<p>  </p> <p>This dissertation focuses on predictive modeling of phonon-mediated thermal transport in thorium dioxide (ThO2) with defects. ThO2 has lately gained attention as it is a suitable model system for more complex nuclear reactor materials such as uranium dioxide and its mixed oxides. The reduction in thermal conductivity of the fuel as a result of irradiation-induced lattice defects is arguably the most important fuel performance metric in regard to reactor efficiency and safety. For this reason, the present work presents a theoretical investigation of thermal conductivity reduction seen in defect-bearing ThO2 and compares directly with experimental measurements. Thermal transport in irradiated ThO2 is first modeled here by a non-transport solution of the linearized Boltzmann transport equation (BTE) within the single-mode relaxation time approximation. Classic models for phonon-defect scattering rates are used to model point defects, voids, and dislocation loops in irradiated ThO2, and the resultant thermal conductivity is directly compared to experimental measurements of irradiated specimens. Our predicted conductivity values agree well with measured values near room temperature. However, discrepancy between our predictions and experimental values exist at lower temperatures where experimentally measured conductivity values seem to reach a saturation level while the model predicts further reduction in thermal conductivity. This discrepancy is most notable in higher irradiation dose samples where the thermal conductivity is almost completely controlled by the dislocation loop density. This hints at the conclusion that classic models for phonon-defect scattering rates which integrate out local variation of the defect strain field and replace this by a defect density may not be adequate to capture all physics of phonon-defect scattering, especially for dislocation loops at low temperatures. This motivated us to model defects through their spatially resolved lattice distortion fields and investigate phonon scattering in those fields in an explicit fashion. A transport solution of the phonon BTE is implemented based upon the Monte Carlo (MC) method, which explicitly tracks the phonon population as it evolves in space and time according to phonon group velocities and scattering rates. An expression for the scattering rate of phonons from an arbitrary strain field is derived from a generalized form of Grüneisen’s law of thermal expansion, and applied to the case of dislocations in ThO2. It is found that the localized strain in the material, resulting from the presence of a crystal defect, leads to a net heat flux into the strained region. This provides evidence for thermal fluxes in the absence of a temperature gradient, a phenomenon that cannot be captured via Fourier’s law. This evidence for material heating owing to the imposed strain of material defects would be immediately applicable to the field of thermoelectrics and defect engineering where large temperature gradients are desirable to improve the thermoelectric efficiency.  Although the model is applied specifically to the case of dislocations in ThO2, the derived phonon scattering rate expression is general and may be applied to any defect for which a strain field may be generated.</p>

<p>A first-principles theory of plasticity in metals currently does not exist. While many plasticity models make reference to rules based on heuristic arguments regarding dislocations (the fundamental mediators of plastic deformation in crystals), the scientific community still does not have a theory of dislocation dynamics which can recover even basic features of plasticity theory. Discrete dislocation dynamics, though a valuable tool for understanding fundamentals topics in dislocation plasticity, becomes unusable beyond ~1.5\% strain due to the line length multiplication inherent in deformation. As a result, it is necessary to develop continuum theories of dislocation dynamics which treat dislocation densities rather than individual dislocations. This thesis examines the foundations of one such continuum theory: line bundle continuum dislocation dynamics, which assumes that dislocations are roughly parallel at every point. First, this assumption is given definite meaning and it is shown from discrete dislocation dynamics data that to be appropriate when modelling dislocation densities on fine length scales (resolving densities on lengths less than 100 nm). Second, it is found that an additional driving force, the correlation stress, emerges from coarse-graining the line bundle dynamics. This correction to the dislocation interactions is dependent on tensorial dislocation correlation functions describing the short-range errors in the products of dislocation densities lying on two slip systems. The full set of these dislocation correlation functions are evaluated from discrete density data with the aid of a novel left-and-right handed classification of slip system interactions in FCC crystals. Lastly, a study of the correlation stress in a representative dislocation system suggests that these stresses are roughly one tenth the magnitude of the mean-field dislocation interaction stress. Taken together, this thesis bridges discrete and continuum models of dislocation dynamics and provides a foundation for future work on a first-principles theory of metal plasticity. </p>

<p>This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist.</p>

<div>The interactions of femtosecond lasers with gold targets were investigated with a numerical method combining molecular dynamics (MD) and the two-temperature model (TTM). Previous works using MD-TTM method did not consider all the thermodynamic parameters and the interatomic potential dependent of the electron temperature simultaneously. Therefore, we developed a LAMMPS function to achieve this. To accurately capture the physics behind the interactions, we also included the electron blast force from free electron pressure and the modified Fourier law with steep electron temperature gradient in our model. For bulk materials, a stress non-reflecting and heat conducting boundary is added between the atomistic and the continuum parts. The modified boundary force in our study greatly reduces the reflectivity of the atomistic-continuum boundary compared with its original form. Our model is the first to consider all these factors simultaneously and manage to predict four femtosecond laser ablation phenomena observed in the experiments. </div><div><br></div><div>In this dissertation, the thermodynamic parameters in the two-temperature model were extensively explored. We considered three different approaches to calculate these parameters: namely interpolation, <i>ab initio</i> calculation, and analytical expression. We found that simple interpolation between solid state and plasma state could lead to high level of inaccuracy, especially for electron thermal conductivity. Therefore, <i>ab initio</i> calculation and analytical expression were used for the calculation of the thermodynamic parameters in more advanced studies. The effects of electron thermal conductivity and electron-phonon coupling factor on electron and lattice temperatures were analyzed.</div><div><br></div><div>Our studies considered electron temperature dependent (ETD) and electron temperature independent (ETI) interatomic potentials. The ETI interatomic potential is easier to implement and therefore it is used in our phase change study to investigate the effects of target thickness on melting. Homogeneous melting occurred for thin films, while melting can be observed through the movement of the solid-liquid interface in thick or bulk materials. However, the ETI potential overestimated the bond strength at high temperatures. Therefore, ablation process was studied with the ETD potential. Three ablation mechanisms were found in our simulations at different laser fluences. Short nonthermal ablation was only observed at the ablation threshold. With increasing laser fluence, spallation was then seen. In high laser fluence regime, phase explosion occurred on the surface and coexisted with spallation.</div><div><br></div><div>Lastly, we researched on the effects of the delay time between two femtosecond laser pulses. Various delay times did not have much influence on melting depth. In low laser fluence regime, with increasing delay time, the target went through nonthermal ablation, to spallation and to no ablation. In high laser fluence regime, longer delay time encouraged phase explosion while suppressed spallation.</div>