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At least 37 records · Page 2

Predicting path-dependent diffusion barrier spectra in vast compositional space of multi-principal element alloys via convolutional neural networks

The emergent multi-principal element alloys (MPEAs) provide a vast compositional space to search for novel materials for technological advances. How to screen promising compositions from such an ample design space for targeted properties is a grand challenge. In this report, we demonstrate the state-of-the-art deep learning technology—convolutional neural network (CNN)—in predicting path-dependent vacancy migration energy barrier spectra, which are critical to diffusion behavior and many high-temperature properties, in the hyperdimensional composition space of MPEAs. The developed CNN model, fully capturing local chemical features surrounding each vacancy, accurately and efficiently predicts migration energy barrier of MPEAs with different degrees of chemical short-range order and at any unseen compositions. By varying the size of the local region encapsulating vacancy in the CNN model, we reveal that the length scale influencing vacancy migration is surprisingly extensive, up to its six nearest neighboring shells. The efforts of the CNN model make it promising for developing a database of diffusion barriers for various MPEA systems, which would have profound implications for accelerating alloy screening and discovering new compositions with desirable properties.

36 MATERIALS SCIENCE↗

Atomistic modeling of interface strengthening in Al-Si eutectic alloys

Al-Si cast alloys are usually composed of α-Al and Al-Si eutectic. Si flakes and Al matrix generally hold cube-on-cube orientation relationship with the primary interface (111) Al ∥(111) Si . Extensive experimental studies demonstrated that Si flakes cannot significantly improve mechanical properties of Al-Si cast alloys. We hypothesize that the weak strengthening effect associated with Si flakes might be attributed to thermomechanical properties of Al-Si interfaces besides their morphologies. To characterize Al-Si interfaces with a large lattice mismatch (> 30%), we proposed the quasi-coincident site lattice (Q-CSL) as reference lattice, and demonstrated that the Q-CSL Al-Si coherent interface has three characteristic coherent structures, one stable and low energy structure and two metastable and high energy structures. The translation vectors for the same type of coherent Q-CSL structures are consistent with three displacement shift complete (DSC) vectors. The two metastable structures can be obtained by shifting the low energy structure with three partial DSC vectors. Semi-coherent interface is composed of the low energy Q-CSL patches and three sets of interface misfit dislocations with Burgers vectors same as the DSC vectors. Atomistic simulations revealed that Al-Si interface exhibits low shear resistance. Ideal shear strength of the Q-CSL coherent interface is 110 MPa and semi-coherent interface is 20 MPa. The low shear resistance is attributed to the glide of interface misfit dislocations. Al-Si interface also exhibits low formation and migration energies of point defects. Owing to low shear strength and low formation and migration energies of point defects, interface sliding or shear readily happen under mechanical loading or during dislocation-interface interactions. Lattice dislocations can cross slip onto or climb along Al-Si interfaces. These reactions decrease the number of accumulated dislocation loops around Si flakes and promote nucleation and emission of lattice dislocations from Al-Si interfaces to matrix, consequently reduce the repulsive force on approaching dislocations and weaken Si flakes strengthening effect. In situ tension and compression tests in a scanning electron microscope reveal relatively weak strengthening effect due to Si flakes, consistent with the computed dislocation interaction with interfaces and shear behavior of interfaces.

36 MATERIALS SCIENCE↗

Radiation-Enhanced Anion Transport in Hematite

The influence of radiation-induced (1 MeV energy H+ to ~0.1 dpa at 450°C), non-equilibrium point defect populations on mass transport is studied with an integrated campaign of experimental and theoretical methods. Using epitaxial thin films of hematite with embedded 18O tracer layers and nanoscale atom probe tomography measurements, it is shown that anion self-diffusion is enhanced by at least 2 orders of magnitude under irradiation compared to thermal diffusion alone. Complementary scanning transmission electron microscopy of vacuum annealed specimens, reveals associated microstructural changes in the oxide films, including local phase transformation to Fe3O4 and the development of nanoscale voids from vacancy coalescence. Point defect formation and migration energies were computed from density functional theory and applied within the context of chemical rate theory to analyze contributions from both interstitial and vacancy mechanisms to self-diffusion in thermal and irradiation conditions. Comparisons are made between calculated, literature and newly measured self-diffusion values, revealing good agreement on the magnitude of radiation-enhanced anion diffusion. Further, the model suggests a transition from vacancy to interstitialcy mechanisms at low temperatures and high oxygen activity, consistent with the varied activation energies reported from prior studies.

iron oxides, isotopic tracers, atom probe tomograp↗

Synthesis and Photophysical Properties of Light-Harvesting Gold Nanoclusters Fully Functionalized with Antenna Chromophores

The development of efficient light-harvesting systems is important to understand the key aspects of solar-energy conversion processes and to utilize them in various photonic applications. In this study, atomically well-defined gold nanoclusters are reported as a new platform to fabricate artificial light-harvesting systems. An efficient amide coupling method is developed to synthesize water-soluble Au 22 clusters fully protected with pyrene chromophores by taking advantage of their facile phase-transfer reaction. The synthesized Au 22 clusters with densely packed 18 pyrene chromophores (Au 22 –PyB 18 ) exhibit triple-emission in blue, green, and red wavelength regions arising respectively from pyrene monomer, pyrene excimer, and Au 22 emission, producing bright white light emission together. The photoluminescence of Au 22 is enhanced by more than tenfold, demonstrating that pyrenes at the periphery efficiently channel the absorbed energy to the luminescent Au 22 at the center. A combination of femtosecond transient absorption and anisotropy measurements of Au 22 –PyB 18 explicitly reveals three main decay components of 220 fs, 3.5 ps, and 160 ps that can be assigned to energy migration between pyrenes and energy transfer processes from pyrene monomer and excimer to the central Au 22 , respectively.

14 SOLAR ENERGY↗

Vacancy formation energies and migration barriers in multi-principal element alloys

Multi-principal element alloys (MPEAs) continue to garner interest as structural and plasma-facing materials due to their structural (phase) stability and increased resistance to radiation damage. Despite sensitivity of mechanical behavior to irradiation and point-defect formation, there has been scant attention on understanding vacancy stability and diffusion in refractory-based MPEAs. Using density-functional theory, we examine vacancy stability and diffusion barriers in body-centered cubic (Mo 0.95 W 0.05 ) 0.85 Ta 0.10 (TiZr) 0.05 . The results in this MPEA show strong dependence on environment, originating from local lattice distortion associated with charge-transfer between neighboring atoms that vary with different chemical environments. We find a correlation between degree of lattice distortion and migration barrier: (Ti, Zr) with less distortion have lower barriers, while (Mo, W) with larger distortion have higher barriers, depending up local environments. Under irradiation, our findings suggest that (Ti, Zr) are significantly more likely to diffuse than (Mo, W) while Ta shows intermediate effect. Finally, material degradation caused by vacancy diffusion can be controlled by tuning composition of alloying elements to enhance creep strength at extreme operating temperatures and harsh conditions.

36 MATERIALS SCIENCE↗

Microstructural evolution of compositionally complex solid-solution alloys under in-situ dual-beam irradiation

Here, this work attempts to link the microstructural evolution of single-phase compositionally complex alloy (CCA) compositions under dual-beam irradiation to their Mn-content via the stacking-fault energy (SFE) and vacancy migration energies. Two alloys, Cr 18 Fe 27 Mn 27 Ni 28 and Cr 15 Fe 35 Mn 15 Ni 35 , along with less compositionally complex pure Ni and Fe 56 Ni 44 binary were irradiated at 500 and 600 °C under dual-beam 1 MeV Kr 2+ and 16 keV He + heavy-ions up to 7 displacements per atom (dpa) with a He/dpa ratio of 0.75 %/dpa using in situ transmission electron microscopy (TEM). Due to the bubble-stabilizing effect of implanted He, bubbles were observed in all irradiations, and populations of faulted interstitial loops were characterized in Cr 18 Fe 27 Mn 27 Ni 28 and Cr 15 Fe 35 Mn 15 Ni 35 . A reduction in swelling was observed in the two CCAs compared to pure Ni and Fe 56 Ni 44 . Although swelling increased from 500 to 600 °C in Fe 56 Ni 44 , Cr 15 Fe 35 Mn 15 Ni 35 and Cr 18 Fe 27 Mn 27 Ni 28 both swelled slightly more at 500 °C. This was attributed to the difference in vacancy mobility, stronger pinning effect of vacancies on He, and the sink strength of faulted dislocation loops. Faulted interstitial loops nucleated with a higher number density and dislocation line density in Cr 15 Fe 35 Mn 15 Ni 35 at both temperatures, and at 600 °C in both materials. The differences in faulted loop population and temperature effect on swelling are correlated to the Mn-content and the measured SFE (20.2 ± 6.7 mJ/m 2 for Cr 18 Fe 27 Mn 27 Ni 28 and 9.2 ± 3.4 mJ/m 2 for Cr 15 Fe 35 Mn 15 Ni 35 ).

36 MATERIALS SCIENCE↗

Industrializable interlayer with catalytic conversion of dead lithium for Ah–level Nickel–rich lithium metal batteries

The growth of lithium (Li) dendrites and the accumulation of dead Li (i.e., Li metal regions which are electronically disconnected from the current collector) significantly undermine the safety and performance of Li metal batteries. This study employs kilogram-scale atomic layer deposition technology to construct zinc oxide with a preferential (002) crystal orientation, which homogeneously forms on commercial carbon nanotube papers. Our approach emphasizes the importance of achieving a moderate Li adsorption energy and low Li migration energy barriers to suppress Li dendrite growth. In this work, we introduce the concept of "catalytic" effect for dead Li reconversion, as validated through time-of-flight secondary ion mass spectrometry, leading to a Li plating/stripping efficiency of 99.89%. The Ah-level Li metal pouch cells with high-nickel positive electrodes achieve a specific energy of 380 Wh kg -1 (based on the mass of the whole pouch cell) and demonstrate stable cycling under demanding conditions. Analysis of the cycled pouch cells confirms the structural integrity and provides insights into the mechanism of the dead Li "catalytic" conversion.

Shen, Huasen [Jianghan University, Wuhan (China)]↗

Accelerated kinetic Monte Carlo: A case study; vacancy and dumbbell interstitial diffusion traps in concentrated solid solution alloys

Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and $\langle$100$\rangle$ dumbbell interstitials in Ni–Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy’s non-monotonic behavior. In contrast, the difference between formation energies of Ni–Ni, Ni–Fe, and Fe–Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition—based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one—is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.

36 MATERIALS SCIENCE↗

Evolution of dislocation loops in irradiated α-Uranium: An atomistically-informed cluster dynamics investigation

An atomistically-informed mean field cluster dynamics model has been developed to investigate the nucleation and growth of prismatic loops in irradiated a-Uranium. TEM analysis of neutron irradiated a-Uranium shows the evolution of self-interstitial atom and vacancy loops on (010) and (100) crystallographic planes, respectively, resulting in an anisotropic lattice swelling of its face-centered orthorhombic crystal. To provide model parameters, the crystallography of loops and the binding energy of point defects to these loops were studied using an angular dependent EAM potential and classical molecular dynamics (MD) simulations. Furthermore, using the bond-boost hyperdynamics method, the anisotropic diffusion of interstitials and vacancies in a-Uranium was investigated. Here, the mechanisms of point defect diffusion and the associated migration energies were reported and compared with previous DFT studies. The energetics and kinetic quantities mentioned above were used in the cluster dynamics model to predict the cluster density as a function of dose rate, dose and temperature and the results were compared to the reported neutron irradiation experiments. The model predictions reveal an accumulation of small sized vacancy loops along with a population of large and growing self-interstitial loops, which closely corresponds to the TEM observations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Kinetic Monte Carlo Simulation of Oxygen Diffusion in Ytterbium Disilicate

Ytterbium disilicate is of interest as a potential environmental barrier coating for aerospace applications, notably for use in next generation jet turbine engines. In such applications, the transport of oxygen and water vapor through these coatings to the ceramic substrate is undesirable if high temperature oxidation is to be avoided. In an effort to understand the diffusion process in these materials, we have performed kinetic Monte Carlo simulations of vacancy-mediated and interstitial oxygen diffusion in Ytterbium disilicate. Oxygen vacancy and interstitial site energies, vacancy and interstitial formation energies, and migration barrier energies were computed using Density Functional Theory. We have found that, in the case of vacancy-mediated diffusion, many potential diffusion paths involve large barrier energies, but some paths have barrier energies smaller than one electron volt. However, computed vacancy formation energies suggest that the intrinsic vacancy concentration is small. In the case of interstitial diffusion, migration barrier energies are typically around one electron volt, but the interstitial defect formation energies are positive, with the result that the disilicate is unlikely to exhibit experience significant oxygen permeability except at very high temperature.

Coatings↗

Design considerations for high entropy alloys in advanced nuclear applications

The demanding operating environments of advanced nuclear reactors require the development of new nuclear materials that can withstand their increased physical, chemical, thermal, and radiation-related challenges. High-entropy alloys (HEAs) have shown often-impressive mechanical, thermomechanical, and corrosion-resistant properties, and offer a massive, unexplored compositional space which allows for the targeted development of application-specific materials. Furthermore, although still in a nascent stage, research has shown that HEAs may exhibit unique irradiation tolerance, including reduced defect production and resistance to irradiation-induced swelling and hardening. The mechanisms behind this increased tolerance are not yet well-understood, although the HEA-specific attributes of a complex energy landscape, reduced thermal conductivity, and shift in defect migration energies and pathways provide promising explanations. Here this work assesses the current and future challenges faced by structural nuclear materials, identifying the specific applications in which HEAs may provide a competitive advantage compared to industry-standard materials with the aid of Ashby material selection maps. Considerations are provided for the design of future nuclear HEAs, including calculations of nuclear-relevant properties to assist in the initial down-selection of elements depending on application requirements (e.g., low neutron capture for in-core applications), narrowing the existing compositional space of HEAs to a manageable scope.

36 MATERIALS SCIENCE↗

Ab Initio Design of High-Entropy Thermal/ Environmental Barrier Coatings

Next generation thermal/environmental barrier coatings (TEBC) require carefully balancing various properties including phase stability, thermal conductivity, coefficient of thermal expansion (CTE), mechanical properties, and resistance against hot corrosion and water vapor recession. This work mainly focuses on rapid design of cost-effective high entropy rare-earth disilicates and aluminum garnets to protect SiC-based ceramic matrix composites and nickel-based superalloys in the hot section of gas turbine engines using density functional theory methods. Our calculations identify several low-cost high entropy TEBC exhibiting ultralow thermal conductivity at 1500 K and desirable CTE while maintaining good mechanical properties, including Er1/2Y3/4Yb3/4Si2O7, Gd1/4Er1/4Y3/4Yb3/4Si2O7, Eu1/4Er1/4Y3/4Yb3/4Si2O7, and (Y1/4Gd1/4Er1/4Yb1/4)3Al5O12. This work also aims to gain fundamental understanding of oxygen diffusion in model disilicates. Minimizing oxidizer (such as water vapor and oxygen) permeability through the EBC layer can significantly decrease the growth rate of thermally grown oxide and extend the service life of the coating system. Oxygen diffusion mechanisms including formation energy of defects under varying oxygen conditions and defect migration energy barriers will be presented.

coefficient of thermal expansion↗

Theoretical Design of Lithium Chloride Superionic Conductors for All-Solid-State High-Voltage Lithium-Ion Batteries

The development of solid electrolytes (SEs) is a promising pathway to improve the energy density and safety of conventional Li ion batteries. Several lithium chloride SEs, Li 3 MCl 6 (M = Y, Er, In, and Sc), have gained popularity due to their high ionic conductivity, wide electrochemical window, and good chemical stability. This study systematically investigated 17 Li 3 MCl 6 SEs to identify novel and promising lithium chloride SEs. Calculation results revealed that 12 Li 3 MCl 6 (M = Bi, Dy, Er, Ho, In, Lu, Sc, Sm, Tb, TI, Tm, and Y) were stable phase with a wide electrochemical stability window and excellent chemical stability against cathode materials and moisture. Li-ion transport properties were examined using bond valence site energy (BVSE) and ab initio molecular dynamics (AIMD) calculation. Li 3 MCl 6 showed the lower migration energy barrier in monoclinic structures, while orthorhombic and trigonal structures exhibited higher energy barriers due to the sluggish diffusion along the two-dimensional path based on the BVSE model. AIMD results confirmed the slower ion migration along the 2D path, exhibiting lower ionic diffusivity and higher activation energy in orthorhombic and trigonal structures. For the further increase of ionic conductivity in monoclinic structures, Li-ion vacancy was formed by the substitution of M 3+ with Zr 4+ . Zr-substituted phase (Li 2.5 M 0.5 Zr 0.5 Cl 6 , M = In, Sc) exhibited up to a fourfold increase in ionic conductivity. This finding suggested that the optimization of Li vacancy in the Li 3 MCl 6 SEs could lead to superionic Li 3 MCl 6 SEs.

25 ENERGY STORAGE↗

Diffusion of alloying and fission atoms in α-U investigated by first-principles calculation

Stability and diffusion of small defect clusters containing alloying or fission atoms (“F” is used to represent both atoms) in an α-uranium (U) crystal are investigated using first-principles calculations. Here, results indicate that different stable defect structures are observed for an interstitial defect and a cluster (F n V m ) containing different alloying or fission atoms and vacancies. An interstitial defect is found to be most stable either at the center of a pyramid pentahedron or in a 〈010〉 mixed dumbbell configuration and the latter one is reported for the first time. Formation energy of a small F n V m cluster depends on the distribution of vacancies. Based on these stable defects, new migration energies and paths have been explored in this work. Anisotropic migration of an interstitial defect by jumping between nearest centers of two pyramid pentahedrons or jumping between two mixed U-Zr dumbbells has been suggested. Furthermore, a new migration-rotation mechanism has been explored for the first time for a FV 2 cluster, resulting in a 3D diffusion. Finally, the effect of substitutional Pu atoms on the migration of a FV 2 cluster suggests that optimizing the Pu concentration may prohibit the diffusion of some alloying or fission atoms, increasing the safe performance of metallic fuels.

3D diffusion↗

Role of a 3D Structure in Energy Transfer in Mixed-Ligand Metal–Organic Frameworks

We present a detailed investigation of the photophysical properties of mixed-ligand pyrene- and porphyrin-based metal–organic frameworks (MOFs) as a function of their 3D structure. Solvothermal reactions between metal salts (InCl 3 , Zr(acac) 4 , and ZrCl 4 ) and suitable ratios of 1,3,6,8-tetrakis(p-benzoic acid)pyrene (TBAPy) and meso-tetrakis- (4-carboxyphenyl)porphyrin (TCPP) were performed to prepare a series of mixed-ligand ROD-7, NU-901, and NU-1000 MOFs. Time-resolved and steady-state fluorescence measurements were conducted on the mixed-ligand MOFs to study their photophysics. Based on the results, we concluded that upon excitation of TBAPy linkers in the MOFs, singlet excitation energy migrates across TBAPy linkers until it finds a TCPP unit. TCPP acts as an energy trap and quenches the excitation. The efficiency of TBAPy-to-TBAPy energy transfer was found to be sensitive to the structural parameters of MOFs. Analysis of steady-state and time-resolved fluorescence data revealed that excitation energy transfer (EET) is most efficient in ROD-7, followed by NU-901 and NU-1000. We propose that topology that invokes the shorter interchromophoric distances between TBAPy linkers in ROD-7 is responsible for its higher EET efficiency. The distance dependence of the EET rate constant (kEET) was investigated to gain insight into the mechanistic aspects of energy transfer in MOFs. This study revealed that (a) energy transfer in MOFs deviates from the classical Förster model and (b) the geometrical arrangement of linkers influences the mechanism of EET in MOFs. A theoretical investigation was also performed to determine energy-transfer rate constants along different directions and assess the directionality of energy transfer in these MOFs. The magnitude of rate constants indicated that energy transfer in ROD-7 should be highly anisotropic along the stacking direction. Furthermore, these findings suggest that ROD-7 is a promising candidate to play the role of the light-harvesting and energy-transfer component in solar energy conversion devices, where directional energy transfer is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Defect Diffusion Graph Neural Networks for Materials Discovery in High-Temperature Energy Applications

Here, the migration of crystallographic defects dictates material properties and performance for a plethora of technological applications. Density functional theory (DFT)-based nudged elastic band (NEB) calculations are a powerful computational technique for predicting defect migration activation energy barriers, yet they become prohibitively expensive for high-throughput screening of defect diffusivities. Without introducing hand-crafted (i.e., chemistry- or structure-specific) descriptors, we propose a generalized deep learning approach to train surrogate models for NEB energies of vacancy migration by hybridizing graph neural networks with transformer encoders and simply using pristine host structures as input. With sufficient training data, computationally efficient and simultaneous inference of vacancy defect thermodynamics and migration activation energies can be obtained to compute temperature-dependent vacancy diffusivities and to down-select candidates for more thorough DFT analysis or experiments. Thus, as we specifically demonstrate for potential water-splitting materials, candidates with desired defect thermodynamics, kinetics, and host stability properties can be more rapidly targeted from open-source databases of experimentally validated or hypothetical materials.

14 SOLAR ENERGY↗

Topological graph-based analysis of solid-state ion migration

To accelerate the development of ion conducting materials, we present a general graph-theoretic analysis framework for ion migration in any crystalline structure. The nodes of the graph represent metastable sites of the migrating ion and the edges represent discrete migration events between adjacent sites. Starting from a collection of possible metastable migration sites, the framework assigns a weight to the edges by calculating the individual migration energy barriers between those sites. Connected pathways in the periodic simulation cell corresponding to macroscopic ion migration are identified by searching for the lowest-cost cycle in the periodic migration graph. To exemplify the utility of the framework, we present the automatic analyses of Li migration in different polymorphs of VO(PO 4 ), with the resulting identification of two distinct crystal structures with simple migration pathways demonstrating overall <300 meV migration barriers.

36 MATERIALS SCIENCE↗

A Novel NASICON‐Type Na 4 MnCr(PO 4 ) 3 Demonstrating the Energy Density Record of Phosphate Cathodes for Sodium‐Ion Batteries

Abstract Sodium‐ion batteries (SIBs) have attracted incremental attention as a promising candidate for grid‐scale energy‐storage applications. To meet practical requirements, searching for new cathode materials with high energy density is of great importance. Herein, a novel Na superionic conductor (NASICON)‐type Na 4 MnCr(PO 4 ) 3 is developed as a high‐energy cathode for SIBs. The Na 4 MnCr(PO 4 ) 3 nanoparticles homogeneously embedded in a carbon matrix can present an extraordinary reversible capacity of 160.5 mA h g −1 with three‐electron reaction at ≈3.53 V during the Na + extraction/insertion process, realizing an unprecedentedly high energy density of 566.5 Wh kg −1 in the phosphate cathodes for SIBs. It is intriguing to reveal the underlying mechanism of the unique Mn 2+ /Mn 3+ , Mn 3+ /Mn 4+ , and Cr 3+ /Cr 4+ redox couples via X‐ray absorption near‐edge structure spectroscopy. The whole electrochemical reaction undergoes highly reversible single‐phase and biphasic transitions with a moderate volume change of 7.7% through in situ X‐ray diffraction and ex situ high‐energy synchrotron X‐ray diffraction. Combining density functional theory (DFT) calculations with the galvanostatic intermittent titration technique, the superior performance is ascribed to the low ionic‐migration energy barrier and desirable Na‐ion diffusion kinetics. The present work can offer a new insight into the design of multielectron‐reaction cathode materials for SIBs.

Zhang, Jian↗