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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.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Theory-guided design of duplex-phase multi-principal-element alloys

Density-functional theory (DFT) is used to identify phase-equilibria in multi-principal-element and high-entropy alloys (MPEAs/HEAs), including duplex-phase and eutectic microstructures. Here, a combination of composition-dependent formation energy and electronic-structure-based ordering parameters were used to identify a transition from FCC to BCC favoring mixtures, and these predictions experimentally validated in the Al-Co-Cr-Cu-Fe-Ni system. A sharp crossover in lattice structure and dual-phase stability as a function of composition were predicted via DFT and validated experimentally. The impact of solidification kinetics and thermodynamic stability was explored experimentally using a range of techniques, from slow (castings) to rapid (laser remelting), which showed a decoupling of phase fraction from thermal history, i.e., phase fraction was found to be solidification rate-independent, enabling tuning of a multi-modal cell and grain size ranging from nanoscale through macroscale. Strength and ductility tradeoffs for select processing parameters were investigated via uniaxial tension and small-punch testing on specimens manufactured via powder-based additive manufacturing (directed-energy deposition). This work establishes a pathway for design and optimization of next-generation multiphase superalloys via tailoring of structural and chemical ordering in concentrated solid solutions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Computational design of high entropy alloy coating for hydrogen turbine applications

This project aims to develop novel high entropy alloy (HEA)-based coatings to protect critical components in hydrogen-fueled turbine power system. The HEA-coatings will demonstrate superior performance in hydrogen combustion environment to commercial NiCoCrAlY coating in current natural gas turbine system. The HEA coating facilitates the formation of a protective scale of alpha-alumina to slow down the inward diffusion of oxidizing species and the outward diffusion of metal elements, and possesses ultrahigh corrosion and spallation resistance to prolong the service lifetime of critical components in hydrogen turbine power system. Aimed to accelerate the discovery of novel HEA coating compositions, high throughput computational modeling including CALPHAD and density functional theory and machine learning are performed to predict phase stability, oxygen permeability, oxidation rate constant, coefficient of thermal expansion, and mechanical properties. Based on the modeling and machine learning prediction, experimental validation is performed. Preliminary results will be presented and approaches to minimize oxidation will be discussed.

alloy design↗
DOE OSTI2020

Chemical short-range order in derivative Cr–Ta–Ti–V–W high entropy alloys from the first-principles thermodynamic study

The development of high-entropy alloys (HEAs) focuses on exploring compositional regions in multi-component systems with all alloy elements in equal or near-equal atomic concentrations. Initially it was based on the main idea that high mixing configurational entropy contributions to the alloy free energy could promote the formation of a single solid solution phase. By using the ab-initio based Cluster Expansion (CE) Hamiltonian model constructed for the quinary bcc Cr–Ta–Ti–V–W system in combination with Monte Carlo (MC) simulations, we show that the phase stability and chemical short-range order (SRO) of the equiatomic quinary and five sub-quaternary systems, as well as their derivative alloys, can dramatically change the order–disorder transition temperatures (ODTT) as a function of alloy compositions. In particular, it has been found, that the equiatomic quaternary Ta–Ti–V–W and Cr–Ta–Ti–W alloys had the lowest order–disorder transition temperature (500 K) among all the analysed equiatomic compositions. In all investigated alloy systems, the strongest chemical ordering has been observed between Cr and V, which led to the conclusion that decreasing the concentration of either Cr or V might be beneficial in terms of decreasing the ODTT. It also predicts that increasing concentration of Ti significantly decreases the ODTT. Our analysis of chemical SRO as a function of alloy composition allows to understand the microstructure evolution of HEAs as a function of temperature in excellent agreement with available experimental observations. Importantly, our free energy of mixing and SRO calculations predict that the origin of precipitates formed by Cr- and V-rich in the sub-quaternary Cr–Ta–V–W system is driven by the thermodynamics. The modelling results are in an excellent agreement with experimental observation of Cr and V segregation in the W 0.38 Ta 0.36 Cr 0.15 V 0.11 alloy which in turns shows an exceptional radiation resistance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Seed-Mediated Colloidal Synthesis of Multimetallic and High-Entropy Alloy Nanocrystal Libraries with Enhanced Catalytic Performance

Engineering colloidally stable multimetallic nanocrystals offers many benefits in a wide range of applications and allows manipulation of physical, chemical, and electronic properties of materials at the nanoscale. Synthesis routes are challenged by the chemical complexity required to temporally and spatially coordinate the reduction and alloying of multiple metal species, which has hampered the development of tunable libraries of colloidal materials to date. Here, in this work, we demonstrate a seed-mediated synthesis method to incorporate five or more metal elements into uniform, colloidally stable nanocrystals. By integrating machine learning-accelerated simulations, the synthesis of shortlisted high-entropy alloy nanocrystals was demonstrated. Multiple seed materials can be used, leading to a library of multimetallic nanocrystals with tunable electronic, physical, and alloy structures. The advantage of this synthetic protocol is highlighted in the preparation of catalytic materials that showed 2 orders of magnitude higher reaction rates than monometallic catalysts and outstanding thermal stability, thus highlighting the promise of this approach for high-performance materials in many areas.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Advanced thermal/environmental barrier coatings of high-entropy rare earth disilicates tuned by strong anharmonicity of Eu 2 Si 2 O 7

Advancing thermal/environmental barrier coating (TEBC) materials with integrated thermal-mechanical functions is paramount for safeguarding SiC-based ceramic matrix composites (CMCs) in high-efficiency gas turbines. Herein, we employ a synergistic approach, combining density functional theory (DFT) methods and combinatorial chemistry techniques, to design high-performance and low-cost RE 2 Si 2 O 7 (RE = rare earth elements) TEBC materials tailored for enhanced compatibility with SiC-based CMCs. Expanding on phase stability of alloying pure RE 2 Si 2 O 7 , the investigation extends to the mechanical and thermal properties of solid solution systems, including Er 1/2 Y 3/4 Yb 3/4 Si 2 O 7 , Gd 1/4 Er 1/4 Y 3/4 Yb 3/4 Si 2 O 7 , and Eu 1/4 Er 1/4 Y 3/4 Yb 3/4 Si 2 O 7 . The solid solution systems exhibit a major reduction in lattice thermal conductivity relative to their pure counterparts, achieving ultralow values of 0.25 to 0.39 W m −1 K −1 at 1500 K. Furthermore, the coefficients of thermal expansion (CTE) of these solid solutions are precisely tuned within the desired range for SiC (4.4 to 5.5 × 10 −6 K −1 ), while maintaining good mechanical properties. Here, in particular, the addition of Eu 2 Si 2 O 7 demonstrates to be an important variable to the tuning of CTE and lattice thermal conductivity by leveraging its strong anharmonicity, presenting a pioneering avenue for fine-tuning material properties. In summary, this research not only identifies promising TEBC materials with superior thermal properties, but also introduces a valuable computational material design methodology for the rapid discovery of complex materials for harsh environments.

36 MATERIALS SCIENCE↗
DOE OSTI2020

First-principles prediction of incipient order in arbitrary high-entropy alloys: exemplified in Ti 0.25 CrFeNiAl

High-temperature disordered multi-component alloys, including high-entropy alloys, experience either segregation or partially-ordered phases to reach low-temperature phases. For Ti 0.25 CrFeNiAl x (0 ≤ x ≤ 1), experiments suggest a partially-ordered B2 phase, whereas CALculation of PHAse Diagrams (CALPHAD) predicts a region of L21+B2 coexistence. We employ first-principles KKR-CPA to assess stability of phases with arbitrary order and a KKR-CPA linear-response theory to predict atomic short-range order (SRO) in the disorder phase that reveals the competing long-range ordered (LRO) phases in a given Bravais lattice. The favorable SRO provides a specific concentration-waves (site occupation probabilities and partially-ordered unit cells) and estimated energy gains that can then be assess directly by KKR-CPA formation enthalpies. Our results are in good agreement with experiments and CALPHAD in Al-poor regions (x ≤ 0.75) and with CALPHAD in Al-rich region (1≥ x >0.75). Our first-principles KKR-CPA and SRO-based concentration-wave analysis is shown to be a powerful and fast method to assess competing LRO phases in complex solid-solution alloys, and our results suggests more careful experiments in Al-rich region are needed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Accelerated Design of Cost-Effective Thermal/Environmental Barrier Coatings based on High-Entropy Rare Earth Disilicates: A First-Principles Study

This project aims to design cost-effective thermal/environmental barrier coatings (TEBC) based on high entropy rare earth disilicates to protect SiC-based ceramic matrix composites from chemical and thermal attack for better performance of components in the hot section of gas turbine engines. To accelerate the alloy design, we utilize first-principles density functional theory (DFT) together with combinatorial chemistry methodology to predict key properties including phase stability, apparent bulk coefficient of thermal expansion (ABCTE), intrinsic lattice thermal conductivity, and temperature-dependent elastic constants. Specifically, this project focuses on β-RE2Si2O7 (RE=Yb, Y, Er, Lu, La, Ce,) with β-Yb2Si2O7 and β-Y2Si2O7 as the benchmark. Our DFT calculations predict that Er1/4Lu1/4Y3/4Yb3/4Si2O7 and Er1/2Lu1/2Y1/2Yb1/2Si2O7 have ultralow lattice thermal conductivity < 0.23 W/m/K at 1500 K and a good match of average ABCTE (5.1 - 5.2×10-6 K-1) with SiC. Owing to the low cost and abundant supply of Ce and La, the A- and G-La2Si2O7/Ce2Si2O7 disilicates are also studied. Our study shows that G-phase Ce2Si2O7 has an ultralow thermal conductivity (0.26 W/m/K at 1500 K) and the apparent bulk ABCTE (≈6.9×10-6 K-1) slightly higher than SiC, demonstrating great potential as low-cost high-performance T/EBC. However, La2Si2O7 and Ce2Si2O7 undergo an A-phase to G-phase polymorphic transition at around 1470 K.

environmental barrier coatings↗
DOE OSTI2025

Conformal high-entropy oxide coatings enable fast and durable surface oxygen reactions

Developing active and durable air electrodes for efficient oxygen reactions is challenging for protonic ceramic cells (PCCs), especially at temperatures below 550°C. Here, in this study, we report a rationally designed conformal coating with a high-entropy PrNi 0.2 Mn 0.2 Co 0.2 Fe 0.2 Cu 0.2 O 3−δ (PNMCFC) perovskite structure on the surface of a state-of-the-art PrBaCo 2 O 5+δ (PBC) air electrode. The formed hybrid air electrode (PNMCFC-PBC) shows faster surface oxygen kinetics and a more stable phase structure in high-humidity air than the bare PBC electrode. Further density functional theory calculations suggest that the conformal coating mitigates Ba segregation at the interface and improves oxygen-related reactions, enhancing overall stability and electrocatalytic performance. The cells with the developed hybrid electrodes show encouraging electrochemical performance at 550°C: a polarization resistance of 0.72 Ω cm 2 , a peak power density of 1.30 W cm −2 , an electrolysis current density of −1.36 A cm −2 at 1.3 V, and reasonable operating stabilities (∼200 h at 550°C).

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

Quantum many-body scars in a Landau level on a thin torus

We review a kinetically constrained pair-hopping model that arises within a Landau level in the quantum Hall effect. At filling ν = 1/3, the model exactly maps onto the so-called “PXP model,” a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors ν = p/(2p+1), and show that the model is equivalent to nonintegrable spin chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

1-dimensional spin chains↗
DOE OSTI2020

Solid-phase hetero epitaxial growth of α-phase formamidinium perovskite

Conventional epitaxy of semiconductor films requires a compatible single crystalline substrate and precisely controlled growth conditions, which limit the price competitiveness and versatility of the process. We demonstrate substrate-tolerant nano-heteroepitaxy (NHE) of high-quality formamidinium-lead-tri-iodide (FAPbI 3 ) perovskite films. The layered perovskite templates the solid-state phase conversion of FAPbI 3 from its hexagonal non-perovskite phase to the cubic perovskite polymorph, where the growth kinetics are controlled by a synergistic effect between strain and entropy. The slow heteroepitaxial crystal growth enlarged the perovskite crystals by 10-fold with a reduced defect density and strong preferred orientation. This NHE is readily applicable to various substrates used for devices. The proof-of-concept solar cell and light-emitting diode devices based on the NHE-FAPbI 3 showed efficiencies and stabilities superior to those of devices fabricated without NHE.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Electronic structure and dynamics of confined atoms

Confined atomic systems are of great importance owing a multitude of possible applications in various areas of science and technology. Of particular interest are atoms encaged in the C 60 molecule, A@C 60 , since the near-spherical symmetry of C 60 simplifies theoretical studies, and the stability of C 60 renders it amenable to experimental examination. Herein a review of investigations of the electronic structure and dynamics of A@C 60 is presented in this manuscript focusing on developments in the last decade. Addressed mainly are how the confinement affects electronic structure properties such as ionization potentials, localization of atomic electrons, Shannon entropy, correlation effects, relativistic interactions, and others. In the area of dynamics, photoionization and e-A@C 60 scattering are reviewed and summarized, and the major effects of confinement on the dynamical properties, e.g., confinement resonances, hybridization, Wigner time delay, are delineated.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Irradiation-Induced Extremes Create Hierarchical Face-/Body-Centered-Cubic Phases in Nanostructured High Entropy Alloys

A nanoscale hierarchical dual-phase structure is reported to form in a nanocrystalline NiFeCoCrCu high-entropy-alloy (HEA) film via ion irradiation. Under the extreme energy deposition and consequent thermal energy dissipation induced by energetic particles, a fundamentally new phenomenon is revealed, in which the original single-phase face-centered-cubic (FCC) structure partially transforms into alternating nanometer layers of a body-centered-cubic (BCC) structure. The orientation relationship follows the Nishiyama–Wasser-man relationship, that is, (011) BCC || (1¯1¯1) FCC and [100] BCC || [11¯0] FCC . Simulation results indicate that Cr, as a BCC stabilizing element, exhibits a tendency to segregate to the stacking faults (SFs). Furthermore, the high densities of SFs and twin boundaries in each nanocrystalline grain serve to accelerate the nucleation and growth of the BCC phase during irradiation. By adjusting the irradiation parameters, desired thicknesses of the FCC and BCC phases in the laminates can be achieved. Finally, this work demonstrates the controlled formation of an attractive dual-phase nanolaminate structure under ion irradiation and provides a strategy for designing new derivate structures of HEAs.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Causal horizons, geodesic completeness and stability in slow contraction cosmology

We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, flat or open slow contraction admits a stable past attractor that asymptotes to Minkowski space and is past geodesically complete, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde–Guth–Vilenkin theorem. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗
DOE OSTI2022

Shock Formation and Vorticity Creation for 3d Euler

Abstract We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.

Mathematics↗
DOE OSTI2025

Final report on assessment of molten salt corrosion testing of unirradiated and ion irradiated advanced manufactured high entropy alloys

Generation IV reactors and future fusion reactor designs have led to more demanding materials performance requirements due to their increased operating temperatures, corrosive coolants, and increased radiation doses compared to the current light-water reactor fleet. Among the innovative nuclear technologies under development, molten salt reactors stand out for their potential to offer superior fuel utilization, intrinsic safety characteristics, and economic viability. Of the proposed Generation IV designs, the gas fast reactor operates at 450 to 850°C and the molten salt reactor operates at 565 to 850°C, with the molten salt reactor design needing molten salt corrosion resistant materials [1, 2]. These increased temperatures and more extreme corrosion environments necessitate higher material performance, such as creep strength, radiation-tolerant microstructures, corrosion resistance, and high-temperature tensile properties. Hastelloy-N, a nickel-based alloy with additions of molybdenum and chromium, has been successfully employed to contain molten fluoride salt at temperatures up to 705°C. However, Hastelloy-N becomes embrittled upon neutron irradiation, primarily due to the accumulation of helium produced by (n,a) transmutation reactions. Furthermore, the corrosive nature of molten fluoride and chloride salts presents a formidable challenge, as these salts can react with and dissolve alloying elements such as Cr, Mo, and Fe, leading to selective leaching, loss of protective oxide layers, and accelerated degradation. High entropy alloys (HEAs) and refractory high entropy alloys (RHEAs) have emerged as a prominent area of interest, due to their ability to achieve tailored chemical compositions for specific applications. Unlike conventional alloys, HEAs are characterized by having multiple principal elements in equimolar or near equimolar ratios, leading to an unconventional alloying strategy [3]. This alloying strategy is believed to promote unique properties, such as single-phase stabilization of chemically compatible elements, lattice distortion effects due to atomic radius differences, and proposed sluggish diffusion effects. For extreme-environment applications, RHEAs have garnered much research interest because of the possibility of creating relatively ductile materials that can operate in extremely high-temperature environments, beyond the operating temperatures where other Ni-based superalloys begin to lose strength [4-6]. Idaho National Laboratory (INL) initiated a joint international effort with the Czech Republic to explore the feasibility of manufacturing HEAs for high-temperature nuclear applications using advanced manufacturing. This effort was funded at INL by the United States Department of Energy's Office of Nuclear Energy under the Advanced Reactor Technologies and Advanced Materials and Manufacturing Technologies (AMMT) Program. The HEAs were specifically designed for the corrosive and irradiation environments experienced in gas-cooled fast reactors, molten salt reactors, and fusion power. These alloys have been manufactured by multiple processes to determine the impact of manufacturing processes on the performance of the alloys in corrosive and irradiation environments. Preliminary molten salt corrosion testing showed that equimolar MoNbTiV and MoNbTi alloys exhibit exceptional performance, with arc-melted variants demonstrating only minimal degradation after 1000 hours of exposure to molten chloride salt at 700°C. Conversely, Nb2TiVZr2 showed significant molten salt corrosion susceptibility and microstructural instability during high-temperature molten salt exposures, and was, therefore deemed unfit for molten salt reactor applications. The MoNbTiV, MoNbTi, and Nb2TiVZr2 alloys were further evaluated through ion irradiation experiments conducted at the Michigan Ion Beam Laboratory at the University of Michigan. The microstructural stability and the evolution of irradiation-induced defects were characterized to assess the irradiation resistance of each of these alloys.

36 - MATERIALS SCIENCE↗
DOE OSTI2024

Phase segregation of a composite air electrode unlocks the high performance of reversible protonic ceramic electrochemical cells

One breakthrough in developing highly efficient air electrodes for reversible protonic ceramic electrochemical cells (R-PCECs) is optimizing the sluggish oxygen reduction and water oxidation reactions. Here, we present a novel composite material with a nominal formula of high-entropy Ce 0.2 Ba 0.2 Sr 0.2 La 0.2 Ca 0.2 CoO 3–δ (CBSLCC) that spontaneously self-assembles to three-phase electrocatalysts composed of deficient Ce 0.2–y Ba 0.2 Sr 0.2–x La 0.2–x Ca 0.2 CoO 3–δ (CD-CBSLCC), CeO 2 , and La 0.5 Sr 0.5 CoO 3–δ (LSC). Mechanistic studies corroborate that oxygen reduction may occur on entire air electrode surfaces, followed by water formation preferentially at or near CD-CBSLCC. The CeO 2 phase could provide or consume protons to facilitate the oxygen evolution/reduction kinetics in R-PCECs. The developed electrodes demonstrate a record-high electrochemical performance in dual modes of fuel cells and electrolysis cells, delivering a peak power density of 1.66 W cm –2 at 600 °C and a current density of –1.76 A cm –2 at 1.3 V and 600 °C. Finally, excellent operational stabilities of the fuel cell (200 h at 600 °C), electrolysis cell (200 h at 600 °C), and reversible cycling (548 h at 550 °C) provide a promising and reliable step towards realizing the commercialization of R-PCECs.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

Here, a conservative discontinuous Galerkin scheme for a non-linear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it has a non-decreasing entropy functional, and conserves particles, momentum and energy. Discretely these conservative properties are maintained exactly as well, independent of numerical resolution. In this work the phase space discretization is performed using a novel version of the discontinuous Galerkin scheme, carefully constructed using concepts of weak equality and recovery. Discrete time advancement is carried out with an explicit time-stepping algorithm, whose stability limits we explore. The formulation and implementation within the long-wavelength gyrokinetic solver of Gkeyll are validated with relaxation tests, collisional Landau-damping benchmarks and the study of 5D gyrokinetic turbulence on helical, open field lines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Emergent Dimer-Model Topological Order and Quasiparticle Excitations in Liquid Crystals: Combinatorial Vortex Lattices

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

36 MATERIALS SCIENCE↗