Search NASA⌕ Search

SEARCH · Search NASA

Results for “polyhedron”

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
DOE OSTI2023

First Moments of a Polyhedron Clipped by a Paraboloid

We provide closed-form expressions for the first moments (i.e., the volume and volume-weighted centroid) of a polyhedron clipped by a paraboloid, that is, of a polyhedron intersected with the subset of the three-dimensional real space located on one side of a paraboloid. These closed-form expressions are derived following successive applications of the divergence theorem and the judicious parametrization of the intersection of the polyhedron’s faces with the paraboloid. Here, we provide means for identifying ambiguous discrete intersection topologies, and propose a corrective procedure for preventing their occurence. Finally, we put our proposed closed-form expressions and numerical approach to the test with millions of random and manually engineered polyhedron/paraboloid intersection configurations. The results of these tests show that we are able to provide robust machine-accurate estimates of the first moments at a computational cost that is within one order of magnitude of that of state-of-the-art half-space clipping algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Synthesis of perovskite polyhedron nanocrystals with equivalent facets and the controlled growth of Pt nanoparticles with differing surface concentration of oxidized Pt 4+ /Pt 2+ species

Co-existence of different surfaces in traditional polycrystalline heterogeneous catalysts imposes a challenge to induce different kinds of catalytic species and average reactivity. Supported metal/oxide model catalyst designed with equivalent well-defined surfaces and active species provides an opportunity to control the uniformity, maintain efficient activity, and understand catalytic mechanisms at the atomic and molecular levels. Herein, sub-20 nm perovskite-structure BaTiO 3 polyhedron nanocuboids and Zr-substituted rhombic dodecahedron nanocrystals were synthesized and employed as the oxide support for the subsequent uniform growth of 1–2 nm Pt nanoparticles. These Pt nanoparticles were well dispersed on the 12 equivalent (110) facets of BaTi 0.75 Zr 0.25 O 3 rhombic dodecahedra and on the 6 equivalent (100) facets of BaTiO 3 nanocuboids. The main active centers on the Pt/BaTi 0.75 Zr 0.25 O 3 catalysts in the oxidized surface layer of Pt (111) facets are Pt 4+ versus Pt 2+ , which is in contrast to the oxidized surface layer of the Pt (100) facets on the Pt/BaTiO 3 cuboids where there are a greater number of Pt 2+ species. Compared with Pt/BaTiO 3 nanocuboids, the Pt/BaTi 0.75 Zr 0.25 O 3 catalysts demonstrated higher CO catalytic oxidation activity with a lower apparent Arrhenius activation energy. Finally, this work advances our ability to synthesize metal/oxide model catalyst that offer equivalent facets and highly uniform active centers with reasonable surface area in order to gain insight in reaction mechanisms.

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

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2-] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Geochemistry & Geophysics↗
DOE OSTI2020

An ab initio molecular dynamics exploration of associates in Ba-Bi liquid with strong ordering trends

Fictive associates are widely used to describe and model liquid phases with strong ordering trends. However, little evidence is known about the assumed associates in most cases. In the present work, an ab initio molecular dynamics (AIMD) study is employed to investigate the characters of the Ba-Bi liquid, in which associates have been assumed in existing thermodynamic modeling. It is found that in the Ba rich melt, the Bi atoms are almost completely surrounded by Ba atoms. The Bi-centered coordination polyhedrons are strongly associated to crystalline structures of Ba 5 Bi 3 and Ba 4 Bi 3 with a longer lifetime than other polyhedrons during the AIMD simulations. In addition, these Bi-centered polyhedrons in Ba rich melt connect with each other through vertex, edge, face, and/or bipyramid sharing to form medium range orders (MRO). In the Bi rich melt, the Ba-centered polyhedrons also form MROs, but they are both structurally and compositionally diverse with a shorter lifetime. These findings from AIMD study provide evidences that there exist a strongly ordering Ba 4 Bi 3 associate and a weakly ordering BaBi 3 associate in the Ba-Bi liquid. Here, the predicted enthalpy of mixing in the liquid agrees well with the results by the CALPHAD modeling in the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-plane moment-of-fluid interface reconstruction in 3D

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

3D interface reconstruction↗
DOE OSTI2021

Bulk Diffusion of Cl through O Vacancies in α-Cr 2 O 3 : A Density Functional Theory Study

Many metals form passive oxides which are broken or weakened by anionic-induced degradation leading to material failure and anionic diffusion is an important step of this degradation process. The diffusion of anionic species through oxides involves a combination of diffusion along grain boundaries, cracks, and channels, as well as bulk diffusion via point defects which is the focus of this study. Using density functional theory, we study bulk diffusion of Cl through O vacancies in α -Cr 2 O 3 as a model system for passive metal oxides. Little is known about Cl diffusion and bonding characteristics, so we benchmark our work through comparison to numerous studies on O diffusion in α -Cr 2 O 3 to analyze similarities and differences between the O and Cl diffusion in the passivation and degradation process of α -Cr 2 O 3 respectively. Unlike O diffusion, the lowest diffusion barrier for Cl is cross-plane diffusion between two (0001) planes through a vacant cation site but the much shorter in-plane diffusion path within the same coordination polyhedron has 35% higher barrier. This work provides the basis for considering the contributions of Cl bulk-diffusion in the overall diffusion kinetics of Cl through α -Cr 2 O 3 .

Oware Sarfo, Kofi↗
DOE OSTI2021

Gravitation and Mesh Adaption

The Gravitation and Mesh Adaptation (GaMA) toolbox consists of a set of Matlab classes for modeling the environment around asteroids and comets. A variety of gravitational models and supporting algorithms from are consolidated alongside a custom meshing utility tailored for the application. This allows the user to work within a single streamlined environment to import and manipulate surface definitions, probe the dynamical environment, integrate trajectories, and post-process results. For other applications, modified surface meshes can be exported. Gravity Models: 1) Werner's analytic polyhedron model 2) Mascon model 3) Gottlieb's spherical harmonic model 4) Approximate polyhedron models 5) Curvilinear surface models 6) Custom composite models Meshing Features: 1) Array-based half-edge data structure 2) Supports curvilinear surface definitions up to degree 4 3) Ray-tracing 4) Coarsening 5) Feature-based refinement 6) Projection 7) Smoothing 8) Mesh quality validity tests 9) Mesh repair Additional Features: 1) Solar radiation pressure model 2) Distant 3rd body model 3) Collision detection 4) Trajectory integration and post-processing 5) Visualization of surface fields

Pearl, Jason↗
DOE OSTI2022

Cutting Corners: Curvilinear-Surface-Based Gravity Models for Asteroids and Comets

We report that asteroids and comets are often highly irregular in shape and can contain large density inhomogenities. For such bodies, the simple point-mass gravity model does not capture the dynamics of the environment and this has driven a need for higher fidelity alternatives. A number of approaches have been developed with one of the most popular being the analytic polyhedral model. The analytic polyhedral model approximates the irregular shaped body as a polyhedron, typically consisting of triangular facets, with some assumed internal density distribution. Several analytic formulations have been derived for the gravitational fields of a constant-density polyhedron. A thorough history of the model is provided in Ref. [6] as well as a comparison of the implementations of Refs. [2–4]. The three versions provide near identical accuracy with the implementation of Werner requiring the fewest transcendental function evaluations suggesting its superior efficiency. Implementations with linear density contrasts and arbitrary polynomial density contrasts have also been developed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A machine learning approach to predict thermal expansion of complex oxides

Although it is of scientific and practical importance, the state-of-the-art of predicting the thermal expansion of oxides over broad temperature and composition ranges by physics-based atomistic simulations is currently limited to qualitative agreements. We present an emerging machine learning (ML) approach to accurately predict the thermal expansion of cubic oxides with a dataset consisting of experimentally measured lattice parameters while using the metal cation polyhedron and temperature as descriptors. High-fidelity ML models that can accurately predict temperature- and composition-dependent lattice parameters of cubic oxides with isotropic thermal expansions have been successfully trained. The ML-predicted thermal expansions of oxides not included in the training dataset have shown good agreement with available experiments. The limitations of the current approach and challenges to go beyond cubic oxides with isotropic thermal expansion are also briefly discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Understanding the Instability of the Halide Perovskite CsPbI 3 through Temperature-Dependent Structural Analysis

Despite the tremendous interest in halide perovskite solar cells, the structural reasons that cause the all-inorganic perovskite CsPbI 3 to be unstable at room temperature remain mysterious, especially since many tolerance-factor-based approaches predict CsPbI 3 should be stable as a perovskite. Here single-crystal X-ray diffraction and X-ray pair distribution function (PDF) measurements characterize bulk perovskite CsPbI3 from 100 to 295 K to elucidate its thermodynamic instability. While Cs occupies a single site from 100 to 150 K, it splits between two sites from 175 to 295 K with the second site having a lower effective coordination number, which, along with other structural parameters, suggests that Cs rattles in its coordination polyhedron. PDF measurements reveal that on the length scale of the unit cell, the Pb-I octahedra concurrently become greatly distorted, with one of the I-Pb-I angles approaching 82° compared to the ideal 90°. The rattling of Cs, low number of Cs-I contacts, and high degree of octahedral distortion cause the instability of perovskite-phase CsPbI 3 . These results reveal the limitations of tolerance factors in predicting perovskite stability and provide detailed structural information that suggests methods to engineer stable CsPbI 3 -based solar cells.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Synthesis of Core@Shell Cu-Ni@Pt-Cu Nano-Octahedra and Their Improved MOR Activity

Fabrication of 3d metal-based core@shell nanocatalysts with engineered Pt-surfaces provides an effective approach for improving the catalytic performance. The challenges in such preparation include shape control of the 3d metallic cores and thickness control of the Pt-based shells. Herein, we report a colloidal seed-mediated method to prepare octahedral CuNi@Pt-Cu core@shell nanocrystals using CuNi octahedral cores as the template. By precisely controlling the synthesis conditions including the deposition rate and diffusion rate of the shell-formation through tuning the capping ligand, reaction temperature, and heating rate, uniform Pt-based shells can be achieved with a thickness of < 1 nm. Furthermore, the resultant carbon-supported CuNi@Pt-Cu core@shell nano-octahedra showed superior activity in electrochemical methanol oxidation reaction (MOR) compared with the commercial Pt/C catalysts and carbon-supported CuNi@Pt-Cu nano-polyhedron counterparts, demonstrating that both the lattice strain and shape effects arising from the as-prepared CuNi@Pt-Cu octahedral nanocatalysts play a crucial role in MOR performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Surface Engineering Strategy to Synthesize Bicomponent Carbons for Rechargeable Zinc-Air Batteries

Atomic Fe-N x moieties and nanosized FeCo species anchored on carbons have each been demonstrated to be among the most effective active components for oxygen reduction and evolution reactions (ORR/OER), respectively in rechargeable zinc -air batteries (ZABs). However, incorporating both of these components in a single catalyst presents a great challenge due to the trade-off in formation between them during hightemperature preparation. Herein, we integrate them into a bicomponent carbon through a surface engineering strategy. In this process, K 3 [Fe(CN) 6 ] is engineered on the surface of a precursor mixture consisting of polyaniline-coated graphene oxide and ZIF-67. This is followed by pyrolysis to produce the bicomponent carbon catalyst of FeCo nanoparticles modified carbon polyhedron (for accelerating the OER), supported on atomically dispersed Fe -N -doped carbon nanosheet (for boosting the ORR). The catalyst exhibits a small potential gap of 0.69 V for OER/ORR. In situ Raman spectroscopy demonstrates that spinel FeCo oxides may be responsible for OER. The use of this catalyst in ZABs achieves high power densities of 225 mW cm -2 in aqueous electrolyte and 164 mW cm -2 in solid-state electrolyte. Additionally, a small and stable voltage gap of 0.712 V at 10 mA cm -2 is maintained after 1035 discharge -charge cycles demonstrating the great application potential in energy devices.

An, Jia-Xing↗
DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗
DOE OSTI2023

Uncovering metallic glasses hidden vacancy-like motifs using machine learning

Vacancies are a ubiquitous type of defect in crystalline materials that can affect their properties and behavior, including atomic diffusivity, deformation processes, thermal conductivity, and electrical conductivity. While well-defined in crystals, it is challenging to identify such topological footprints in the amorphous structure of metallic glasses (MGs). Here, we uncover an unforeseen vacancy-like structural motif named Q7, which refers to an atomic Voronoi polyhedron with seven quadrangular faces, by investigating MG local atomic configurations with the help of machine learning. The Q7 motif exhibits characteristics similar to crystalline vacancies and plays a significant role in short-range structural disorder in MGs. The atoms at the center of the Q7 motif display larger local entropy, atomic volume, and local tension. Additionally, its concentration follows an Arrhenius-like relationship with temperature, accurately indicating the glass transition temperature, and is strongly correlated with the yield and failure of MGs during mechanical deformation. The discovery of the Q7 motif provides new insights into understanding the intricate relationship between local disorder and structural relaxation in MGs, offering a remarkable ability to predict their thermal and mechanical behavior. This potentially paves the way for enhancements in the design and manufacturing processes of MGs and other amorphous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Deciphering the Distribution and Crystal-Chemical Environment of Arsenic, Lead, Silica, Phosphorus, Tin, and Zinc in a Porous Ferrihydrite Grain Using Transmission Electron Microscopy and Atom Probe Tomography

Here the interaction of contaminants and nutrients with soil constituents is controlled by processes in intergranular and intragranular pore spaces of organic matter or/and common secondary minerals such as ferrihydrite, ~Fe 3+ 10 O 14 (OH) 2 . This contribution shows that distribution and clustering of the contaminants As, P, Pb, Si, Sn, and Zn in a porous ferrihydrite grain is greatly affected by the heterogeneous size distribution and chemical composition of the pores as well as the ability of their polyhedra to polymerize with the same type of polyhedron. Transmission electron microscopy (TEM) and atom probe tomography (APT) studies are conducted on focused ion beam (FIB) sections extracted from a porous ferrihydrite grain from the smelter-impacted topsoil in Sudbury, Ontario, Canada. The ferrihydrite grain has pore spaces ranging in diameter from tens to hundreds of nanometers. TEM and scanning-TEM studies indicate that the surfaces of the pore walls are enriched in Si. APT data in conjunction with First Near Neighbor (1NN) analyses indicate different degrees of clustering of Pb, As, Sn, Zn, Si, and P within the sample and selected domains. Careful evaluations of 3D atomic plots and 1NN distances indicates the occurrence of polymerized arsenite-, silica-, Sn-, and Zn-polyhedra within pore spaces of the ferrihydrite. Deciphering adsorption, polymerization, and nucleation processes in porous Fe-(hydr)oxides and other soil constituents requires multianalytical approaches and, in this regard, we discuss the advantages and disadvantages of the combination of TEM and APT for characterizing complex environmental samples at the atomic to nanometer scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Organic Modulators Enable Morphological Diversity in Colloidal Crystals Engineered with DNA

Colloidal crystal engineering with DNA is a powerful way of generating a wide variety of crystals spanning over 90 different symmetries. However, in many cases, crystals with well-defined habits are difficult, if not impossible, to make, in part due to rapid crystal defect formation and propagation. This is especially true in the case of face-centered cubic (FCC) structures. Herein, we report a strategy that uses formamide as a chemical modulator to slow down colloidal crystal growth, which decreases defect formation and yields higher-quality crystals. Formamide forms hydrogen bonds with DNA bases and destabilizes the DNA duplex; in the context of colloidal crystallization, formamide leads to the disassembly of undercoordinated particles (defect architectures) and facilitates their reassembly into structures with the maximum number of nearest-neighbor contacts and DNA bonds. Here, when targeting an FCC lattice comprised of DNA-modified spherical 20 nm particles, formamide promotes the formation of its Wulff polyhedron (a truncated octahedron), never observed before in colloidal crystal engineering with DNA. Importantly, kinetic habits, including tetrahedra, octahedra, icosahedra, and decahedra, are also observed depending on formamide concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗