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DOE OSTI2022

Efficient Probabilistic Computing with Stochastic Perovskite Nickelates

Probabilistic computing has emerged as a viable approach to solve hard optimization problems. Devices with inherent stochasticity can greatly simplify their implementation in electronic hardware. In this report we demonstrate intrinsic stochastic resistance switching controlled via electric fields in perovskite nickelates doped with hydrogen. The ability of hydrogen ions to reside in various metastable configurations in the lattice leads to a distribution of transport gaps. With experimentally characterized p-bits, a shared-synapse p-bit architecture demonstrates highly parallelized and energy-efficient solutions to optimization problems such as integer factorization and Boolean satisfiability. The results introduce perovskite nickelates as scalable potential candidates for probabilistic computing and showcase the potential of light-element dopants in next-generation correlated semiconductors.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2026

Dynamic control of quantum phases in two-dimensional materials via Floquet engineering

The dynamical engineering of quantum states through periodic optical driving, known as Floquet engineering, has emerged as a powerful frontier in condensed matter physics, offering a pathway to realize material properties inaccessible in static equilibrium. This review provides a comprehensive overview of recent theoretical and experimental advances in the optical manipulation of two-dimensional (2D) quantum materials. We begin by systematically reviewing the evolution of the field from its pioneering applications in graphene and twisted moiré superlattices, highlighting the experimental realization of the light-induced anomalous Hall effect (AHE) to the complex spin-valley physics in transition metal dichalcogenides (TMDs). Furthermore, we briefly examine recent advances in 2D magnetic materials, demonstrating how optical driving can actively compete with intrinsic magnetism to dynamically switch magnetic orders and topological invariants. Moreover, we discuss the emerging frontiers of multi-frequency driving, quantum optimal control theory (QOCT), and ultrafast lightwave electronics. We highlight how tailored waveforms, such as bicircular light fields, and sub-cycle attosecond control can selectively break spatial symmetries to generate novel nonlinear photocurrents, mitigate dissipation, and extend the boundaries of quantum control well beyond the perturbative steady-state regime. Finally, we summarize the key experimental challenges for Floquet engineering, including effects such as heating and scattering, which limit coherent quantum control.

Wang, Wenpeng [Northeastern University, Shenyang, ↗

DOE OSTI2025

An unusual Co–S bond links B 12 chaperones in an interprotein complex

Chaperones in trafficking pathways ensure specificity of transition metal loading and protection against adventitious side reactions. In B 12 , an essential cofactor for humans, a cobalt ion is coordinated to a >1.3 kDa tetrapyrrolic scaffold, posing logistical challenges for its translocation. In this study, we report the 3.4 Å crystal structure of the human MMACHC and MMADHC B 12 chaperones, tethered via a rarely seen covalent cobalt–sulfur bond. B 12 is bound in the base-off state to MMACHC, with Cys-261 on MMADHC serving as the upper axial ligand; the lower-axial position is vacant. The propensity of thiolato-cobalamin derivatives bound to MMACHC to undergo spontaneous decomposition via general acid catalysis or reduction/oxidation chemistry is averted in the interprotein complex with MMADHC. An exposed face in the complex suggests an exit route for B 12 . No known clinical variants localize to the interprotein interface, consistent with the cobalt–sulfur bond being key to forming the high-affinity complex.

Science & Technology - Other Topics↗

DOE OSTI2024

Exact-Two-Component Complete Active Space Method with Variational Treatment of Magnetic Field and Spin–Orbit Coupling: Application to X-ray Magnetic Circular Dichroism Spectroscopy

We introduce an exact-two-component complete active space self-consistent-field (X2C-CASSCF) method formulated under the restricted-magnetic-balance condition. This framework allows for the nonperturbative treatment of static magnetic fields using gauge-including atomic orbitals (GIAOs). The GIAO-X2C-CASSCF methodology effectively captures all microstates within the same 2J + 1-degenerate manifold and their splitting in a static magnetic field, which are not accessible through single-reference-based methods. We also present mathematical recursive expressions for evaluating one-electron relativistic integrals by using GIAOs in the presence of a finite magnetic field. Benchmark studies include oxygen and nitrogen K-edge X-ray magnetic circular dichroism spectroscopy (XMCD) for closed-shell organic compounds, as well as L-edge XMCD spectroscopy for the high-spin open-shell transition metal ion Mn 2+ and the tetrahedral Mn(II)O 4 6– complex.

Chemical calculations↗

DOE OSTI2020

Spatially Resolved Investigation of Mixed Valence and Insulator-to-Metal Transition in an Organic Salt

Using scanning tunneling microscopy/spectroscopy (STM/STS), we investigate the evolution of electronic structures across the boundaries of 7,7,8,8-tetracyanoquinodimethane (TCNQ) and K-TCNQ assemblies on a weakly interacting substrate. Despite the semiconducting/insulating nature of TCNQ (TCNQ 0 ) and K-TCNQ (TCNQ -1 ), a continuum metallic-like density of states extending deep (~1.5 nm) into the TCNQ assembly is observed near domain boundary. We attribute the formation of these states to the abrupt change of molecular valence, which perturbs the electrostatics of the junction and creates local electric fields as evidenced by the band bending near domain boundary. To the best of our knowledge, this study provides the first microscopic understanding of the crucial physics occurring near domain boundaries of mixed valence in K-TCNQ, or broadly speaking charge transfer complexes, which highlights these boundaries as potential “weak” points to initiate the electric field induced insulator-to-metal transition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Formic Acid: A Hydrogen-Bonding Cocatalyst for Formate Decomposition

Hydrogen bonding accelerates many catalytic reactions by orienting intermediates, stabilizing transition states, and even opening reaction pathways. However, most mechanistic studies regarding the decomposition of formic acid (FA), a promising hydrogen storage material, neglect hydrogen-bonding interactions even though FA is a strong hydrogen-bond donor and acceptor. Here, we probe the formation of bimolecular hydrogen-bonded complexes between FA and formate (FA–HCOO complexes) adsorbed on metal surfaces and how these complexes affect HCOO* decomposition. Using first-principles density functional theory (DFT) calculations on 12 close-packed (111)/(0001) and 8 open (100) surfaces of 12 transition metals—Ag, Au, Co, Cu, Ir, Ni, Os, Re, Pd, Pt, Rh, and Ru, we—show that FA–HCOO complexes are generally thermodynamically stable, even at elevated temperatures and pressures. We then illustrate that these complexes produce infrared spectroscopic signatures consistent with as yet unassigned experimental peaks. We last demonstrate that by stabilizing the dangling bond of monodentate HCOO*, these complexes significantly lower the barriers for rotation of HCOO* from a bidentate to a monodentate configuration, the rate-limiting step for HCOO* decomposition on many surfaces. FA thus acts as a cocatalyst for HCOO* decomposition. Our results may guide the community toward improved catalysts for reactions involving HCOO* such as FA decomposition, methanol steam reforming, and the water gas shift reaction. More broadly, our work highlights the ability of hydrogen bonding to modify the adsorbed structures of intermediates and lower the barriers for their reaction on heterogeneous catalysts. Lastly, this phenomenon can be relevant for other reactions involving ammonia, alcohols, and carboxylic acids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Novel Valence Transition in Elemental Metal Europium around 80 GPa

We report valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized 4f electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of 4f electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic (C2/c) to an orthorhombic phase ($Pnma$). We show that the valence transition occurs when the pressure-dependent energy gap between 4f and 5d electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Photo-exfoliation of MoS 2 quantum dots from nanosheets: an in-situ transmission electron microscopy study

Fabrication of transition metal dichalcogenide (TMD) quantum dots (QDs) is complex and requires submerging of powders in binary solvents and the constant tuning of wavelength and pulsed frequency of light to achieve a desired reaction. Here,iInstead of liquid state photoexfoliation, we utilize infrared laser irradiation of free-standing MoS 2 flakes in transmission electron microscope (TEM) to achieve solid-state multi-level photoexfoliation of QDs. By investigating the steps involved in photochemical reaction between the surface of MoS 2 and the laser beam, we gain insight into each step of the photoexfoliation mechanism and observe high yield production of QDs, led by an inhomogeneous crystalline size distribution. Additionally, by using a laser with a lower energy than the indirect optical transition of bulk MoS 2 , we conclude that the underlying phenomena behind the photoexfoliation is from multi-photon absorption achieved at high optical outputs from the laser source. These findings provide an environmentally friendly synthesis method to fabricate QDs for potential applications in biomedicine, optoelectronics, and fluorescence sensing.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Bimetallic Coinage Metal Complexes of Tetradentate ortho Ter arylene Ligands

The synthesis, structural and photophysical properties of five bimetallic coinage metal complexes of three tetradentate charge-transfer (CT) ligands are presented. The ligand structures incorporate donor/acceptor moieties electronically decoupled by ortho connection to a bridging biphenylene group. The M M distances observed in the crystal structures of the bimetallic complexes are shorter than the sum of the Van der Waals radii of the metal ions, suggesting stabilizing interactions between the d10 metal centers. Additionally, short distances between the bridging biphenylene and metal atoms suggest arylene metal interactions. Bimetallic Cu, Ag, and Au complexes of the ligand incorporating a carbazole donor and pyridyl acceptor (N2R22-) show absorption and emission energies that trend with the ionization potential of each metal, indicating metal character in the excited state. These properties contrast with our previously reported mononuclear Zn complex of N2R22-The structural and photophysical properties of five bimetallic d10 coinage metal complexes were presented. The M M distances observed in the crystal structures of the bimetallic complexes are shorter than the sum of the metals’ Van der Waals radii, suggesting attractive interactions between the d10 metal centers. Additionally, short distances between the bridging biphenylene and metal atoms suggest arylene metal interactions. The absorption and emission spectra of the bimetallic complexes redshift based on the oxidation potential of the metal ion. This suggests involvement of metal based orbitals in the excited state transitions of the bimetallic complexes, which was corroborated by molecular modeling. High photoluminescent quantum yields were observed in solution and in rigid media (up to PL = 0.75), and the excited state lifetimes in solution were found to exceed several microseconds.

Shariaty, Darius Allen [University of Southern Cal↗

DOE OSTI2025

Density Functional Tight Binding Insights into Plasmonic Silver–Platinum Nanoparticles and Alloys for Enhanced Photocatalysis

Developing accurate and efficient Slater-Koster (SK) tight-binding parameter sets is essential for quantum plasmonic studies of alloyed metal nanoparticles, as conventional time dependent density functional theory (TD-DFT) calculations are computationally prohibitive for larger clusters. In this work, we develop and validate density functional tight binding (DFTB) parameter sets for both ground state (GS-SK) and excited state (ES-SK) calculations to study the structural, electronic, and optical properties of silver (Ag), platinum (Pt), and Ag–Pt nanoalloys. Our investigation of the ground state properties demonstrates that the GS-SK parameters enable DFTB to closely reproduce the electronic structures of platinum clusters with diverse sizes and geometries – showing qualitative agreement with DFT for density of states (DOS) profiles and energy levels. The ES-SK parameters accurately describe excited-state properties compared to TD-DFT reference calculations, including the broad, featureless absorption profiles of Pt that are dominated by interband transitions. Using the ES-SK parameters within a real-time TD-DFTB framework, we compute size-dependent optical absorption spectra of Ag, Pt and Ag-Pt nanocubes containing up to 1099 atoms (size ∼4.18 nm). A detailed study of Ag–Pt and Pt-Ag core–shell nanoparticles shows quenching of the Ag plasmon resonance even at monolayer coverage for Ag-Pt, but not for Pt-Ag. We also show how to define submonolayer Ag-core Pt-shell cubic structures that have similar optical properties to those generated experimentally for much larger particles, which offers potential for describing plasmon-enhanced photocatalysis. Collectively, the GS-SK and ES-SK parameter sets provide an accurate, computationally efficient approach for modeling the complex optical and electronic behavior of noble–transition metal nanostructures and their alloys.

SPR↗

DOE OSTI2022

Revealing the Influence of Diverse Secondary Metal Cations on Redox-Active Palladium Complexes

Incorporation of redox-inactive metals into redox-active complexes and catalysts attracts attention for engendering new reactivity modes, but this strategy has not been extensively investigated beyond the first-row of the transition metals. In this report the isolation and characterization of the first series of heterobimetallic complexes of palladium with mono-, di-, and tri-valent redox-inactive metal ions are reported. A Reinhoudt-type heteroditopic ligand with a salen-derived [N 2 ,O 2 ] binding site for Pd and a crown-ether-derived [O 6 ] site has been used to prepare isolable adducts of the Lewis acidic redox-inactive metal ions (M n+ ). Comprehensive data from single-crystal X-ray diffraction analysis reveal distinctive trends in the structural properties of the heterobimetallic species, including an uncommon dependence of the Pd … M distance on Lewis acidity. The reorganization energy associated with reduction of the heterobimetallic species is strongly modulated by Lewis acidity, with the slowest heterogeneous electron transfer kinetics associated with the strongest incorporated Lewis acids. This hitherto unexplored reorganization energy penalty for electron transfer contrasts with prior thermodynamic studies, revealing that kinetic parameters should be considered in studies of reactivity involving heterobimetallic species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Cationic α-Diimine Nickel and Palladium Complexes Incorporating Phenanthrene Substituents: Highly Active Ethylene Polymerization Catalysts and Mechanistic Studies of syn/anti Isomerization

α-Diimine palladium complexes incorporating phenanthryl- and 6,7-dimethylphenanthrylimino groups have been synthesized and characterized. The (diimine)PdMeCl complexes prepared from 2,3-butanedione and acenaphthenequinone bearing the unsubstituted phenanthrylimino groups, 12a and 14a, respectively, exist as a mixture syn and anti isomers in a ca. 1:1 ratio. Separation and X-ray diffraction analysis of 14a-syn and 14a-anti isomers confirms the syn/anti assignments. The barrier to interconversion of 14a-syn and 14a-anti via ligand rotation, ΔG ‡ , was found to be 25.5 kcal/mol. The corresponding (diimine)PdMeCl complex prepared from acenaphthenequinone and incorporating the 6,7-dimethylphenanthrylimino group exists solely as the anti isomer, 14b, due to steric crowding which destabilizes the syn isomer. Analogous (diimine)NiBr2 complexes were prepared from 2,3-butanedione incorporating the phenanthrylimino group, 16a, and the 6,7-dimethylphenanthrylimino group, 16b. Nickel-catalyzed polymerizations of ethylene were carried out by activation of the dibromide complexes 16a and 16b using various aluminum alkyl activators. Complex 16a yields a bimodal distribution polymer, the low molecular weight fraction originating from the syn isomer and the high molecular weight fraction arising from the anti isomer. Polymerizations carried out by 16b yield only high molecular weight polymers with monomodal distributions due to the existence of a single isomer (anti) as the active catalyst. All polymers are linear or nearly so. All catalysts are highly active but catalysts derived from 16b are somewhat more active than 16a and exhibit turnover frequencies general over 10 6 and up to 5 × 10 6 per hour (40 °C, 27.2 atm ethylene, 15 min). Here, active palladium ethylene oligomerization catalysts were generated by conversion of the neutral methyl chloride complexes 14a and 14b to the cationic nitrile complexes 15a and 15b via halide abstraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Uniaxial tensile mechanical properties from a scratch on ultra-fine grained tungsten

We demonstrate that surface-based mechanical testing can be used to quantify a wide range of mechanical properties determined using traditional uniaxial tension experiments. These include mapping of dynamic stress–strain behaviour, which can be used as a screening tool for uniaxial tensile ductility (uniform elongation), fracture toughness (K C ), which is shown to be in good agreement with reported plane-strain K IC , as well work-hardening exponents (n), activation volumes (V) energies (Q) and strain-rate sensitivity (m) exponents as a function of temperature. Advantages of the surface-based approach are the ability to work with significantly smaller volumes and accommodate processing defects like pores, voids and cracks. These methods are applied to ultra-fine grained tungsten (average grain size of 650 nm), as it is an ideal candidate for alloy development efforts in advanced energy systems. Tungsten is a useful baseline as it exhibits a near-ambient temperature (approx. 200°C) ductile-to-brittle transition temperature (DBTT), enabling validation efforts for the proposed methods, and extraordinary material properties, including the highest melting temperature of any metal and complex temperature and strain-rate dependencies linked to transitions in dislocation mechanisms.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Single vs double atom catalyst for N 2 activation in nitrogen reduction reaction: A DFT perspective

Abstract Ammonia synthesis through electrochemical reduction of nitrogen molecules is a promising strategy to significantly reduce the energy consumption in traditional industrial process. Detailed mechanism study of multistep complex nitrogen reduction reaction is prerequisite for the design of highly efficient catalyst. Stable atomically dispersed catalyst with unique geometric and electronic structure is suitable for the mechanism clarification of such a complex reaction. In this study, d ‐block transition‐metal (TM) anchored C 2 N single layer catalyst is investigated by the density functional theory (DFT) calculation. Both single TM‐anchored single atom catalyst (SAC) and double TM‐anchored double atom catalyst (DAC) exhibit good thermodynamic stability in atomically dispersed catalyst. In the case of SACs, IVB metals (Ti, Zr, Hf) exhibit the highest reactivity and lowest overpotential. While in the case of DACs, Cr─Cr system leads to the NH 3 formation, but V─V system leads to the N 2 H 4 formation. The SACs show much lower overpotential and stronger activation of N 2 molecule than the DACs due to the different activation mechanisms: traditional σ ‐donation/ π ‐backdonation N 2 activation mechanism is found in SACs, while a new π ‐donation/π‐backdonation N 2 activation mechanism is found in the DACs. The present work demonstrates that the different catalytic effect for NRR between SAC and DAC and their corresponding electronic structure origin, which gives more insight into the single atom catalyst. image

Qian, Yumin↗

DOE OSTI2023

First-Principles Examination of Multiple Criteria of Organic Solvent Oxidative Stability in Batteries

Oxidative instability of the liquid electrolyte at or near battery cathode oxide surfaces has significant detrimental effects on batteries. Organic solvent molecules are often the fuel and precursors of such degradation processes, releasing electrons and protons that react with cathode oxides and electrolyte anions. These reactions contribute to cathode–electrolyte interphase (CEI) film formation, transition-metal ion dissolution, and phase transformation of the surface regions of the cathode. Here we apply density functional theory calculations to examine four criteria of oxidative stability (oxidation potential, hydrogen removal energies, and initial reactivity on two types of oxide facets) using four different solvent/additive molecules (ethylene carbonate, fluoroethylene carbonate, 1,3-dioxolane, and dimethyl ether). The ranking of molecular stability differs with each criterion. Surprisingly, the all-oxygen-terminated basal planes of layered oxides exhibit lower reaction barriers than spinel surface facets with exposed transition-metal cations, especially for ether solvents; the calculations also suggest basal planes contribute to the dissolution of transition-metal ions. Further, the structure–degradation relation complexity underscores the challenge of understanding the function of the CEI but also offers a guide to future degradation-mitigation strategies including facet engineering. Our predictions and models help establish a framework for future studies relevant to high-voltage conditions.

25 ENERGY STORAGE↗

DOE OSTI2023

Well-Defined Iron Sites in Crystalline Carbon Nitride

Carbon nitride materials can be hosts for transition metal sites, but Mössbauer studies on iron complexes in carbon nitrides have always shown a mixture of environments and oxidation states. Here we describe the synthesis and characterization of a crystalline carbon nitride with stoichiometric iron sites that all have the same environment. The material (formula C 6 N 9 H 2 Fe 0.4 Li 1.2 Cl, abbreviated PTI/FeCl 2 ) is derived from reacting poly(triazine imide)·LiCl (PTI/LiCl) with a low-melting FeCl 2 /KCl flux, followed by anaerobic rinsing with methanol. X-ray diffraction, X-ray absorption and Mössbauer spectroscopies, and SQUID magnetometry indicate that there are tetrahedral high-spin iron(II) sites throughout the material, all having the same geometry. As a result, the material is active for electrocatalytic nitrate reduction to ammonia, with a production rate of ca. 0.1 mmol cm –2 h –1 and Faradaic efficiency of ca. 80% at −0.80 V vs RHE.

Anions↗

DOE OSTI2021

The Cosmic Ultraviolet Baryon Survey (CUBS) – III. Physical properties and elemental abundances of Lyman-limit systems at z < 1

ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the Cosmic Ultraviolet Baryon Survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicity constraints for the low density, highly ionized phase remains challenging due to the uncertain $N\mathrm{(H\, {\small I})}$, we demonstrate that the cool-phase gas in LLSs has a median metallicity of $\mathrm{[\alpha /H]_{1/2}}=-0.7^{+0.1}_{-0.2}$, with a 16–84 percentile range of [α/H] = (−1.3, −0.1). Furthermore, the wide range of inferred elemental abundance ratios ([C/α], [N/α], and [Fe/α]) indicate a diversity of chemical enrichment histories. Combining the absorption data with deep galaxy survey data characterizing the galaxy environment of these absorbers, we discuss the physical connection between star-forming regions in galaxies and diffuse gas associated with optically thick absorption systems in the z < 1 circumgalactic medium.

Zahedy, Fakhri S. (ORCID:0000000178692551)↗

DOE OSTI2026

Chemical complexity suppresses interstitial solute segregation to screw dislocation cores in the bcc NbTaTiHfZr high-entropy alloy

Recent reports suggest that interstitial solute additions to body-centered cubic (bcc) high-entropy alloys (HEAs) may enhance their mechanical properties. However, details of interactions between interstitial atoms and dislocations in these HEAs remain incompletely understood. Using first-principles calculations, we examine the energetics of C, N, and O interstitial solutes in elemental bcc metals and NbTaTiHfZr, focusing on their segregation in screw dislocation cores. We examine two types of core sites and show that the low-energy configuration and associated segregation energy depend on the transition metal group. In NbTaTiHfZr, we find that chemical complexity substantially suppresses interstitial segregation in dislocation cores, as fluctuations in bulk solute energies induce energetically favorable sites that disfavor segregation to core sites. Local chemical order further enhances this effect by promoting solute clustering away from dislocation cores. These findings reveal fundamental differences between the behavior of interstitial atoms in elemental metals and HEAs, with implications for high-temperature plasticity and dynamic strain aging.

Body-centered cubic transition metals↗