Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and on...Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P_(2)O_(7) unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.展开更多
Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions be...Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with a...Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.展开更多
This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensiona...This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.展开更多
CO_(2) is the most cost-eff ective and abundant carbon resource,while the reverse water-gas reaction(rWGS)is one of the most eff ective methods of CO_(2) utilization.This work presents a comparative study of rWGS acti...CO_(2) is the most cost-eff ective and abundant carbon resource,while the reverse water-gas reaction(rWGS)is one of the most eff ective methods of CO_(2) utilization.This work presents a comparative study of rWGS activity for perovskite systems based on AFeO_(3)(where A=Ce,La,Y).These systems were synthesized by solution combustion synthesis(SCS)with diff erent ratios of fuel(glycine)and oxidizer(φ),diff erent amounts of NH 4 NO_(3),and the addition of alumina or silica as supports.Various techniques,including X-ray diff raction analysis,thermogravimetric analysis,Fourier transform infrared spectroscopy(FTIR),scanning electron microscopy,energy-dispersive X-ray spectroscopy,N 2-physisorption,H_(2) temper-ature-programmed reduction,temperature-programmed desorption of H_(2) and CO_(2),Raman spectroscopy,and in situ FTIR,were used to relate the physicochemical properties with the catalytic performance of the obtained composites.Each specifi c perovskite-containing system(either bulk or supported)has its own optimalφand NH_(4) NO_(3) amount to achieve the highest yield and dispersion of the perovskite phase.Among all synthesized systems,bulk SCS-derived La-Fe-O systems showed the highest resistance to reducing environments and the easiest hydrogen desorption,outperforming La-Fe-O produced by solgel combustion(SGC).CO_(2) conversion into CO at 600°C for bulk ferrite systems,depending on the A-cation type and preparation method,follows the order La(SGC)<Y<Ce<La(SCS).The diff erences in properties between La-Fe-O obtained by the SCS and SGC methods can be attributed to diff erent ratios of oxygen and lanthanum vacancy contributions,hydroxyl coverage,morphology,and free iron oxide presence.In situ FTIR data revealed that CO_(2) hydrogenation occurs through formates generated under reaction conditions on the bulk system based on La-Fe-O,obtained by the SCS method.γ-Al_(2)O_(3) improves the dispersion of CeFeO_(3) and LaFeO_(3) phases,the specifi c surface area,and the quantity of adsorbed H_(2) and CO_(2).This led to a signifi cant increase in CO_(2) conversion for supported CeFeO_(3) but not for the La-based system compared to bulk and SiO_(2)-supported perovskite catalysts.However,adding alumina increased the activity per mass for both Ce-and La-based perovskite systems,reducing the amount of rare-earth components in the catalyst and thereby lowering the cost without substantially compromising stability.展开更多
基金National Natural Science Foundation of China,Grant/Award Numbers:21972108,U20A20249,U22A20438Changzhou Science and Technology Bureau,Grant/Award Number:CM20223017Innovation and Technology Commission(ITC)of Hong Kong,The Innovation&Technology Fund(ITF)with Project No.ITS/126/21。
文摘Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P_(2)O_(7) unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.
文摘Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.
基金the two referees for very helpful comments and suggestions to improve the quality of the paper.This work was partially supported by the Natural Science Foundation of Zhejiang province of China(LY21A010017)the National Natural Science Foundation of China(12071106,12171130).
文摘This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.
基金The research was carried out within the State Assignment of the Ministry of Science and Higher Education of the Russian Federation(project No.FFUG-2024-0036)。
文摘CO_(2) is the most cost-eff ective and abundant carbon resource,while the reverse water-gas reaction(rWGS)is one of the most eff ective methods of CO_(2) utilization.This work presents a comparative study of rWGS activity for perovskite systems based on AFeO_(3)(where A=Ce,La,Y).These systems were synthesized by solution combustion synthesis(SCS)with diff erent ratios of fuel(glycine)and oxidizer(φ),diff erent amounts of NH 4 NO_(3),and the addition of alumina or silica as supports.Various techniques,including X-ray diff raction analysis,thermogravimetric analysis,Fourier transform infrared spectroscopy(FTIR),scanning electron microscopy,energy-dispersive X-ray spectroscopy,N 2-physisorption,H_(2) temper-ature-programmed reduction,temperature-programmed desorption of H_(2) and CO_(2),Raman spectroscopy,and in situ FTIR,were used to relate the physicochemical properties with the catalytic performance of the obtained composites.Each specifi c perovskite-containing system(either bulk or supported)has its own optimalφand NH_(4) NO_(3) amount to achieve the highest yield and dispersion of the perovskite phase.Among all synthesized systems,bulk SCS-derived La-Fe-O systems showed the highest resistance to reducing environments and the easiest hydrogen desorption,outperforming La-Fe-O produced by solgel combustion(SGC).CO_(2) conversion into CO at 600°C for bulk ferrite systems,depending on the A-cation type and preparation method,follows the order La(SGC)<Y<Ce<La(SCS).The diff erences in properties between La-Fe-O obtained by the SCS and SGC methods can be attributed to diff erent ratios of oxygen and lanthanum vacancy contributions,hydroxyl coverage,morphology,and free iron oxide presence.In situ FTIR data revealed that CO_(2) hydrogenation occurs through formates generated under reaction conditions on the bulk system based on La-Fe-O,obtained by the SCS method.γ-Al_(2)O_(3) improves the dispersion of CeFeO_(3) and LaFeO_(3) phases,the specifi c surface area,and the quantity of adsorbed H_(2) and CO_(2).This led to a signifi cant increase in CO_(2) conversion for supported CeFeO_(3) but not for the La-based system compared to bulk and SiO_(2)-supported perovskite catalysts.However,adding alumina increased the activity per mass for both Ce-and La-based perovskite systems,reducing the amount of rare-earth components in the catalyst and thereby lowering the cost without substantially compromising stability.
