UMD Theses and Dissertations
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Item Tuning Crystallographic and Magnetic Symmetry in Lithium Transition Metal Phosphates and Thiophosphates(2022) Diethrich, Timothy; Rodriguez, Efrain E.; Chemistry; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Ferroic ordering needs no introduction; ferromagnetic, ferroelectric, and ferroelastic materials have had a significant impact on the materials science community for many years. While these three main types of ferroic ordering are well known, there is a fourth and final, lesser known ferroic ordering known as ferrotoroidicity. A ferrotoroidic material undergoes a spontaneous, physical alignment of toroidal moments under a critical temperature. This study is focused on broadening our current understanding of ferrotoroidics by studying two families of materials: LiMPO4, and Li2MP2S6, where M = Fe, Mn, and Co. While these two materials initially appear to be similar in some regards, many differences can be observed as a deeper dive is taken into their crystallography and magnetic structures. For a toroidal moment to exist, a specific orientation of magnetic moments is required, because of this, only certain magnetic point groups are allowed. For example, LiFePO4 has an “allowed” magnetic point group of m’mm, while it’s delithiated counterpart FePO4 has a “forbidden” magnetic point group of 222. This work has found that by using a new selective oxidation technique, lithium concentration can be controlled in the Li1−xFexMn1−xPO4 solid solution series. Neutron powder diffraction and representational analysis were used to find the magnetic point groups of each member of this series. In the end, each structure was solved and the largest transition temperature to date was reported for a potential ferrotoroidic material. The magnetic exchange interactions can be used to describe the magnetic phase changes that occuracross the Li1−xFexMn1−xPO4 series. The second group of materials in this study is the lithium transition metal thiophosphates of the formula Li2MP2S6, where M = Fe, Co. The structure of Li2FeP2S6 has been previously studied but no magnetic properties of this material have been reported. In addition, neither the structural nor magnetic properties have been reported for the cobalt analog. Single crystalXRD was used to confirm the previously reported crystal structure of Li2FeP2S6 and to find the novel crystal structure of Li2CoP2S6; both crystallize in a trigonal P31m space group. While isostructural in some regard, there are some crucial differences between these materials. The site occupancies are different, resulting in non-trivial charge balances and a unique thiophosphate distortion. Originally, these materials were chosen because their nuclear structure was predicted to host long-range antiferromagnetic order and potentially ferrotoroidic order. Contrary to expectations, magnetic susceptibility and field dependent measurements demonstrated paramagnetic behavior for both the iron and the cobalt sample down to 2 K. This result was further confirmed by a lack of magnetic reflections in the time-of-flight neutron powder diffraction data. While the phosphates and the thiophosphates demonstrated very different structural andmagnetic results, they both remain relevant materials for not only ferrotoroidics, but also magnetoelectrics, spintronics, quantum materials, and much more.Item SHADOW MOIRÉ USING NON-ZERO TALBOT DISTANCE AND APPLICATION OF DIFFRACTION THEORY TO MOIRÉ INTERFEROMETRY(2005-03-02) Han, Chang woon; Han, Bongtae; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)When shadow moiré is practiced in industry for the warpage of microelectronic devices, the required high basic measurement sensitivity limits a dynamic range due to the diffraction effect of the reference grating. An extensive understanding of the contrast and intensity of shadow moiré fringes is required to achieve optical configurations for the measurements. In Part I, an exact mathematical description for the contrast and intensity of shadow moiré fringe is developed using a diffraction theory for a monochromatic light source first. The analysis is extended to study the effect of a broad spectrum light source on the contrast and intensity of shadow moiré fringes. The effect of an aperture on the fringe contrast is defined to propose a complete expression for the contrast of shadow moiré fringe. The mathematical analysis is exploited to define the systematic error from the non-sinusoidal intensity distribution of shadow moiré fringe when the displacement resolution is enhanced using the phase-shifting technique. The results of the mathematical analysis provide a guideline for optimum optical configurations for the required basic measurement sensitivity, which results in a novel technique, called high sensitivity shadow moiré using non-zero Talbot distance (SM-NT). The SM-NT increases the dynamic range substantially and allows the warpage measurements of high-end microelectronics devices, which is not possible with the conventional shadow moiré using the zero Talbot distance. In an achromatic moiré interferometry system, a compensator grating is translated to achieve phase-shifting. The phase-shifting in the achromatic system cannot be explained by the existing theories of moiré interferometry based on the concept of optical path length. In Part II, a diffraction theory is used to explain the phase shifting in the achromatic system. The results reveal that the amount of translation of the compensator grating is proportional to the diffraction order and the frequency of the compensator grating. The diffraction theory based the mathematical description is extended further to define the mini-order diffractions associated with a general deformations. The discrete Fourier transform is employed to characterize the mini-order from a generally deformed grating. The results explain that the magnitude of strain is only parameter to control the angle of mini-order.