Search NASA⌕ Search

SEARCH · Search NASA

Results for “Polyhedra”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A geometric modeler based on a dual-geometry representation polyhedra and rational b-splines

For speed and data base reasons, solid geometric modeling of large complex practical systems is usually approximated by a polyhedra representation. Precise parametric surface and implicit algebraic modelers are available but it is not yet practical to model the same level of system complexity with these precise modelers. In response to this contrast the GEOMOD geometric modeling system was built so that a polyhedra abstraction of the geometry would be available for interactive modeling without losing the precise definition of the geometry. Part of the reason that polyhedra modelers are effective is that all bounded surfaces can be represented in a single canonical format (i.e., sets of planar polygons). This permits a very simple and compact data structure. Nonuniform rational B-splines are currently the best representation to describe a very large class of geometry precisely with one canonical format. The specific capabilities of the modeler are described.

Klosterman, A. L.↗
DOE OSTI2023

Cation coordination polyhedra lead to multiple lengthscale organization in aqueous electrolytes

Understanding multiple lengthscale correlations in the pair distribution functions (PDFs) of aq. electrolytes is a persistent challenge. Here, the coordination chemistry of polyoxoanions supports an ion-network of cation-coordination polyhedra in NaNO 3(aq) and NaNO 2(aq) that induce long-range solution structure. Further, oxygen correlations associated with Na + -coordination polyhedra have two characteristics lengthscales; 3.5–5.5 Å and 5.5–7.5 Å, the latter solely associated oligomers. The PDF contraction between 5.5–7.5 Å observed in many electrolytes is attributed to the distinct O···O correlation found in dimers and dimer subunits within oligomers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Low Thermal Conductivity in Heteroanionic Materials with Layers of Homoleptic Polyhedra

Although BiAgOSe, an analogue of a well-studied thermoelectric material BiCuOSe, is thermodynamically stable, its synthesis is complicated by the low driving force of formation from the stable binary and ternary intermediates. Here we have developed a “subtraction strategy” to suppress byproducts and produce pure phase BiAgOSe using hydrothermal methods. Electronic structure calculations and optical characterization show that BiAgOSe is an indirect bandgap semiconductor with a bandgap of 0.95 eV. The prepared sample exhibits lower lattice thermal conductivities (0.61 W·m –1 ·K –1 at room temperature and 0.35 W·m –1 ·K –1 at 650 K) than BiCuOSe. Further, lattice dynamical simulations and variable temperature diffraction measurements demonstrate that the low lattice thermal conductivity arises from both the low sound velocity and high phonon–phonon scattering rates in BiAgOSe. These in turn result primarily from the soft Ag–Se bonds in the edge-sharing AgSe 4 tetrahedra and large sublattice mismatch between the quasi-two-dimensional [Bi 2 O 2 ] 2+ and [Ag 2 Se 2 ] 2– layers. These results highlight the advantages of manipulating the chemistry of homoleptic polyhedra in heteroanionic compounds for electronic structure and phonon transport control.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Altering the solubility of metal–organic polyhedra via pendant functionalization of Cp 3 Zr 3 O(OH) 3 nodes

Here, the chemistry of zirconium-based metal-organic polyhedra (ZrMOPs) is often limited by their poor solubilities. Despite their attractive features—including high yielding and facile syntheses, predictable topologies, high stability, and tunability—problematic solubilities have caused ZrMOPs to be under-studied and under-applied. Although these cages have been synthesized with a wide variety of carboxylate-based bridging ligands, we explored a new method for ZrMOP functionalization via node-modification, which we hypothesized could influence solubility. Herein, we report ZrMOPs with benzyl-, vinylbenzyl-, and trifluoromethylbenzyl-pendant groups decorating cyclopentadienyl moieties. The series was characterized by 1 H/ 19 F NMR, high-resolution mass spectrometry, infrared spectroscopy, and single-crystal X-ray diffraction. The effects of node functionalities on ZrMOP solubility were quantified using inductively coupled plasma mass spectrometry. Substitution caused a decrease in water solubility, but for certain organic solvents, e.g. DMF, solubility could be enhanced by ~20×, from 16 μM for the unfunctionalized cage to 310 μM for the vinylbenzyl- and trifluoromethylbenzyl-cages.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Space-tiled colloidal crystals from DNA-forced shape-complementary polyhedra pairing

Generating space-filling arrangements of most discrete polyhedra nanostructures of the same shape is not possible. However, if the appropriate individual building blocks are selected (e.g., cubes), or multiple shapes of the appropriate dimensions are matched (e.g., octahedra and tetrahedra) and their pairing interactions are subsequently forced, space-filled architectures may be possible. With flexible molecular ligands (polyethylene glycol–modified DNA), the shape of a polyhedral nanoparticle can be deliberately altered and used to realize geometries that favor space tessellation. In this work, 10 new colloidal crystals were synthesized from DNA-modified nanocrystal building blocks that differed in shapes and sizes, designed to form space-filling architectures with micron-scale dimensions. The insights and capabilities provided by this new strategy substantially expand the scope of colloidal crystals possible and provide an expanded tool kit for researchers interested in designing metamaterials.

Science & Technology - Other Topics↗
DOE OSTI2026

Many paths, similar destinations: viruses and bacterial microcompartments form polyhedra inside cells

A large number of biological entities assemble into icosahedral structures, and these are ubiquitous throughout nature. Examples include eukaryotic and prokaryotic viral capsids and more recently discovered bacterial microcompartments. Viral capsids and bacterial microcompartments are both composed of pentameric and hexameric subunits; however, they differ in the type of cargo they encapsulate: nucleic acid or protein. Also, both depart from strict icosahedral symmetry: while this is less common in viruses, among bacterial microcompartments, diverse and heterogeneous polyhedra are common. We review shared principles and key distinctions between the self-directed assembly of various icosahedral architectures and their polyhedral variants in nature and explore the concept that there are multiple paths, influenced by their cargo, to arriving at similar protein cage morphologies.

bacterial microcompartments↗
DOE OSTI2024

Syntheses and crystal structures of four new d 0 transition metal tellurites

Four new d 0 transition metal tellurites, namely InVTeO 6 (1), β-InVTe 2 O 8 (2), FeVTe 2 O 8 (3), and Fe 2 MoTe 2 O 10 (4), were synthesized under hydrothermal conditions, and their crystal structures were determined using single-crystal X-ray diffraction. Compound 1 crystallizes in the noncentrosymmetric space group P2 1 2 1 2 1 (No. 19), with unit cell parameters of a = 5.0759(2) Å, b = 8.5030(3) Å, c = 11.6376(5) Å, V = 502.28(3) Å 3 , and Z = 4, while the other three compounds crystallize in centrosymmetric structures, with space group Cmca and unit cell parameters of a = 7.0633(7) Å, b = 8.962(1) Å, c = 20.162(2) Å, V = 1276.3(2) Å 3 , and Z = 8 for compound 2, space group P2 1 /n and unit cell parameters of a = 7.8901(2) Å, b = 4.9617(1) Å, c = 16.4290(3) Å, β = 93.6198(8)°, V = 641.88(2) Å 3 , and Z = 4 for compound 3, and space group Pnma and unit cell parameters of a = 8.7878(2) Å, b = 6.1327(2) Å, c = 15.2423(4) Å, V = 821.45(4) Å 3 , and Z = 4 for compound 4. Compound 3 adopts a two-dimensional (2D) sheet structure composed of FeO 6 octahedra, VO 4 tetrahedra, and TeO 4 polyhedra. The other three compounds exhibit three-dimensional (3D) framework structures: Compound 1 is built from InO 6 octahedra, VO 4 tetrahedra, TeO 4 polyhedra; Compound 2 consists of InO 6 octahedra, VO 5 square pyramids, and TeO 3 polyhedra; and Compound 4 is composed of FeO 6 octahedra, MoO 6 octahedra, and TeO 3 polyhedra. The band structures, density of states, and electron localization functions of all four compounds were calculated. The vibrational spectra were examined for compounds 1, 2, and 4. Furthermore, powder X-ray diffraction, element analysis, and thermogravimetric analysis were conducted for compound 4.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Collision detection for spacecraft proximity operations

Collision Detection for Spacecraft Proximity Operations This thesis describes the development of a new collision detection algorithm to be used when two spacecraft are operating in the same vicinity. The two spacecraft are modelled as unions of convex polyhedra, where the polyhedron resulting from the union may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. The algorithm determines if a collision is possible and, if so, predicts the time when the collision will take place. The theoretical basis for the new collision detection algorithm is the C-function formulation of the configuration space approach recently introduced by researchers in robotics. Three different types of C-functions are defined that model the contacts between the vertices, edges, and faces of the polyhedra representing the two spacecraft. These C-functions are used to formulate three "collision" conditions. The first of these conditions limits the points representing potential collisions to the zeros of the C-functions. The new algorithm is fundamentally a search for the smallest zero of any C-function that satisfies the second and third collision conditions. The C-functions are shown to be transcendental functions of time for the assumed trajectory of the moving spacecraft. The zeros of these functions cannot be expressed in dosed form. Therefore, numerical search procedures are developed to find aLl of the zeros of a C-function in specified bounded intervals of time. These bounded intervals of time are found by examining the second and third collision conditions. The capabilities of the new algorithm are demonstrated for several example cases. These include examples of collisions determined by zeros of each of the three different types of C-functions. In addition to predicting the time of first contact of the polyhedra, the algorithm identifies the features of the two polyhedra that are touching at this time. The new collision detection algorithm is the first such algorithm that is capable of solving the collision detection problem exactly for the case where the moving object has constant linear and angular velocities. This is a significant improvement on previous collision detection algorithms described in the literature. In particular, the ability to handle constant angular velocity represents a more realistic type of rotational motion than those which have been used in other algorithms.

Robin M Vaughan↗
DOE OSTI2022

The Euler characteristic as a basis for teaching topology concepts to crystallographers

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V – E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χ m ) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χ m has an elegant topological interpretation through the concept of orbifolds. Alternatively, χ m can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss–Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A New Sodium Thioborate Fast Ion Conductor: Na 3 B 5 S 9

Abstract We report a new sodium fast‐ion conductor, Na 3 B 5 S 9 , that exhibits a high Na ion total conductivity of 0.80 mS cm −1 (sintered pellet; cold‐pressed pellet=0.21 mS cm −1 ). The structure consists of corner‐sharing B 10 S 20 supertetrahedral clusters, which create a framework that supports 3D Na ion diffusion channels. The Na ions are well‐distributed in the channels and form a disordered sublattice spanning five Na crystallographic sites. The combination of structural elucidation via single crystal X‐ray diffraction and powder synchrotron X‐ray diffraction at variable temperatures, solid‐state nuclear magnetic resonance spectra and ab initio molecular dynamics simulations reveal high Na‐ion mobility (predicted conductivity: 0.96 mS cm −1 ) and the nature of the 3D diffusion pathways. Notably, the Na ion sublattice orders at low temperatures, resulting in isolated Na polyhedra and thus much lower ionic conductivity. This highlights the importance of a disordered Na ion sublattice—and existence of well‐connected Na ion migration pathways formed via face‐sharing polyhedra—in dictating Na ion diffusion.

Zhou, Laidong↗
DOE OSTI2023

A New Sodium Thioborate Fast Ion Conductor: Na 3 B 5 S 9

Abstract We report a new sodium fast‐ion conductor, Na 3 B 5 S 9 , that exhibits a high Na ion total conductivity of 0.80 mS cm −1 (sintered pellet; cold‐pressed pellet=0.21 mS cm −1 ). The structure consists of corner‐sharing B 10 S 20 supertetrahedral clusters, which create a framework that supports 3D Na ion diffusion channels. The Na ions are well‐distributed in the channels and form a disordered sublattice spanning five Na crystallographic sites. The combination of structural elucidation via single crystal X‐ray diffraction and powder synchrotron X‐ray diffraction at variable temperatures, solid‐state nuclear magnetic resonance spectra and ab initio molecular dynamics simulations reveal high Na‐ion mobility (predicted conductivity: 0.96 mS cm −1 ) and the nature of the 3D diffusion pathways. Notably, the Na ion sublattice orders at low temperatures, resulting in isolated Na polyhedra and thus much lower ionic conductivity. This highlights the importance of a disordered Na ion sublattice—and existence of well‐connected Na ion migration pathways formed via face‐sharing polyhedra—in dictating Na ion diffusion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Bifunctional Metal‐Organic Nanoballs Featuring Lewis Acidic and Basic Sites as a New Platform for One‐Pot Tandem Catalysis

Abstract The design and synthesis of polyhedra using coordination‐driven self‐assembly has been an intriguing research area for synthetic chemists. Metal‐organic polyhedra are a class of intricate molecular architectures that have garnered significant attention in the literature due to their diverse structures and potential applications. Hereby, we reportCu‐MOP, a bifunctional metal‐organic cuboctahedra built using 2,6‐dimethylpyridine‐3,5‐dicarboxylic acid and copper acetate at room temperature. The presence of both Lewis basic pyridine groups and Lewis acidic copper sites imparts catalytic activity to Cu‐MOP for the tandem one‐pot deacetalization‐Knoevenagel/Henry reactions. The effect of solvent system and time duration on the yields of the reactions was studied, and the results illustrate the promising potential of these metal‐organic cuboctahedra, also known as nanoballs for applications in catalysis.

Chemistry↗
DOE OSTI2022

Grain incompatibility determines the local structure of amorphous grain boundary complexions

Amorphous grain boundary complexions lack long-range crystalline order but are not featureless, as distinct gradients in structural short-range order have been reported through their thickness. In this work, we test the hypothesis that the distribution of short-range order is determined by the confining crystals using atomistic simulations of both Cu-Zr bicrystals and a random polycrystal. Voronoi polyhedra with structures similar to that of perfect face-centered cubic serve as signatures of high structural order and are only found at the amorphous-crystalline transition regions. The density of the ordered structural motifs within a specific amorphous-crystalline transition region is found to not be directly determined by the orientation and symmetry of the grain which touches it, but rather by the incompatibility between the two confining grains. Further, ordered polyhedra density is found to be inversely related to grain incompatibility, meaning that large incompatibilities between the confining crystals lead to less order in the amorphous-crystalline transition region. The finding that the entire grain-film-grain system must be considered to understand local structure unequivocally demonstrates that amorphous complexions are not simply a collection of independent phases which happen to nucleate at a grain boundary. Rather, an amorphous grain boundary complexion is a single entity that finds a local equilibrium configuration.

36 MATERIALS SCIENCE↗