This investigation is designed to find quaternion operators which will generate selected space groups and which are more convenient to manipulate in some important types of problems.

Nuclear magnetic resonance techniques can provide highly accurate information about the local environment of both liquid and solid samples. In the first half of this dissertation research, solid state NMR has provided experimental evidence for turbostratic disorder in layered covalent organic solids. Additionally, comparison with candidate structures allowed a proposed correction to the accepted structure of Covalent Organic Framework-5. The second half of the dissertation work emphasized liquid NMR spectroscopy applied to doped iron oxides (IOs). In particular, the effect of IOs on water proton T2 relaxation times were determined as a measure of contrast agent efficacy. Both types of data lend towards structure elucidation for material efficiency.

<p>The high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.</p> / Dissertation

Precession photography was used to determine the lattice parameters, the crystal system, the space group and the structure of an artificial Sr-labradorite of composition: Ab27, SrAn73. C= 7.107Å, Ɣ= 90 degrees, β= 115.834 degrees. The crystal system is monoclinic, space group= C2/ m and structure is albite type, reflections being restricted to the 'a' type. The abundance, lithophile characteristics and appropriate ionic radii of elements in Groups IA and IIA are the factors governing their presence as cations of feldspars in nature. The structures of feldspars are discussed as a function of the relative proportion of cations of a charge of +1 and +2. The crystal symmetry (i.e. monoclinicity or triclinicity) is discussed as a function of the ionic radius of the cation. / Thesis / Bachelor of Science (BSc)

Acetylenedicarboxylic acid monopotassium salt, ADCA-K, was polymerized by radiation induced solid-state and chemical initiator induced solution polymerization methods. Radiation induced solid-state polymerization was carried out by Co-60 g-radiation at room temperature. The powder polymer obtained was soluble in water but insoluble in common organic solvents. The solution polymerization initiated by benzoylperoxide was carried out in an oil bath at 90&deg / C. The polymer obtained was soluble in water but insoluble in dimethylsulfoxide. In the first stage of the polymerization, H2O, CO and/or CO2 gases were evolved and the polymerization was proceeded on the acetylene group. The polymers obtained were characterized by FT-IR, DSC, TGA-FTIR, NMR and DP-MS methods. The crystal structure effect on polymerization was investigated by X-Ray method. The monomer is monoclinic with a space group of C2/c. The unit cell parameters are a=795.4, b=1192.6, c=591.8 pm and b=105.40. Polymer showed a partial polycrystalline structure. The larger fraction of polymer has identical crystal structure to that of the monomer. Therefore, polymerization takes place a topotactic mechanism.

The systematic investigation of the x-ray diffraction symmetry of scapolites covering the whole range of solid solution show that all scapolites possess space group P4(2)/n, except the pure end-members, marialite and meionite, which will possess space group I4/m, if they exist. The intensity of the weak superlattice reflections violating the body-centred symmetry, continuously increases from zero at the marialite end-member as Me% increases, reaches a maximum around 37%+/-2% Me then approximately symmetrically decreases to 75% Me followed by a slower decrease to zero at the meionite end-member. Hence, all the intermediate scapolites of the marialite-meionite series actually have a pseudosymmetric structure, i. e., a pseudobody-centred structure, and as the chemical composition approaches both end-members, the scapolite structure approaches the structure with a body-centred lattice. The weak super-lattice reflections are directly related to the following two correlated factors: (1) the relative order-disorder of A1 and Si distribution in the tetrahedral framework, and (2) the structural distortion from the body-centred symmetry. Accompanied with the above facts is the systematic deviation of cell dimensions from the linear regression in such a way that the further the structure deviates from the body-centred symmetry, the smaller the cell volume and the a(o) become relative to the evaluated one from the linear regression. Scapolites are regarded as a continuous, perfect solid solution with a long-range disordering, and unlikely to be composed of submicroscopic twins or different domains. The structural analyses and refinements of three scapolites (ON8, 20% Me; XL, 52% Me; ON45, 93% Me) have been carried out by using 3-dimensional intensity data collected by integrated precession film techniques (ON8, ON45) and an automated single-crystal diffractometer (XL), and using the full-matrix least0squares method. The result has clarified the ambiguities arising from the previous studies and showed that the crystal structure is essentially continuous along the marialite-meionite series, with a slight structural variation as a function of chemical composition and ordering of Al, Si. Several important quantitative relationships regarding the crystal structure and crystal chemistry of the scapolite solid solution series have been established, namely, (1) the relationship between the superlattice intensity r(ΣI(h+k+l=2n+1)/ΣI(h+k+l=2n)) and the chemical index % Me. (2) the exponential relationship between the superlattice intensity ration r and the atomic displacement from the mirror plane consistent with the space group I4/m. (3) The linear relationship between the superlattice intensity ratio r and the difference of Al occupancy between T2 and T3 sites. (4) The Al occupancy (%) of tetrahedral sites as a function of the chemical composition of scapolites. The ordering of Al-Si, the c-axis displacement of (Ca, Na), the tilting of CO3 and the relative amount of CO3 and Cl in the same scapolite are all inter-related. The mechanism to cause all such related structural phenomena and even the abnormal stoichiometry of scapolite can all be interpreted in terms of the internal strain created by the two greatly different anions, Cl- and CO3-,sharing the same set of equivalent sites. / Thesis / Doctor of Philosophy (PhD)

In a crystalline ordered magnet, coherent excitations called spin waves, or magnons, propagate in the material forming band structures in an analogous way to electrons. Spin waves can possess non trivial topology associated with novel response functions of fundamental and potential technological interest. In particular, topologically protected surface states of magnons offer a new path towards coherent spin transport for spintronics applications. One of the central issues in this area is to establish the conditions under which band topology can arise in magnons and explore its variety. In this work we harness the full power of symmetry as applied to magnetism, to facilitate the discovery of new topological magnon models and materials. We show how to efficiently identify such systems by adapting the electronic topological quantum chemistry scheme to magnons, using constraints imposed by time reversal and crystalline symmetries to determine possible gapped and nodal topology in magnon models. Further, we explore enhanced symmetries beyond this paradigm, which are nevertheless natural for magnons: the spin-space groups. Exploring spin-space symmetry, which has wholly or partially decoupled magnetic and lattice degrees of freedom, reveals a proliferation of nodal points, lines, and planes beyond the standard crystalline symmetries. Linear spin wave theory is one of the most valuable techniques to study magnons, however, it can fail in different scenarios. Because of its importance to the community, we explore cases where it contains spurious symmetries which can potentially hide important physics in the spectra, like topology. We provide therefore a simple way to identify and resolve such cases within the linear theory. Finally, a pressing issue in magnons is the experimental detection and manipulation of topological surface states. Even more, the characterisation of generic 2D magnetism is an open problem. We contribute to this by devising an experimental setup based on quasi-particle interference which potentially could solve this long-lasting challenge. / Kohärente Anregungen, wie Spinwellen, auch Magnonen genannt, formen Bandstrukturen in kristallin geordneten Materialien. Diese Magnonen können eine nicht triviale Topologie aufwei- sen, welche neuartige Antwortfunktionen erzeugen können. Sie sind daher von technologischem Interesse. Insbesondere die topologisch geschützten Oberflächenzustände der Magnonen ermöglichen eine Realisierung von kohärentem Spin Transport und erlauben eine potentielle Anwendung in der Spintronik. Zentraler Punkt der aktuellen Forschung sind Bedingungen, unter denen eine nicht triviale Magnon-Bandtopologie entstehen kann und welche Möglichkeiten diese eröffnen. In dieser Arbeit untersuchen wir diese neuartigen topologischen Phasen für verschiedene Mo- delle unter Nutzung verschiedener Symmetrien. Die Erweiterung des elektronischen “topological quantum chemistry” Ansatzes für Magnonen erlaubt eine effiziente Identifikation dieser topologischen Eigenschaften. Der Ansatz basiert auf verschiedenen Einschränkungen, welche von der Zeitumkehr und kristallinen Symmetrien induziert werden. Darüber hinaus untersuchen wir die Anwendung von weiteren Symmetrien, welche relevant für Magnonen sind: die Spin-Raumgruppen. Die Erforschung der Spin-Raum-Symmetrie, welche magnetische Freiheitsgrade und Gittersyme- trien ganz oder teilweise entkoppelt, führt zur Ausbreitung von Knotenpunkten, Linien und Ebenen jenseits der standardmäßigen Kristallsymmetrien. Die lineare Spinwellentheorie ist eine der erfolgreichsten Methoden zur Untersuchung von Magnonen, kann jedoch unter verschiedenen Umständen versagen, da künstliche Symmetrien essenzielle Physik, wie beispielsweise topologische Eigenschaften, verbergen. Ansätze, die im Rahmen dieser Dissertation erarbeitet worden sind, helfen dabei, solche Fälle zu identifizieren und zu verstehen. Aktuelle Experimente zur Manipulation topologischer Oberflächenzustände von Magnonen, sowie die allgemeine Untersuchung von Magnetismus in zwei Dimensionen, fehlen. Daher präsentieren wir einen möglichen experimentellen Aufbau, basierend auf Quasi-Teilchen-Interferenz, welcher einen möglichen Ausweg aufzeigt.

The Protein Data Bank (PDB) is the definitive electronic repository for experimentally-derived protein structures, composed mainly of those determined by X-ray crystallography. Approximately 200 new structures are added weekly to the PDB, and at the time of writing, it contains approximately 97,000 structures. This represents an expanding wealth of high-quality information but there seem to be few bioinformatics tools that consider and analyse these data as an ensemble. This thesis explores the development of three efficient, fast algorithms and software implementations to study protein structure using the entire PDB. The first project is a crystal-form matching tool that takes a unit cell and quickly (< 1 second) retrieves the most related matches from the PDB. The unit cell matches are combined with sequence alignments using a novel Family Clustering Algorithm to display the results in a user-friendly way. The software tool, Nearest-cell, has been incorporated into the X-ray data collection pipeline at the Diamond Light Source, and is also available as a public web service. The bulk of the thesis is devoted to the study and prediction of protein disorder. Initially, trying to update and extend an existing predictor, RONN, the limitations of the method were exposed and a novel predictor (called MoreRONN) was developed that incorporates a novel sequence-based clustering approach to disorder data inferred from the PDB and DisProt. MoreRONN is now clearly the best-in-class disorder predictor and will soon be offered as a public web service. The third project explores the development of a clustering algorithm for protein structural fragments that can work on the scale of the whole PDB. While protein structures have long been clustered into loose families, there has to date been no comprehensive analytical clustering of short (~6 residue) fragments. A novel fragment clustering tool was built that is now leading to a public database of fragment families and representative structural fragments that should prove extremely helpful for both basic understanding and experimentation. Together, these three projects exemplify how cutting-edge computational approaches applied to extensive protein structure libraries can provide user-friendly tools that address critical everyday issues for structural biologists.