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
Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating ...Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating combustion, the desired nanocrystalline perovskite LaMnO3 was obtained and no further calcination was carried out. The possible processes of combustion reaction were discussed according to the principle of propellant chemistry. The autocombustion and thermal decomposition of the precursor were investigated using the TG-DTA and FT-IR techniques. The influences of glycine-nitrate molar ratio and heat-treatment temperature on the perovskite phase formation and crystallite size of as-burnt powder were studied by XRD. The morphology and size of the as-burnt powder before and after milling were characterized and compared by TEM.展开更多
Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theres...Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.展开更多
The effects of cerium nitrite on corrosion behaviors of carbon steel in simulated concrete pore solutions were studied with the methods of linear polarization, electrochemical impedance spectroscopy and surface analys...The effects of cerium nitrite on corrosion behaviors of carbon steel in simulated concrete pore solutions were studied with the methods of linear polarization, electrochemical impedance spectroscopy and surface analysis. In pore solutions in the presence of Ce（NO3）3？6H2O, the corrosion potential, polarization resistance and impedance of carbon steel obviously increased in contrast to the situation in the absence of cerium salts. The pore solution with [NO2-] / [Cl-] = 0.3 and 0.1% Ce（NO3）3？6H2O, carbon steel shows better corrosion resistance than that in the pore solution with [NO2-] / [Cl-] = 0.6, which indicates that a small amount of Ce（NO3）3？6H2O in pore solutions can effectively promote passivation of the steel and reduce the threshold [NO2-] / [Cl-] ratio for corrosion control. The surface layer formed in cerium salt containing pore solutions is more compact and smooth and 1.36%Ce is examined on the sample surface. The addition of 0.1% Ce（NO3）3？6H2O in pore solutions can decrease the corrosion rate of steel in pore solutions and has little influence on pH change of the solutions. However, more cerium nitrate addition above 0.1% may result in pH decrease of the solution.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Project supported bythe National Natural Science Foundation of China (50306008) and the Fund fromthe Preli minary Research Project of General Equipment Ministry (41328030507)
文摘Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating combustion, the desired nanocrystalline perovskite LaMnO3 was obtained and no further calcination was carried out. The possible processes of combustion reaction were discussed according to the principle of propellant chemistry. The autocombustion and thermal decomposition of the precursor were investigated using the TG-DTA and FT-IR techniques. The influences of glycine-nitrate molar ratio and heat-treatment temperature on the perovskite phase formation and crystallite size of as-burnt powder were studied by XRD. The morphology and size of the as-burnt powder before and after milling were characterized and compared by TEM.
文摘Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.
基金the National Natural Science Foundation of China(No.50731004)Technology Support Programs of China(No.2007BAB27B04-N43CTT)
文摘The effects of cerium nitrite on corrosion behaviors of carbon steel in simulated concrete pore solutions were studied with the methods of linear polarization, electrochemical impedance spectroscopy and surface analysis. In pore solutions in the presence of Ce（NO3）3？6H2O, the corrosion potential, polarization resistance and impedance of carbon steel obviously increased in contrast to the situation in the absence of cerium salts. The pore solution with [NO2-] / [Cl-] = 0.3 and 0.1% Ce（NO3）3？6H2O, carbon steel shows better corrosion resistance than that in the pore solution with [NO2-] / [Cl-] = 0.6, which indicates that a small amount of Ce（NO3）3？6H2O in pore solutions can effectively promote passivation of the steel and reduce the threshold [NO2-] / [Cl-] ratio for corrosion control. The surface layer formed in cerium salt containing pore solutions is more compact and smooth and 1.36%Ce is examined on the sample surface. The addition of 0.1% Ce（NO3）3？6H2O in pore solutions can decrease the corrosion rate of steel in pore solutions and has little influence on pH change of the solutions. However, more cerium nitrate addition above 0.1% may result in pH decrease of the solution.
