The sintering behavior of close-packed spheres

The sintering behavior and microstructural evolution of a powder compact is influenced strongly by initial properties, such as the relative density, the particle and pore size distribution, and the powder packing. While the influence of the former parameters on the microstructural evolution has been investigated in some detail, the impact of the initial packing of the powder has been mostly overlooked. However, research has shown that the sintering behavior of a powder can be significantly improved if the powder is regularly packed. This has been shown for monodisperse spherical TiO2 particles [1], which sintered 10 times faster and exhibited almost no grain growth compared to ordinary TiO2. Similar observations has been made for homogeneously packed Al2O3 [2], SiO2 [3], as well as a number of other materials [4]. Monodispersed spherical TiO2 particles have been shown to order in face-centered cubic (fcc) arrays, while the SiO2 powder forms stacked planes of hexagonal close-packed (hcp) particles. Close packing of monodispersed silica has also been observed [5]. Sintering of two-dimensional close packing cylinders has also been demonstrated experimentally [6–8] and numerically modeled [9,10], and the sintering of particle clusters in three dimensions has also been studied [11]

Strain in the mesoscale kinetic Monte Carlo model for sintering

Shrinkage strains measured from microstructural simulations using the mesoscale kinetic Monte Carlo (kMC) model for solid state sintering are discussed. This model represents the microstructure using digitized discrete sites that are either grain or pore sites. The algorithm used to simulate densification by vacancy annihilation removes an isolated pore site at a grain boundary and collapses a column of sites extending from the vacancy to the surface of sintering compact, through the center of mass of the nearest grain. Using this algorithm, the existing published kMC models are shown to produce anisotropic strains for homogeneous powder compacts with aspect ratios different from unity. It is shown that the line direction biases shrinkage strains in proportion the compact dimension aspect ratios. A new algorithm that corrects this bias in strains is proposed; the direction for collapsing the column is determined by choosing a random sample face and subsequently a random point on that face as the end point for an annihilation path with equal probabilities. This algorithm is mathematically and experimentally shown to result in isotropic strains for all samples regardless of their dimensions. Finally, the microstructural evolution is shown to be similar for the new and old annihilation algorithms.Comment: 6 pages, 6 figure

Localized Energy Estimates for Wave Equations on Higher Dimensional Black Holes

A robust measure of decay and dispersion for the wave equation is provided by the localized energy estimates, which have been essential in proving, e.g. the Strichartz estimates on black hole backgrounds. We study localized energy estimates for the wave equation on (1+4)-dimensional Myers-Perry space-times, which represent a family of rotating asymptotically at black holes with spherical horizon topology and generalize the well-known Kerr space-times to higher dimensions. Because of the extra dimension, the Myers-Perry family is parameterized by two angular momentum parameters, which we assume to be sufficiently small relative to the mass of the black hole, essentially allowing us to treat the space-time as a perturbation of the Schwarzschild black hole. This investigation is motivated by the nonlinear stability problem for the Kerr family of black holes, which may be easier to understand in higher dimensions. Typically, the localized energy estimates are proved by commuting the wave operator with a suitable first-order differential operator and integrating by parts. However, the underlying black hole geometry introduces a number of difficulties related to the trapping phenomenon, which is a known obstruction to dispersion and necessitates a loss in decay. This phenomenon is manifest along the event horizon of the Schwarzschild/Kerr black holes, but its effect is rendered negligible due to the celebrated red-shift effect. More delicate analysis is required to deal with trapping that occurs along e.g., the so-called photon sphere in the Schwarzschild geometry. Localized energy estimates on higher dimensional Schwarzschild black holes were proved by Laul-Metcalfe in [34] using a single differential multiplier, but their method relies fundamentally on the fact that the trapped null geodesics lie on a sphere. On the Myers-Perry space-time, the nature of the trapped set is much more complicated and must be described in phase space rather than by position alone, and consequently a single differential multiplier is insufficient to prove the desired result. Once it is determined that all trapped geodesics lie on surfaces of constant r, we can adapt the method of Tataru and Tohaneanu in [62], which perturbs off the Schwarzschild case by instead commuting with an appropriate pseudodifferential operator to generate a positive commutator near the trapped set. This describes joint work with Parul Laul, Jason Metcalfe, and Mihai Tohaneanu [35].Bachelor of Scienc

The experience of seizures:epilepsy and non-epileptic attack disorder

This thesis comprises of a literature review, a research paper and a critical appraisal of the research process. In the literature review, a meta-synthesis methodology was used to identify and synthesise 15 studies that explored the experiences of living with epilepsy. Three themes emerged; ‘making sense of epilepsy: “it affects your perception of yourself”’; ‘the cost of epilepsy: “getting epilepsy has put me in poverty”’; and ‘significance of others in coping with epilepsy; “my family have always helped me”’. Findings are discussed in terms of the impact of epilepsy on identity and self, the losses that individuals have experienced as a consequence of epilepsy, and the ways in which perceived support from others can be helpful or unhelpful. The research paper utilised interpretative phenomenological analysis, whereby six participants who had received a diagnosis of non-epileptic attack disorder (NEAD) were interviewed, to explore how they had made sense of it. Three themes emerged; “NEAD is a confusing diagnosis; “all it means is it’s not epilepsy”’; ‘Legitimising the illness: feeling “like a bit of a fraud”’; and ‘NEAD as a challenge to identity: “I want to be more me again”’. Findings suggest that making sense of a diagnosis of NEAD is a challenging process, which differs from person to person. The clinical implications of these findings are discussed. The critical appraisal discusses the comparisons between the findings of the literature review and research paper. Reflections about epistemology are offered, alongside reflections on the research process as a whole

The experience of adjusting to Acquired Brain Injuries

This thesis comprises of a literature review, a research paper and a critical appraisal of the research process. In the literature review, a meta-synthesis methodology was utilised to identify and synthesise 25 studies that explored the experiences of coping and adjusting to a Traumatic Brain Injury (TBI). Four themes emerged; Immediate impact of injury: “I didn’t know what one should do as a human being”; Extrinsic factors that influenced recovery process; “Without him, I’m not sure I would have managed to live anymore”; Intrinsic factors that influenced recovery process: “Come on, snap out of it and do what you’ve got to do” and Post-injury growth: “I am glad I had my accident because it’s made me into a better person”. Findings are discussed in terms of the impact of loss experienced because of the injury, the impact on the participants’ identity, and the intrinsic and extrinsic factors that supported coping and adjustment. The research paper utilised interpretative phenomenological analysis, whereby six participants who had received a diagnosis of encephalitis were interviewed, to explore how they had made sense of the diagnostic process, experiences of receiving the diagnosis and the impact it had on their coping and adjustment to the illness. Three themes emerged ‘Being on a wild goose chase- challenges with getting the diagnosis’, ‘The emotional rollercoaster experience and ‘significance of information and others’. Findings suggest that encephalitis is a complex condition and the diagnostic journey is filled with many uncertainties fuelled by inadequate knowledge and understanding. Certain factors facilitate and hinder adjustment to the condition. The clinical implications of these findings are discussed. The critical appraisal discusses the comparisons between the findings of the literature review and research paper. Reflections about epistemology are discussed, alongside reflections on the research process as a whole

Processing and testing of high toughness silicon nitride ceramics

High toughness silicon nitride ceramics were processed with the addition of small quantities of beta-Si3N4 whiskers in a commercially available alpha-Si3N4 powder. These whiskers grew preferentially during sintering resulting in large, elongated beta-grains, which acted to toughen the matrix by crack deflection and grain pullout. The fracture toughness of these samples seeded with beta-Si3N4 whiskers ranged from 8.7 to 9.5 MPa m(exp 0.5) depending on the sintering additives