<p> In this thesis, we investigated a recent and interesting issue in magnetism; spin ice, which is a term used for systems where there is a analogy between their magnetic structure and the proton structure of water ice. Until now, only three spin ices, Dy2Ti2O7, Ho2Ti2O7, and Ho2Sn2O7, have been discovered. In 2002, Ho2Ru2O7 was proposed as a candidate spin ice by Bansal et al. Given the similar structure and experimental behaviors of Ho2Ru2O7 and known spin ice systems, it has been an issue whether Ho2Ru2O7 is the fourth spin ice.</p> <p> In order to determine whether the new candidate is spin ice or not, the magnetic characteristics of Ho2Ru2O7 have been investigated. The frustrated system Ho2Ru2O7 has a pyrochlore structure with magnetic spins located on lattice of corner sharing tetrahedra. The crystal field originated <1 1 1> anisotropy of this sites and ferromagnetic interaction of spins give the preference of a two spin in and two spin out to a center of the tetrahedra.</p> <p> High quality polycrystalline samples were prepared and crystal growth attempts were made, then various measurements have been conducted. DC susceptibility data were used to determine the effective magnetic moment and value of Weiss temperature(θ). Zero field cooled (ZFC) and field cooled (FC) susceptibility data show a small irreversibility below 95K, which indicate ruthenium antiferromagnetic ordering. AC susceptibility measurements show a strong frequency dependence of the susceptibility which is a feature characteristic of spin glass or superparamagnetic materials.</p> <p> Specific heat experiments were conducted to also confirm the existence of Ru magnetic ordering at 95 K. The Debye temperature is estimated to be ~441 K.</p> <p> μSR measurements were conducted at TRIUMF. The measurements of Ho2Ru2O7 show signatures of ruthenium ordering near 95K and holmium near 1.4K. In agreement with previous neutron scattering experiment we conclude that the ground state of Ho2Ru2O7 is antiferromagnetic rather than spin ice. Presumably the ruthenium ordering acts to preclude the holmium moments entering the spin ice state.</p> / Thesis / Master of Science (MSc)

Recently it has been concluded that the SiO₄ silicate tetrahedra in crystals behave as rigid bodies. This conclusion is based on analyses of the atomic displacement factors of Si and O atoms obtained from single crystal diffraction experiments wherein the amplitudes of atomic vibrations are ascribed to translational, librational and screw-correlated modes of motion for the entire SiO₄ group. If the displacement ellipsoids are considered to represent time averaged quadratic surfaces of equal configurational potential energy about the mean position of an atom, then an analysis of the these displacements should provide detailed information about the SiO₄ group and the crystal. The apparent SiO bond lengths recorded for silicates over a range of temperatures are typically either invariant or exhibit a contraction with increasing temperature. A rigid-body thermal analysis was completed for the tetrahedra in nine silicates whose structures have been determined over a range of temperatures from 15 K to 1250 K and whose tetrahedra seem to behave as rigid units. The coordinates provided by the analysis yield bond lengths and polyhedral volumes corrected for the librational motion of each silicate tetrahedron. The bond lengths and volumes estimated for tetrahedra with four bridging oxygens seem to increase with temperature at a faster rate than those with four nonbridging oxygen atoms. Those for tetrahedra with two or three nonbridging oxygen atoms tend to increase at an intermediate rate. An analysis of the rigid-body motion of coordinated polyhedra yields a simple but accurate expression for correcting bond lengths for thermal vibrations. Observed anisotropic displacement parameters for Si and O atoms indicate that the SiO₄ tetrahedra in quartz behave as rigid bodies. A configurational potential energy curve, constructed from the librational components of the rigid body motion of the tetrahedra, shows a double well for α quartz and a single well for β quartz when plotted as a function of the displacement of the O atom with temperature. The configurational energetics of α and β quartz are examined with a theoretical potential energy function based on parameters obtained from molecular orbital calculations. The calculations indicate that the temperature behavior of a quartz is governed by the energetics of the SiOSi angle, in contrast to β quartz which is governed by the energetics of the SiO bond. The mechanism of the α ⇌ β transition is examined in terms of the experimental and modeled configurational potential energy curves. Evidence for the proposal that π bonding is the driving mechanism for the transition is lacking. Structural and volume compressibility data for α-cristobalite were determined by single crystal X-ray diffraction methods for pressures up to ~1.6 GPa, where cristobalite undergoes a reversible phase transition. The bulk modulus was determined to be 11.5(7) GPa with a pressure derivative of 9(2). The SiOSi angle shows a greater decrease than observed for quartz and coesite while the SiO bond lengths and the OSiO angles remain essentially unchanged. The responses of V/V₀ and SiOSi angle to pressure for the silica polymorphs are compared and it is found that the percentage decrease in the volume is linearly correlated with the percentage decrease in the SiOSi angle, regardless of the framework structure type. A mathematical modeling of the energies of the structural changes that are induced by pressure suggests that the contribution to the total energy ascribed to Si0Si angle bending terms is the same in quartz and cristobalite. / Ph. D.

This thesis describes the synthesis of a host of polynuclear iron complexes synthesised with phenolic oxime ligands, fundamentally developing the coordination chemistry of iron with these ligands. The metallic cores that occur within iron phenolic oxime clusters were found to contain almost exclusively oxo-centred triangles and oxo-centred tetrahedra. We found that we could alter the reaction conditions or derivatise the ligands and develop these basic building blocks into more elaborate arrays, exerting a degree of control over creating larger or smaller clusters. Chapter one describes the syntheses, structures and magnetic properties of new iron complexes alongside previously synthesised related complexes (4, 5, 8, 9 and 15) containing salicylaldoxime (saoH2) or derivatised salicylaldoximes (RsaoH2). These are [Fe3O(OMe)(Ph-sao)2Cl2(py)3]·2MeOH (1·2MeOH), [Fe3O(OMe)(Ph-sao)2Br2(py)3]·Et2O (2·Et2O), [Fe4(Ph-sao)4F4(py)4]·1.5MeOH (3·1.5MeOH), [Fe6O2(OH)2(Et-sao)2(Et-saoH)2(O2CPh)6] (4), [HNEt3]2[Fe6O2(OH)2(Et-sao)4(O2CPh(Me)2)6]·2MeCN (5·2MeCN), [Fe6O2(O2CPh)10(3-tBut-5-NO2-sao)2(H2O)2]·2MeCN (6·2MeCN), [Fe6O2(O2CCH2Ph)10(3-tBut-sao)2(H2O)2]·5MeCN (7·5MeCN), {[Fe6Na3O(OH)4(Me-sao)6(OMe)3(H2O)3(MeOH)6]·MeOH}n (8·MeOH) and [HNEt3]2[Fe12Na4O2(OH)8(sao)12(OMe)6(MeOH)10] (9). The predominant building block appears to be the triangular [Fe3O(R-sao)3]+ species which can self-assemble into more elaborate arrays depending on reaction conditions. The four hexanuclear and two octanuclear complexes of formulae [Fe8O2(OMe)4(Mesao) 6Br4(py)4]·2Et2O·MeOH (10·2Et2O·MeOH), [Fe8O2(OMe)3.85(N3)4.15(Mesao) 6(py)2] (11), [Fe6O2(O2CPh-4-NO2)4(Me-sao)2(OMe)4Cl2(py)2] (12), [Fe6O2(O2CPh-4-NO2)4(Et-sao)2(OMe)4Cl2(py)2]·2Et2O·MeOH (13·2Et2O·MeOH), [HNEt3]2[Fe6O2(Me-sao)4(SO4)2(OMe)4(MeOH)2] (14) and [HNEt3]2[Fe6O2(Etsao) 4(SO4)2(OMe)4(MeOH)2] (15) all are built from series of edge-sharing [Fe4( μ4- O)]10+ tetrahedra. Complexes 10 and 11 display a new μ4-coordination mode of the oxime ligand and join a small group of Fe-phenolic oxime complexes with nuclearity greater than six. Chapter three then introduces co-ligands to the reaction scheme to compete with the salicylaldoxime ligands for metal coordination sites. Five tetranuclear and two nononuclear complexes are stabilised with salicylaldoxime (saoH2) or derivatised salicylaldoximes (R-saoH2) in conjunction with either 1,4,7- triazocyclononane (tacn), 2-hydroxymethyl pyridine (hmpH) or 2,6-pyridine dimethanol (pdmH2), [Fe4O2(sao)4(tacn)2]·2MeOH (16·MeOH), [Fe4O2(Mesao) 4(tacn)2]·2MeCN (17·2MeCN), [Fe4O2(Et-sao)4(tacn)2]·MeOH (18·MeOH), [Fe9NaO4(Et-sao)6(hmp)8]·3MeCN·Et2O (19·3MeCN·Et2O), [Fe4 (Etsao) 4(hmp)4]·Et-saoH2 (20·Et-saoH2), [Fe4(Ph-sao)4(hmp)4]·2MeCN (21·2MeCN) [Fe9O3(sao)(pdm)6(N3)7(H2O)] (22). Chapter four straps two salicylaldoxime units together in the 3-position, using ligands with aliphatic a,W-aminomethyl links, allowing the assembly of the polynuclear complexes [Fe7O2(OH)6(H2L1)3(py)6](BF4)5·6H2O·14MeOH (23·6H2O·14MeOH), [Fe6O(OH)7(H2L2)3][(BF4)3]·4H2O·9MeOH (24·4H2O·9MeOH) and [Mn6O2(OH)2(H2L1)3(py)4(MeCN)2](BF4)5(NO3)·3MeCN·H2O·5py (25·3MeCN·H2O·5py). In each case the metallic skeleton of the cluster is based on a trigonal prism in which two [MIII 3O] triangles are tethered together via three helically twisted double-headed oximes. The latter are present as H2L2- in which the oximic and phenolic O-atoms are deprotonated and the amino N-atoms protonated, with the oxime moieties bridging across the edges of the metal triangles. Both the identity of the metal ion and the length of the straps connecting the salicylaldoxime units have a major impact on the nuclearity and topology of the resultant cage, with, perhaps counter-intuitively, the longer straps producing the “smallest” clusters.

We prove a couple of conjectures raised by J. J. Seidel in On the volume of a hyperbolic simplex, Stud. Sci. Math. Hung. (21, 243249, 1986). These conjectures concern the volume of ideal hyperbolic tetrahedra in hyperbolic 3-space and are related to the following general framework. Since explicit formulae for geometric quantities in hyperbolic space (distance, area, volume, etc.) typically involve sophisticated transcendental functions, it is desirable (and quite useful in practice) to expresses these geometric quantities as monotonic functions of algebraic maps. Seidels Speculation 1 says that the volume of an ideal tetrahedron in hyperbolic 3-space depends only on the determinant and permanent of the doubly stochastic Gram matrix of its vertices; Speculation 4 claims that the mentioned volume is monotone in both the determinant and permanent. We are able to give affirmative answers to Speculations 1 and 4 by parameterizing the classifying space of (labelled) ideal tetrahedra in a suitable way. / Provamos duas conjecturas apresentadas por J. J. Seidel em On the volume of a hyperbolic simplex, Stud. Sci. Math. Hung. (21, 243249, 1986). Estas conjecturas referem ao volume de tetraedros ideais no 3-espaço hiperbólico e estão relacionadas com o seguinte quadro geral. Como fórmulas explícitas para grandezas geométricas no espaço hiperbólico (distancia, área, volume, etc.) tipicamente envolvem funções transcendentais sofisticadas, é desejável (e, na prática, bastante útil) expressar tais grandezas geométricas como aplicações monótonas de mapas algébricos. A Especulação 1 de Seidel diz que o volume de um tetraedro ideal no 3-espaço hiperbólico depende apenas do determinante e do permanente da matriz de Gram duplamente estocástica G de seus vértices; a Especulação 4 afirma que o referido volume é monótono tanto no determinante quanto no permanente de G. Damos respostas afirmativas ás Especulações 1 e 4 ao parametrizar o espaço classificador de tetraedros ideais (marcados) de maneira adequada.

We prove a couple of conjectures raised by J. J. Seidel in On the volume of a hyperbolic simplex, Stud. Sci. Math. Hung. (21, 243249, 1986). These conjectures concern the volume of ideal hyperbolic tetrahedra in hyperbolic 3-space and are related to the following general framework. Since explicit formulae for geometric quantities in hyperbolic space (distance, area, volume, etc.) typically involve sophisticated transcendental functions, it is desirable (and quite useful in practice) to expresses these geometric quantities as monotonic functions of algebraic maps. Seidels Speculation 1 says that the volume of an ideal tetrahedron in hyperbolic 3-space depends only on the determinant and permanent of the doubly stochastic Gram matrix of its vertices; Speculation 4 claims that the mentioned volume is monotone in both the determinant and permanent. We are able to give affirmative answers to Speculations 1 and 4 by parameterizing the classifying space of (labelled) ideal tetrahedra in a suitable way. / Provamos duas conjecturas apresentadas por J. J. Seidel em On the volume of a hyperbolic simplex, Stud. Sci. Math. Hung. (21, 243249, 1986). Estas conjecturas referem ao volume de tetraedros ideais no 3-espaço hiperbólico e estão relacionadas com o seguinte quadro geral. Como fórmulas explícitas para grandezas geométricas no espaço hiperbólico (distancia, área, volume, etc.) tipicamente envolvem funções transcendentais sofisticadas, é desejável (e, na prática, bastante útil) expressar tais grandezas geométricas como aplicações monótonas de mapas algébricos. A Especulação 1 de Seidel diz que o volume de um tetraedro ideal no 3-espaço hiperbólico depende apenas do determinante e do permanente da matriz de Gram duplamente estocástica G de seus vértices; a Especulação 4 afirma que o referido volume é monótono tanto no determinante quanto no permanente de G. Damos respostas afirmativas ás Especulações 1 e 4 ao parametrizar o espaço classificador de tetraedros ideais (marcados) de maneira adequada.

<p>In order to achieve results that are reliable when using the finite element method one has to use an acceptable element mesh with respect to the shape and size of the elements. As a help to produce an acceptable mesh there are quality criteria that must be fulfilled in most pre-processors.</p><p>One objective with this thesis is to perform a sensitivity study that can be used as a basis for a Mesh guideline for chassis parts which is requested from engineers at Volvo 3P. The software used in the sensitivity study is ANSA as pre-processor, Nastran as solver and Metapost as post-processor.</p><p>In the first part of the sensitivity study three different models are used for studying quality criteria such as aspect ratio, skewness, mid point alignment, mid point deviation and element size. Solid elements of second order, which are used in the three models, can be generated in two ways, which constitutes another part of the sensitivity study. They may either be generated from the beginning or can be converted from first order elements. This means geometrically that if second order elements where generated from the beginning the element mesh would follow the shape of the component in a better way compared to the other method.</p><p>Recently a pre- and post-processing program called SimLab was introduced on the market. Since SimLab supports geometry import from several CAD-systems without loss of feature information, the automatic element mesh generation is supposed to be better as the mesh generator has access to more information concerning the geometry. An evaluation of SimLab is the second major objective of the thesis. More specifically, the evaluation concerns the possibility of using the software at Volvo 3P.</p><p>Results show a surprising insensitivity regarding the criteria and that the method of generating second order elements from the beginning is to be preferred. SimLab is a new program with big potential and the conclusion is that it is possible to use it at Volvo 3P.</p>

In order to achieve results that are reliable when using the finite element method one has to use an acceptable element mesh with respect to the shape and size of the elements. As a help to produce an acceptable mesh there are quality criteria that must be fulfilled in most pre-processors. One objective with this thesis is to perform a sensitivity study that can be used as a basis for a Mesh guideline for chassis parts which is requested from engineers at Volvo 3P. The software used in the sensitivity study is ANSA as pre-processor, Nastran as solver and Metapost as post-processor. In the first part of the sensitivity study three different models are used for studying quality criteria such as aspect ratio, skewness, mid point alignment, mid point deviation and element size. Solid elements of second order, which are used in the three models, can be generated in two ways, which constitutes another part of the sensitivity study. They may either be generated from the beginning or can be converted from first order elements. This means geometrically that if second order elements where generated from the beginning the element mesh would follow the shape of the component in a better way compared to the other method. Recently a pre- and post-processing program called SimLab was introduced on the market. Since SimLab supports geometry import from several CAD-systems without loss of feature information, the automatic element mesh generation is supposed to be better as the mesh generator has access to more information concerning the geometry. An evaluation of SimLab is the second major objective of the thesis. More specifically, the evaluation concerns the possibility of using the software at Volvo 3P. Results show a surprising insensitivity regarding the criteria and that the method of generating second order elements from the beginning is to be preferred. SimLab is a new program with big potential and the conclusion is that it is possible to use it at Volvo 3P.

Optimal partitioning of three-dimensional (3-D) mesh applications necessitates dynamically determining and optimizing for the most time-inhibiting factors, such as load imbalance and communication volume. One challenge is to create an analytical model where the programmer can focus on optimizing load imbalance or communication volume to reduce execution time. Another challenge is the best individual performance of a specific mesh refinement demands precise study and the selection of the suitable computation strategy. Very-large-scale finite element method (FEM) applications require sophisticated capabilities for using the underlying parallel computer's resources in the most efficient way. Thus, classifying these requirements in a manner that conforms to the programmer is crucial. / This thesis contributes a simulation-based approach for the algorithm analysis and design of parallel, 3-D FEM mesh refinement that utilizes Petri Nets (PN) as the modeling and simulation tool. PN models are implemented based on detailed software prototypes and system architectures, which imitate the behaviour of the parallel meshing process. Subsequently, estimates for performance measures are derived from discrete event simulations. New communication strategies are contributed in the thesis for parallel mesh refinement that pipeline the computation and communication time by means of the workload prediction approach and task breaking point approach. To examine the performance of these new designs, PN models are created for modeling and simulating each of them and their efficiencies are justified by the simulation results. Also based on the PN modeling approach, the performance of a Random Polling Dynamic Load Balancing protocol has been examined. Finally, the PN models are validated by a MPI benchmarking program running on the real multiprocessor system. The advantages of new pipelined communication designs as well as the benefits of PN approach for evaluating and developing high performance parallel mesh refinement algorithms are demonstrated.

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