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NASA NTRS2002

Generalized Reliability Methodology Applied to Brittle Anisotropic Single Crystals

A generalized reliability model was developed for use in the design of structural components made from brittle, homogeneous anisotropic materials such as single crystals. The model is based on the Weibull distribution and incorporates a variable strength distribution and any equivalent stress failure criteria. In addition to the reliability model, an energy based failure criterion for elastically anisotropic materials was formulated. The model is different from typical Weibull-based models in that it accounts for strength anisotropy arising from fracture toughness anisotropy and thereby allows for strength and reliability predictions of brittle, anisotropic single crystals subjected to multiaxial stresses. The model is also applicable to elastically isotropic materials exhibiting strength anisotropy due to an anisotropic distribution of flaws. In order to develop and experimentally verify the model, the uniaxial and biaxial strengths of a single crystal nickel aluminide were measured. The uniaxial strengths of the <100> and <110> crystal directions were measured in three and four-point flexure. The biaxial strength was measured by subjecting <100> plates to a uniform pressure in a test apparatus that was developed and experimentally verified. The biaxial strengths of the single crystal plates were estimated by extending and verifying the displacement solution for a circular, anisotropic plate to the case of a variable radius and thickness. The best correlation between the experimental strength data and the model predictions occurred when an anisotropic stress analysis was combined with the normal stress criterion and the strength parameters associated with the <110> crystal direction.

Salem, Jonathan A.↗

DOE OSTI2022

The impact of anisotropic thermal expansion on the isothermal annealing of polycrystalline α -uranium

Although grain growth impacts microstructural evolution in a wide variety of materials systems, the effect of anisotropic thermal expansion on grain boundary mobility and texture evolution has not been widely studied. Anisotropic thermal expansion occurs in multiple non-cubic metals, and the thermomechanical processing behavior of these materials can be better understood with further study into the impact of thermal expansion on grain boundary mobility and texture evolution. In this work, we develop a mesoscale phase field model of grain growth that includes the effect of anisotropic thermal expansion, which is applied to study polycrystalline α-uranium, a highly anisotropic metal. Three-dimensional simulations on polycrystalline a-uranium with and without thermal expansion eigenstrains are performed to study the grain boundary mobility and texture evolution as a function of temperature. A strain-free temperature of 933 K is selected, and the system is studied at within the range of 873 – 933 K at intervals of ten degrees, resulting in increasing thermal eigenstrain with decreasing temperature. We also estimate a grain boundary mobility prefactor and activation energy based on existing experimental data of isothermal annealing of α-uranium. The grain boundary mobility is found to display significant deviation from Arrhenius behavior with the inclusion of thermal expansion eigenstrain as the amount of thermal eigenstrain (and thus elastic strain energy within the system) increases. This result explains an experimentally observed grain boundary mobility deviation from Arrhenius behavior. Furthermore, the texture evolution is affected, such that the grain orientations become less random with increasing thermal eigenstrain, which could explain experimentally observed texture behavior. These results indicate that the effect of thermal expansion should be considered when predicting the thermomechanical processing behavior of α-uranium and other materials with anisotropic thermal expansion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Anisotropic Optical and Frictional Properties of Langmuir–Blodgett Film Consisting of Uniaxially-Aligned Rod-Shaped Cellulose Nanocrystals

Langmuir–Blodgett (LB) film deposition gives an opportunity to control the packing density and orientation of anisotropic nanoparticles at a monolayer level, allowing accurate characterization of their anisotropic material properties. Additionally, the uniaxial deposition of rod-shaped cellulose nanocrystals (CNCs) over a macroscopically large area is achieved by aligning the long axis of CNCs on the LB trough with the direction of the maximum drag force within the meniscus during the vertical pulling of the substrate from the LB trough. On the uniaxially-aligned LB films, anisotropic linear and non-linear optical properties of CNCs are obtained using Mueller matrix spectroscopy and sum frequency generation spectroscopy, respectively, and explained with time-dependent density functional theory calculations. Also, the frictional anisotropy of the LB film is measured using atomic force microscopy and explained theoretically. The findings of this study will be valuable for preparation of anisotropic nanoparticle thin films with uniform arrangements and utilization of their anisotropic material properties.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Anisotropy of localized states in an anisotropic disordered medium

Highlights: • Mobility edges of the Anderson transition are unaffected by anisotropy alone. • The critical exponent of the Anderson localization transition is also unaffected. • Anderson localized eigenstates in an anisotropic medium retain substantial anisotropy. • Their anisotropy is weaker than expected from purely geometric considerations. • Modes with the longest lifetimes are found to be the most anisotropic. We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the localization transition are found to be unaffected by the anisotropy provided that the determinant of the anisotropy tensor is kept equal to one upon introducing the anisotropy. Localized modes have anisotropic spatial shapes although their anisotropy is weaker than the one expected from purely geometric considerations. The modes with the longest lifetimes are found to be the most anisotropic and their anisotropy increases with the size of the disordered medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Monitoring spatiotemporal evolution of fractures during hydraulic stimulations at the first EGS collab testbed using anisotropic elastic-waveform inversion

The EGS Collab project acquired continuous active-source seismic monitoring (CASSM) data before, during, and after hydraulic stimulations at the first testbed at the depth of 4850 ft (1478 m) at the Sanford Underground Research Facility in Lead, South Dakota, for monitoring fracture creation and evolution. CASSM acquisition was conducted using 24 hydrophones, 18 accelerometers, and 17 piezoelectric sources within four fracture-parallel wells and two orthogonal wells. 3D anisotropic traveltime tomography and anisotropic elastic-waveform inversion of the campaign cross-borehole seismic data show that the rock within the stimulation region is a heterogeneous horizontal transverse isotropic medium. Here we use these inversion results as the initial models and apply 3D anisotropic first-arrival traveltime tomography and 3D anisotropic elastic-waveform inversion to the CASSM data acquired after each stimulation in May, 2018 and December, 2018. We observe the spatiotemporal evolution of seismic velocities and anisotropic parameters caused by hydraulic fracture stimulations, showing the regions of rock alternation caused by hydraulic fracture stimulation.

15 GEOTHERMAL ENERGY↗

DOE OSTI2023

Computational design of isotropic and anisotropic ultralow thermal conductivity polymer foams

Current state-of-the-art commercial polymer thermal insulation foam exhibits a thermal conductivity of 24 mW·m -1 ·K -1 (equivalently thermal resistivity of R-6/in.), similar to that of static air. To further optimize building energy efficiency, achieving even lower thermal conductivity is needed, which is, however, highly challenging. This paper presents computational evidence that demonstrates the feasibility of achieving an ultra-low thermal conductivity of less than 14.4 mW·m -1 ·K -1 (equivalently R-10/in.) using isotropic and anisotropic foam cell designs. For the isotropic design, we have identified analytical effective medium approximation (EMA) models within the accuracy of ±5% as finite element analysis (FEA) in predicting the effective thermal conductivity of foams with various porosities and filler gases. For the anisotropic design, we have developed and validated new EMA models against FEA in predicting the effective thermal conductivity of general anisotropic cuboids and Voronoi foams. For both isotropic and anisotropic designs, the design spaces for 18, 16, and 14.4 mW·m -1 ·K -1 (equivalently R-8, R-9 and R-10/in.) using various filler gases are obtained. It is found that polymer foams can be improved to achieve ultralow thermal conductivity by reducing CO 2 concentration, reducing radiation, increasing porosity, and using anisotropic pore geometry. In conclusion, these findings contribute to the development of highly efficient thermal insulation materials, enhancing building energy efficiency and promoting sustainable construction practices.

42 ENGINEERING↗

DOE OSTI2021

Anisotropic neutron response of trans-stilbene and impact on a handheld dual particle imager

Here this manuscript details measurements of the anisotropic light-output response of trans-stilbene, henceforth referred to as stilbene, along the three primary crystal planes and analyzes how this anisotropic response impacts neutron image reconstruction in a handheld dual particle imager (H2DPI). A prototype H2DPI composed of stilbene pillars (6 x 6 x 50 mm 3 ) coupled to silicon photomultipliers was built and is capable of imaging both fast neutrons and gamma rays from kilogram quantities of special nuclear material. Stilbene was chosen as the scintillating medium for the imager because of its pulse shape discrimination capability, time resolution and relatively high light output. A drawback to using stilbene, however, is the anisotropic response. A recoiling proton from a neutron elastic-scattering event in stilbene will yield different amounts of scintillation light depending on the direction of the recoiling proton with respect to the crystal lattice. This manuscript analyzes how this anisotropic response impacts neutron image reconstruction in 4π. The light output in the three primary crystal planes of stilbene were independently measured 6–7 times for proton recoil energies ranging from 0.5–5.0 MeV using a quasi-monoenergetic time-of-flight neutron source. The measured light-output data in the three crystal planes were fit with a semi-empirical function based on Birks’ formula. These fits were used to reconstruct the location of a 252 Cf source in front of the imager (0°, -0.8°), to the left of the imager (-90°, -0.8°) and directly above the imager (0°, 90°) to determine if it is necessary to apply the directionally-dependent response of stilbene to accurately reconstruct source locations. A bootstrapping technique was applied to the measured data sets to produce 1000 images composed of 2000 cone projections for each source location and each measured light-output curve. List-mode maximum likelihood expectation maximization was applied to each image; the highest pixel location and the full width at half maximum (FWHM) were then recorded. The average and standard deviations of these parameters were taken for each set of images. The maximum difference in the average azimuthal pixel location when varying between the appropriate and incorrect light-output curves for the source locations at (0°, -0.8°) and (-90°, -0.8°) were respectively found to be 1.85 ± 1.39° and 2.03 ± 1.78°. All other pixel locations and FWHMs were within a single standard deviation of uncertainty. Taken together, the anisotropic response of stilbene has negligible impact on the neutron image reconstruction capability of the H2DPI.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Iron-assisted growth of anisotropic ZnO nanostructures

Anisotropic nanostructures offer a promising pathway to modulate structure-function relationships of materials. However, the correlation between growth direction of high-quality anisotropic nanostructures, the synthesis conditions and mechanisms controlling their growth, and their magnetic and optical properties remain underexplored. In this study, we developed an iron-assisted anisotropic growth method to form zinc oxide nanostructures on the O-polar (0001̄) surface, resulting in two distinct ZnO-based nanostructures: hand-shaped nanostructures and truncated hexagonal nanopyramids. In contrast to most reports of anisotropic nanostructure synthesis, which primarily focus on morphology control through ligand-ligand interactions, the current study probes the effects of doping on anisotropic growth, and how doping, along with ligand-ligand interactions and facet-specific ligand binding, control nanostructure morphology. The reaction mechanisms leading to formation of these novel structures were thoroughly probed by systematically manipulating synthesis parameters. A two-step formation mechanism was identified: first, a hexagonal platform forms through an initial homogeneous nucleation process, followed by secondary heterogeneous nucleation, which results in metastable secondary nanostructures growing on the oxygen-rich template. Optical and magnetic properties of these Fe/ZnO nanostructures were characterized. Our findings provide a new strategy that uses a magnetic element as a dopant to build new nanostructures of ZnO with controllable size and shape growing on an oxygen-rich crystal plane. These materials could have applications in novel technologies where both optoelectronic and magnetic properties are of interest.

Xuan, Zhengxi↗

DOE OSTI2023

The anisotropic nature of singlet fission in single crystalline organic semiconductors

The escalating global energy predicament implores for a revolutionary resolution—one that converts sunlight into electricity—holding the key to supreme conversion efficiency. This comprehensive review embarks on the exploration of the principle of generating multiple excitons per absorbed photon, a captivating concept that possesses the potential to redefine the fundamental confines of conversion efficiency, albeit its application remains limited in photovoltaic devices. At the nucleus of this phenomenon are two principal processes: multiple exciton generation (MEG) within quantum-confined environments, and singlet fission (SF) inside molecular crystals. The process of SF, characterized by the cleavage of a single photogenerated singlet exciton into two triplet excitons, holds promise to potentially amplify photon-to-electron conversion efficiency twofold, thereby laying the groundwork to challenge the detailed balance limit of solar cell efficiency. Our discourse primarily dissects the complex nature of SF in crystalline organic semiconductors, laying special emphasis on the anisotropic behavior of SF and the diffusion of the subsequent triplet excitons in single-crystalline polyacene organic semiconductors. We initiate this journey of discovery by elucidating the principles of MEG and SF, tracing their historical genesis, and scrutinizing the anisotropy of SF and the impact of quantum decoherence within the purview of functional mode electron transfer theory. We present an overview of prominent techniques deployed in investigating anisotropic SF in organic semiconductors, including femtosecond transient absorption microscopy and imaging as well as stimulated Raman scattering microscopies, and highlight recent breakthroughs linked with the anisotropic dimensions of Davydov splitting, Herzberg–Teller effects, SF, and triplet transport operations in single-crystalline polyacenes. Through this comprehensive analysis, our objective is to interweave the fundamental principles of anisotropic SF and triplet transport with the current frontiers of scientific discovery, providing inspiration and facilitating future ventures to harness the anisotropic attributes of organic semiconductor crystals in the design of pioneering photovoltaic and photonic devices.

Chemistry↗

DOE OSTI2022

Observation of anisotropic Dirac cones in the topological material Ti 2 Te 2 P

Anisotropic bulk Dirac (or Weyl) cones in three-dimensional systems have recently gained intense research interest as they are examples of materials with tilted Dirac (or Weyl) cones indicating the violation of Lorentz invariance. In contrast, the studies on anisotropic surface Dirac cones in topological materials which contribute to anisotropic carrier mobility have been limited. By employing angle-resolved photoemission spectroscopy and first-principles calculations, we reveal the anisotropic surface Dirac dispersion in a tetradymite material Ti 2 Te 2 P on the (001) plane of the Brillouin zone. We observe quasielliptical Fermi pockets at the M ¯ point of the Brillouin zone forming the anisotropic surface Dirac cones. Our calculations of the Z 2 indices confirm that the system is topologically nontrivial with multiple topological phases in the same material. In addition, the observed nodal-line-like feature formed by bulk bands makes this system topologically rich.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Numerical Modeling of Anisotropic Elastic-Wave Sensitivity Propagation for Optimal Design of Time-Lapse Seismic Surveys

Reliable subsurface time-lapse seismic monitoring is crucial for many geophysical applications, such as enhanced geothermal system characterization, geologic carbon utilization and storage, and conventional and unconventional oil/gas reservoir characterization, etc. In this work, we develop an elastic-wave sensitivity propagation method for optimal design of cost-effective time-lapse seismic surveys considering the fact that most of subsurface geologic layers and fractured reservoirs are anisotropic instead of isotropic. For anisotropic media, we define monitoring criteria using qP- and qS-wave sensitivity energies after decomposing qP- and qS-wave components from the total elastic-wave sensitivity wavefield using a hybrid time- and frequency-domain approach. Geophones should therefore be placed at locations with significant qP- and qS-wave sensitivity energies for cost-effective time-lapse seismic monitoring in an anisotropic geology setting. Our numerical modeling results for a modified anisotropic Hess model demonstrate that, compared with the isotropic case, subsurface anisotropy changes the spatial distributions of elastic-wave sensitivity energies. Consequently, it is necessary to consider subsurface anisotropies when designing the spatial distribution of geophones for cost-effective time-lapse seismic monitoring. This finding suggests that it is essential to use our new anisotropic elastic-wave sensitivity modeling method for optimal design of time-lapse seismic surveys to reliably monitor the changes in subsurface reservoirs, fracture zones or target monitoring regions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

Anisotropic parametrized post-Newtonian gravitational metric field

The anisotropic generalization of the parameterized post-Newtonian (PPN) gravitational metric field is made for the case of theories with energy and momentum conservation laws. Such an anisotropic metric field will generally result in two-tensor or bimetric theories of gravity in an anisotropic universe. New anisotropic 3 x 3 spatial PPN matrices are introduced into the general metric expansion. Earth gravimeter measurements strongly restrict some anisotropies, while anisotropic inertial and gravitational mass for celestial bodies result from other combinations of the PPN matrices.

Nordtvedt, K., Jr.↗

NASA NTRS2007

Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR

An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.

Marcum, David L.↗

NASA NTRS2011

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

Nemeth, Michael P.↗

NASA NTRSDate not supplied

Anisotropic Goal-Based Mesh Adaptation Metric Clarification and Development

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows to control discretization error for reliable simulation results. Multiple independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics have matured. Goal-based metrics target estimated error in output functions, such as lift and drag, through the guidance of an adjoint solution. A unification of goal-based anisotropic metrics is presented for steady viscous flows, which is an active area of research. These goal-based metrics drive robust and efficient anisotropic mesh adaptation for the calculation of output functions. The super-convergent functional output error behavior of stabilized finite-element methods is exploited without a formal proof, and evidence of super-convergence is shown in numerical experiments. Mesh adapted drag and lift outputs for two simple bodies in compressible viscous flow show convergence of error to less than a single drag count. Asymptotic behavior established for relatively coarse meshes shows the efficiency of this goal-based metric when compared to solution interpolation error control and expert-guided meshing. Anisotropic mesh adaptation techniques are applied to a transport aircraft in a high-lift configuration where variation between approaches decreases with mesh refinement, but asymptotic behavior is not observed with available resources.

goal-based↗

DOE OSTI2020

Method of making iron nitride powder with anisotropic shape

Techniques are disclosed for milling an iron-containing raw material in the presence of a nitrogen source to generate anisotropically shaped particles that include iron nitride and have an aspect ratio of at least 1.4. Techniques for nitridizing an anisotropic particle including iron, and annealing an anisotropic particle including iron nitride to form at least one a″-Fe16N2 phase domain within the anisotropic particle including iron nitride also are disclosed. In addition, techniques for aligning and joining anisotropic particles to form a bulk material including iron nitride, such as a bulk permanent magnet including at least one a″-Fe16N2 phase domain, are described. Milling apparatuses utilizing elongated bars, an electric field, and a magnetic field also are disclosed.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Iron nitride powder with anisotropic shape

Techniques are disclosed for milling an iron-containing raw material in the presence of a nitrogen source to generate anisotropically shaped particles that include iron nitride and have an aspect ratio of at least 1.4. Techniques for nitridizing an anisotropic particle including iron, and annealing an anisotropic particle including iron nitride to form at least one α″-Fe16N2 phase domain within the anisotropic particle including iron nitride also are disclosed. In addition, techniques for aligning and joining anisotropic particles to form a bulk material including iron nitride, such as a bulk permanent magnet including at least one α″-Fe16N2 phase domain, are described. Milling apparatuses utilizing elongated bars, an electric field, and a magnetic field also are disclosed.

Wang, Jian-Ping↗

DOE OSTI2022

On the effect of scalar flux weighing of linearly anisotropic scattering matrices in few-group transport calculations

The majority of the codes available for homogenized group constant generation for deterministic transport calculations apply the approximation of scalar flux weighting during energy group condensation of higher-order anisotropic scattering matrices. In this paper, we discuss the effect of scalar flux weighting of the linearly anisotropic scattering matrices in the frame of S P{sub 3} and S{sub 12} calculations performed for a two-dimensional VVER-440 reactor benchmark. To compare group constants generated for two neutron energy groups, an infinite pin cell was homogenized with Serpent 2 and ERANOS ECCO. Serpent 2 applies scalar flux, while ERANOS ECCO performs current weighting of the linearly anisotropic scattering matrices during energy group condensation. For analyzing the effect of the various weighting options, three simple reactor models were built assuming different core sizes using standard rectangular assemblies with 15*15 fuel pins. Diffusion, SP{sub 3} and S{sub 12} calculations were performed for the 3 models using group constants generated with Serpent 2 and ERANOS ECCO. The effect of scalar flux weighting of linearly anisotropic scattering matrices is shown by comparing the decrease in reactivity due to the decreased reactor size, as well as the assembly power distribution to reference results obtained with Serpent 2 Monte Carlo calculations. Neglecting higher than linearly anisotropic scattering and indirect application of diffusion coefficients in higher-order transport calculations is advised if angular flux-moment spectra weighted higher-order scattering matrices cannot be generated. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗