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
The microstructure of hypoeutectic Al-9.21wt.%Si alloy solidified under 5.5 GPa was studied. The results show that the solidification microstructure is refined. The primary a phase is the extended solid solution. The ...The microstructure of hypoeutectic Al-9.21wt.%Si alloy solidified under 5.5 GPa was studied. The results show that the solidification microstructure is refined. The primary a phase is the extended solid solution. The solid solubility of Si in α phase is up to 8.26wt.%. The growth mode of the α phase is cellular, and this cellular growth mechanism is interpreted in terms of the decrease of the diffusivity and the extended solid solution under high pressure. By calculation, it can be known that the the diffusivity of solute in the liquid under normal pressure is as high as two hundred times that under high pressure. The microhardness of the hypoeutectic Al-Si alloy solidified under high pressure is higher than that of solidified under normal pressure. After annealing, Si precipitates from the solid solution, the microhardness of the alloy decrease, but, still higher than that of solidified under normal pressure.展开更多
In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous b...In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.展开更多
The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be ...The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.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.
基金supported by the National Natural Science Foundation of China(grant No.59571040)
文摘The microstructure of hypoeutectic Al-9.21wt.%Si alloy solidified under 5.5 GPa was studied. The results show that the solidification microstructure is refined. The primary a phase is the extended solid solution. The solid solubility of Si in α phase is up to 8.26wt.%. The growth mode of the α phase is cellular, and this cellular growth mechanism is interpreted in terms of the decrease of the diffusivity and the extended solid solution under high pressure. By calculation, it can be known that the the diffusivity of solute in the liquid under normal pressure is as high as two hundred times that under high pressure. The microhardness of the hypoeutectic Al-Si alloy solidified under high pressure is higher than that of solidified under normal pressure. After annealing, Si precipitates from the solid solution, the microhardness of the alloy decrease, but, still higher than that of solidified under normal pressure.
基金supported by the National NSF of China(11571088)NSF of Zhejiang Province(LY13A010020)Program(HNUEYT2013)
文摘In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.
基金Project supported by the National Natural Science Foundation of China (No.12071106) and the Science Foundation of the Ministry of Education of China.
文摘The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.
