transverse Ising model, two-dimensional electron gas
Cluster Approach Applied to the One-Dimensional Anderson-Hubbard Model
S. Johri and R. Bhatt developed a real-space renormalization group approach aimed at extracting the localized single-particle eigenstates of the Anderson model from a large system by identifying clusters of resonant site potentials. E. Campbell generalized this real-space renormalization group approach using standard perturbation theory. Both approaches were intended to approximate the single-particle density of states of the Anderson model. In this thesis, we aimed to test the potential of applying a similar real-space renormalization group approach to calculate the density of states of the interacting Anderson-Hubbard model. Our interest in the density of states of this model is due to a V-shaped zero-bias anomaly in two-dimensional systems. A real-space renormalization group approach is best applied to a one-dimensional system. We found that the zero-bias anomaly is not V-shaped in one-dimension. To test the potential of a real-space renormalization group approach, we used the cluster approach which is the same as the non-interacting renormalization group approach but without the perturbation theory and found that for strong disorder this technique could accurately calculate the density of states over a wide range of energies but deviated from exact results at the band edge, at $\omega=\pm U$ and near $\omega=0$. The first two inaccuracies will be reduced with a proper real-space renormalization group approach. We suspect that the last inaccuracy is associated with long range physics and may be difficult to recover. We also developed a technique that adjusts the identification of clusters in the cluster approach to improve the computation time of the density of states with minimal loss of accuracy in a tunable range around the Fermi level. We found that this technique significantly reduced the computation time and was able to preserve the density of states near the Fermi level, except at the smallest energies near $\omega=0$. Author Keywords: Anderson-Hubbard model, renormalization group, Strong electron correlations, Zero-bias anomaly
Advanced broadband CARS microscopy based on a supercontinuum-generating photonic crystal fiber
I have developed and improved a coherent anti-Stokes Raman scattering (CARS) microscope based on the spectral focusing (SF) technique. The CARS microscope uses an 800 nm oscillator and a photonic crystal fibre module to generate the supercontinuum Stokes. The photonic crystal fibre was originally designed to generate light beyond 945 nm which is useful for CARS microscopy in the CH/OH frequencies but essentially prevents access to the important fingerprint region at lower frequencies. With expert and nontraditional approaches to generating supercontinuum with sufficient power at wavelengths below 945 nm, I substantially extend the usefulness of the module for SF-CARS microscopy deep into the fingerprint region. Moreover, with the invention of a dynamic supercontinuum generation scheme we call "spectral surfing," I improve both the brightness of the CARS signal and extend the accessible CARS frequency range to frequencies as low as 350 cm$^{-1}$ and as high as 3500 cm$^{-1}$---all in a single scan-window. I demonstrate the capabilities of our broadband SF-CARS system through CARS and four-wave mixing hyperspectroscopy on samples such as astaxanthin, lily pollen and glass; liquid chemicals such as benzonitrile, nitrobenzene and dimethyl sulfoxide; and on pharmaceutical samples such as acetaminophen, ibuprofen, and cetirizine. Furthermore, In search of more useful Stokes supercontinuum sources, I compare the performance of two commercial photonic crystal fibre modules for use in SF-CARS applications, ultimately finding that one module provides better spectral characteristics for static supercontinuum use, while the other provides improved characteristics when spectral surfing is implemented. Author Keywords: coherent anti-Stokes Raman scattering, nonlinear microscopy, scanning microscopy, spectroscopy, supercontinuum generation, vibrational spectroscopy
Phosphoric Acid Chemically Activated Waste Wood
Activated Carbon (AC) is commonly produced by gasification, but there has been increasing interest in chemical activation due to its lower activation temperatures and higher yields. Phosphoric acid, in particular, succeeds in both these areas. Phosphoric acid activated carbon (PAC) can be environmentally sustainable, and economically favourable, when the phosphoric acid used in the activation is recycled. This thesis describes the digestion and activation of waste wood using phosphoric acid, as well as methods used to recover phosphoric acid, functionalize the produced activated carbon with iron salts and then test their efficacy on the adsorption of target analytes, selenite and selenate. In order to achieve an efficient phosphoric acid based chemical activation, further understanding of the activation process is needed. A two-step phosphoric acid activation process with waste wood feed stock was examined. The filtrate washes of the crude product and the surface composition of the produced PAC were characterized using X-ray Photoelectron Spectroscopy (XPS), Fourier Transform-Infrared spectroscopy (FT-IR), Ion Chromatography (IC), and 31P Nuclear Magnetic Resonance (NMR). XPS of the unwashed PAC contained 13.3 atomic percent phosphorous, as phosphoric acid, while the washed sample contained 1.4 atomic percent phosphorous as PO43-, and P2O74-. Using 31P NMR, phosphoric acid was identified as the primary phosphorous species in the acidic 0.1 M HCl washings, with pyrophosphates also appearing in the second 0.1 M NaOH neutralizing wash, and finally a weak signal from phosphates with an alkyl component also appearing in the DI wash. IC showed high concentrations of phosphoric acid in the 0.1 M HCl wash with progressively lower concentrations in both the NaOH and DI washes. Total phosphoric acid recovery was 96.7 % for waste wood activated with 25 % phosphoric acid, which is higher than previous literature findings for phosphoric acid activation. The surface areas of the PAC were in the 1500-1900 m2g-1 range. Both pre and post activation impregnation of iron salts resulted in iron uptake. Pre-activation resulted in only iron(III) speciation while post-activation impregnation of iron(II)chloride did result in iron(II) forming on the PAC surface. The pre-activated impregnated PAC showed little to no adsorption of selenite and selenate. The post-activation impregnated iron(II)chloride removed up to 12.45 ± 0.025 mg selenium per g Iron-PAC. Competitive ions such as sulfate and nitrate had little effect on selenium adsorption. Phosphate concentration did affect the uptake. At 250 ppm approximately 75 % of adsorption capacity of both the selenate and the selenite solutions was lost, although selenium was still preferentially adsorbed. Peak adsorption occurred between a pH of 4 and 11, with a complete loss of adsorption at a pH of 13. Author Keywords: Activated Carbon, doping, Iron, phosphoric acid, selenium
Molecular Dynamics Simulations of Aqueous and Confined Systems Relevant to the Supercritical Water Cooled Nuclear Reactor
Supercritical water (SCW) is the intended heat transfer fluid and potential neutron moderator in the proposed GEN-IV Supercritical Water Cooled Reactor (SCWR). The oxidative environment poses challenges in choosing appropriate design materials, and the behaviour of SCW within crevices of the passivation layer is needed for developing a corrosion control strategy to minimize corrosion. Molecular Dynamics simulations have been employed to obtain diffusion coefficients, coordination number and surface density characteristics, of water and chloride in nanometer-spaced iron hydroxide surfaces. Diffusion models for hydrazine are evaluated along with hydration data. Results demonstrate that water is more likely to accumulate on the surface at low density conditions. The effect of confinement on the water structure diminishes as the gap size increases. The diffusion coefficient of chloride decreases with larger surface spacing. Clustering of water at the surface implies that the SCWR will be most susceptible to pitting corrosion and stress corrosion cracking. Author Keywords: Confinement, Diffusion, Hydration, MD Simulations, Supercritcal Water
Model for the Differential Susceptibility of Strontium Titanate
The appearance of a two-dimensional electron gas (2DEG) in oxide interfaces between strontium titanate (STO) and other materials has become a major area of study. The behaviour of the 2DEG in STO is not well understood in part because the dielectric properties of STO are not well characterized. The differential susceptibility has a major impact on the electric fields within strontium titanate, and therefore to understand the 2DEG a better understanding of the susceptibility is needed. An expression for the soft mode phonon frequency of bulk strontium titanate is derived and used to model the susceptibility as a function of spatially homogeneous electric field, temperature and wavevector. This model is used to discuss the effect of spatially inhomogeneous electric fields and the local vs. nonlocal nature of the susceptibility. The critical exponents and the free energy are determined and discussed. Author Keywords: critical exponents, differential susceptibility, quantum paraelectric, strontium titanate
Correlating density of states features with localization strength in disordered interacting systems
Johri and Bhatt found singular behavior near the band edge in the density of states as well as in the inverse participation ratio of the Anderson model. These singularities mark a transition to an energy range dominated by resonant states. We study the interacting case using an ensemble of two-site Anderson-Hubbard systems. We find the ensemble-averaged density of states and generalized inverse participation ratio have more structure than in the non-interacting case because there are more transitions and in particular the transitions depend on the ground state. Nonetheless, there are regions of sharp decline in the generalized inverse participation ratio associated with specific density of state features. Moreover these features move closer to the Fermi level with the addition of interactions making them more experimentally accessible. Unfortunately resonances unique to interacting systems cannot be specifically identified. Author Keywords: Correlated electrons, Disorder, Localization
Investigation of Using Phase Change Materials for Thermal Energy Storage in Adiabatic Compressed Air Energy Storage
There is an increasing global need for grid scale electrical energy storage to handle the implementation of intermittent renewable energy sources. Adiabatic compressed air energy storage is an emerging technology with similar performance to pumped hydro except it has the issue of heat loss during the compression stage. Previously, it has been considered to use sensible heat storage materials to store the heat created by compression in a thermal energy storage unit until energy is required, and then transfer the heat back to the air. This research proposes to instead use phase change materials to store the heat of compression, as this will reduce entropy generation and maximize roundtrip exergy efficiency. Different configurations and placements of the phase change materials are considered and exergy analyses are presented. The thermodynamic equations are derived and optimal setup conditions including amount of latent heat and melting temperatures are calculated. Author Keywords: Compressed Air Energy Storage, Energy Storage, Exergy, Phase Change Materials
Experiments have observed a two-dimensional electron gas at the interface of two insulating oxides: strontium titanate (SrTiO3) and lanthanum aluminate (LaAlO3). These interfaces exhibit metallic, superconducting, and magnetic behaviours, which are strongly affected by impurities. Motivated by experiments, we introduce a simple model in which impurities lie at the interface. We treat the LaAlO3 as an insulator and model the SrTiO3 film. By solving a set of self-consistent Hartree equations for the charge density, we obtain the band structure of the SrTiO3 film. We then study the relative contributions made by the occupied bands to the two-dimensional conductivity of the LaAlO3/SrTiO3 interface. We find that the fractional conductivity of each band depends on several parameters: the mass anisotropy, the filling, and the impurity potential. Author Keywords: conductivity, impurities, insulating oxides, Two-dimensional electron gases


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Format: 2021/05/16