Antimony(Sb)is an intriguing anode material for Li-ion batteries(LIBs)owing to its high theoretical capacity of 660 m Ah·g^(-1)and appropriate working potential of~0.8 V(vs.Li^(+)/Li).However,just like all alloyi...Antimony(Sb)is an intriguing anode material for Li-ion batteries(LIBs)owing to its high theoretical capacity of 660 m Ah·g^(-1)and appropriate working potential of~0.8 V(vs.Li^(+)/Li).However,just like all alloying materials,the Sb anode suffers from huge volume expansion(230%)during repeated insertion/extraction of Li+ions,resulting in structural deterioration and rapid capacity decay.In this work,a novel amorphous Sb/C composite with atomically dispersed Sb particles in carbon matrix is prepared via a straightforward high-energy ball milling approach.The intimate intermixing of amorphous Sb with C provides homogeneous element distribution and isotropic volume expansion during cycling,resulting in persistent structural stability.Meanwhile,the disordered structure of amorphous material shortens the diffusion distance of lithium ions/electrons,promoting fast reaction kinetics and rate capability.Benefiting from the aforementioned effects,the amorphous Sb/C exhibits a high reversible capacity of537.4 m Ah·g^(-1)at 0.1 A·g^(-1)and retains 201.0 m Ah·g^(-1)at an ultrahigh current rate of 10.0 A·g^(-1).Even after 1500deep cycles at 2.0 A·g^(-1),the amorphous Sb/C electrode still maintains 86.3%of its initial capacity,which outperforms all existing Sb-based anodes reported so far.Postmortem analysis further reveals a greatly reduced volume variation of merely 34.6%for the amorphous Sb/C electrode,much lower than that of 223.1%for crystalline Sb materials.This study presents a new approach to stabilizing Sb-based alloy anodes and contributes to the construction of high-performance amorphous anode materials for LIBs,enabling advanced energy storage.展开更多
The definitions of θ-ray pattern proposed to establish some new results matrix and θ-ray matrix are firstly on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A ...The definitions of θ-ray pattern proposed to establish some new results matrix and θ-ray matrix are firstly on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A ∈ C^n×n and nonempty α （n） = {1,2,... ,n} are proposed such that A is an invertible H-matrix if A（α） and A/α are both invertible H-matrices. Furthermore, the important results on Schur complement for general H-matrices are presented to give the different necessary and sufficient conditions for the matrix A E HM and the subset α C （n） such that the Schur complement matrix A/α∈ HI^n-｜α｜ or A/α ∈ Hn-｜α｜^M or A/α ∈ H^n-｜ α｜^S.展开更多
基金supported by the National Natural Science Foundation of China(Nos.22279093 and 22075216)the Natural Science Foundation of Hubei Province,China(No.2022CFB096)the Fundamental Research Funds for Central University(Nos.2042022gf0005 and 2042021kf0194)。
文摘Antimony(Sb)is an intriguing anode material for Li-ion batteries(LIBs)owing to its high theoretical capacity of 660 m Ah·g^(-1)and appropriate working potential of~0.8 V(vs.Li^(+)/Li).However,just like all alloying materials,the Sb anode suffers from huge volume expansion(230%)during repeated insertion/extraction of Li+ions,resulting in structural deterioration and rapid capacity decay.In this work,a novel amorphous Sb/C composite with atomically dispersed Sb particles in carbon matrix is prepared via a straightforward high-energy ball milling approach.The intimate intermixing of amorphous Sb with C provides homogeneous element distribution and isotropic volume expansion during cycling,resulting in persistent structural stability.Meanwhile,the disordered structure of amorphous material shortens the diffusion distance of lithium ions/electrons,promoting fast reaction kinetics and rate capability.Benefiting from the aforementioned effects,the amorphous Sb/C exhibits a high reversible capacity of537.4 m Ah·g^(-1)at 0.1 A·g^(-1)and retains 201.0 m Ah·g^(-1)at an ultrahigh current rate of 10.0 A·g^(-1).Even after 1500deep cycles at 2.0 A·g^(-1),the amorphous Sb/C electrode still maintains 86.3%of its initial capacity,which outperforms all existing Sb-based anodes reported so far.Postmortem analysis further reveals a greatly reduced volume variation of merely 34.6%for the amorphous Sb/C electrode,much lower than that of 223.1%for crystalline Sb materials.This study presents a new approach to stabilizing Sb-based alloy anodes and contributes to the construction of high-performance amorphous anode materials for LIBs,enabling advanced energy storage.
基金Acknowledgements This work was supported in part by the Science Foundation of the Education Department of Shaanxi Province of China （No. 2013JK0593）, the Scientific Research Foundation of Xi＇an Polytechnic University （No. BS1014）, the China Postdoctoral Science Foundation （No. 20110491668）, and the National Natural Science Foundations of China （Grant Nos. 11201362, 11271297, 11101325, 11171270）.
文摘The definitions of θ-ray pattern proposed to establish some new results matrix and θ-ray matrix are firstly on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A ∈ C^n×n and nonempty α （n） = {1,2,... ,n} are proposed such that A is an invertible H-matrix if A（α） and A/α are both invertible H-matrices. Furthermore, the important results on Schur complement for general H-matrices are presented to give the different necessary and sufficient conditions for the matrix A E HM and the subset α C （n） such that the Schur complement matrix A/α∈ HI^n-｜α｜ or A/α ∈ Hn-｜α｜^M or A/α ∈ H^n-｜ α｜^S.
