abstract: Niobium is the primary material for fabricating superconducting radio-frequency (SRF) cavities. However, presence of impurities and defects degrade the superconducting behavior of niobium twofold, first by nucleating non-superconducting phases and second by increasing the residual surface resistance of cavities. In particular, niobium absorbs hydrogen during cavity fabrication and promotes precipitation of non-superconducting niobium hydride phases. Additionally, magnetic flux trapping at defects leads to a normal conducting (non-superconducting) core which increases surface resistance and negatively affects niobium performance for superconducting applications. However, undelaying mechanisms related to hydride formation and dissolution along with defect interaction with magnetic fields is still unclear. Therefore, this dissertation aims to investigate the role of defects and impurities on functional properties of niobium for SRF cavities using first-principles methods. Here, density functional theory calculations revealed that nitrogen addition suppressed hydrogen absorption interstitially and at grain boundaries, and it also decreased the energetic stability of niobium hydride precipitates present in niobium. Further, hydrogen segregation at the screw dislocation was observed to transform the dislocation core structure and increase the barrier for screw dislocation motion. Valence charge transfer calculations displayed a strong tendency of nitrogen to accumulate charge around itself, thereby decreasing the strength of covalent bonds between niobium and hydrogen leading to a very unstable state for interstitial hydrogen and hydrides. Thus, presence of nitrogen during processing plays a critical role in controlling hydride precipitation and subsequent SRF properties. First-principles methods were further implemented to gain a theoretical perspective about the experimental observations that lattice defects are effective at trapping magnetic flux in high-purity superconducting niobium. Full-potential linear augmented plane-wave methods were used to analyze the effects of magnetic field on the superconducting state surrounding these defects. A considerable amount of trapped flux was obtained at the dislocation core and grain boundaries which can be attributed to significantly different electronic structure of defects as compared to bulk niobium. Electron redistribution at defects enhances non-paramagnetic effects that perturb superconductivity, resulting in local conditions suitable for flux trapping. Therefore, controlling accumulation or depletion of charge at the defects could mitigate these tendencies and aid in improving superconductive behavior of niobium. / Dissertation/Thesis / Doctoral Dissertation Materials Science and Engineering 2019

This thesis describes a portfolio of work aimed at the high field applications of superconductors and can be split into four main topics: The thermal stability of technical superconductors. This section investigates the effects of thermal perturbations on technical superconducting wire used in MRI scanner construction. The ultimate aim of this section is to predict how the architecture of the wire may affect its thermal stability. To this end a detailed finite element analysis model was constructed, verified by detailed experimental data, which could then be used to quickly and easily vary the wire’s parameters. Design of a high field pulsed electromagnetic coil for flux trapping in superconductors. This section details the design, construction and testing of a novel pulsed high field magnet. The design uses finite element analysis to predict the electromagnetic, thermal and structural properties of the coil. Explosive testing of high tensile fibres used in the construction of the high field coil. This section describes the refinement and use of a novel method for testing the mechanical properties of high tensile fibres in cylindrical geometries by using highly pressurized copper vessels. Pulsed field magnetization of bulk high temperature superconductors. This section discusses the process of magnetizing bulks of high temperature superconductors by using pulsed magnetic fields. It investigates how the trapped field varies with the magnitude and rise-time of the magnetizing field, sample temperature and time after magnetization.

Understanding and characterising the diffusive transport of capillary oxygen and nutrients in striated muscles is key to assessing angiogenesis and investigating the efficacy of experimental and therapeutic interventions for numerous pathological conditions, such as chronic ischaemia. In articular, the influence of both muscle tissue and microvascular heterogeneities on capillary oxygen supply is poorly understood. The objective of this thesis is to develop mathematical and computational modelling frameworks for the purpose of extending and generalising the current use of histology in estimating the regions of tissue supplied by individual capillaries to facilitate the exploration of functional capillary oxygen supply in striated muscles. In particular, we aim to investigate the balance between local capillary supply of oxygen and oxygen demand in the presence of various anatomical and functional heterogeneities, by capturing tissue details from histological imaging and estimating or predicting regions of capillary supply. Our computational method throughout is based on a finite element framework that captures the anatomical details of tissue cross sections. In Chapter 1 we introduce the problem. In Chapter 2 we develop a theoretical model to describe oxygen transport from capillaries to uniform muscle tissues (e.g. cardiac muscle). Transport is then explored in terms of oxygen levels and capillary supply regions. In Chapter 3 we extend this modelling framework to explore the influence of the surrounding tissue by accounting for the spatial anisotropies of fibre oxygen demand and diffusivity and the heterogeneity in fibre size and shape, as exemplified by mixed muscle tissues (e.g. skeletal muscle). We additionally explore the effects of diffusion through the interstitium, facilitated--diffusion by myoglobin, and Michaelis--Menten kinetics of tissue oxygen consumption. In Chapter 4, a further extension is pursued to account for intracellular heterogeneities in mitochondrial distribution and diffusive parameters. As a demonstration of the potential of the models derived in Chapters 2--4, in Chapter 5 we simulate oxygen transport in myocardial tissue biopsies from rats with either impaired angiogenesis or impaired arteriolar perfusion. Quantitative predictions are made to help explain and support experimental measurements of cardiac performance and metabolism. In the final chapter we summarize the main results and indicate directions for further work.