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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↗

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↗

DOE OSTI2025

Anisotropic growth of Ni 2 (Cr,Mo) ordered phase in proton irradiated Ni-Cr-Mo alloys

Ni-Cr-Mo alloys are widely used in the nuclear industry as structural materials due to their high temperature strength and corrosion resistance. Ni-based alloys containing around 33 at.% (Cr+Mo) developed a long-range ordered Ni 2 (Cr,Mo) phase after thermal aging and/or irradiation. The ordering mechanism for thermally-aged Ni 2 (Cr,Mo) phase is well-understood, characterized to be sluggish, homogeneous, and isotropic. The ordering mechanism for irradiation-induced Ni 2 (Cr,Mo) phase is not fully understood, characterized as having rapid formation and demonstrating anisotropic precipitation. Here, this work elucidates the anisotropic precipitation and anisotropic precipitation mechanism of Ni 2 (Cr,Mo) after proton irradiation in Ni-Cr-Mo alloys. Selected area electron diffraction and bright-field scanning transmission electron microscopy imaging are used to image superlattice reflections from the ordered phase and irradiation-induced defects, respectively. A higher degree of anisotropic precipitation is observed with increasing dislocation loop and void size; a phenomenon not observed in thermally aged samples.

36 - MATERIALS SCIENCE↗

DOE OSTI2023

Effects of anisotropic shale creep on the stress and permeability evolution of a geological nuclear waste repository

To ensure long-term safety and performance, geological nuclear waste repositories require low-permeability barriers such as bentonite buffers and/or shale host rock. Shale is not only known for its low permeability but also for its trend to undergo time-dependent deformation (i.e., creep), which could heal damage, but the effects of shale creep on the long-term performance of nuclear waste repositories have not been clearly understood. In particular, the anisotropic nature of shale (i.e., bedding) could have a significant effect on its creep behavior, and consequently, on the long-term performance of nuclear waste repositories. In this research, numerical simulations were carried out with the objective of showing the effects of anisotropic shale creep on the stress and permeability evolution of a generic geological nuclear waste repository in shale. The TOUGH-FLAC simulator, a thermo-hydromechanically (THM) coupled numerical code, was used for the simulations. To achieve the objective, comparisons were performed between the results of anisotropic shale creep simulations and those of different simulation cases, namely, no creep (i.e., elastic), isotropic creep, and long-term creep shale cases. Results of the comparisons show that the elastic and isotropic creep shale cases respectively led to the overestimation and underestimation of stress and permeability in the repository, whereas the long-term creep shale case, which accumulated greater creep in later periods than in earlier periods, helped to keep large shear and tensile stresses from developing while maintaining compressive spherical stress, resulting in consistently low permeability levels. These results indicate that performance assessments with elastic and isotropic creep formation models will provide the upper and lower bound estimates of stress and permeability, while more reasonable estimates will be given by an anisotropic creep formation model, and that shale with long-term creep characteristics will be beneficial in many aspects of the safety and performance of nuclear waste repositories.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

An All-Ceramic, Anisotropic, and Flexible Aerogel Insulation Material

To exploit the high-temperature superinsulation potential of anisotropic thermal management materials, the incorporation of ceramic aerogel into the aligned structural networks is indispensable. Yet, the long-standing obstacle to exploring ultralight superinsulation ceramic aerogels is the inaccessibility of its mechanical elasticity, stability, and anisotropic thermal insulation. Here, we report a recoverable, flexible ceramic fiber-aerogel composite with anisotropic lamellar structure, where the interfacial cross-linking between ceramic fiber and aerogel is important in its superinsulation performance. The resulting ultralight aerogel composite exhibits a density of 0.05 g/cm 3 , large strain recovery (over 50%), and low thermal conductivity (0.0224 W m –1 K –1 ), while its hydrophobicity is achieved by in situ trichlorosilane coating with the water contact angle of 135°. The hygroscopic tests of such aerogel composites demonstrate a reversible thermal insulation. The mechanical elasticity and stability of the anisotropic composites, with its soundproof performance, shed light on the low-cost superelastic aerogel manufacturing with scalability for energy saving building applications.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

3D printing of anisotropic Sm–Fe–N nylon bonded permanent magnets

Abstract Fabricating a bonded magnet with a near‐net shape in suitable thermoplastic polymer binders is of paramount importance in the development of cost‐effective energy technologies. In this work, anisotropic Sm 2 Fe 17 N 3 (Sm–Fe–N) bonded magnets are additively printed using SmFeN anisotropic magnetic particles in a polymeric binder polyamide‐12 (PA12). The anisotropic SmFeN bonded magnets are fabricated by Big Area Additive Manufacturing followed by post‐printing alignment in a magnetic field. Optimal post‐alignment results in an enhanced remanence of ∼0.68 T in PA12 reflected in a parallel‐oriented (aligned) measured direction. The maximum energy product achieved for the additively printed anisotropic bonded magnet of Sm–Fe–N in PA12 polymer is 78.8 KJ m −3 . Our results show advanced processing flexibility with 3D printing of the development of SmFeN nylon bonded magnets designed for applications with no critical rare earth magnets.

42 ENGINEERING↗

DOE OSTI2022

The complex heavy-quark potential in an anisotropic quark-gluon plasma — Statics and dynamics

We generalize a complex heavy-quark potential model from an isotropic QCD plasma to an anisotropic one by replacing the Debye mass m> D with an anisotropic screening mass depending on the quark pair alignment with respect to the direction of anisotropy. Such an angle-dependent mass is determined by matching the perturbative contributions in the potential model to the exact result obtained in the Hard-Thermal-Loop resummed perturbation theory. An advantage of the resulting potential model is that its angular dependence can be effectively described by using a set of angle-averaged screening masses as proposed in our previous work. Consequently, one could solve a one-dimensional Schrödinger equation with a potential model built by changing the anisotropic screening masses into the corresponding angle-averaged ones, and reproduce the full three-dimensional results for the binding energies and decay widths of low-lying quarkonium bound states to very high accuracy. Finally, turning to dynamics, we demonstrate that the one-dimensional effective potential can accurately describe the time evolution of the vacuum overlaps obtained using the full three-dimensional anisotropic potential. This includes the splitting of different p-wave polarizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Coupled Thermo-Hydrological-Mechanical-Chemical Behavior of Anisotropic Granite for Geologic Disposal of High-Level Radioactive Waste: A Core-Scale Laboratory Investigation

The coupled thermo-hydrological-mechanical-chemical (THMC) behavior of rock within an Excavation Damaged Zone (EDZ) is critical for the safety and long-term performance of a geological repository for high-level radioactive wastes. While many laboratory experiments have been conducted to investigate EDZ rocks, the flow and deformation characteristics resulting from anisotropic rock textures and microcrack distribution under triaxial loading and elevated temperatures remain poorly understood. Particularly, cracks at various scales serve as fast paths for fluid flow and solute transport and present as focal points of mechanical weakness, which complicate the coupled THMC processes in anisotropic EDZ rocks and challenge modeling predictions. Here, in this study, a series of core-scale experiments was conducted on three granite samples under repository-relevant conditions. These rock samples were obtained from the Grimsel Underground Research Laboratory (URL), featured by anisotropic minerals (represented by bedding layers) and microcrack distributions and coarse cm-scale grain sizes. During the experiments, samples were subjected to an elevated temperature at 90 °C and different triaxial loading conditions either by radial (normal to bedding layers) or axial (parallel to bedding layers) compaction. Water was injected into the samples, and the rock permeability evolutions and effluent water chemistry were monitored closely. For intact samples, thermal expansion of minerals at 90 °C resulted in a large, 75% irreversible permeability reduction and rock strengthening under radial compaction, while thermal impact was limited to a 15% permeability reduction under axial compaction. In contrast, for a sample containing open cracks, the growth of fractures during the experiment resulted in an abrupt permeability increase and fast failure at 90 °C. The effluent water chemistry indicates much more considerable mineral dissolution from large shear sliding than that in rocks dominated by mechanical compaction. These results helped better understand the coupled THMC processes in anisotropic rocks containing cracks, evaluate the behaviors of EDZ rocks, and predict the long-term evolution of EDZ for the performance of the repositories.

Coupled THMC processes↗