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In this thesis, we study the effects of doping in two-dimensional quantum antiferromagnets. We consider cases where the undoped parent compound is a Mott insulator with long-range antiferromagnetic order and focus on the low-doping situations. The limit of localized impurities is studied in a system consisting of a host magnet and two additional weakly coupled spins. We derive the effective Hamiltonian describing the interaction between these impurities as a function of their distance and show that it exhibits xyz anisotropy, leading to NMR and EPR line broadening. We calculate the magnetization disturbance in the host magnet induced by a single impurity and find that it always enhances Neel order. Relaxing the localization constraint, we investigate the single-hole dynamics of the t-J model on the honeycomb lattice. Using exact diagonalizations, series expansion and the self-consistent Born approximation, we calculate the quasi-particle dispersion, bandwidth and residues and compare our findings with the well-established results for the square lattice. Similar to the latter case, we find an almost flat band along the edges of the magnetic Brillouin zone and well-defined hole pockets around the corners. The most important part of this thesis is devoted to the magnetic properties of lightly doped La2-xSrxCuO4, the simplest and by far most studied cuprate superconductor. Starting from the undoped parent compound, we calculate the spin-wave spectrum and the spin-flop transitions in a uniform magnetic field at zero temperature. We then consider the low-doping regime and derive the effective field theory describing the spin dynamics in insulating La2-xSrxCuO4, x ≤ 0.055, at low temperature. The spin structure resulting from the spiral solution of the extended t-J model, obtained by taking into account the Coulomb trapping of holes by Sr ions, is confined in the copper-oxide planes. Our solution explains why the incommensurate structure is directed along the orthorhombic b axis and allows us to calculate the positions and shapes of the neutron scattering peaks numerically. These results are in perfect agreement with experimental data. We also show that topological defects (spin vortex-antivortex pairs) are an intrinsic property of the spin-glass ground state.

<p><strong>Abstract</strong></p><p>The behavior for MoSi₂ based high temperature heating elements for resistive heating has been examined in elevated temperature and low oxygen content environment. MoSi₂ spontaneously forms a protective SiO₂ scale at high temperature if the amount of oxygen in the ambient atmosphere is sufficient according to the following reaction:</p><p>5MoSi₂ + 7O₂(g)  7SiO₂ + Mo₅Si₃</p><p>If the oxygen content at a specific temperature is too low, SiO(g) is more stable than SiO₂ and the following reaction will occur instead:</p><p>2SiO₂  2SiO(g) + O₂(g)</p><p>Then surface will be Si-deplated and finally, the base material will be exposed. Si and Mo will oxidize and degas from the surface as SiO and MoO₃ with severe diameter reduction of the heating element as a result. It is therefore of high interest to find the relationship between the maximum element temperature and the oxygen content in the ambient atmosphere to be able to fully exploit the potential of the heating elements and also to aid and help diagnose customer complaints.</p><p> </p><p>After 14 full scale tests in a custom made atmospheric furnace, the following equation could be calculated:</p><p>p(O₂) = 1.748·10^{0.01677·T·log(e)-10}</p><p>The equation gives the minimum oxygen content at a specified temperature. The equation is based on 100 hours tests at atmospheric pressure, gas flow rate of 4 liter per minute, varying temperature and varying oxygen content. Nitrogen has been used as carrier gas for the oxygen.</p>

The microstructural evolution and mechanical properties at elevated temperatures of a recently fabricated fine-grained AA6xxx aluminium sheet were evaluated and compared to the commercially fabricated sheet of the same alloy in the T4P condition. The behaviour of the fine-grained and T4P sheets was compared at elevated temperatures between 350°C and 550°C, as well as room temperature. Static exposure to elevated temperatures revealed that the precipitate structure of the fine-grained material did not change extensively. The T4P material, however, underwent extensive growth of precipitates, including a large amount of grain boundary precipitation. At room temperature, the T4P material deformed at much higher stresses than the FG material, but achieved lower elongations. Deformation at elevated temperatures revealed that the fine-grained material achieved significantly larger elongations to failure than the T4P material in the temperature range of 350°C-450°C. Both materials behaved similarly at 500°C and 550°C. Above 500°C, the grain size was greatly reduced in the T4P material, and only a slightly increased in the fine-grained material. At temperatures above 450°C, the elongation to failure in both materials generally increased with increasing strain-rate. The poor performance of the T4P material at low temperatures was attributed to the precipitate characteristics of the sheet, which lead to elevated stresses and increased cavitation. The deformation mechanism of both materials was found to be controlled by dislocation climb, accommodated by the self diffusion of aluminium at 500°C and 550°C. The deformation mechanism in the fine-grained material transitioned to power law breakdown at lower temperatures. At 350°C to 450°C, the T4P material behaved similarly to a particle hardened material with an internal stress created by the precipitates. The reduction in grain size of the T4P material after deformation at 500°C and 550°C was suggested to be caused by dynamic recovery/recrystallization. The role of a finer grain-size in the deformation behaviour at elevated temperatures was mainly related to enhanced diffusion through grain boundaries. The differences in the behaviour of the two materials were mainly attributed to the difference in the precipitation characteristics of the materials.

Abstract The behavior for MoSi2 based high temperature heating elements for resistive heating has been examined in elevated temperature and low oxygen content environment. MoSi2 spontaneously forms a protective SiO2 scale at high temperature if the amount of oxygen in the ambient atmosphere is sufficient according to the following reaction: 5MoSi2 + 7O2(g)  7SiO2 + Mo5Si3 If the oxygen content at a specific temperature is too low, SiO(g) is more stable than SiO2 and the following reaction will occur instead: 2SiO2  2SiO(g) + O2(g) Then surface will be Si-deplated and finally, the base material will be exposed. Si and Mo will oxidize and degas from the surface as SiO and MoO3 with severe diameter reduction of the heating element as a result. It is therefore of high interest to find the relationship between the maximum element temperature and the oxygen content in the ambient atmosphere to be able to fully exploit the potential of the heating elements and also to aid and help diagnose customer complaints.   After 14 full scale tests in a custom made atmospheric furnace, the following equation could be calculated: p(O2) = 1.748·100.01677·T·log(e)-10 The equation gives the minimum oxygen content at a specified temperature. The equation is based on 100 hours tests at atmospheric pressure, gas flow rate of 4 liter per minute, varying temperature and varying oxygen content. Nitrogen has been used as carrier gas for the oxygen.

The microstructural evolution and mechanical properties at elevated temperatures of a recently fabricated fine-grained AA6xxx aluminium sheet were evaluated and compared to the commercially fabricated sheet of the same alloy in the T4P condition. The behaviour of the fine-grained and T4P sheets was compared at elevated temperatures between 350°C and 550°C, as well as room temperature. Static exposure to elevated temperatures revealed that the precipitate structure of the fine-grained material did not change extensively. The T4P material, however, underwent extensive growth of precipitates, including a large amount of grain boundary precipitation. At room temperature, the T4P material deformed at much higher stresses than the FG material, but achieved lower elongations. Deformation at elevated temperatures revealed that the fine-grained material achieved significantly larger elongations to failure than the T4P material in the temperature range of 350°C-450°C. Both materials behaved similarly at 500°C and 550°C. Above 500°C, the grain size was greatly reduced in the T4P material, and only a slightly increased in the fine-grained material. At temperatures above 450°C, the elongation to failure in both materials generally increased with increasing strain-rate. The poor performance of the T4P material at low temperatures was attributed to the precipitate characteristics of the sheet, which lead to elevated stresses and increased cavitation. The deformation mechanism of both materials was found to be controlled by dislocation climb, accommodated by the self diffusion of aluminium at 500°C and 550°C. The deformation mechanism in the fine-grained material transitioned to power law breakdown at lower temperatures. At 350°C to 450°C, the T4P material behaved similarly to a particle hardened material with an internal stress created by the precipitates. The reduction in grain size of the T4P material after deformation at 500°C and 550°C was suggested to be caused by dynamic recovery/recrystallization. The role of a finer grain-size in the deformation behaviour at elevated temperatures was mainly related to enhanced diffusion through grain boundaries. The differences in the behaviour of the two materials were mainly attributed to the difference in the precipitation characteristics of the materials.

Designing a fit-for-purpose drilling fluid for high-pressure, high-temperature (HP/HT) operations is one of the greatest technological challenges facing the oil and gas industry today. Typically, a drilling fluid is subjected to increasing temperature and pressure with depth. While higher temperature decreases the drilling fluid’s viscosity due to thermal expansion, increased pressure increases its viscosity by compression. Under these extreme conditions, well control issues become more complicated and can easily be masked by methane and hydrogen sulfide solubility in oil-base fluids frequently used in HP/HT operations. Also current logging tools are at best not reliable since the anticipated bottom-hole temperature is often well above their operating limit. The Literature shows limited experimental data on drilling fluid properties beyond 350°F and 20,000 psig. The practice of extrapolation of fluid properties at some moderate level to extreme-HP/HT (XHP/HT) conditions is obsolete and could result in significant inaccuracies in hydraulics models. This research is focused on developing a methodology for testing drilling fluids at XHP/HT conditions using an automated viscometer. This state-of-the-art viscometer is capable of accurately measuring drilling fluids properties up to 600°F and 40,000 psig. A series of factorial experiments were performed on typical XHP/HT oil-based drilling fluids to investigate their change in rheology at these extreme conditions (200 to 600°F and 15,000 to 40,000 psig). Detailed statistical analyses involving: analysis of variance, hypothesis testing, evaluation of residuals and multiple linear regression are implemented using data from the laboratory experiments. I have developed the FluidStats program as an effective statistical tool for characterizing drilling fluids at XHP/HT conditions using factorial experiments. Results from the experiments show that different drilling fluids disintegrate at different temperatures depending on their composition (i.e. weighting agent, additives, oil/water ratio etc). The combined pressure-temperature effect on viscosity is complex. At high thresholds, the temperature effect is observed to be more dominant while the pressure effect is more pronounced at low temperatures. This research is vital because statistics show that well control incident rates for non- HP/HT wells range between 4% to 5% whereas for HP/HT wells, it is as high as 100% to 200%. It is pertinent to note that over 50% of the world’s proven oil and gas reserves lie below 14,000 ft subsea according to the Minerals Management Service (MMS). Thus drilling in HP/HT environment is fast becoming a common place especially in the Gulf of Mexico (GOM) where HP/HT resistant drilling fluids are increasingly being used to ensure safe and successful operations.

published_or_final_version / Physics / Master / Master of Philosophy

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

No description available.