Transition metal phosphides(TMPs)have emerged as promising electrocatalysts to enhance the slow kinetic process of oxygen evolution reaction(OER).Framelike hollow nanostructures(nanoframes,NFs)provide the open structu...Transition metal phosphides(TMPs)have emerged as promising electrocatalysts to enhance the slow kinetic process of oxygen evolution reaction(OER).Framelike hollow nanostructures(nanoframes,NFs)provide the open structure with more accessible active sites and sufficient channels into the interior volume.Here,we report the fabrication of bimetallic Co-Fe phosphide NFs(Co-Fe-P NFs)via an intriguing temperature-controlled strategy for the preparation of precursors followed by phosphidation.The precursors,Co-Fe Prussian blue analogues(Co-Fe PBAs)are prepared by a precipitation method with Co^(2+)and[Fe(CN)_(6)]^(3−),which experience a structural conversion from nanocubes to NFs by increasing the aging temperature from 5 to 35℃.The experimental results indicate that this conversion is attributable to the preferentially epitaxial growth on the edges and corners of nanocubes,triggered by intramolecular electron transfer at an elevated aging temperature.The as-prepared Co-Fe-P NFs catalyst shows remarkable catalytic activity toward OER with a low overpotential of 276 mV to obtain a current density of 10 mA cm^(−2),which is superior to the reference samples(Co-Fe-P nanocubes)and most of the recently reported TMPs-based electrocatalysts.The synthetic strategy can be extended to fabricate Co-Fe dichalcogenide NFs,thereby holding a great promise for the broad applications in energy storage and conversion systems.展开更多
It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q...It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.展开更多
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced...We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the nae continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak,intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.展开更多
基金supported by the National Natural Science Foundation of China(21872105 and 22072107)the Natural Science Foundation of Zhejiang Province(LQ20B030001 and LY20E020002)。
文摘Transition metal phosphides(TMPs)have emerged as promising electrocatalysts to enhance the slow kinetic process of oxygen evolution reaction(OER).Framelike hollow nanostructures(nanoframes,NFs)provide the open structure with more accessible active sites and sufficient channels into the interior volume.Here,we report the fabrication of bimetallic Co-Fe phosphide NFs(Co-Fe-P NFs)via an intriguing temperature-controlled strategy for the preparation of precursors followed by phosphidation.The precursors,Co-Fe Prussian blue analogues(Co-Fe PBAs)are prepared by a precipitation method with Co^(2+)and[Fe(CN)_(6)]^(3−),which experience a structural conversion from nanocubes to NFs by increasing the aging temperature from 5 to 35℃.The experimental results indicate that this conversion is attributable to the preferentially epitaxial growth on the edges and corners of nanocubes,triggered by intramolecular electron transfer at an elevated aging temperature.The as-prepared Co-Fe-P NFs catalyst shows remarkable catalytic activity toward OER with a low overpotential of 276 mV to obtain a current density of 10 mA cm^(−2),which is superior to the reference samples(Co-Fe-P nanocubes)and most of the recently reported TMPs-based electrocatalysts.The synthetic strategy can be extended to fabricate Co-Fe dichalcogenide NFs,thereby holding a great promise for the broad applications in energy storage and conversion systems.
基金supported by Natural Science Foundation of Hebei Province(Grant No.A2012205079)Science Foundation of Hebei Normal University(Grant No.L2011B02)the 100 Talents Program of the Chinese Academy of Sciences for support
文摘It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.
基金supported by Engineering and Physical Sciences Research Council (EPSRC) (Grant No. EP/J001392/1)the Danish Council for Independent Research under the Sapere Aude program
文摘We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the nae continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak,intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.
