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All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2021

The crystal structure of a new calcium aluminate phase containing formate

A new calcium aluminate phase containing formate ions was synthesized and its crystal structure determined. This new phase is indicated as M-phase and was firstly observed in Portland cement pastes hydrated in presence of Ca-formate and in excess of water. The crystal structure of the M-phase was successfully solved in the R-3 space group of the trigonal system on the basis of synchrotron X-ray single crystal diffraction data. The structural model was confirmed by Rietveld refinement of the powder diffraction data acquired on the synthesized pure sample. The crystal structure of the M-phase is similar to that of ettringite, being characterized by columns of AlO{sub 6} octahedra alternating with groups of three edge-sharing CaO{sub 7} polyhedra. The formate ions (HCOO){sup −} share two oxygens with Ca polyhedra and are located in the interspace between the columns. The crystal structure of the M-phase testifies the strong interaction occurring between small organic molecules as formate and the calcium aluminate components of Portland cement.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Mechanisms and stability of Li dynamics in amorphous Li-Ti-P-S-based mixed ionic–electronic conductors: A machine learning molecular dynamics study

Mixed ionic–electronic conductors (MIECs) exhibit both high ionic and electronic conductivity to improve the battery performance. In this work, we investigate the mechanism and stability of transport channels in our recently developed MIEC material, amorphous Ti-doped lithium phosphorus sulfide (LPS), using molecular dynamics (MD) simulations with a 99% accurate machine-learning force field (MLFF) trained on ab initio MD data. The achieved MLFF helps efficient large-scale MD simulations on LPS with three Ti concentrations (10%, 20%, and 30%) and six temperatures (25°C to 225°C) to calculate ionic conductivity, activation energy, Li-ion transport mechanism, and configurational entropy. Results show that ionic conductivities and activation energies are consistent with our recent experimental values. Moreover, Li-ion transport occurs via free-volume diffusion facilitated by the formation of disordered Li-S polyhedra. The enhanced stability of transport channels at 10% and 20% Ti doping, compared to 0% and 30%, is observed by analyzing the vibrational and configurational entropy of these disordered Li-S polyhedra. Overall, this study highlights the utility of MLFF-based large-scale MD simulations in explaining the transport mechanism and the stability of Li-ion in Ti-doped LPS electrolyte with significant computational efficiency.

And configuration entropy↗
DOE OSTI2023

IrGe 4 : A Predicted Weyl-Metal with a Chiral Crystal Structure

Polycrystalline IrGe4 was synthesized by annealing elements at 800 °C for 240 h, and the composition was confirmed by energy-dispersive X-ray spectroscopy. IrGe 4 adopts a chiral crystal structure (space group P3 1 21) instead of a polar crystal structure (P3 1 ), which was corroborated by the convergent-beam electron diffraction and Rietveld refinements using synchrotron powder X-ray diffraction data. The crystal structure features layers of IrGe 8 polyhedra along the b axis, and the layers are connected by edge- and corner-sharing. Each layer consists of corner-shared [Ir 3 Ge 20 ] trimers, which are formed by three IrGe 8 polyhedra connected by edge-sharing. Temperature-dependent resistivity indicates metallic behavior. The magnetoresistance increases with increasing applied magnetic field, and the nonsaturating magnetoresistance reaches 11.5% at 9 T and 10 K. The Hall resistivity suggests that holes are the majority carrier type, with a carrier concentration of 4.02 × 10 21 cm –3 at 300 K. In conclusion, electronic band structures calculated by density functional theory reveal a Weyl point with a chiral charge of +3 above the Fermi level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Role of Fe Doping on Local Structure and Electrical and Magnetic Properties of PbTiO 3

In this work, the local structure and multiferroic properties of iron-doped lead titanate (PbTi 1-x Fe x O 3-δ ) samples was investigated over the entire composition range (x = 0-1). Inherent polarization in PbTiO 3 decreases due to Fe 3+ incorporation up to the solubility limit (x similar to 0.3), although homogeneous doping persists only up to x = 0.1. Ti prefers highly distorted oxygen octahedra for any x value, while Fe prefers more symmetric O-deficient polyhedra (Fe-O n ). The charge compensating oxygen vacancies induce local tilting of the Fe-O n polyhedra beyond a critical x value (x ≥ 0.2), promoting magnetic interaction between two adjacent Fe atoms. The strain induced by local heterogeneity could act as a coupling force between magnetic and ferroelectric properties. Fe-rich clusters evolve into ferromagnetic PbFe 12 O 19 with increased Fe doping. PbTi 1-x Fe x O 3-δ (x ≥ 0.3) samples therefore have separate origins for the ferroelectric (PbTi 1-x Fe x O 3-δ ) and magnetic (PbFe 12 O 19 ) phases.

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

Elucidating the local structure of Li 1+ x Al x Ti 2– x (PO 4 ) 3 and Li 3 Al x Ti 2– x (PO 4 ) 3 ( x = 0, 0.3) via total scattering

Li 1+x Al x Ti 2–x (PO 4 ) 3 (LATP) and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3) are promising candidates in all-solid-state batteries due to their high room temperature conductivity of 10 –3 S cm –1 and air- and moisture-stability. They also exhibit unusual thermal expansion properties, with Li 1+x Al x Ti 2–x (PO 4 ) 3 showing near-zero thermal expansion along the a axis while Li 3 Al x Ti 2–x (PO 4 ) 3 exhibits polynomial positive thermal expansion along the a axis and polynomial negative thermal expansion along the c axis. A crucial component to understanding these properties is understanding the local structure. Total scattering is a powerful analytical technique as it provides information on the long-range, average structure as well as the local structure. Here, we report the first X-ray and neutron total scattering experiments performed on Li 1+x Al x Ti 2–x (PO 4 ) 3 and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3). We show that the PO 4 and TiO 6 polyhedra experience very little expansion of the P/Ti–O bonds up to 800 °C, nor is there much expansion when the Li content increases significantly. The minor thermal expansion of the nearest-neighbor bonds of the polyhedra is revealed to be the reason behind the unusual thermal expansion properties, causing the near-zero thermal expansion along a in Li 1+x Al x Ti 2–x (PO 4 ) 3 and moving as whole units in Li 3 Al x Ti 2–x (PO 4 ) 3 . The structural robustness of the framework is also the reason for the increased conductivity as Li content increases, as the framework remains undistorted as Li content increases, permitting Li-ion mobility as the number of charge carriers increases. Finally, this suggests that phosphate-based framework materials beyond LATP would also be a good material space to explore for new Li-ion (and other ion-) conducting materials.

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

Effect of rare earth size on network structure and glass forming ability in binary aluminum garnets

Rare earth aluminate glasses are potentially useful for optical, luminescence, and laser applications. As reluctant glass formers, these materials exhibit unconventional atomic structures. To better understand how their structures correlate with glass formation, we investigate two rare earth aluminum garnet melts, La 3 Al 5 O 12 (LAG) and Yb 3 Al 5 O 12 (YbAG), which represent the relative extremes of good and poor glass forming ability in rare earth aluminates. Structural models have been refined to high-energy X-ray diffraction data over 1340–2740 K. Both melts contain mixtures of AlO 4 , AlO 5 , and AlO 6 polyhedra, with larger fractions of [5] Al and [6] Al in YbAG. Extrapolation of the Al–O coordination distributions to the glass transition match closely with 27 Al nuclear magnetic resonance measurements of (La 1−z Y z ) 3 Al 5 O 12 glasses, z = 0 to 1. During cooling, the mean coordination numbers increase for La–O in LAG from 6.45(8) to 6.98(8) and for Yb–O in YbAG from 6.02(8) to 6.21(8). Linkedness among Al–O polyhedra at ∼2450 K is mostly corner-sharing, with 9% edge-sharing in LAG and 19% in YbAG. Among [4] Al units, both melts have 6% edge-sharing that convert to all corner-sharing upon cooling. Network connectivity is compared using a newly defined metric, K n , that is similar to the Q n distribution but that accounts for the edge-sharing and triply bonded oxygen present in these melts. The lower glass forming ability in YbAG as compared to LAG correlates with more edge-sharing, associated with the larger fractions of [5] Al and [6] Al, and lower connectivity among [4] Al units.

Wilke, Stephen K. [Materials Development, Inc., Ar↗
DOE OSTI2025

Structure of molten ytterbium aluminum garnet

Rare earth aluminum garnets are important materials in optical, dielectric, and thermal barrier applications. To advance the understanding of their melt processing and glass forming ability, we report the atomic structure of molten Yb 3 Al 5 O 12 over 1770–2630 K, which spans the equilibrium and supercooled liquid regimes. The melt density at T m = 2283 K is 5.50 g cm –3 , measured via silhouette imaging of electrostatically levitated drops over 1010–2420 K. Four separate structure measurements were made with aerodynamically levitated melts using x-ray and neutron diffraction with isotope substitution of Yb ( 172 Yb, 174 Yb, or nat Yb). Empirical potential structure refinement models were developed, which are in excellent agreement with the experiments. Coordination environments for Al–O are predominantly 4- and 5-coordinate, with a mean coordination of n AlO = 4.43(8), while Yb–O environments mostly range from 5- to 8-coordinate, with n YbO = 6.26(8). The cation–oxygen polyhedra are connected primarily by corner-sharing, with edge-sharing constituting up to ~1/3 of the connectivity among polyhedra with Yb or higher-coordinated Al–O. Structurally, the –Al–O– network in molten Yb 3 Al 5 O 12 appears conducive to glass formation: n OAl = 1.85(3), there are 1.86 AlO x –AlO x connections per Al atom (e.g., a mixture of Q 3 and Q 4 units), and the modal ring size is six cations. These characterize a network that is somewhat less constrained compared to SiO 2 glass, yet Yb 3 Al 5 O 12 cannot be quenched into crystal-free glass. Here, aluminum garnet compositions with larger rare earth cations do form glass, so these characterizations help reveal the structural characteristics corresponding to the limit of glass forming ability in rare earth aluminates.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Crystal structure of calcium-ferrite type NaAlSiO4 up to 45 GPa

Abstract Alkali-rich aluminous high-pressure phases including calcium-ferrite (CF) type NaAlSiO4 are thought to constitute ~20% by volume of subducted mid-ocean ridge basalt (MORB) under lower mantle conditions. As a potentially significant host for incompatible elements in the deep mantle, knowledge of the crystal structure and physical properties of CF-type phases is therefore important to understanding the crystal chemistry of alkali storage and recycling in the Earth’s mantle. We determined the evolution of the crystal structure of pure CF-NaAlSiO4 and Fe-bearing CF-NaAlSiO4 at pressures up to ~45 GPa using synchrotron-based, single-crystal X-ray diffraction. Using the high-pressure lattice parameters, we also determined a third-order Birch-Murnaghan equation of state, with V0 = 241.6(1) Å3, KT0 = 220(4) GPa, and KT0′ = 2.6(3) for Fe-free CF, and V0 = 244.2(2) Å3, KT0 = 211(6) GPa, and KT0′ = 2.6(3) for Fe-bearing CF. The addition of Fe into CF-NaAlSiO4 resulted in a 10 ± 5% decrease in the stiffest direction of linear compressibility along the c-axis, leading to stronger elastic anisotropy compared with the Fe-free CF phase. The NaO8 polyhedra volume is 2.6 times larger and about 60% more compressible than the octahedral (Al,Si)O6 sites, with K0NaO8 = 127 GPa and K0(Al,Si)O6 ~304 GPa. Raman spectra of the pure CF-type NaAlSiO4 sample shows that the pressure coefficient of the mean vibrational mode, 1.60(7) cm–1/GPa, is slightly higher than 1.36(6) cm−1/GPa obtained for the Fe-bearing CF-NaAlSiO4 sample. The ability of CF-type phases to contain incompatible elements such as Na beyond the stability field of jadeite requires larger and less-compressible NaO8 polyhedra. Detailed high-pressure crystallographic information for the CF phases provides knowledge on how large alkali metals are hosted in alumina framework structures with stability well into the lowermost mantle.

Geochemistry & Geophysics↗
NASA NTRS1991

Collision detection for spacecraft proximity operations

A new collision detection algorithm has been developed for use when two spacecraft are operating in the same vicinity. The two spacecraft are modeled as unions of convex polyhedra, where the resulting polyhedron many 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. Contacts between the vertices, faces, and edges of the polyhedra representing the two spacecraft are shown to occur when the value of one or more of a set of functions is zero. The collision detection algorithm is then formulated as a search for the zeros (roots) of these functions. Special properties of the functions for the assumed relative trajectory are exploited to expedite the zero search. The new algorithm is the first algorithm that can solve the collision detection problem exactly for relative motion with constant angular velocity. This is a significant improvement over models of rotational motion used in previous collision detection algorithms.

Vaughan, Robin M.↗
NASA NTRS1993

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Gedney, Stephen D.↗
NASA NTRS2010

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.

Lane, John E.↗
NASA NTRS2019

Bounding Methods for Heterogeneous Lidar-derived Navigational Geofences

Safe Unmanned Aerial Vehicle (UAV) operations near the ground require navigation methods that avoid fixed obstacles such as buildings, power lines and trees. Aerial lidar surveys of ground structures are available with the precision and accuracy to geolocate obstacles, but the high volume of raw survey data can exceed the compute power of onboard processors and the rendering ability of ground-based flight planning maps. Representing ground structures with bounding polyhedra instead of point clouds greatly reduces the data size and can enable effective obstacle avoidance, as long as the bounding geometry envelopes the structures with high spatial fidelity. This report describes in detail four methods to compute bounding geometries of ground obstacles from lidar point clouds. The four methods are: 1) 2.5D Maximum Elevation Box, 2) 2.5D Ground Map Extrusion, 3) 3D Bounding Cylinder, and 4) 3D Bounding Box. The methods are applied to five point cloud datasets from lidar surveys of UAV flight research sites in Georgia and Virginia with an average point spacing that ranges from 0.1m to 0.6m. The methods are assessed using survey areas with geometrically heterogeneous ground structures: buildings, vegetation, power lines, and sub-meter structures such as road signs and guy wires. The 2.5D Maximum Elevation Box method is useful for simple structures. The 2.5D Ground Map Extrusion method efficiently encloses vegetation, but requires handdrawn ground footprints. The 3D Bounding Cylinder method excels at enclosing linear structures such as power lines and fences. The 3D Bounding Box method excels at enclosing planar structures such as buildings. The methods are compared on the basis of data compression and boundary fidelity on selected areas. The 2.5D methods yield the highest data compression but the polyhedra produced by them enclose significant amounts of empty space. Boundary fidelity is superior for the 3D methods, though this fidelity comes at the cost of a roughly thirtyfold lower data compression ratio than the 2.5D Maximum Elevation Box method. A mix of these output geometries is proposed for autonomous UAV navigation with limited on-board computing. Both the accuracy and spatial detail of emerging satellite-based survey technology lower than that of aerial lidar scanning survey technology. Sub-meter structures and thin linear structures are not reliably mapped at present by satellite-based surveys.

Moore, Andrew J.↗
DOE OSTI2023

Fundamentals of SrCoO 3-δ Based Oxygen Deficient Perovskites as Cathodes for Solid Oxide Fuel Cells

The local structure and oxygen stoichiometry in oxide systems have a profound impact on oxygen electrocatalysis encountered in metal-air batteries and solid oxide fuel cells (SOFCs). However, this knowledge is often obtained under conditions different from the real working conditions of the material, resulting in misinterpretation and misunderstanding. This PhD dissertation aims to obtain the structure and oxygen-stoichiometry information of a class of perovskite oxides under their real working conditions in solid oxide fuel cells. Several perovskite oxides were selected for the study: Sr 0.9 Y 0.1 CoO 3-δ (SYC10), Sr 0.9 Y 0.3 CoO 3-δ (SYC30), SrCo 0.9 Nb 0.1 O 3-δ (SCN10) and SrCo 0.9 Ta0.1O 3-δ (SCT10). The local crystal structure and oxygen stoichiometry of these materials were systematically characterized with in-situ neutron diffraction (ND). The oxygen stoichiometry was also measured by thermogravimetric analysis (TGA) and iodometric titration methods. To establish the correlation among structure, oxygen stoichiometry and oxygen reduction reaction (ORR) activity, high temperature electrochemical impedance spectroscopy, oxygen permeation and single cell testing were also performed. In chapter 2, SYC10 is described to have a more symmetrical structure and $V_o^{··}$ distribution, and higher $V_o^{··}$ concentration than SYC30. Molecular orbital energy analysis based on the local structure of the ORR-active Co1-polyhedra indicates SYC30 has a higher Fermi level relative to O-2p energy level in the active Co1-polyhedra, and thus a higher motional enthalpy for $V_o^{··}$ migration. However, the ORR activity of Y-doped SrCoO 3-δ (SCO) are found uncompetitive with other popular catalysts. In chapter 3 and 4, systematic structural studies are presented for Nb and Ta-doped SCO, namely SCN10 and SCT10, respectively. The methodology of unrevealing the structure-activity relationships in chapter 2 is also found applicable to SYC10, SCN10 and SCT10 as presented in chapter 5. The electrochemical tests indicate that SCT10 is the best catalyst due to its excellent thermal and electrochemical stability. In chapter 6, SCT10 is evaluated in a real solid oxide fuel cell in the form of nanoscaled SCT10 layer coating on the commercial (La 0.6 Sr 0.4 ) 0.95 Co 0.2 Fe 0.8 O 3-δ (LSCF). The bilayer structured cathode shows excellent properties of coarsening-resistant, Sr-segregation-free and high ORR-activity.

Yang, Tianrang↗
DOE OSTI2020

An efficient method to integrate polynomials over polytopes and curved solids

Here in this paper, we present an efficient approach to compute the integral of monomials and polynomials over polyhedra and regions defined by parametric curved boundary surfaces. We use Euler's theorem for homogeneous functions in combination with Stokes's theorem to reduce the integration of a monomial over a three-dimensional solid to its boundary. If the solid is a polytope, through a recursive application of these theorems, the integral is further reduced to just the evaluation of the monomial and its derivatives at the vertices of the polytope. The present approach is simpler than existing techniques that rely on repeated use of the divergence theorem, which require the antiderivative of the monomials and the projection of these functions onto hyperplanes. For convex and nonconvex polytopes, our approach does not introduce any approximation for the integration of monomials. For curved solid regions bounded by surfaces that admit a parameterization, the same approach yields simplified formulas to compute the integral of any homogeneous function, including monomials. For surfaces parameterized by polynomial surfaces (such as Bezier surface triangles and B-spline patches), the method yields machine-precision accuracy for the volumetric integration of monomials with an appropriate quadrature rule. Numerical examples over regions bounded by polynomial surfaces and rational surfaces are presented to establish the accuracy and efficiency of the method.

97 MATHEMATICS AND COMPUTING↗