Sodium superionic conductors(NASICONs)have attracted enormous attention owing to their excellent ionic diffusion and structural stability.However,the high cost of vanadium,limited capacity due to fewer redox reactions...Sodium superionic conductors(NASICONs)have attracted enormous attention owing to their excellent ionic diffusion and structural stability.However,the high cost of vanadium,limited capacity due to fewer redox reactions,and low electronic conductivity restrict their practical application.Herein,we designed Na_(3.5)V_(0.5)Mn_(0.5)Fe_(0.5)Ti_(0.5)(PO_(4))3 (NVMFTP)medium entropy NASICON with multi-electron reactions as a fast sodium storage cathode for sodium-ion batteries(SIBs).The incorporation of Fe,Mn and Ti not only reduces the cost but also activates multi-redox reactions of V^(2+)/V^(3+),Ti^(3+)/Ti^(4+),Fe^(2+)/Fe^(3+),V^(3+)/V^(4+),Mn^(2+)/Mn^(3+),V^(4+)/V^(5+).Owing to distinctive structural design with medium entropy,the NVMFTP delivered 168 mAh·g^(−1) at 0.5C with a remarkable rate capability of 93.51 mAh·g^(−1) at 60C and steady long-term cycling performance till 5000 cycles.More importantly,NVMFTP takes only 11 min to achieve 80%SOC at 5C.The in-situ and ex-situ X-ray diffraction(XRD)further demonstrate reversible multi-electron reaction mechanisms of slow charging and fast charging.NVMFTP/HC full cell shows 110 mAh·g^(−1) capacity and 208 Wh·kg^(−1) energy density.This study will provide comprehensive insight into developing low-cost,cutting-edge materials for SIBs.展开更多
Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaus...Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaussian diffusion models,concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula,or HJB equations.The explicit solutions to the related forward-backward equations are also given.展开更多
基金supported by the National Natural Science Foundation of China(Nos.52027801 and 92263203)the National Key R&D Program of China(Nos.2022YFA1203902 and 2022YFA1200093)and the China-Germany Collaboration Project(No.M-0199)。
文摘Sodium superionic conductors(NASICONs)have attracted enormous attention owing to their excellent ionic diffusion and structural stability.However,the high cost of vanadium,limited capacity due to fewer redox reactions,and low electronic conductivity restrict their practical application.Herein,we designed Na_(3.5)V_(0.5)Mn_(0.5)Fe_(0.5)Ti_(0.5)(PO_(4))3 (NVMFTP)medium entropy NASICON with multi-electron reactions as a fast sodium storage cathode for sodium-ion batteries(SIBs).The incorporation of Fe,Mn and Ti not only reduces the cost but also activates multi-redox reactions of V^(2+)/V^(3+),Ti^(3+)/Ti^(4+),Fe^(2+)/Fe^(3+),V^(3+)/V^(4+),Mn^(2+)/Mn^(3+),V^(4+)/V^(5+).Owing to distinctive structural design with medium entropy,the NVMFTP delivered 168 mAh·g^(−1) at 0.5C with a remarkable rate capability of 93.51 mAh·g^(−1) at 60C and steady long-term cycling performance till 5000 cycles.More importantly,NVMFTP takes only 11 min to achieve 80%SOC at 5C.The in-situ and ex-situ X-ray diffraction(XRD)further demonstrate reversible multi-electron reaction mechanisms of slow charging and fast charging.NVMFTP/HC full cell shows 110 mAh·g^(−1) capacity and 208 Wh·kg^(−1) energy density.This study will provide comprehensive insight into developing low-cost,cutting-edge materials for SIBs.
文摘Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaussian diffusion models,concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula,or HJB equations.The explicit solutions to the related forward-backward equations are also given.
