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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The mobility of small, over-pressurized helium bubbles in tungsten at 2000 K

Fusion reactor environments inevitably lead to the formation of high-pressure helium bubbles whose nucleation, growth, and diffusion strongly impact the performance of plasma-facing components. Here this research describes a diffusion mechanism of over-pressurized bubbles via a sequence of Frenkel pair nucleation, self-interstitial migration, and Frenkel pair annihilation. Molecular dynamics was used to simulate the diffusion of small bubbles in tungsten at 2000 K with helium-per-vacancy ratios in the range of 4.5 to 7. The diffusion coefficients are calculated and their dependence on helium content, number of vacancies, and number of attached self-interstitials is characterized. It is found that bubbles are most mobile when the nucleation/annihilation rates of Frenkel pairs are nearly equal and when the bubbles nucleate and annihilate a single self-interstitial. All bubbles experience a peak diffusivity, which can be as high as 10 -11 m 2 /s decreasing with bubble size. The calculated diffusion coefficients provide valuable insight into the mobility of small, high-pressure bubbles, and can be used as input parameters in mesoscale models to improve predictions of plasma-surface interactions. (LA-UR-21-21881)

36 MATERIALS SCIENCE↗
DOE OSTI2021

Regulating crystallization to maintain balanced carrier mobility via ternary strategy in blade-coated flexible organic solar cells

Regulating the crystallization of donor and acceptor to maintain balanced carrier mobility is of great importance to fabricate efficient organic solar cells (OSCs). Herein, the balanced crystallinity between donor and acceptor was finely controlled in blade-coated OSCs. By adding high crystalline FOIC into PBDB-T:ITIC system, a balanced carrier mobility was achieved, resulting in the much improved fill factor. The optimized ternary device exhibits an increased current density, due to the enhanced light-harvesting efficiency with complementary absorption and the morphology change. Morphology characterization demonstrated that the ternary film exhibits a highly balanced crystallinity between the donor and acceptor on account of the formation of acceptor alloy. Moreover, the ternary film not only possesses a small domain size, but also exhibits a high domain purity as compared to both binary films. Encouragingly, a highest power conversion efficiency (PCE) of 10.68% was obtained for the blade-coated ternary OSCs. In addition, the blade-coated flexible large-area (105 mm 2 ) OSC based on PBDB-T:ITIC:FOIC ternary system also exhibits a high PCE of 9.81%, showing great potential in the high-throughput fabrication of OSCs.

14 SOLAR ENERGY↗
DOE OSTI2023

Revising the dynamic energy budget theory with a new reserve mobilization rule and three example applications to bacterial growth

Dynamic energy budget (DEB) theory has been applied to model a wide range of organisms, including microbes. In the standard DEB model, biomass is partitioned into reserve and structural compartments, where reserve biomass is mobilized in a pseudolinear manner (while the reserve biomass density, defined as the ratio between reserve and structural biomass, decays linearly) to drive maintenance and the growth of structural biomass (and extracellular enzyme production if it is considered). However, the linear dynamics of the reserve biomass density makes the standard DEB model incapable of explaining the slowdown of microbial growth at high reserve density that is caused by macromolecular crowding effect which reduces biochemical reaction rates (a typical situation occurs when microbes are experiencing severe moisture stress) and is inconsistent with the observation that intracellular enzymatic reactions generally follow non-linear kinetics. By partitioning biomass into reserve, kinetic, and structural compartments, we show here that the Equilibrium Chemistry Approximation (ECA) kinetics can be used to represent enzymatically catalyzed reserve biomass mobilization that can then drive the kinetic and structural biomass synthesis. This revised DEB model better represents the tradeoff in ribosome allocation for structural growth and internal enzyme production, is structurally compatible with metabolic models of cell individuals, and includes the standard DEB model and the popular compromise model as special cases for representing population growth. We then applied the revised DEB model to interpret components of bacterial respiration, their dependence on substrate availability, and emergent microbial carbon use efficiency dynamics for an exponentially growing population. We found that the revised DEB model enables a better understanding of bacterial substrates use (carbon in our examples) than that can be derived from a few other models in the literature. In particular, the revised DEB model explains why carbon use efficiency may first increase, then plateau, and finally decrease with growth rate (and substrate uptake rate), as a function of proteomics. Additionally, the revised DEB model explains why the kinetic biomass compartment needs to be divided to reasonably incorporate proteomic control of microbial growth.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Stability and mobility of tungsten clusters on tungsten (110) surface: Ab initio and atomistic simulations

Quantifying the surface transport properties of tungsten (W) is of prime importance to understand the formation of nano-fuzz in fusion plasma-facing conditions. The stability and mobility of W adatom clusters (W n , n = 2-9) on the W(110) surface has been investigated by computer simulations, including ab initio calculations using density functional theory (DFT) and molecular statics (MS) simulations with multiple W interatomic potentials. The DFT results demonstrate that the sequential binding energy generally increases with number of W adatoms, except for the 5 th and 7 th W adatoms. The most common elemental migration steps of W n (n>2) clusters are observed to consist of monomer and dimer hops, while larger W n clusters can also diffuse by dissociation and recombination of smaller clusters. The threshold migration energy of W 9 is the highest, then followed by W 8 , W 4 , and W 6 , while W 3 , W 5 , and W 7 have similar migration energies. Compared to DFT, each interatomic potential evaluated overestimates the binding energies of W n clusters. Additionally, the embedded-atom potential developed by Juslin and Wirth adequately predicts the threshold migration energy of W n (n>2) clusters, although it predicts different underlying migration mechanisms. The results show that interaction mechanism between W adatoms controls the stability and mobility of W n clusters on the W(110) surface.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Learning From User Behavior: A Survey-Assist Algorithm for Longitudinal Mobility Data Collection

GPS-based travel surveys are widely used in mobility studies to gather crucial qualitative data, like purpose, transportation mode and replaced mode. However, survey response still poses a burden to users, especially in long-term mobility studies, leading to response fatigue. We explore a survey-assist strategy to ease this burden by a novel, user-level modeling approach that leverages past responses from each user to predict responses for new trips, without relying on external data sources like GIS data. We investigate three main algorithms for predicting responses: (i) clustering trips and extrapolating responses for similar trips, (ii) using random forest classification, and (iii) clustering that uses a hybrid algorithm to determine spatial structure, which is then fed as input to a classic random forest classifier. The clustering approach can flexibly predict responses for even complex qualitative survey questions; it achieved F-scores of 65%. The random forest pipeline uses architecture that restricts it to predicting three predetermined survey questions: trip purpose, mode, and replaced mode. However, it achieved F-scores of 78%. While the survey-assist approach has been implemented by several proprietary systems, to our knowledge, this is the first exploration in the academic literature. It follows that this is also the first rigorous evaluation of multiple algorithms that can implement the approach. The evaluation uses a large scale, publicly available, longitudinal dataset consisting of ~ 92k trips from 235 users over a period of roughly one and a half years. With this approach, travel surveys can be pre-filled with the predicted responses for each trip, thus streamlining the survey process for users. Combined with an active learning system that requests user input on low-confidence predictions, models can be updated and improved over time to better support the long-term collection of longitudinal qualitative data.

clustering↗
DOE OSTI2020

Joint Design of Multimodal Transit Networks and Shared Autonomous Mobility Fleets

Providing quality transit service to travelers in low-density areas, particularly travelers without personal vehicles, is a constant challenge for transit agencies. The advent of fully-autonomous vehicles (AVs) and their inclusion in mobility service fleets may allow transit agencies to offer better service and/or reduce their own capital and operational costs. This study focuses on the problem of allocating resources between transit patterns and operating (or subsidizing) shared-use AV mobility services (SAMSs) in a large metropolitan area. To address this question, a joint transit network redesign and SAMS fleet size determination problem (JTNR-SFSDP) is introduced, and a bi-level mathematical programming formulation and solution approach are presented. The upper-level problem modifies a transit network frequency setting problem (TNFSP) formulation via incorporating SAMS fleet size as a decision variable and allowing the removal of bus routes. The lower-level problem consists of a dynamic combined mode choice-traveler assignment problem (DCMC-TAP) formulation. The heuristic solution procedure involves solving the upper-level problem using a nonlinear programming solver and solving the lower-level problem using an iterative agent-based assignment-simulation approach. To illustrate the effectiveness of the modeling framework, this study uses traveler demand from Chicago along with the regions existing multimodal transit network. The computational results indicate significant traveler benefits, in terms of improved average traveler wait times, associated with optimizing the joint design of multimodal transit networks and SAMS fleets compared with the initial transit network design.

bi-level programming↗
DOE OSTI2021

Exploring the impacts of conformer selection methods on ion mobility collision cross section predictions

The prediction of structure dependent molecular properties, such as collision cross sections as measured using ion mobility spectrometry, are crucially dependent on the selection of the correct population of molecular conformers. Here, we report an in-depth evaluation of multiple conformation selection techniques, including simple averaging, Boltzmann weighting, lowest energy selection, low energy threshold reductions, and similarity reduction. Generating 50,000 conformers each for 18 molecules, we used the In Silico Chemical Library Engine (ISiCLE) to calculate the collision cross sections for the entire dataset. First, we employed Monte Carlo simulations to understand the variability between conformer structures as generated using simulated annealing. Then we employed Monte Carlo simulations to the aforementioned conformer selection techniques applied on the simulated molecular property—the ion mobility collision cross section. Based on our analyses, we found Boltzmann weighting to be a good tradeoff between precision and theoretical accuracy. Combining multiple techniques revealed that energy thresholds and root-mean-squared deviation-based similarity reductions can save considerable computational expense while maintaining property prediction accuracy. Molecular dynamic conformer generation tools like AMBER can continue to generate new lowest energy conformers even after tens of thousands of generations, decreasing precision between runs. This reduced precision can be ameliorated and theoretical accuracy increased by running density functional theory geometry optimization on carefully selected conformers.

Nielson, Felicity F.↗
DOE OSTI2020

Mobility of Radionuclides in Fractured Carbonate Rocks: Lessons from a Field-Scale Transport Experiment

Current research on radionuclide disposal is mostly conducted in granite, clay, saltstone, or volcanic tuff formations. These rock types are not always available to host a geological repository in every nuclear waste-generating country, but carbonate rocks may serve as a potential alternative. To assess their feasibility, a forced gradient cross-borehole tracer experiment was conducted in a saturated fractured chalk formation. The mobility of stable Sr and Cs (as analogs for their radioactive counterparts), Ce (an actinide analog), Re (a Tc analog), bentonite particles, and fluorescent dye tracers through the flow path was analyzed. The migration of each of these radionuclide analogs (RAs) was shown to be dependent upon their chemical speciation in solution, their interactions with bentonite, and their sorption potential to the chalk rock matrix. The brackish groundwater resulted in flocculation and immobilization of most particulate RAs. Nevertheless, the high permeability of the fracture system allowed for fast overall transport times of all aqueous RAs investigated. This study suggests that the geochemical properties of carbonate rocks may provide suitable conditions for certain types of radionuclide storage (in particular, brackish, high-porosity, and low-permeability chalks). Nevertheless, careful consideration should be given to high-permeability fracture networks that may result in high radionuclide mobility.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Hydrophilic and Apolar Hydration in Densely Grafted Cationic Brushes and Counterions with Large Mobilities

We employ all-atom molecular dynamics (MD) simulation framework to unravel water microstructure and ion properties for cationic [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] (PMETAC) brushes with chloride ions as counterions. First, we identify locally separate water domains (or first hydration shells) each around the {N(CH 3 ) 3 } + and the C=O functional groups of the PMETAC chain and one around the Cl - ion. These first hydration shells around the respective moieties overlap and the extent of the overlap depends on the nature of the species triggering it. Second, despite the overlap, the water molecules in these domains demonstrate disparate properties dictated by the properties of the atoms/groups around which they are located. For example, the presence of the methyl groups make the {N(CH 3 ) 3 } + group trigger apolar hydration as evidenced by the corresponding orientation of the dipole of the water molecules around the {N(CH 3 ) 3 } + moiety. These water molecules around the N(CH 3 ) 3 } + group also have enhanced tetrahedrality as compared to the water molecules constituting the hydration layer around the C=O group and the Cl - counterion. Our simulations also identify that there is an intervening water layer between the Cl - ion and {N(CH 3 ) 3 } + group: this layer prevents the Cl - ion from coming very close to the {N(CH 3 ) 3 } + group. As a consequence, there is a significantly large mobility of the Cl - ions inside the PMETAC brush layer. Furthermore, the C=O group of the PE chain, due to the partial negative charge on the oxygen atom and the specific structure of the PMETAC brush system, demonstrates strongly hydrophilic behavior and enforces a specific dipole response of water molecules analogous to that experienced by water around anionic species of high charge density. As a result, our findings confirm that PMETAC brushes undergo hydrophilic hydration at one site, apolar hydration at another site, and ensures large mobility of the supported Cl- counterions.

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

Side Chain Engineering of Near-IR Aza-BODIPY Dyes Enables Processable Films with High Hole Mobility in Diodes

Boron chelated azadipyrromethene (Aza-BODIPY) derivatives are promising candidates for near-infrared optoelectronic applications due to their tunable absorption, electron-deficient core, and strong π-conjugation. Here, in this work, we synthesized and studied a series of 1-naphthylethynyl-substituted aza-BODIPY molecules featuring hexyl or hexyloxy solubilizing groups at either the proximal or the distal phenyl positions. These substitutions were designed to improve the solubility, film formation, and optoelectronic properties. We found that solubilizing groups not only enabled uniform solution-processed films but also fine-tuned key properties, such as absorption onset, oxidation potential, and energy levels. Charge transport analysis showed consistently high hole mobilities (∼10 –3 cm 2 /V s) across all substituted derivatives when CuI was used as the hole transport layer, regardless of film morphology. In contrast, electron mobilities tended to be low and inconsistent, partly because of the relatively poor-quality films on the ZnO electron transport layer. Overall, we have shown that solubilizing groups enable film solution-casting and can fine-tune the properties of these near-infrared aza-BODIPY derivatives.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Role of Intradomain Heterogeneity on Ion and Polymer Dynamics in Block Polymer Electrolytes: Investigating Interfacial Mobility and Ion-Specific Dynamics and Transport

Block polymers show promise as solid-state battery electrolytes due to the optimization of conductive and mechanical properties enabled via tuning of block chemistry and length. We investigate a polystyrene-block-poly(oligo-oxyethylene methacrylate) (PS-b-POEM) electrolyte doped with various lithium salts to investigate the role of molecular structure on ion transport properties and on local ion dynamics and associations. Anion charge becomes more delocalized with increasing size, reducing the coupling between salt ions while increasing coupling between ion and polymer chain motions and creating a more mobile overall environment. We observe support for this ion-polymer coupling via 1 H, 7 Li and 19 F NMR spectroscopy, from which we obtain ion-specific mobility transition temperatures that differ from the polymer glass transition temperature. We also note faster transport and weaker local energetic interactions with anion size using temperature-dependent NMR diffusometry. 1 H NMR spectroscopy further elucidates polymer chain dynamics and enables quantification of the temperature-dependent fraction of the conducting block that is immobile near the PS-POEM domain interface. As a result, NMR thus represents a species-specific and timescale-specific platform to quantify phase and interface behavior, and to correlate ion-specific transport with polymer chain dynamics.

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

Reducing Pb and Cl Mobility in Waste-to-Energy Fly Ashes via Chlorellestadite Formation

Sustainably sourced development minerals are vital to meeting the demand for low-carbon construction materials. A potential waste material that can be a low-carbon construction material for cementitious systems is waste-to-energy fly ash (WTE ash), a by-product of waste incineration. WTE ash contains chloride-bearing species and heavy metals, which can promote steel reinforcement corrosion and present long-term leaching risks. Here, we present a new multi-step ash treatment protocol involving dissolution and heating to transform the non-readily removable chlorides in WTE ash to Chlorellestadite (Ca 10 (SiO 4 ) 3 (SO 4 ) 3 Cl 2 ). Our results suggest that this transformation significantly reduces chloride release from WTE ash in an alkaline cement-like environment by over two orders of magnitude, from 1500 mg/l to less than 10 mg/l. This transformation also significantly reduces Pb mobility after treatment (from > 5 mg/l to < 0.5 mg/l), likely caused by the crystallo-chemical incorporation of Pb in Chlorellestadite. In contrast to the existing ash treatment methods, the proposed ash treatment protocol minimizes heavy metals volatilization while simultaneously reducing Pb mobility and chloride release through Chlorellestadite formation. Furthermore, these findings overcome limitations preventing the commercial use of WTE ash and thus opening up pathways towards a circular economy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Role of the Mobile Active Site Flap in IMP Dehydrogenase Inhibitor Binding

Inosine 5′-monophosphate dehydrogenase (IMPDH) is a promising antibiotic target. This enzyme catalyzes the NAD-dependent oxidation of inosine 5′-monophosphate (IMP) to xanthosine 5′-monophosphate (XMP), which is the rate-limiting step in guanine nucleotide biosynthesis. Bacterial IMPDH-specific inhibitors have been developed that bind to the NAD + site. These inhibitors display varied affinities to different bacterial IMPDHs that are not easily rationalized by X-ray crystal structures of enzyme–inhibitor complexes. Inspection of X-ray crystal structures of 25 enzyme–inhibitor complexes, including 10 newly described, suggested that a mobile active site flap may be a structural determinant of inhibitor potency. Saturation transfer difference NMR experiments also suggested that the flap may contact the inhibitors to varying extents in different IMPDHs. Flap residue Leu413 contacted some inhibitors but was not structured in the crystal structures of other inhibitor complexes. The substitution of Leu413 with Phe or Ala in Bacillus anthracis IMPDH had inhibitor-selective effects, suggesting residue 413 could be a structural determinant of affinity. Curiously, the Ala substitution increased the potency of most inhibitors, even those that contacted Leu413 in the crystal structures. Presteady-state and steady-state kinetics experiments showed that the Leu413Ala substitution had comparable effects on inhibitor binding to the noncovalent E·IMP complex and the covalent intermediate E-XMP*, suggesting that the flap had similar interactions in both complexes. These results demonstrate that contacts do not necessarily indicate favorable interactions, and poorly structured mobile regions should not be discounted when assessing binding determinants.

Conformation↗
DOE OSTI2021

Unraveling the Unconventional Order of a High-Mobility Indacenodithiophene-Benzothiadiazole Copolymer

We report a new class of donor–acceptor (D-A) copolymers found to produce high charge carrier mobilities competitive with amorphous silicon (>1 cm 2 V –1 s –1 ) exhibit the puzzling microstructure of substantial local order, however lacking long-range order and crystallinity previously deemed necessary for achieving high mobility. Here, we demonstrate the application of low-dose transmission electron microscopy to image and quantify the nanoscale and mesoscale organization of an archetypal D-A copolymer across areas comparable to electronic devices (≈9 μm 2 ). The local structure is spatially resolved by mapping the backbone (001) spacing reflection, revealing nanocrystallites of aligned polymer chains throughout nearly the entire film. Analysis of the nanoscale structure of its ordered domains suggests significant short- and medium-range order and preferential grain boundary orientations. Moreover, we provide insights into the rich, interconnected mesoscale organization of this new family of D-A copolymers by analysis of the local orientational spatial autocorrelations.

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

Chemically Stable Polyarylether-Based Metallophthalocyanine Frameworks with High Carrier Mobilities for Capacitive Energy Storage

Covalent organic frameworks (COFs) with efficient charge transport and exceptional chemical stability are emerging as an import class of semiconducting materials for opto-/electronic devices and energy-related applications. However, the limited synthetic chemistry to access such materials and the lack of mechanistic understanding of carrier mobility greatly hinder their practical applications. Herein, we report the synthesis of three chemically stable polyarylether-based metallophthalocyanine COFs (PAE-PcM, M = Cu, Ni, and Co) and facile in situ growth of their thin films on various substrates (i.e., SiO 2 /Si, ITO, quartz) under solvothermal conditions. We show that PAE-PcM COFs thin films with van der Waals layered structures exhibit p -type semiconducting properties with the intrinsic mobility up to ~19.4 cm 2 V -1 s -1 and 4 orders of magnitude of increase in conductivity for PAE-PcCu film (0.2 S m -1 ) after iodine doping. Density functional theory calculations reveal that the carrier transport in the framework is anisotropic, with the out-of-plane hole transport along columnar stacked phthalocyanine more favorable. Furthermore, PAE-PcCo shows the redox behavior maximumly contributes ~88.5% of its capacitance performance, giving rise to a high surface area normalized capacitance of ~19 μF cm -2 . Overall, this work not only offers fundamental understandings of electronic properties of polyarylether-based 2D COFs but also paves the way for their energy-related applications.

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

Effects of Temperature Fluctuations on Surface Mobility of Atomic Steps and Oxidation Dynamics in High-Temperature Alloys

In contrast to the traditional perspective that thermal fluctuations are insignificant in surface dynamics, here we report their influence on surface reaction dynamics. Using real-time low-energy electron microscopy imaging of NiAl(100) under both vacuum and O 2 atmospheres, we demonstrate that transient temperature variations substantially alter the direction of atom diffusion between the surface and bulk, leading to markedly different oxidation outcomes. During heating, substantial outward diffusion of atoms from the bulk to the surface results in step growth. Conversely, cooling induces considerable inward diffusion of adatoms, producing a distinct oxide morphology. In both scenarios, initially formed oxide islands impede local atomic step mobility, thereby increasing step length due to mass transfer between the surface and bulk, with atomic steps acting as adatom sinks during heating and sources during cooling. Furthermore, we show that this pinning effect on atomic step mobility can be mitigated by applying persistent temperature fluctuations. As a result, understanding these nuances is vital for accurately predicting and dynamically manipulating the performance of active materials in various chemical processes under transient thermal conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order

Abstract Refractory high-entropy alloys (RHEAs) are designed for high elevated-temperature strength, with both edge and screw dislocations playing an important role for plastic deformation. However, they can also display a significant energetic driving force for chemical short-range ordering (SRO). Here, we investigate mechanisms underlying the mobilities of screw and edge dislocations in the body-centered cubic MoNbTaW RHEA over a wide temperature range using extensive molecular dynamics simulations based on a highly-accurate machine-learning interatomic potential. Further, we specifically evaluate how these mechanisms are affected by the presence of SRO. The mobility of edge dislocations is found to be enhanced by the presence of SRO, whereas the rate of double-kink nucleation in the motion of screw dislocations is reduced, although this influence of SRO appears to be attenuated at increasing temperature. Independent of the presence of SRO, a cross-slip locking mechanism is observed for the motion of screws, which provides for extra strengthening for refractory high-entropy alloy system.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantum octets in high mobility pentagonal two-dimensional PdSe 2

Two-dimensional (2D) materials have drawn immense interests in scientific and technological communities, owing to their extraordinary properties and their tunability by gating, proximity, strain and external fields. For electronic applications, an ideal 2D material would have high mobility, air stability, sizable band gap, and be compatible with large scale synthesis. Here we demonstrate air stable field effect transistors using atomically thin few-layer PdSe 2 sheets that are sandwiched between hexagonal BN (hBN), with large saturation current > 350 μA/μm, and high field effect mobilities of ~ 700 and 10,000 cm 2 /Vs at 300 K and 2 K, respectively. At low temperatures, magnetotransport studies reveal unique octets in quantum oscillations that persist at all densities, arising from 2-fold spin and 4-fold valley degeneracies, which can be broken by in-plane and out-of-plane magnetic fields toward quantum Hall spin and orbital ferromagnetism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗