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This thesis reports an \textit{ab initio} study of the Ge(111)-5$\times$5 reconstruction, which forms on top of a Si(111)-7$\times$7 substrate. Detailed descriptions of the structural and electronic properties of this surface, obtained from density-functional calculations, are presented and analyzed. A study of In clusters on this surface is performed, and compared with recent experimental work on this system. The effect of surface strain as well as the issue of the Si-Ge interface is addressed. Also, a preliminary investigation of some dynamical aspects of an In atom on the 5$\times$5 surface is presented. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2007-10-26 14:14:48.513 / NSERC HPCVL WestGrid

Morrison has constructed a geometric relationship between K3 surfaces with large Picard number and abelian surfaces. In particular, this establishes that the period spaces of certain families of lattice polarized K3 surfaces (which are closely related to the moduli spaces of lattice polarized K3 surfaces) and lattice polarized abelian surfaces are identical. Therefore, we may study the moduli spaces of such K3 surfaces via the period spaces of abelian surfaces. In this thesis, we will answer the following question: from the moduli space of abelian surfaces with endomorphism structure (either a Shimura curve or a Hilbert modular surface), there is a natural map into the moduli space of abelian surfaces, and hence into the period space of abelian surfaces. What sort of relationship exists between the moduli spaces of abelian surfaces with endomorphism structure and the moduli space of lattice polarized K3 surfaces? We will show that in many cases, the endomorphism ring of an abelian surface is just a subring of the Clifford algebra associated to the N\'eron-Severi lattice of the abelian surface. Furthermore, we establish a precise relationship between the moduli spaces of rank 18 polarized K3 surfaces and Hilbert modular surfaces, and between the moduli spaces of rank 19 polarized K3 surfaces and Shimura curves. Finally, we will calculate the moduli space of E_8^2 + <4>-polarized K3 surfaces as a family of elliptic K3 surfaces in Weierstrass form and use this new family to find families of rank 18 and 19 polarized K3 surfaces which are related to abelian surfaces with real multiplication or quaternionic multipliction via the Shioda-Inose construction. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2011-08-12 14:38:04.131

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Recent high-pressure experiments on iridium show a transition to a 14 atomic layer superlattice structure. Since iridium has a high bulk modulus, it is used in many high-pressure applications, for instance as a gasket for high-temperature, high-pressure diamond anvil cell experiments. The effects of pressure on this material are hence of interest. Of the transition metals, the iridium surface has been one of the most extensively studied surfaces experimentally. The field ion microscope has made it possible to observe in detail the behaviour of adatoms on the surface, and has led to interesting discoveries of the nature of atomic adsorption on the lr(111) surface. A number of theoretical and semi-empirical studies have been made on this topic. However, none of these studies take atomic relaxations into account in a satisfactory manner, and therefore do not give a complete understanding of the process of incorporation of adatoms onto the surface. In the present work, first-principles total energy calculations based on the plane wave pseudopotential method within the framework of the density functional theory are employed in the study of the bulk properties of iridium, and the crystal phases and defect structures of iridium under pressure. The bond-orientation model is extended to include the effects of pressure, and used to compute all of the ~2n defect structures of iridium as a function of atomic volume. Allowance for full atomic relaxations is made in computing the ideal and relaxed surface formation energies of the three low-index surfaces of iridium, and in investigating the nature of adsorption of single adatoms on the lr(111) surface. The formation energy of a vacancy on the Ir(111) surface is also computed. This is the first time such a calculation has been made. / Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 2003.

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