Digital objects in rhombic dodecahedron grid

Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system

From Pure Oxides to Mixed Oxides: Model Systems for Structural and Catalytic Studies

As pure oxides and mixed oxide systems play an ever-increasing role in a variety of research fields ranging from catalysis over electrochemical applications to microelectronics, the present contribution aims at introducing a straightforward concept for the easy and reproducible preparation of well-defined and well-structured thin film model systems both for pure and mixed oxide systems. Exploiting the special structural and surface properties of vacuum-cleaved NaCl (001) growth templates, the concept is exempli-fied for the formation of nano-spheres (Ga2O3), nano-pyramids (In2O3), plates and needles (V2O5) and den-dritic structures (Ga2O3-WO3). Careful tuning of the preparation conditions (substrate temperature, depo-sition rate, oxygen partial pressure or post-annealing temperature) allows the formation of special particle morphologies at much lower substrate temperatures (less than 400°C) than previously and usually applied. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3504

Structural characterization of multimetallic nanoparticles

Bimetallic and trimetallic alloy nanoparticles have enhanced catalytic activities due to their unique structural properties. Using in situ time-resolved synchrotron based x-ray diffraction, we investigated the structural properties of nanoscale catalysts undergoing various heat treatments. Thermal treatment brings about changes in particle size, morphology, dispersion of metals on support, alloying, surface electronic properties, etc. First, the mechanisms of coalescence and grain growth in PtNiCo nanoparticles supported on planar silica on silicon were examined in detail in the temperature range 400-900°C. The sintering process in PtNiCo nanoparticles was found to be accompanied by lattice contraction and L10chemical ordering. The mass transport involved in sintering is attributed to grain boundary diffusion and its corresponding activation energy is estimated from the data analysis. ^ Nanoscale alloying and phase transformations in physical mixtures of Pd and Cu ultrafine nanoparticles were also investigated in real time with in situ synchrotron based x-ray diffraction complemented by ex situ high-resolution transmission electron microscopy. PdCu nanoparticles are interesting because they are found to be more efficient as catalysts in ethanol oxidation reaction (EOR) than monometallic Pd catalysts. The combination of metal support interaction and reactive/non-reactive environment was found to determine the thermal evolution and ultimate structure of this binary system. The composition of the as prepared Pd:Cu mixture in this study was 34% Pd and 66% Cu. At 300°C, the nanoparticles supported on silica and carbon black intermix to form a chemically ordered CsCl-type (B2) alloy phase. The B2 phase transforms into a disordered fcc alloy at higher temperature (\u3e450°C). The alloy nanoparticles supported on silica and carbon black are homogeneous in volume, but evidence was found of Pd surface enrichment. In sharp contrast, when supported on alumina, the two metals segregated at 300°C to produce almost pure fcc Cu and Pd phases. Upon further annealing of the mixture on alumina above 600°C, the two metals interdiffused, forming two distinct disordered alloys of compositions 30% and 90% Pd. The annealing atmosphere also plays a major role in the structural evolution of these bimetallic nanoparticles. The nanoparticles annealed in forming gas are larger than the nanoparticles annealed in helium due to reduction of the surface oxides that promotes coalescence and sintering. ^ The nanoscale composition and structure of alloy catalysts affect heterogeneous catalysis. We also studied Pd:Cu nanoparticle mixtures of different compositions. In Pd:Cu of composition ratio 1:1, ordered B2 phase is formed during annealing at 450C. During the ramped annealing from 450°C to 750°C, the B2 phase transforms into two different alloys, one alloy rich in copper and the other rich in Pd. This structural evolution is different from that of Pd-Cu system in bulk. In the 3:1 composition, the B2 phase dominates in the isothermal anneal at 450C but a disordered alloy fcc phase is also formed. On annealing to 750°C, the disordered fcc phase grows at the expense of the B2 phase. These findings have important applications for the thermal activation of Pd-Cu nanocatalysts for EOR reactions

Numeric simulation of atom probe tomography

Die Arbeit beschreibt einen neuen Ansatz zur Simulation von Messdaten, wie sie bei Experimenten mit der Atomsondentomographie erzeugt werden. Derartige Simulationen stellen einen komplementären Ansatz dar, mit dessen Hilfe die Interpretation von Messergebnissen verbessert werden soll. Die atomare Struktur der zu untersuchenden Probe wird maßstabsgerecht durch Wigner-Seitz-Zellen beschrieben. Aus der Berechnung der Trajektorien feldemittierter Ionen ergeben sich zweidimensionale Detektorkoordinaten. Eine Analyse der Trajektorien zeigt vergleichbare Abbildungseigenschaften, wie sie auch mit anderen Simulationsverfahren und in Experimenten ermittelt wurden. Die Flexibilität in der Beschreibung der Probenstruktur beim hier verwendeten Ansatz zeigt sich insbesondere darin, dass realistische Felddesorptionsbilder für beliebige Gitterstrukturen und -orientierungen berechnet werden können (z.B. kubisch, hexagonal, amorphe Strukturen, Korngrenzen)

MODEL STUDY OF PLATINUM NANOPARTICLE INTERACTIONS WITH γ-ALUMINA SINGLE CRYSTAL SUPPORTS

Pt/γ-Al2O3 is arguably the most important heterogeneous catalyst system, as it is used in numerous technologically important processes, including oil refining, catalytic converters and fuel cells. Hence, many investigators have studied Pt/γ-Al2O3 both experimentally and theoretically. Yet, a significant gap exists between experiment and theory since theory models well defined finite systems whereas the commercially available γ-Al2O3 is polycrystalline with ill-defined morphologies, crystallography and impurities. The goal of this thesis project is to synthesize a model Pt/γ-Al2O3 heterogeneous catalyst system which is in the appropriate size regime for theoretical modeling. The critical challenge of this project is the creation of single crystal γ-Al2O3 thin films. To achieve this goal, the growth of single crystal γ-Al2O3 thin film on NiAl(110) surface was systematically investigated by oxidation in dry ambient air to determine the optimal oxidation parameters to form a reasonably flat, defect-free, single crystal γ-Al2O3 film. We determined that the optimal oxidation condition was 850℃ for 1 hour in air that produced an 80 nm thick film with an RMS value of 10 nm. The model Pt/ γ-Al2O3 system was produced by e-beam evaporation of Pt nanoparticles onto the surface of the γ-Al2O3. We characterized the Pt/γ-Al2O3 by transmission electron microscopy techniques for morphological and electronic structure of the nanoparticles and interfaces, respectively. We provide two feasibility studies of obtaining benchmark parameters that could be used by theorists: (1) the interfacial energy through a Wulff-Kashiew analysis of the supported Pt nanoparticles’ shapes and (2) information on the density of states at the interface using electron energy loss spectroscopy. During the course of this study, we also discovered aspects of NiAl oxidation kinetics in the intermediate temperature regime of 650-950℃ where only γ-Al2O3 forms, not the thermodynamically stable α-Al2O3. For example, crystallinity, epitaxy, and surface roughness of the oxide depends on the oxidation temperature due to temperature-dependent strain and relative diffusion behaviors

Scanning transmission electron microscopy tomography and 4D-stem applied to the study of chiral and self-assembled nanoparticles

Over recent years, advances in nanotechnology have led to an increased interest towards engineering nanomaterials with defined morphologies, for applications where the nanoparticle shape plays a significant role in processes, such as in catalysis, drug delivery and optics. Therefore, it is essential to resolve the 3D morphology and structure of these materials in order to gain understanding about their physical and chemical properties for further optimization. Following this line of research, this thesis explores a set of experiments that makes use of Scanning Transmission Electron Microscopy (STEM), incorporating both STEM tomography and 4D-STEM techniques. These techniques were used to investigate the origin of chiral shapes in Tellurium (Te) bipyramidal nanoparticles, where it was determined that the chiral geometries of the nanoparticles arise from growth mediated by screw dislocations rather than chiral ligands used in their synthesis. Gold (Au) nanoparticle self-assembled superlattices were studied by electron tomography and their lattice structure was investigated through determination of the 3D nanoparticle positions. The superlattices were found to have different crystalline structures for different molecular weights of their protective ligands. Finally, gold nanoparticles that seemed to have a twisted bipyramidal geometry were investigated through electron tomography. A model was built from the reconstructed cross-sections which supported the conclusion that the asymmetry in the shape resulted from the arrangement of the facets rather than a twist. The analyses performed in this thesis were custom-developed building upon general electron microscopy and mathematical concepts, enabling their application towards different systems and materials

Finite Element Modeling Driven by Health Care and Aerospace Applications

This thesis concerns the development, analysis, and computer implementation of mesh generation algorithms encountered in finite element modeling in health care and aerospace. The finite element method can reduce a continuous system to a discrete idealization that can be solved in the same manner as a discrete system, provided the continuum is discretized into a finite number of simple geometric shapes (e.g., triangles in two dimensions or tetrahedrons in three dimensions). In health care, namely anatomic modeling, a discretization of the biological object is essential to compute tissue deformation for physics-based simulations. This thesis proposes an efficient procedure to convert 3-dimensional imaging data into adaptive lattice-based discretizations of well-shaped tetrahedra or mixed elements (i.e., tetrahedra, pentahedra and hexahedra). This method operates directly on segmented images, thus skipping a surface reconstruction that is required by traditional Computer-Aided Design (CAD)-based meshing techniques and is convoluted, especially in complex anatomic geometries. Our approach utilizes proper mesh gradation and tissue-specific multi-resolution, without sacrificing the fidelity and while maintaining a smooth surface to reflect a certain degree of visual reality. Image-to-mesh conversion can facilitate accurate computational modeling for biomechanical registration of Magnetic Resonance Imaging (MRI) in image-guided neurosurgery. Neuronavigation with deformable registration of preoperative MRI to intraoperative MRI allows the surgeon to view the location of surgical tools relative to the preoperative anatomical (MRI) or functional data (DT-MRI, fMRI), thereby avoiding damage to eloquent areas during tumor resection. This thesis presents a deformable registration framework that utilizes multi-tissue mesh adaptation to map preoperative MRI to intraoperative MRI of patients who have undergone a brain tumor resection. Our enhancements with mesh adaptation improve the accuracy of the registration by more than 5 times compared to rigid and traditional physics-based non-rigid registration, and by more than 4 times compared to publicly available B-Spline interpolation methods. The adaptive framework is parallelized for shared memory multiprocessor architectures. Performance analysis shows that this method could be applied, on average, in less than two minutes, achieving desirable speed for use in a clinical setting. The last part of this thesis focuses on finite element modeling of CAD data. This is an integral part of the design and optimization of components and assemblies in industry. We propose a new parallel mesh generator for efficient tetrahedralization of piecewise linear complex domains in aerospace. CAD-based meshing algorithms typically improve the shape of the elements in a post-processing step due to high complexity and cost of the operations involved. On the contrary, our method optimizes the shape of the elements throughout the generation process to obtain a maximum quality and utilizes high performance computing to reduce the overheads and improve end-user productivity. The proposed mesh generation technique is a combination of Advancing Front type point placement, direct point insertion, and parallel multi-threaded connectivity optimization schemes. The mesh optimization is based on a speculative (optimistic) approach that has been proven to perform well on hardware-shared memory. The experimental evaluation indicates that the high quality and performance attributes of this method see substantial improvement over existing state-of-the-art unstructured grid technology currently incorporated in several commercial systems. The proposed mesh generator will be part of an Extreme-Scale Anisotropic Mesh Generation Environment to meet industries expectations and NASA\u27s CFD visio

Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios