Kinetics of solid-state reduction of chromite overburden

The demand for alternative low-grade iron ores is on the rise due to the rapid depletion of high-grade natural iron ore resources and the increased need for steel usage in daily life.However,the use of low-grade iron ores is a constant clinical task for industry metallurgists.Direct smelting of low-grade ores consumes a substantial amount of energy due to the large volume of slag generated.This condition can be avoided by direct reduction followed by magnetic separation(to separate the high amount of gangue or refractory and metal parts)and smelting.Chromite overburden(COB)is a mine waste generated in chromite ore processing,and it mainly consists of iron,chromium,and nickel(<1wt%).In the present work,the isothermal and non-isothermal kinetics of the solid-state reduction of self-reduced pellets prepared using low-grade iron ore(COB)were thoroughly investigated via thermal analysis.The results showed that the reduction of pellets followed a firstorder autocatalytic reaction control mechanism in the temperature range of 900-1100℃.The autocatalytic nature of the reduction reaction was due to the presence of nickel in the COB.The apparent activation energy obtained from the kinetics results showed that the solid-state reactions between COB and carbon were the rate-determining step in iron oxide reduction.

Solid-state reduction kinetics and mechanism of pre-oxidized vanadium-titanium magnetite concentrate

The solid-state reduction kinetics of pre-oxidized vanadium-titanium magnetite concentrate was studied. The phase and microstructure of the reduction product were characterized by XRD, SEM and EDS methods, based on which the mechanism of the solid-state reduction was investigated. The results showed that using coal as reductant at 950-1100 °C, the solid-state reduction of the pre-oxidized vanadium-titanium magnetite concentrate was controlled by interface chemical reaction and the apparent activation energy was 67.719 k J/mol. The mineral phase transformation during the reduction process can be described as follows： pre-oxidized vanadium-titanium magnetite concentrate → ulvospinel → ilmenite → Fe Ti2O5 →（FenTi1-n）Ti2O5. M3O5-type（M can be Fe, Ti, Mg, Mn, etc） solid solutions would be formed during the reduction process of the pre-oxidized vanadium-titanium magnetite concentrate at 1050 °C for 60 min. The poor reducibility of iron in M3O5 solid solutions is the main reason to limit the reduction property of pre-oxidized vanadium-titanium magnetite concentrate.

Mechanism of vanadic titanomagnetite solid-state reduction

The influence mechanism of vanadic titanomagnetite solid-state reduction was studied in this paper.Optical microscopy(OM),scanning electron microscope(SEM),and X-ray diffraction(XRD)were used to characterize the structure and phases of the samples.The results show that the dense structure is not the reason that limits the reducibility of Panxi vanadic titanomagnetite.Metallization rate of 93%was achieved when it was reduced at 1100℃for 100 min.After pre-oxidation,Fe_(9)TiO_(15)and Fe_(2)O_(3)are the main phases of samples.Pre-oxidation could destroy the dense structure of vanadic titanomagnetite and increase the specific surface area of particles.However,reducibility of vanadic titanomagnetite is not improved obviously by pre-oxidation,with metallization rate increasing only 1%under the same reduction conditions,and the generated metallic iron grains are smaller.Phase transformation of vanadic titanomagnetite at different reduction temperatures shows that the presence of FeTi_(2)O_(5)is the main reason that limits the reducibility of Panxi vanadic titanomagnetite.

12.6μm-Thick Asymmetric Composite Electrolyte with Superior Interfacial Stability for Solid-State Lithium-Metal Batteries

Solid-state lithium metal batteries(SSLMBs)show great promise in terms of high-energy-density and high-safety performance.However,there is an urgent need to address the compatibility of electrolytes with high-voltage cathodes/Li anodes,and to minimize the electrolyte thickness to achieve highenergy-density of SSLMBs.Herein,we develop an ultrathin(12.6μm)asymmetric composite solid-state electrolyte with ultralight areal density(1.69 mg cm^(−2))for SSLMBs.The electrolyte combining a garnet(LLZO)layer and a metal organic framework(MOF)layer,which are fabricated on both sides of the polyethylene(PE)separator separately by tape casting.The PE separator endows the electrolyte with flexibility and excellent mechanical properties.The LLZO layer on the cathode side ensures high chemical stability at high voltage.The MOF layer on the anode side achieves a stable electric field and uniform Li flux,thus promoting uniform Li^(+)deposition.Thanks to the well-designed structure,the Li symmetric battery exhibits an ultralong cycle life(5000 h),and high-voltage SSLMBs achieve stable cycle performance.The assembled pouch cells provided a gravimetric/volume energy density of 344.0 Wh kg^(−1)/773.1 Wh L^(−1).This simple operation allows for large-scale preparation,and the design concept of ultrathin asymmetric structure also reveals the future development direction of SSLMBs.

Advances in All-Solid-State Lithium-Sulfur Batteries for Commercialization

Solid-state batteries are commonly acknowledged as the forthcoming evolution in energy storage technologies.Recent development progress for these rechargeable batteries has notably accelerated their trajectory toward achieving commercial feasibility.In particular,all-solid-state lithium-sulfur batteries(ASSLSBs)that rely on lithium-sulfur reversible redox processes exhibit immense potential as an energy storage system,surpassing conventional lithium-ion batteries.This can be attributed predominantly to their exceptional energy density,extended operational lifespan,and heightened safety attributes.Despite these advantages,the adoption of ASSLSBs in the commercial sector has been sluggish.To expedite research and development in this particular area,this article provides a thorough review of the current state of ASSLSBs.We delve into an in-depth analysis of the rationale behind transitioning to ASSLSBs,explore the fundamental scientific principles involved,and provide a comprehensive evaluation of the main challenges faced by ASSLSBs.We suggest that future research in this field should prioritize plummeting the presence of inactive substances,adopting electrodes with optimum performance,minimizing interfacial resistance,and designing a scalable fabrication approach to facilitate the commercialization of ASSLSBs.

How Does Stacking Pressure Affect the Performance of Solid Electrolytes and All-Solid-State Lithium Metal Batteries?

All-solid-state lithium metal batteries(ASSLMBs)with solid electrolytes(SEs)have emerged as a promising alternative to liquid electrolyte-based Li-ion batteries due to their higher energy density and safety.However,since ASSLMBs lack the wetting properties of liquid electrolytes,they require stacking pressure to prevent contact loss between electrodes and SEs.Though previous studies showed that stacking pressure could impact certain performance aspects,a comprehensive investigation into the effects of stacking pressure has not been conducted.To address this gap,we utilized the Li_(6)PS_(5)Cl solid electrolyte as a reference and investigated the effects of stacking pressures on the performance of SEs and ASSLMBs.We also developed models to explain the underlying origin of these effects and predict battery performance,such as ionic conductivity and critical current density.Our results demonstrated that an appropriate stacking pressure is necessary to achieve optimal performance,and each step of applying pressure requires a specific pressure value.These findings can help explain discrepancies in the literature and provide guidance to establish standardized testing conditions and reporting benchmarks for ASSLMBs.Overall,this study contributes to the understanding of the impact of stacking pressure on the performance of ASSLMBs and highlights the importance of careful pressure optimization for optimal battery performance.

Atom substitution of the solid-state electrolyte Li_(10)GeP_(2)S_(12)for stabilized all-solid-state lithium metal batteries

Solid-state electrolyte Li_(10)GeP_(2)S_(12)(LGPS)has a high lithium ion conductivity of 12 mS cm^(-1)at room temperature,but its inferior chemical stability against lithium metal anode impedes its practical application.Among all solutions,Ge atom substitution of the solid-state electrolyte LGPS stands out as the most promising solution to this interface problem.A systematic screening framework for Ge atom substitution including ionic conductivity,thermodynamic stability,electronic and mechanical properties is utilized to solve it.For fast screening,an enhanced model Dop Net FC using chemical formulas for the dataset is adopted to predict ionic conductivity.Finally,Li_(10)SrP_(2)S_(12)(LSrPS)is screened out,which has high lithium ion conductivity(12.58 mS cm^(-1)).In addition,an enhanced migration of lithium ion across the LSr PS/Li interface is found.Meanwhile,compared to the LGPS/Li interface,LSrPS/Li interface exhibits a larger Schottky barrier(0.134 eV),smaller electron transfer region(3.103?),and enhanced ability to block additional electrons,all of which contribute to the stabilized interface.The applied theoretical atom substitution screening framework with the aid of machine learning can be extended to rapid determination of modified specific material schemes.

Strong synergy between physical and chemical properties:Insight into optimization of atomically dispersed oxygen reduction catalysts

Atomically dispersed catalysts exhibit significant influence on facilitating the sluggish oxygen reduction reaction(ORR)kinetics with high atom economy,owing to remarkable attributes including nearly 100%atomic utilization and exceptional catalytic functionality.Furthermore,accurately controlling atomic physical properties including spin,charge,orbital,and lattice degrees of atomically dispersed catalysts can realize the optimized chemical properties including maximum atom utilization efficiency,homogenous active centers,and satisfactory catalytic performance,but remains elusive.Here,through physical and chemical insight,we review and systematically summarize the strategies to optimize atomically dispersed ORR catalysts including adjusting the atomic coordination environment,adjacent electronic orbital and site density,and the choice of dual-atom sites.Then the emphasis is on the fundamental understanding of the correlation between the physical property and the catalytic behavior for atomically dispersed catalysts.Finally,an overview of the existing challenges and prospects to illustrate the current obstacles and potential opportunities for the advancement of atomically dispersed catalysts in the realm of electrocatalytic reactions is offered.

Cu-Based Materials for Enhanced C_(2+) Product Selectivity in Photo-/Electro-Catalytic CO_(2) Reduction: Challenges and Prospects

Carbon dioxide conversion into valuable products using photocatalysis and electrocatalysis is an effective approach to mitigate global environmental issues and the energy shortages. Among the materials utilized for catalytic reduction of CO_(2), Cu-based materials are highly advantageous owing to their widespread availability, cost-effectiveness, and environmental sustainability. Furthermore, Cu-based materials demonstrate interesting abilities in the adsorption and activation of carbon dioxide, allowing the formation of C_(2+) compounds through C–C coupling process. Herein, the basic principles of photocatalytic CO_(2) reduction reactions(PCO_(2)RR) and electrocatalytic CO_(2) reduction reaction(ECO_(2)RR) and the pathways for the generation C_(2+) products are introduced. This review categorizes Cu-based materials into different groups including Cu metal, Cu oxides, Cu alloys, and Cu SACs, Cu heterojunctions based on their catalytic applications. The relationship between the Cu surfaces and their efficiency in both PCO_(2)RR and ECO_(2)RR is emphasized. Through a review of recent studies on PCO_(2)RR and ECO_(2)RR using Cu-based catalysts, the focus is on understanding the underlying reasons for the enhanced selectivity toward C_(2+) products. Finally, the opportunities and challenges associated with Cu-based materials in the CO_(2) catalytic reduction applications are presented, along with research directions that can guide for the design of highly active and selective Cu-based materials for CO_(2) reduction processes in the future.

In-situ interfacial passivation and self-adaptability synergistically stabilizing all-solid-state lithium metal batteries

The function of solid electrolytes and the composition of solid electrolyte interphase(SEI)are highly significant for inhibiting the growth of Li dendrites.Herein,we report an in-situ interfacial passivation combined with self-adaptability strategy to reinforce Li_(0.33)La_(0.557)TiO_(3)(LLTO)-based solid-state batteries.Specifically,a functional SEI enriched with LiF/Li_(3)PO_(4) is formed by in-situ electrochemical conversion,which is greatly beneficial to improving interface compatibility and enhancing ion transport.While the polarized dielectric BaTiO_(3)-polyamic acid(BTO-PAA,BP)film greatly improves the Li-ion transport kinetics and homogenizes the Li deposition.As expected,the resulting electrolyte offers considerable ionic conductivity at room temperature(4.3 x 10~(-4)S cm^(-1))and appreciable electrochemical decomposition voltage(5.23 V)after electrochemical passivation.For Li-LiFePO_(4) batteries,it shows a high specific capacity of 153 mA h g^(-1)at 0.2C after 100 cycles and a long-term durability of 115 mA h g^(-1)at 1.0 C after 800 cycles.Additionally,a stable Li plating/stripping can be achieved for more than 900 h at 0.5 mA cm^(-2).The stabilization mechanisms are elucidated by ex-situ XRD,ex-situ XPS,and ex-situ FTIR techniques,and the corresponding results reveal that the interfacial passivation combined with polarization effect is an effective strategy for improving the electrochemical performance.The present study provides a deeper insight into the dynamic adjustment of electrode-electrolyte interfacial for solid-state lithium batteries.

Numerical Study on Reduction in Aerodynamic Drag and Noise of High-Speed Pantograph

Reducing the aerodynamic drag and noise levels of high-speed pantographs is important for promoting environmentally friendly,energy efficient and rapid advances in train technology.Using computational fluid dynamics theory and the K-FWH acoustic equation,a numerical simulation is conducted to investigate the aerodynamic characteristics of high-speed pantographs.A component optimization method is proposed as a possible solution to the problemof aerodynamic drag and noise in high-speed pantographs.The results of the study indicate that the panhead,base and insulator are the main contributors to aerodynamic drag and noise in high-speed pantographs.Therefore,a gradual optimization process is implemented to improve the most significant components that cause aerodynamic drag and noise.By optimizing the cross-sectional shape of the strips and insulators,the drag and noise caused by airflow separation and vortex shedding can be reduced.The aerodynamic drag of insulator with circular cross section and strips with rectangular cross section is the largest.Ellipsifying insulators and optimizing the chamfer angle and height of the windward surface of the strips can improve the aerodynamic performance of the pantograph.In addition,the streamlined fairing attached to the base can eliminate the complex flow and shield the radiated noise.In contrast to the original pantograph design,the improved pantograph shows a 21.1%reduction in aerodynamic drag and a 1.65 dBA reduction in aerodynamic noise.

A dynamic database of solid-state electrolyte(DDSE)picturing all-solid-state batteries

All-solid-state batteries(ASSBs)are a class of safer and higher-energy-density materials compared to conventional devices,from which solid-state electrolytes(SSEs)are their essential components.To date,investigations to search for high ion-conducting solid-state electrolytes have attracted broad concern.However,obtaining SSEs with high ionic conductivity is challenging due to the complex structural information and the less-explored structure-performance relationship.To provide a solution to these challenges,developing a database containing typical SSEs from available experimental reports would be a new avenue to understand the structureperformance relationships and find out new design guidelines for reasonable SSEs.Herein,a dynamic experimental database containing>600 materials was developed in a wide range of temperatures(132.40–1261.60 K),including mono-and divalent cations(e.g.,Li^(+),Na^(+),K^(+),Ag^(+),Ca^(2+),Mg^(2+),and Zn^(2+))and various types of anions(e.g.,halide,hydride,sulfide,and oxide).Data-mining was conducted to explore the relationships among different variates(e.g.,transport ion,composition,activation energy,and conductivity).Overall,we expect that this database can provide essential guidelines for the design and development of high-performance SSEs in ASSB applications.This database is dynamically updated,which can be accessed via our open-source online system.

Oxygen‑Coordinated Single Mn Sites for Efficient Electrocatalytic Nitrate Reduction to Ammonia

Electrocatalytic nitrate reduction reaction has attracted increasing attention due to its goal of low carbon emission and environmental protection.Here,we report an efficient NitRR catalyst composed of single Mn sites with atomically dispersed oxygen(O)coordination on bacterial cellulose-converted graphitic carbon(Mn-O-C).Evidence of the atomically dispersed Mn-(O-C_(2))_(4)moieties embedding in the exposed basal plane of carbon surface is confirmed by X-ray absorption spectroscopy.As a result,the as-synthesized Mn-O-C catalyst exhibits superior NitRR activity with an NH_(3)yield rate(RNH_(3))of 1476.9±62.6μg h^(−1)cm^(−2)at−0.7 V(vs.reversible hydrogen electrode,RHE)and a faradaic efficiency(FE)of 89.0±3.8%at−0.5 V(vs.RHE)under ambient conditions.Further,when evaluated with a practical flow cell,Mn-O-C shows a high RNH_(3)of 3706.7±552.0μg h^(−1)cm^(−2)at a current density of 100 mA cm−2,2.5 times of that in the H cell.The in situ FT-IR and Raman spectroscopic studies combined with theoretical calculations indicate that the Mn-(O-C_(2))_(4)sites not only effectively inhibit the competitive hydrogen evolution reaction,but also greatly promote the adsorption and activation of nitrate(NO_(3)^(−)),thus boosting both the FE and selectivity of NH_(3)over Mn-(O-C_(2))_(4)sites.

Research on a Monte Carlo global variance reduction method based on an automatic importance sampling method

Global variance reduction is a bottleneck in Monte Carlo shielding calculations.The global variance reduction problem requires that the statistical error of the entire space is uniform.This study proposed a grid-AIS method for the global variance reduction problem based on the AIS method,which was implemented in the Monte Carlo program MCShield.The proposed method was validated using the VENUS-Ⅲ international benchmark problem and a self-shielding calculation example.The results from the VENUS-Ⅲ benchmark problem showed that the grid-AIS method achieved a significant reduction in the variance of the statistical errors of the MESH grids,decreasing from 1.08×10^(-2) to 3.84×10^(-3),representing a 64.00% reduction.This demonstrates that the grid-AIS method is effective in addressing global issues.The results of the selfshielding calculation demonstrate that the grid-AIS method produced accurate computational results.Moreover,the grid-AIS method exhibited a computational efficiency approximately one order of magnitude higher than that of the AIS method and approximately two orders of magnitude higher than that of the conventional Monte Carlo method.

Single-atom catalysts for the electrochemical reduction of carbon dioxide into hydrocarbons and oxygenates

The electrochemical reduction of carbon dioxide offers a sound and economically viable technology for the electrification and decarbonization of the chemical and fuel industries.In this technology,an electrocatalytic material and renewable energy-generated electricity drive the conversion of carbon dioxide into high-value chemicals and carbon-neutral fuels.Over the past few years,single-atom catalysts have been intensively studied as they could provide near-unity atom utilization and unique catalytic performance.Single-atom catalysts have become one of the state-of-the-art catalyst materials for the electrochemical reduction of carbon dioxide into carbon monoxide.However,it remains a challenge for single-atom catalysts to facilitate the efficient conversion of carbon dioxide into products beyond carbon monoxide.In this review,we summarize and present important findings and critical insights from studies on the electrochemical carbon dioxide reduction reaction into hydrocarbons and oxygenates using single-atom catalysts.It is hoped that this review gives a thorough recapitulation and analysis of the science behind the catalysis of carbon dioxide into more reduced products through singleatom catalysts so that it can be a guide for future research and development on catalysts with industry-ready performance for the electrochemical reduction of carbon dioxide into high-value chemicals and carbon-neutral fuels.

The photo-decomposition and self-restructuring dynamic equilibrium mechanism of Cu_(2)(OH)_(2)CO_(3)for stable photocatalytic CO_(2)reduction

Developing suitable photocatalysts and understanding their intrinsic catalytic mechanism remain key challenges in the pursuit of highly active,good selective,and long-term stable photocatalytic CO_(2)reduction(PCO_(2)R)systems.Herein,monoclinic Cu_(2)(OH)_(2)CO_(3)is firstly proven to be a new class of photocatalyst,which has excellent catalytic stability and selectivity for PCO_(2)R in the absence of any sacrificial agent and cocatalysts.Based on a Cu_(2)(OH)_(2)^(13)CO_(3)photocatalyst and 13CO_(2)two-sided^(13)C isotopic tracer strategy,and combined with in situ diffused reflectance infrared Fourier transform spectroscopy(DRIFTS)analysis and density functional theory(DFT)calculations,two main CO_(2)transformation routes,and the photo-decomposition and self-restructuring dynamic equilibrium mechanism of Cu_(2)(OH)_(2)CO_(3)are definitely revealed.The PCO_(2)R activity of Cu_(2)(OH)_(2)CO_(3)is comparable to some of state-of-the-art novel photocatalysts.Significantly,the PCO_(2)R properties can be further greatly enhanced by simply combining Cu_(2)(OH)_(2)CO_(3)with typical TiO_(2)to construct composites photocatalyst.The highest CO_(2)and CH_(4)production rates by 7.5 wt%Cu_(2)(OH)_(2)CO_(3)-TiO_(2)reach 16.4μmol g^(-1)h^(-1)and 116.0μmol g^(-1)h^(-1),respectively,which are even higher than that of some of PCO_(2)R systems containing sacrificial agents or precious metals modified photocatalysts.This work provides a better understanding for the PCO_(2)R mechanism at the atomic levels,and also indicates that basic carbonate photocatalysts have broad application potential in the future.

Porous metal oxides in the role of electrochemical CO_(2) reduction reaction

The global energy-related CO_(2) emissions have rapidly increased as the world economy heavily relied on fossil fuels.This paper explores the pressing challenge of CO_(2) emissions and highlights the role of porous metal oxide materials in the electrocatalytic reduction of CO_(2)(CO_(2)RR).The focus is on the development of robust and selective catalysts,particularly metal and metal-oxide-based materials.Porous metal oxides offer high surface area,enhancing the accessibility to active sites and improving reaction kinetics.The tunability of these materials allows for tailored catalytic behavior,targeting optimized reaction mechanisms for CO_(2)RR.The work also discusses the various synthesis strategies and identifies key structural and compositional features,addressing challenges like high overpotential,poor selectivity,and low stability.Based on these insights,we suggest avenues for future research on porous metal oxide materials for electrochemical CO_(2) reduction.

Understanding Bridging Sites and Accelerating Quantum Efficiency for Photocatalytic CO_(2) Reduction

We report a novel double-shelled nanoboxes photocatalyst architecture with tailored interfaces that accelerate quantum efficiency for photocatalytic CO_(2) reduction reaction(CO_(2)RR)via Mo–S bridging bonds sites in S_(v)–In_(2)S_(3)@2H–MoTe_(2).The X-ray absorption near-edge structure shows that the formation of S_(v)–In_(2)S_(3)@2H–MoTe_(2) adjusts the coordination environment via interface engineering and forms Mo–S polarized sites at the interface.The interfacial dynamics and catalytic behavior are clearly revealed by ultrafast femtosecond transient absorption,time-resolved,and in situ diffuse reflectance–Infrared Fourier transform spectroscopy.A tunable electronic structure through steric interaction of Mo–S bridging bonds induces a 1.7-fold enhancement in S_(v)–In_(2)S_(3)@2H–MoTe_(2)(5)photogenerated carrier concentration relative to pristine S_(v)–In_(2)S_(3).Benefiting from lower carrier transport activation energy,an internal quantum efficiency of 94.01%at 380 nm was used for photocatalytic CO_(2)RR.This study proposes a new strategy to design photocatalyst through bridging sites to adjust the selectivity of photocatalytic CO_(2)RR.

Surface engineering of ZnO electrocatalyst by N doping towards electrochemical CO_(2) reduction

The discovery of efficient,selective,and stable electrocatalysts can be a key point to produce the largescale chemical fuels via electrochemical CO_(2) reduction(ECR).In this study,an earth-abundant and nontoxic ZnO-based electrocatalyst was developed for use in gas-diffusion electrodes(GDE),and the effect of nitrogen(N)doping on the ECR activity of ZnO electrocatalysts was investigated.Initially,a ZnO nanosheet was prepared via the hydrothermal method,and nitridation was performed at different times to control the N-doping content.With an increase in the N-doping content,the morphological properties of the nanosheet changed significantly,namely,the 2D nanosheets transformed into irregularly shaped nanoparticles.Furthermore,the ECR performance of Zn O electrocatalysts with different N-doping content was assessed in 1.0 M KHCO_(3) electrolyte using a gas-diffusion electrode-based ECR cell.While the ECR activity increased after a small amount of N doping,it decreased for higher N doping content.Among them,the N:ZnO-1 h electrocatalysts showed the best CO selectivity,with a faradaic efficiency(FE_(CO))of 92.7%at-0.73 V vs.reversible hydrogen electrode(RHE),which was greater than that of an undoped Zn O electrocatalyst(FE_(CO)of 63.4%at-0.78 V_(RHE)).Also,the N:ZnO-1 h electrocatalyst exhibited outstanding durability for 16 h,with a partial current density of-92.1 mA cm^(-2).This improvement of N:ZnO-1 h electrocatalyst can be explained by density functional theory calculations,demonstrating that this improvement of N:ZnO-1 h electrocatalyst comes from(ⅰ)the optimized active sites lowering the free energy barrier for the rate-determining step(RDS),and(ⅱ)the modification of electronic structure enhancing the electron transfer rate by N doping.

Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.