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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 73 records · Page 4

Voltage-Based Strategies for Preventing Battery Degradation under Diverse Fast-Charging Conditions

Maintaining safe operating conditions is a key challenge for high-performance lithium-ion battery applications. The lithium-plating reaction remains a risk during charging, but limited studies consider the highly variable charging conditions possible in commercial cells. Here we combine pseudo-2D electrochemical modeling with data visualization methods to reveal important relationships between the measurable cell voltage and difficult-to-predict Li-plating onset criteria. An extensively validated model is used to compute Li plating for thousands of multistep charging conditions spanning diverse rates, temperatures, states-of-charge, and cell aging. Here we observe an empirical cell operating voltage limit below which plating does not occur across all conditions, and this limit varies with the battery state-of-charge and aging. A model sensitivity analysis also indicates that, when comparing two charging voltage profiles, the capacity difference at 4.0 V correlates well with the difference in the plating onset capacity. These results encourage simple strategies for Li-plating prevention that are complementary to existing battery controls.

25 ENERGY STORAGE↗

The Carnegie Supernova Project I: Spectroscopic analysis of stripped-envelope supernovae

An analysis leveraging 170 optical spectra of 35 stripped-envelope (SE) core-collapse supernovae (SNe) observed by the Carnegie Supernova Project I and published in a companion paper is presented. Mean template spectra were constructed for the SNe IIb, Ib, and Ic subtypes, and parent ions associated with designated spectral features are identified with the aid of the spectral synthesis code SYNAPPS. Our modeled mean spectra suggest the ~6150 Å feature in SNe IIb may have an underlying contribution due to silicon, while the same feature in some SNe Ib may have an underlying contribution due to hydrogen. Standard spectral line diagnostics consisting of pseudo-equivalent widths (pEWs) and blue-shifted Doppler velocity were measured for each of the spectral features. Correlation matrices and rolling mean values of both spectral diagnostics were constructed. A principle component analysis (PCA) was applied to various wavelength ranges of the entire dataset and suggests clear separation among the different SE SN subtypes, which follows from trends previously identified in the literature. In addition, our findings reveal the presence of two SNe IIb subtypes, a select number of SNe Ib displaying signatures of weak, high-velocity hydrogen, and a single SN Ic with evidence of weak helium features. Our PCA results can be leveraged to obtain robust subtyping of SE SNe based on a single spectrum taken during the so-called photospheric phase, separating SNe IIb from SNe Ib with ~80% completion.

79 ASTRONOMY AND ASTROPHYSICS↗

Site-Specific Structure at Multiple Length Scales in Kagome Quantum Spin Liquid Candidates

Realizing a quantum spin liquid (QSL) ground state in a real material is a leading issue in condensed matter physics research. In this pursuit, it is crucial to fully characterize the structure and influence of defects, as these can significantly affect the fragile QSL physics. In this work, we perform a variety of cutting-edge synchrotron x-ray scattering and spectroscopy techniques, and we advance new methodologies for site-specific diffraction and L-edge Zn absorption spectroscopy. The experimental results along with our first-principles calculations address outstanding questions about the local and long-range structures of the two leading kagome QSL candidates, Zn-substituted barlowite Cu 3 Zn x Cu 1-x (OH) 6 FBr and herbertsmithite Cu 3 Zn(OH) 6 Cl 2 . On all length scales probed, there is no evidence that Zn substitutes onto the kagome layers, thereby preserving the QSL physics of the kagome lattice. Our calculations show that antisite disorder is not energetically favorable and is even less favorable in Zn-barlowite compared to herbertsmithite. Site-specific x-ray diffraction measurements of Zn-barlowite reveal that Cu 2+ and Zn 2+ selectively occupy distinct interlayer sites, in contrast to herbertsmithite. Using the first measured Zn L-edge inelastic x-ray absorption spectra combined with calculations, we discover a systematic correlation between the loss of inversion symmetry from pseudo-octahedral (herbertsmithite) to trigonal prismatic coordination (Zn-barlowite) with the emergence of a new peak. Overall, our measurements suggest that Zn-barlowite has structural advantages over herbertsmithite that make its magnetic properties closer to an ideal QSL candidate: its kagome layers are highly resistant to nonmagnetic defects while the interlayers can accommodate a higher amount of Zn substitution.

36 MATERIALS SCIENCE↗

Evaluation of Impedance Measurement Using Spread Spectrum Time Domain Reflectometry

We evaluate the feasibility of spectral time domain reflectometry (STDR) and spread spectrum time domain reflectometry (SSTDR) as a new modality for impedance measurement to test energized/noisy systems over a very broad frequency spectrum (near dc to gigahertz) as well as multiple channels in parallel. We simulate how the S/SSTDR signal parameters (signal-to-noise ratio (SNR) frequency and length of the pseudo-noise (PN) signals) affect the accuracy and usable frequency band for reflection coefficient and impedance measurement. An initial measurement validation is included. Here, we conclude with a recommendation of what will be required for a viable multichannel impedance (and reflection, transmission coefficient) measurement system for either energized or nonenergized systems, in noisy environments, that can test multiple channels simultaneously.

14 SOLAR ENERGY↗

The Physics behind Precipitation Onset Bias in CMIP6 Models: The Pseudo-Entrainment Diagnostic and Trade-Offs between Lapse Rate and Humidity

Conditional instability and the buoyancy of plumes drive moist convection but have a variety of representations in model convective schemes. Vertical thermodynamic structure information from Atmospheric Radiation Measurement (ARM) sites and reanalysis (ERA5), satellite-derived precipitation (TRMM3b42), and diagnostics relevant for plume buoyancy are used to assess climate models. Previous work has shown that CMIP6 models represent moist convective processes more accurately than their CMIP5 counterparts. However, certain biases in convective onset remain pervasive among generations of CMIP modeling efforts. Here we diagnose these biases in a cohort of nine CMIP6 models with sub-daily output, assessing conditional instability in profiles of equivalent potential temperature θ e and saturation equivalent potential temperature θ es in comparison to a plume model with different mixing assumptions. Most models capture qualitative aspects of the θ es vertical structure, including a substantial decrease with height in the lower free troposphere associated with the entrainment of subsaturated air. We define a “pseudo-entrainment” diagnostic that combines subsaturation and a θ es measure of conditional instability similar to what entrainment would produce under the small-buoyancy approximation. This captures the trade-off between larger θ es lapse rates (entrainment of dry air) and small subsaturation (permits positive buoyancy despite high entrainment). This pseudo-entrainment diagnostic is also a reasonable indicator of the critical value of integrated buoyancy for precipitation onset. Models with poor θ e /θ es structure (those using variants of the Tiedtke Scheme) or low entrainment runs of CAM5, and models with low subsaturation, such as NASA-GISS, lie outside the observational range in this diagnostic.

54 ENVIRONMENTAL SCIENCES↗

Precise measurements of branching fractions for $ {\mathrm{D}}_{\mathrm{s}}^{+} $ meson decays to two pseudoscalar mesons

We measure the branching fractions for seven $D$$^{+}_{s}$ two-body decays to pseudo-scalar mesons, by analyzing data collected at √s = 4.178 ~ 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fractions are determined to be $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \hbox{'}\right)=\left(2.68\pm 0.17\pm 0.17\pm 0.08\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta \hbox{'}{\pi}^{+}\right)=\left(37.8\pm 0.4\pm 2.1\pm 1.2\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(1.62\pm 0.10\pm 0.03\pm 0.05\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to \eta {\pi}^{+}\right)=\left(17.41\pm 0.18\pm 0.27\pm 0.54\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{K}_S^0\right)=\left(15.02\pm 0.10\pm 0.27\pm 0.47\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}_S^0{\pi}^{+}\right)=\left(1.109\pm 0.034\pm 0.023\pm 0.035\right)\times {10}^{-3},\\ {}\mathcal{B}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(0.748\pm 0.049\pm 0.018\pm 0.035\right)\times {10}^{-3},\end{array}} $$ B D s + → K + η ' = 2.68 ± 0.17 ± 0.17 ± 0.08 × 10 - 3 , B D s + → η ' π + = 37.8 ± 0.4 ± 2.1 ± 1.2 × 10 - 3 , B D s + → K + η = 1.62 ± 0.10 ± 0.03 ± 0.05 × 10 - 3 , B D s + → η π + = 17.41 ± 0.18 ± 0.27 ± 0.54 × 10 - 3 , B D s + → K + K S 0 = 15.02 ± 0.10 ± 0.27 ± 0.47 × 10 - 3 , B D s + → K S 0 π + = 1.109 ± 0.034 ± 0.023 ± 0.035 × 10 - 3 , B D s + → K + π 0 = 0.748 ± 0.049 ± 0.018 ± 0.035 × 10 - 3 , where the first uncertainties are statistical, the second are systematic, and the third are from external input branching fraction of the normalization mode $ {D}_s^{+} $ D s + → K + K - π + . Precision of our measurements is significantly improved compared with that of the current world average values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Analysis of the Ion Conversion Mechanisms in the Effluent of Atmospheric Pressure Plasma Jets in Ar with Admixtures of O 2 , H 2 O and Air

Ionic species in atmospheric pressure plasma jets (APPJs) play an important role in plasmasurface and plasma-liquid interactions, nonetheless, they have not received the same attention as their neutral reactive species counterparts. In this work, a molecular beam mass spectrometer (MBMS) was used to characterize the ion compositions in the effluent of an APPJ operating in ambient air for different feed gases including Ar + O 2 , Ar + air and Ar + H 2 O mixtures inspired by gas compositions used for biomedical applications. Changes in compositions of positive and negative ions as a function of nozzle-to-substrate distance along the plasma plume were analyzed and compared with a pseudo-1D plug flow model. Positive and negative ions were detected up to distances of 12 mm from the visible plasma plume tip. The measurements enable to follow the ion conversion pathways in the effluent of the APPJs as a function of distance from the nozzle. The trends in ion yield obtained from a pseudo-1D plug flow model showed generally a good agreement with the experimentally observed trends after addition of ionic reactions to the previously reported reaction set but also some distinctive differences were observed. The dominant positive ions in the far effluent are water ion clusters, the most stable ion for all gas mixtures investigated, while a large variety of negative ions was found for different gas mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Borexino and general neutrino interactions

We derive constraints on all possible general neutrino-electron interactions (scalar, vector, pseudo-scalar, axial-vector and tensor) using the recent real time Borexino event rate measurements of pp, pep and Be7 solar neutrinos. Some of the limits improve from TEXONO and CHARM-II for incoming electron and muon neutrinos while the rest remains weaker for Borexino and those for the tau flavor are the first ones. Future improvements by next-generation solar neutrino experiments are also studied. The limits extend the physics reach of solar neutrino measurements to TeV-scale physics. Finally, the different properties of the new interactions for Dirac and Majorana neutrinos are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nondestructive Evaluation (NDE) of Cable Anomalies using Frequency Domain Reflectometry (FDR) and Spread Spectrum Time Domain Reflectometry (SSTDR)

This report presents a comparative assessment of the performance of frequency domain reflectometry (FDR) and spread spectrum time domain reflectometry (SSTDR) in detecting a wide range of electrical cable anomalies. All tests and results reported herein were performed at the PNNL Accelerated and Real-Time Environmental Nodal Assessment (ARENA) cable and motor test bed. The primary objective of this work was to evaluate the effectiveness of SSTDR, a fledgling cable monitoring technique that shows promise for application in online monitoring of energized cable systems, against FDR, an offline technique widely employed in the nuclear power plant (NPP) industry. FDR tests are becoming more widely used in nuclear power plant cable aging management and test programs – particularly for low voltage cables. FDR capabilities for these kinds of tests have been reported by PNNL and others. The FDR test is performed on de-energized cables by connecting the FDR instrument to two of the cable conductors, or one conductor and the shield. A broad band low voltage (< 5 V) chirp is introduced in the cable, and any reflected response is captured in the frequency domain. The captured reflection is then processed by performing an inverse Fourier transform to a time domain response which can then be converted to a distance response based on the cable velocity of propagation (VoP). SSTDR measurements are functionally similar to FDR measurements in that a broad-band voltage signal composed of a square or sine wave modulated pseudo-random sequence of chips (< 5 volts), is injected onto one of the cable conductors. The injected signal will experience partial energy reflection and transmission at each impedance discontinuity along the transmission line. Any reflected response is detected by computing a cross-correlation between the reflected signals and a delayed copy of the incident SSTDR signal. the time delay for the reflected signal to experience the best matched correlation with the incident signal, indicates the travel time for the signal to reach a change in impedance. By knowing this time delay and velocity of propagation (VoP) of the signal, one can compute the physical distance. A big advantage that SSTDR measurements have over other methods is the ability to be connected to energized or live wires (currently up to 1kV) thereby enabling online monitoring of cables. SSTDR has been used successfully in several applications, e.g., aircraft, rail, and photovoltaic systems. In this work FDR and SSTDR cable assessment techniques were used to characterize a variety of cable anomalies and faults including: (1) Presence or absence of a motor; (2) Ground faults and short circuit faults; (3) Moist environments and water ingress faults; (4) Accelerated thermal aging. Both shielded and non-shielded cables were evaluated in this report. Offline measurements were made using FDR and online measurements were made by SSTDR for a range of test scenarios. Based on the results across all cable anomalies evaluated in this study, FDR displayed high sensitivity towards cable condition assessment, while SSTDR showed promise for future application in monitoring NPP cable systems. However, further developments are suggested to improve the resolution and sensitivity of SSTDR towards faults and anomalies in low voltage cables.rt presents a comparative

42 ENGINEERING↗

Cosmic birefringence test of the Hubble tension

A cosmic pseudo-Nambu-Goldstone boson has been proposed to resolve the four-sigma discrepancy between precision measurements of the expansion rate of the universe. We show this solution may also produce a cosmic birefringence (CB) signal in the polarization of the cosmic microwave background (CMB); observations of the CB power spectrum and cross-correlation with the CMB can independently confirm the presence of this new boson. In this work, we find significant new contributions to the CB signal, and show that future CMB experiments will greatly improve sensitivity to CB and Hubble tension scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparison of theory with the experimental characterization of the spatial frequency response of interferometers using a binary pseudo-random array sample

Experimental evaluations of the surface height response of an interference microscope using a binary pseudo-random array test sample are compared with a theory based on a Fourier optics model. Measurements of key instrument characteristics, including the illumination, imaging, and obscuring apertures of three different Mirau objectives, support the theoretical calculations. Agreement between experimental and theoretical modeling confirms the predictability of the spatial frequency response for the purpose of specification and optimization of instrument configuration for specific metrology tasks. The results also provide confidence in methods of compensating for the decrease in instrument response with spatial frequency.

Calibration↗

Thermodynamic evaluation and modeling of the CeF 3 -LaF 3 -LiF-NaF system

The thermodynamic properties of the LiF-NaF-CeF 3 -LaF 3 pseudo-quaternary system have been evaluated, and models for the relevant phases have been revised or newly developed. The solid solubility of NaF in LaF 3 and CeF 3 was described in the model based on reported phase-equilibria observations and results from density functional theory calculations. The Gibbs energy functions for the NaCeF 4 and NaLaF 4 phases have been updated with recently reported thermochemical measurements. The Gibbs energy functions and model relations for the LiF-NaF-LaF 3 and LiF-NaF-CeF 3 pseudo-ternary systems were successfully optimized based on thermochemical properties and phase equilibria observations.

CALPHAD↗

Correlating hidden local structural distortion with antiferroelectric-ferroelectric transition in PbZrO 3 -based perovskites

Externally stimulated antiferroelectric-ferroelectric (AFE-FE) transition makes AFE materials attractive for many applications ranging from energy storage to sensing. This transition-mediated macroscopic electrical characteristics have been extensively investigated, yet the underlying structural evolution remains poorly understood. Herein, we study the local- and long-range structural evolutions in the Nb-doped Pb(Zr,Sn,Ti)O 3 perovskites by in-situ X-ray total scattering and diffraction, which show three different types of AFE-FE transitions. The evolution of long-range structure from diffraction and local structure identified by atomic pair distribution function (PDF) are consistent well with the phase transition behavior indicated by macroscopic polarization/strain measurements, while discrepancies exist. Interestingly, frequently employed long-range structure picture that the uniform AFE pseudo-tetragonal to FE rhombohedral transformation is insufficient to understand the distinct composition-dependent AFE-FE transition behaviours. Instead, the reversibility of this transition correlates with the chemically sensitive local atomic displacements revealed by newly developed in-situ PDF. The critical electric field of transition is associated with the local structural differences between the AFE and FE state. The macroscopic electrostrains can be well estimated by the phase transition associated lattice strain and domain alignment from in-situ synchrotron XRD data, while the local strains calculated from in-situ PDFs are found to be much lower. Finally, these results provide a fresh insight into the AFE-FE transition, and advance the understanding of structure-property relationships in AFE materials.

36 MATERIALS SCIENCE↗

NaCo 2 (SeO 3 ) 2 (OH): competing magnetic ground states of a new sawtooth structure with 3d 7 Co 2+ ions

While certain magnetic sublattices have long been known theoretically to give rise to emergent physics via competing magnetic interactions and quantum effects, finding such configurations in real materials is often deeply challenging. Here we report the synthesis and characterization of a new such material, NaCo 2 (SeO 3 ) 2 (OH) which crystallizes with a highly frustrated sublattice of sawtooth Co 2+ chains. Single crystals of NaCo 2 (SeO 3 ) 2 (OH) were synthesized using a low-temperature hydrothermal method. X-ray single crystal structure analysis reveals that the material crystallizes in orthorhombic space group of Pnma (no. 62). Its crystal structure exhibits one-dimensional chains of corner-sharing isosceles triangles that are made of two crystallographically distinct 3d 7 Co 2+ sites (Co(1) and Co(2)). The chains run along the b-axis and are interconnected via [SeO 3 ] groups to form a three-dimensional structure mediating super-exchange interactions. The temperature dependent magnetization data show a ferromagnetic-like (FM) transition at 11 K (T 1 ) followed by an antiferromagnetic (AFM) transition at about 6 K (T 2 ). Neutron-powder diffraction measurements reveal that at T 1 = 11 K only the Co(2) site orders magnetically, forming ferromagnetic zigzag chains along the b-axis. Below T 2 = 6 K, both Co(1) and Co(2) sites order in a nearly orthogonal configuration, with Co(1) moments lying inside the plane of the sawtooth chain while Co(2) moments cant out of the plane. The canting of the magnetic moments leads to a net ferromagnetic component along b-axis, parallel to the chain direction. The ordered moments are fully compensated in the ac-plane. Inelastic neutron scattering measurements reveal crystal field excitations that are consistent with the presence of a spin–orbital entangled pseudo-spin state J eff = 1/2 for the Co 2+ ions. Low-energy spin-wave excitations are observed below the second magnetic transition. The analysis of powder excitation spectrum suggests complex exchange interactions that go beyond a Heisenberg Hamiltonian model with nearest neighbor couplings. Our results demonstrate the richness of the magnetic properties of sawtooth-type structures and encourage the study of similar structures with different oxyanion groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pseudo-Dirac neutrinos and relic neutrino matter effect on the high-energy neutrino flavor composition

We show that if neutrinos are pseudo-Dirac, they can potentially affect the flavor ratio predictions for the high-energy astrophysical neutrino flux observed by IceCube. In this context, we point out a novel matter effect induced by the cosmic neutrino background (CνB) on the flavor ratio composition. Specifically, the active-sterile neutrino oscillations over the astrophysical baseline lead to an energy-dependent flavor ratio at Earth due to the CνB matter effect, which is in principle distinguishable from the vacuum oscillation effect, provided there is an asymmetry between the neutrino and antineutrino number densities, as well as a local CνB overdensity. Considering the projected precision of the 3-neutrino oscillation parameter measurements and improved flavor triangle measurements, we show that the next-generation neutrino telescopes, such as KM3NeT and IceCube-Gen2, can in principle probe the pseudo-Dirac neutrino hypothesis and the CνB matter effect.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurement of the very rare K+ → $ {\pi}^{+}\nu \overline{\nu} $ decay

The NA62 experiment reports the branching ratio measurement BR K + → π + ν ν ¯ = 10.6 - 3.4 + 4.0 stat ± 0.9 syst × 10 - 11 at 68% CL, based on the observation of 20 signal candidates with an expected background of 7.0 events from the total data sample collected at the CERN SPS during 2016–2018. This provides evidence for the very rare K + → π + ν ν ¯ decay, observed with a significance of 3.4 σ . The experiment achieves a single event sensitivity of (0 . 839 ± 0 . 054) × 10 - 11 , corresponding to 10.0 events assuming the Standard Model branching ratio of (8 . 4 ± 1 . 0) × 10 - 11 . This measurement is also used to set limits on BR( K + → π + X ), where X is a scalar or pseudo-scalar particle. Details are given of the analysis of the 2018 data sample, which corresponds to about 80% of the total data sample.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Methane Quantification Performance of the Quantitative Optical Gas Imaging (QOGI) System Using Single-Blind Controlled Release Assessment

Quantitative optical gas imaging (QOGI) system can rapidly quantify leaks detected by optical gas imaging (OGI) cameras across the oil and gas supply chain. A comprehensive evaluation of the QOGI system’s quantification capability is needed for the successful adoption of the technology. This study conducted single-blind experiments to examine the quantification performance of the FLIR QL320 QOGI system under near-field conditions at a pseudo-realistic, outdoor, controlled testing facility that mimics upstream and midstream natural gas operations. The study completed 357 individual measurements across 26 controlled releases and 71 camera positions for release rates between 0.1 kg Ch 4 /h and 2.9 kg Ch 4 /h of compressed natural gas (which accounts for more than 90% of typical component-level leaks in several production facilities). The majority (75%) of measurements were within a quantification factor of 3 (quantification error of –67% to 200%) with individual errors between –90% and 831%, which reduced to –79% to +297% when the mean of estimates of the same controlled release from multiple camera positions was considered. Performance improved with increasing release rate, using clear sky as plume background, and at wind speeds ≤1 mph relative to other measurement conditions.

42 ENGINEERING↗

Physics-Informed Machine-Learning Prediction of Curie Temperatures and Its Promise for Guiding the Discovery of Functional Magnetic Materials

High-performance permanent magnets with a high Curie temperature, containing less critical materials, are integral to zero-carbon energy solutions. We built a machine-learning model trained over available experimentally measured Curie temperature values to predict the T C of multicomponent magnetic materials. We chose two compositions from a pseudo-binary (Zr 1–x Ce x )Fe 2 system, namely, (Zr 0.16 Ce 0.84 )Fe 2 and (Zr 0.94 Ce 0.06 )Fe 2 , to experimentally validate the ability of our model to predict the Curie temperature of novel compounds. We also provided a detailed discussion on the correlation of the Curie temperature with the de Gennes scaling factor in rare-earth intermetallic compounds and its breakdown below a certain rare-earth content. The electronic structure calculations (density of states and Fermi surface) were performed using the density functional theory on selected compounds (Zr 0.16 Ce 0.84 )Fe 2 and (Zr 0.94 Ce 0.06 )Fe 2 to understand the electronic origin of a strong magnetic exchange. We found that the change in the electronic density of states and electron/hole fillings at the Fermi level directly correlate with the Curie temperature. Notably, our model was able to capture these key electronic structure trends, which show that physics-informed machine learning can play a crucial role in designing new high-performance magnets with improved properties for environmentally sustainable applications.

36 MATERIALS SCIENCE↗