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At least 613 records · Page 34

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DOE OSTI2020

Exploiting the Spinel Structure for Li-ion Battery Applications: A Tribute to John B. Goodenough

This review provides a personal account of career-long efforts, interwoven with the contributions of others, to exploit the [B 2 ]O 4 framework of an A[B 2 ]O 4 spinel structure for lithium-ion battery applications, where A = Li, and B is one or more metal cations. The narrative begins at the Council for Scientific and Industrial Research (CSIR) in South Africa in the mid-1970s when, in response to the Middle East oil crisis, worldwide efforts were turned to develop high-temperature sodium and lithium batteries to power electric vehicles. In 1981, results in CSIR's program on a high-temperature lithium battery led to a collaborative project on room-temperature lithium cells with Prof. John B. Goodenough at Oxford University, where studies of Fe 3 O 4 , Mn 3 O 4 , and LiMn 2 O 4 cathodes led to the recognition of the broad utility of the [B2]O4 spinel framework as an anode, cathode, or solid electrolyte for rechargeable lithium cells. This finding has had a profound and lasting impact, influencing further ideas and discoveries at the CSIR, Argonne National Laboratory, and elsewhere. The narrative emphasizes the compositional versatility of the spinel structure and the opportunities to tailor the electrochemical potential and stability of a Li-ion cell.

25 ENERGY STORAGE↗

DOE OSTI2020

$CP$ violation from $τ, t$ and $b$ dimension-6 Yukawa couplings — interplay of baryogenesis, EDM and Higgs physics

We explore the implications of the Standard Model effective field theory (SMEFT) with dimension-six terms involving the Higgs boson and third-generation fermion fields on the rate of Higgs boson production and decay into fermions, on the electric dipole moments (EDMs) of the electron, and on the baryon asymmetry of the Universe. We study the consequences of allowing these additional terms for each flavor separately and for combinations of two flavors. We find that a complex $\tau$ Yukawa coupling can account for the observed baryon asymmetry $Y_B^{\rm obs}$ within current LHC and EDM bounds. A complex $b$ ($t$) Yukawa coupling can account for $4\%$ ($2\%$) of $Y_B^{\rm obs}$, whereas a combination of the two can reach $12\%$. Combining $\tau$ with either $t$ or $b$ enlarges the viable parameter space owing to cancellations in the EDM and in either Higgs production times decay or the total Higgs width, respectively. Interestingly, in such a scenario there exists a region in parameter space where the SMEFT contributions to the electron EDM cancel and collider signal strengths are precisely SM-like, while producing sufficient baryon asymmetry. Measuring $CP$ violation in Higgs decays to $\tau$ leptons is the smoking gun for this scenario.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Measurement of the cross section for $\text{t}\bar{\text{t}}$ production with additional jets and b jets in pp collisions at $\sqrt{s}=$ 13 TeV

Measurements of the cross section for the production of top quark pairs in association with a pair of jets from bottom quarks $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}}\right) $ and in association with a pair of jets from quarks of any flavor or gluons $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}}\right) $ and their ratio are presented. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{−1}$. The measurements are performed in a fiducial phase space and extrapolated to the full phase space, separately for the dilepton and lepton+jets channels, where lepton corresponds to either an electron or a muon. The results of the measurements in the fiducial phase space for the dilepton and lepton+jets channels, respectively, are $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ = 2.36±0.02 (stat)±0.20 (syst) pb and 31.0±0.2 (stat)±2.9 (syst) pb, and for the cross section ratio 0.017 ± 0.001 (stat) ± 0.001 (syst) and 0.020 ± 0.001 (stat) ± 0.001 (syst). The values of $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}} $ are determined from the product of the $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ and the cross section ratio, obtaining, respectively, 0.040±0.002 (stat)±0.005 (syst) pb and 0.62±0.03 (stat)±0.07 (syst) pb. These measurements are the most precise to date and are consistent, within the uncertainties, with the standard model expectations obtained using a matrix element calculation at next-to-leading order in quantum chromodynamics matched to a parton shower.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Structure of the polysaccharide sheath from the B race of the green microalga Botryococcus braunii

The green microalga Botryococcus braunii forms a colony of cells held together by an intricate extracellular matrix. This extracellular matrix also acts as a storage location for liquid hydrocarbons initially produced inside the cells. These hydrocarbons can be used as feedstocks to produce transportation fuels. In the B race of B. braunii, the extracellular matrix is composed of several elements: a cross-linked hydrocarbon network filled with the liquid hydrocarbons, a retaining wall to hold the hydrocarbons in the extracellular matrix, an arabinogalactan polysaccharide fibrillar sheath that extends outward from the retaining wall, and a single protein known as polysaccharide associated protein is found at the base of the polysaccharide fibers where they connect to the retaining wall. During growth, colonies of the B race of B. braunii shed fragments of the retaining wall with polysaccharide fibrils attached into the media. Here we describe the isolation and structural analysis of these polysaccharides using a series of chemical degradations in combination with glycosyl residue composition and linkage analysis, as well as 2-dimensional nuclear magnetic resonance spectroscopy. The results demonstrate that the polysaccharide is highly branched, consisting of a galactan backbone with short branches comprised of Dgalactopyranose, L-arabinofuranose, 4-O-methyl-D-glucopyranuronic acid, and 6-deoxy-D-altropyranose. To our knowledge, this is the first description of 6-deoxyaltrose in algae or plants.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Seismic monitoring of EGS fracture stimulations at Utah FORGE (Part 1): Time-lapse variations of b-values and Shear-wave Splitting Rates of induced microearthquakes

Characterizing geologic formations near geothermal wells is crucial for efficient extraction of subsurface geothermal energy resources. To monitor effective fracture stimulation of enhanced geothermal systems (EGS), we analyze a catalog of induced microearthquakes to characterize seismicity induced by Phase 2C fracture stimulations of the Utah FORGE project and derive the b-values for 424 induced microearthquakes in three stages of fracture stimulation. Here, we find the time-lapse variations of these b-values. We apply eigenvector rotation and waveform correlation to 3C geophone data to separate fast S 1 and slow S 2 waves, determine their directions, measure their lag time, and calculate the S-wave splitting rate (SSR) for six induced microearthquakes in Stage 1 and 21 in Stage 3. Both SSR values and b-values increase with time. The increase in these values may be related to heavily fractured zones created by fracture stimulations during Stage 2 injections. Large and highly variable SSR values in Stage 3 may reflect heterogeneities in the fracture zones. Time-lapse variations of SSR values and b-values may be one of the most useful approaches to monitoring and characterizing the effectiveness and efficiency of various types of fracture stimulations.

58 GEOSCIENCES↗

DOE OSTI2020

Enhanced negative thermal expansion of boron-doped Fe 43 Mn 28 Ga 28.97 B 0.03 alloy

Enhanced negative thermal expansion (NTE) properties are achieved by introducing a little amount of boron in the Fe 43 Mn 28 Ga 28.97 B 0.03 alloy. As a result, this alloy shows a giant NTE coefficient of alpha(1) = -79.7 x 10 -6 K -1 in a wide temperature range from 277 K to 136 K. Compared to the NTE characteristics in Fe 43 Mn 28 Ga 29 , the NTE operation temperature window has expanded by 74% with the corresponding coefficient of thermal expansion increased by 57% within the NTE temperature window for the boron-doped Fe 43 Mn 28 Ga28.97B0.03. Additionally, in-situ synchrotron high-energy X-ray diffraction results suggest that by boron substitution, the large unit cell volume change across martensitic transformation and the wide phase transition temperature interval are responsible for the pronounced NTE behavior in Fe 43 Mn 28 Ga 28.97 B 0.03 . Moreover, for the Fe 43 Mn 28 Ga 28.97 B 0.03 NTE material, the compressive strength and strain are significantly improved compared with that of Fe 43 Mn 28 Ga 29 . The present study indicates that Fe 43 Mn 28 Ga 28.97 B 0.03 with enhanced NTE across martensitic transformation may be used for practical application as thermal-expansion compensators.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Structural stability of mechanically alloyed amorphous (FeCoNi) 70 Ti 10 B 20 under high-temperature and high-pressure

Nanostructured (FeCoNi) 70 Ti 10 B 20 (at%) alloy was synthesized by mechanical alloying from elemental powder mixture of Fe, Co, Ni, Ti and B using ball milling. The effect of ball milling time on the evolution of structure and morphology was investigated by X-ray diffraction, scanning and transmission electron microscopy and differential thermal analysis. It was observed that the formation of solid solution of (FeCoNi) 70 Ti 10 B 20 started from the very onset of the milling process. Crystallite size and lattice strains seemed to be leveled off after 20 h of milling with no further major changes. The milling process for longer periods introduced severe plastic deformations causing formation of amorphous phase of (FeCoNi) 70 Ti 10 B 20 . The amorphous alloy composition was confirmed by energy dispersive X-ray spectroscopy analysis that showed an excellent homogeneity of the alloying elements. The phase stability of the mechanically alloyed amorphous sample was further verified by employing high-temperature and high-pressure studies. The alloy samples heat-treated at 700 °C revealed crystallization of the amorphous phase. However, synchrotron-based high-pressure ambient temperature X-ray diffraction studies confirmed that the amorphous phase of the alloy remained stable up to the pressure of 30 GPa. Here, the 50 h milled sample after being annealed at 350 °C showed improvement in the soft magnetic properties of the alloy, which was due to the probable elimination of the residual stress in the amorphous phase of the alloy powders.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Theory meets experiment: Insights into structure and magnetic properties of Fe 1-x Ni x B alloy

Here, we studied the structural and magnetic properties of the solid solution Fe 1-x Ni x B through theoretical and experimental approaches. Powder X-ray diffraction, X-ray Pair Distribution Function analysis, and energy dispersive X-ray spectroscopy reveal that the Fe 1-x Ni x B solid solution crystallizes in the β-FeB structure type up to x = 0.6–0.7 and exhibits anisotropic unit cell volume contraction with increasing Ni concentration. Magnetic measurements showed a transition from ferromagnetism to paramagnetism around x = 0.7. For x = 0.5, the low (< 0.3 μ B ) magnetic moments suggest itinerant magnetism despite the relatively high Curie temperature (up to 225 K). Theoretical calculations indicated different types of magnetic orderings depending on the Fe/Ni atomic order, with the antiferromagnetic state being stable for ordered FeNiB 2 , whereas the ground state is ferromagnetic for the disordered alloy. Calculations also predicted the coexistence of low- and high-spin states in Fe atoms around the composition with x = 0.5, in line with the experimental evidence from 57 Fe Mössbauer spectroscopy. The two magnetically distinct Fe sites for x = 0.3, 0.4, and 0.5 observed by 57 Fe Mössbauer spectroscopy can also be interpreted as two magnetically different regions or clusters. The formation of these clusters could affect the critical behavior near a quantum magnetic transition based on a potential ferromagnetic quantum critical point identified computationally and experimentally near x = 0.64. This work highlights the complex interplay between structure and magnetism in Fe 1-x Ni x B alloys, suggesting areas for future research on quantum critical behavior.

Bhaskar, Gourab [Iowa State Univ., Ames, IA (Unite↗

DOE OSTI2021

The detrimental effect of elemental contaminants when using B additions to improve the creep properties of a Ni-based superalloy

The effect of Si contamination when using B to improve the creep properties of a Ni-based superalloy was investigated using advanced characterization techniques and first-principles simulations on alloys with high and low B levels with varying Si contents. The positive effect of B segregation along grain boundaries on the creep properties was mitigated by the presence of Si which showed a similar segregation preference. Density functional theory calculations were used for validation by calculating grain boundary cleavage energies. Silicon was shown to decrease grain boundary cohesion which offsets the positive effect of B.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Topological Frustration as a New Parameter to Tune Morphology Revealed through Exploring the Continuum between A-B-C 3-Arm Star and Linear Triblock Polymers

Block polymers assemble into a variety of phase-separated morphologies based on volume fraction (φ) and interactions (χ) of the respective blocks. The arrangement of three different polymer blocks could either be a 3-arm star, with each block having one terminus attached to a common junction point or a linear A-B-C architecture. A versatile strategy is reported to synthesize a series of well-defined graft polymers that lie along the unexplored continuum between a 3-arm star and an A-B-C linear triblock polymer architecture. Using the technique of single-molecule insertion, precise control over the position of graft arm C along the B chain was achieved. A series of discrete graft polymers (PMMA-b-PS-g-PEO) with fixed φ and prescribed ω values that lie on the continuum between a 3-arm star (ω = 0) and linear triblock polymer (ω = 1) were synthesized. Morphological studies using small-angle X-ray scattering and conventional and energy-filtered transmission electron microscopy reveal the transition between lamellae, perforated lamellae, and cylindrical morphologies with systematic variation in the ω values, a trend attributed to the topological frustration and the associated χ values between the three blocks. Molecular dynamic simulations of coarse-grained models were found to predict phase diagrams that are consistent with the experimentally observed morphologies. Furthermore, our results suggest that changes in ω lead to topological frustration which is an important additional new design parameter that can be used to tune the morphology of multiblock polymers in addition to φ and χ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Propagation of Chorus Waves Generated in Minimum‐B Pockets

Abstract We present the first ray tracing results of chorus waves generated in minimum‐B pockets. A new ray tracer is developed to accommodate an arbitrary magnetic field model, which enables us to construct minimum‐B pocket geometries using the Tsyganenko (1989) model. Rays with different frequencies and initial wave normal angles are launched from minimum‐B pockets and traced under different geomagnetic activity and hot electron density conditions. Our results indicate that chorus waves generated from minimum‐B pockets are usually highly localized and thus are unlikely to be detected unless the spacecraft is very close to the source region. These waves are also very unlikely to propagate into the plasmasphere. The propagation distances generally decrease with increasing geomagnetic activity.

Kang, Ning↗

DOE OSTI2024

The effect of low temperature on poly(3-methyl- N -vinylcaprolactam)- b -poly( N -vinylpyrrolidone) diblock copolymer nanovesicles assembled from all-aqueous media

Nanosized polymeric vesicles (polymersomes) self-assembled from double hydrophilic copolymers of poly(3-methyl-N-vinylcaprolactam) n -b-poly(N-vinylpyrrolidone) m (PMVC n -b-PVPON m ) using all aqueous media are a promising platform for biomedical applications, because of their superior stability over liposomes in vivo and high loading capacity. Herein, we explored the temperature-sensitive behavior of PMVC 58 -b-PVPON 65 vesicles using transmission electron microscopy (TEM), dynamic light scattering (DLS), atomic force microscopy (AFM), and small-angle neutron scattering (SANS) in response to lowering the solution temperature from 37 to 25, 20, 14 and 4 °C. The copolymer vesicles with an average size of 350 nm at 37 °C were assembled from the diblock copolymer dissolved in aqueous solution at 4 °C. We show that while the polymersome's size gradually decreases upon the temperature decrease from 37 to 4 °C, the average shell thickness increases from 17 nm to 25 nm, respectively. SANS study revealed that the PMVC 58 -b-PVPON 65 vesicle undergoes a gradual structure evolution from a dense-shell vesicle at 37–25 °C to a highly-hydrated shell vesicle at 20–14 °C to molecular chain aggregates at 4 °C. From SANS contrast matching study, this vesicle behavior is found to be driven by the gradual rehydration of PMVC block at 37–14 °C. The shell hydration at 20–14 °C also correlated with the 4.4-fold decrease in the relative fluorescence intensity from vesicle-encapsulated fluorescent dye, indicating ~80% of the dye release within 12 hours after the vesicle exposure to 14 °C. No significant (<5%) dye release was observed for the vesicle solutions at 37–20 °C, indicating excellent cargo retention inside the vesicles. Our study provides new fundamental insights on temperature-sensitive polymer vesicles and demonstrates that the copolymer assembly into polymersomes can be achieved by decreasing a copolymer aqueous solution temperature below 14 °C followed by solution exposure to ≥20 °C. This type of all-aqueous assembly, instead of nanoprecipitation from organic solvents or solvent exchange, can be highly desirable for encapsulating a wide range of biological molecules, including proteins, peptides, and nucleic acids, into stable polymer vesicles without a need for organic solvents for dissolution of the copolymers that are amphiphilic at physiologically relevant temperatures of 20–37 °C.

36 MATERIALS SCIENCE↗

DOE OSTI2025

The possibility of hydrogen-water demixing in Uranus, Neptune, K2-18 b and TOI-270 d

Context. The internal structures of Uranus and Neptune remain unknown. In addition, sub-Neptunes are now thought to be the most common type of exoplanets. Improving our understanding of the physical processes that govern the interiors of such planets is therefore essential. Phase separation between planetary constituents may occur, in particular, hydrogen-water immiscibility in cold, water-rich intermediate-mass planets. Aims. We assess whether hydrogen-water demixing could occur in Uranus, Neptune, K2-18 b and TOI-270 d, and investigate its effect on the planetary evolution and inferred internal structure. Methods. We couple planetary evolution models with recent ab initio calculations of the hydrogen-water phase diagram, allowing for temperature shifts to account for uncertainties in miscibility gaps. Results. We find that demixing may occur and could lead to a complete depletion of water in the outermost regions of Uranus and Neptune. Temperature offsets of up to 1100 K lead to a depleted region comprising as much as 16% of the planet’s mass, and an increase in planetary radius by nearly 20%. For K2-18 b, our models suggest that hydrogen-water demixing is ongoing and may explain the absence of water features in its JWST spectrum. A temperature offset of 500 K is required to get a complete depletion of water in the atmosphere of K2-18b. TOI-270d may also have experienced hydrogen-water demixing. When applying a similar temperature offset on the phase diagram as for K2-18 b, we find a partial depletion of water in the atmosphere of TOI-270 d, consistent with JWST’s detection of water. Conclusions. Hydrogen-water immiscibility may play a key role in shaping the structure and evolution of both Solar System giant planets like Uranus and Neptune, and cold/temperate exoplanets such as K2-18 b and TOI-270 d. Accounting for such internal processes is crucial to accurately interpret atmospheric observations from current (e.g., JWST) and upcoming (e.g., ARIEL) missions.

planets and satellites: composition↗

DOE OSTI2020

Structural changes upon magnetic ordering in magnetocaloric AlFe 2 B 2

With a Curie temperature just above room temperature, AlFe 2 B 2 is a useful magnetocaloric material composed of earth-abundant elements. Here, we employ temperature-dependent high-resolution synchrotron X-ray diffraction to establish with high certainty that the paramagnetic to ferromagnetic transition in AlFe 2 B 2 is of second order, showing no discontinuity in lattice parameters or cell volume. Nevertheless, the lattice parameters undergo anisotropic changes across the transition with distinct differences in the thermal expansion coefficients. While the $a$ and $b$ lattice parameters show a positive thermal expansion, $c$ shows a negative thermal expansion. We link these changes to the respective interatomic distances to determine the contribution of magnetism to the anisotropic structural evolution. The work underpins the possible role of magnetostructural coupling in driving the magnetocaloric effect in AlFe 2 B 2 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Anisotropic E × B shearing rate in a magnetic island

We derive the E × B shearing rate associated with vortex flow inside a macroscopic magnetic island (MI) in axisymmetric toroidal geometry. Due to the elongation of the MI and incompressibility of the E × B flow, the shearing rate near X-points is much lower than that near the mid-plane (x-axis of the local Cartesian coordinate) of the MI on the same flux surface. Furthermore, the rate formally vanishes at the X-points where the local poloidal magnetic field associated with the MI stagnates. Here, this calculation of E × B shearing profile and, in particular, minimal E × B shear near the X-points is consistent with the recent experimental finding that turbulence tends to spread into an MI through regions around the X-points and can contribute to more thorough quantitative interpretation of the results from experiments and simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Production of warm ions in electron beam generated E × B plasma

Several recent experiments have demonstrated low-damage processing of 2D materials, such as graphene and single crystal diamond, using electron beam (e-beam) generated plasmas with applied crossed electric and magnetic (E × B) fields. Here, the low damage of these sensitive materials is commonly attributed to the low energy of ions incident to the substrate surface and the ion confinement in E x B fields. In this work, measurements of atom and ion velocity distribution functions in an e-beam E × B plasma at sub-mTorr argon pressures using a laser-induced fluorescence diagnostic revealed the presence of a warm population of ions with temperatures of ~ 1 eV that are sufficient to destroy the ion confinement in E × B fields and drive the ion flux by cross field diffusion in the direction opposite to the applied electric field, toward the plasma-bounded walls or substrate. Thus, it is this nearly ambipolar diffusion process that is responsible for the flux of charged particles impinging on the wall/substrate surface.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Laser-initiated p – 11 B fusion reactions in petawatt high-repetition-rate laser facilities

Driving of the nuclear fusion reaction p + 11 B → 3α + 8.7 MeV under laboratory conditions by interaction between high-power laser pulses and matter has become a popular field of research, owing to its numerous potential applications: as an alternative to deuterium–tritium for fusion energy production, astrophysics studies, and alpha-particle generation for medical treatment. One possible scheme for laser-driven p– 11 B reactions is to direct a beam of laser-accelerated protons onto a boron (B) sample (the so-called “pitcher-catcher” scheme). This technique has been successfully implemented on large high-energy lasers, yielding hundreds of joules per shot at low repetition. We present here a complementary approach, exploiting the high repetition rate of the VEGA III petawatt laser at CLPU (Spain), aiming at accumulating results from many interactions at much lower energy, to provide better control of the parameters and the statistics of the measurements. Despite a moderate energy per pulse, our experiment allowed exploration of the laser-driven fusion process with tens (up to hundreds) of laser shots. The experiment provided a clear signature of the reactions involved and of the fusion products, accumulated over many shots, leading to an improved optimization of the diagnostics for experimental campaigns of this type. In this paper, we discuss the effectiveness of laser-driven p– 11 B fusion in the pitcher–catcher scheme, at a high repetition rate, addressing the challenges of this experimental scheme and highlighting its critical aspects. Our proposed methodology allows evaluation of the performance of this scheme for laser-driven alpha particle production and can be adapted to high-repetition-rate laser facilities with higher energy and intensity.

Alpha particles↗

DOE OSTI2024

Bi-modal particle size distribution for high energy product hybrid Nd–Fe–B—Sm–Fe–N bonded magnets

In this work, we have demonstrated high energy product bonded magnet by leveraging the variation in sizes between Nd-Fe-B and Sm-Fe-N, as well as their hard magnetic properties. The hybrid anisotropic bonded magnets contain 70 vol% of magnet powder (Dy-free Nd-Fe-B and Sm-Fe-N) and 30 vol% of nylon. The objective of the work was to create bi-modal and bi-compositional bonded magnets in which the fine (3μm) particles of Sm-Fe-N would be used to fill the voids between the bigger Nd-Fe-B (105μm) particles, thus improve packing density. The magnetic hysteresis loop did not show significant signs of decoupled interactions between the magnetic phases. It was also found that the performance of the bonded magnet was most enhanced at 1:4 ratio of Nd-Fe-B and Sm-Fe-N. At that ratio, maximum density of 5 g/cm 3 and the highest (BH) max value of 18.5 MGOe were obtained, although the intrinsic coercivity decreased, relative to the trend seen for other ratios. This work advances the opportunity to expand the use of Sm-Fe-N in bonded magnet applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗