Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
Browse
5 results
Search Results
Item Broken-symmetry phases of matter and their effects on electronic and magnetic properties(Montana State University - Bozeman, College of Letters & Science, 2023) Peterson, Sean Fahlman; Chairperson, Graduate Committee: Yves U. Idzerda; This is a manuscript style paper that includes co-authored chapters.Physical symmetries inherent to a material are often reflected in its electronic and magnetic properties. The in-plane four-fold rotational symmetry of thin-film ferromagnets inherent to their tetragonal lattice is also exhibited by their cubic anisotropy. The magnetization as a function of applied magnetic field can be calculated via the Stoner- Wohlfarth model. These calculated hysteresis loops were fit to measured hysteresis loops to determine anisotropy constants consistent with known values. An electronic nematic state reduces the in-plane four-fold rotational symmetry of materials by inducing a structural transition from tetragonal to orthorhombic/monoclinic, with two-fold symmetry. This reduced symmetry persists in the electronic thermal transport. Nematicity enhances nearest-neighbor hopping along one axis and reduces it along the other. This results in a deformed Fermi surface compressed (elongated) along the axis of stronger (weaker) electron hopping. This drags van Hove singularities through the Fermi level, affecting quasiparticle lifetimes. Calculating conductivity from the Boltzmann kinetic equation, nematicity enhances thermal transport along one axis and diminishes it along the other. Additionally, s-wave superconductivity coexisting with nematicity creates a feedback on the superconducting gap with a d-wave instability, which can lead to gapless excitations. In the case of weak feedback, nematic superconductors behave like fully-gapped superconductors along both axes, where transport decreases exponentially with temperature. Once gapless excitations form, transport along both axes becomes T -linear at low-T . Similarly, striped antiferromagnetism (AFM2 and AFM3) reduces the rotational symmetry of a square unit cell to a larger two-fold symmetric magnetic cell. Modeling the band structure with a tight- binding model and considering a smaller periodicity in momentum-space, gaps the Fermi surface along one axis. Calculating conductivity reveals diminished transport along one axis and enhanced thermal transport along the other. Considering d-wave superconductivity in this model results in two cases. One has highly anisotropic transport with greatly enhanced T -linear transport along one axis and diminished transport decreasing exponentially with temperature along the other. The second has weakly anisotropic transport with diminished T -linear conductivity along both axes. The symmetry of a material's properties, such as magnetic anisotropy and thermal transport, are intrinsically linked to their crystalline, electronic, and magnetic symmetries.Item Designing pattern formation through anisotropy(Montana State University - Bozeman, College of Letters & Science, 2019) Gaussoin, Anthony Danwayne; Chairperson, Graduate Committee: Scott McCallaWhen governed by appropriate potentials, systems of particles interacting pairwise in three dimensions self assemble into diverse patterns near the surface of a sphere. The resulting structure of these minimal energy states can be altered through anisotropic effects. This leads to the inverse problem of finding anisotropic potentials that produce specific targeted equilibrium structures. To study this problem, continuous versions of the discrete particle interaction equations are employed so that a leading order approximation can be obtained. Linear stability is then determined through a Fourier type analysis in terms of spherical harmonics. This allows us to solve the linearized inverse problem: for a targeted equilibrium structure, where the particles congregate along a finite set of spherical harmonics, construct an anisotropic potential that induces the same finite set of linear instabilities. Several examples of anisotropic potentials that cause known linear instabilities are presented. The resulting minimal energy configurations are approximated through a gradient descent of the discrete particle energy. These numerical experiments corroborate that the linear instabilities can be used to predict the minimal energy structure in the full nonlinear dynamics. Solving the linearized inverse problem yields a clear path to designing pattern formation through anisotropic effects.Item Intergranular water and permeability of the Lake Vostok accretion ice, Eastern Antarctica(Montana State University - Bozeman, College of Engineering, 2005) Jepsen, Steven Michael; Chairperson, Graduate Committee: Edward E. AdamsThe relative importance of nonhydrostatic stress and lattice-rejected impurities on the phase equilibrium of intergranular liquid water in the Vostok accretion ice, Eastern Antarctica, was examined in this study. In addition, experiments were conducted to examine the influence of intergranular water in ice on the permeability of a Light Non-Aqueous Phase Liquid (LNAPL) hydrocarbon. Sub-grain scale stresses in the Vostok accretion ice were simulated with anisotropic elastic and elastocreep finite element (FE) models and compared to X-ray dislocation topographs. The phase equilibrium conditions were solved separately using stresses simulated by the FE models and ice chemistry data obtained from literature. The permeability of ice to JP-8 aviation fuel, the primary component of drilling fluid used in the Vostok borehole, was tested in three Fuel-Ice (FI) Experiments on unfractured ice in dark conditions near the melting point. The shear stresses simulated by the elastic FE model indicated plastic deformation, via basal glide, in the Vostok accretion ice. This finding was supported by observed dislocation densities exceeding 107 m-2, with higher values reported in literature. The elasto-creep FE model indicated onset of intergranular melt, at scales ₃ 1% the crystal size, in the lower few meters of the westernmost accretion ice. Model predictions of strain rate and internal melt were in reasonable agreement with literature data on polycrystalline ice. Based on an impurity model, which assumed hydrostatic stress, millimeter-size intergranular water veins were predicted in the lower few dekameters of accretion ice. The FI Experiments indicated that these water veins in ice provide conduits for rapid (> 16 cm hr-1) infiltration of JP-8 fuel in dark conditions near the melting point. This transport mechanism, referred to as fuel-tunneling, involved the formation of intergranular tubes, 1-2 mm in diameter, that were absent from experiments using ice grown from distilled water. It was concluded that intergranular water veins in ice near the melting point provide tunneling conduits for LNAPL hydrocarbons. This fuel-tunneling may be accelerated in the basal-most part of the accretion ice due to intergranular melting from both deviatoric stress and mechanical anisotropy. These results have implications for environmentally-clean penetration methods of subglacial lake exploration.Item Fabric tensors and effective properties of granular materials with application to snow(Montana State University - Bozeman, College of Engineering, 2011) Shertzer, Richard Hayden; Chairperson, Graduate Committee: Edward E. AdamsGranular materials e.g., gravel, sand, snow, and metallic powders are important to many engineering analysis and design problems. Such materials are not always randomly arranged, even in a natural environment. For example, applied strain can transform a randomly distributed assembly into a more regular arrangement. Deviations from random arrangements are described via material symmetry. A random collection exhibits textural isotropy whereas regular patterns are anisotropic. Among natural materials, snow is perhaps unique because thermal factors commonly induce microstructural changes, including material symmetry. This process temperature gradient metamorphism produces snow layers that can exhibit anisotropy. To adequately describe the behavior of such layers, mathematical models must account for potential anisotropy. This feature is absent from models specifically developed for snow, and, in most granular models in general. Material symmetry is quantified with fabric tensors in the constitutive models proposed here. Fabric tensors statistically characterize directional features in the microstructure. For example, the collective orientation of intergranular bonds impacts processes like conduction and loading. Anisotropic, microstructural models are analytically developed here for the conductivity, diffusivity, permeability, and stiffness of granular materials. The methodology utilizes homogenization an algorithm linking microscopic and macroscopic scales. Idealized geometries and constitutive assumptions are also applied at the microscopic scale. Fabric tensors tying the granular arrangement to affected material properties are a natural analysis outcome. The proposed conductivity model is compared to measured data. Dry dense snow underwent temperature gradient metamorphism in a lab. Both the measured heat transfer coefficient and a developing ice structure favored the direction of the applied gradient. Periodic tomography was used to calculate microstructural variables required by the conductivity model. Through the fabric tensor, model evolution coincides with measured changes in the heat transfer coefficient. The model also predicts a different conductivity in directions orthogonal to the gradient due to developing anisotropy. Models that do not consider directional microstructural features cannot predict such behavior because they are strictly valid for isotropic materials. The conclusions are that anisotropy in snow can be significant, fabric tensors can characterize such symmetry, and constitutive models incorporating fabric tensors offer a more complete description of material behavior.Item Size dependence of the magnetic properties of cobalt oxide nanoparticles mineralized in protein cages(Montana State University - Bozeman, College of Letters & Science, 2005) Resnick, Damon Aaron; Chairperson, Graduate Committee: Yves U. IdzerdaA major question in the physics of magnetic nanoparticles is how the size affects the magnetic properties in magnetic nanoparticle systems. In particular, the magnetic properties can be affected by finite-size effects or surface effects. It is this author's belief that surface effects and not finite-size effects play the dominate role. This study is a specific example of how to try to answer this question by looking at different sizes of Co 3O 4 nanoparticles. In order to answer this question as well as better understand this system, different antiferromagnetic Co 3O 4 nanoparticles of 4.35 nm and 6.3 nm in diameter were synthesized. These particles were determined to be relatively uniform and monodispersed. In this study, Transmission Electron Microscopy (TEM), electron diffraction (ED) and X-ray Absorption Spectroscopy (XAS) were used to study the physical and electronic structure of the nanoparticles. Alternating Current Magnetic Susceptibility (ACMS) was used to measure the magnetic anisotropy energy density of the different size nanoparticles. It was found that the anisotropy energy density increases with decreasing size, from 1.09 x10 4 J/m 3 for the 6.3 nm particles to 7.53x10 4 J/m 3 for the 4.35 nm particles, consistent with the importance of surface anisotropy with decreasing particle size. Vibrating Sample Magnetometry (VSM) was used to measure the Neel temperature and coercive field of the different particles. It was found that the Neel temperature decreases with decreasing size, from 40 K to 15 K, consistent with a simple surface approximation of the finite-size scaling theory, while the coercive field increased with decreasing particle size consistent with a surface model. The main conclusion of this work is that surface effects and not finite-size effects play a major role in the change of the magnetic properties with size in Co 3O 4 nanoparticles. The evidence also suggests that the increase in the anisotropy energy density is due to the creation of a surface anisotropy component normal to the surface of the particles.