On self-affine tiles that are homeomorphic to a ball

Let M be a 3×3 integer matrix which is expanding in the sense that each of its eigenvalues is greater than 1 in modulus and let D?Z^(3)be a digit set containing|det M|elements.Then the unique nonempty compact set T=T(M,D)defined by the set equation MT=T+D is called an integral self-affine tile if its interior is nonempty.If D is of the form D={0,v,...,(|det M|-1)v},we say that T has a collinear digit set.The present paper is devoted to the topology of integral self-affine tiles with collinear digit sets.In particular,we prove that a large class of these tiles is homeomorphic to a closed 3-dimensional ball.Moreover,we show that in this case,T carries a natural CW complex structure that is defined in terms of the intersections of T with its neighbors in the lattice tiling{T+z:z∈Z^(3)}induced by T.This CW complex structure is isomorphic to the CW complex defined by the truncated octahedron.

Thermal annealing synthesis of double-shell truncated octahedral Pt-Ni alloys for oxygen reduction reaction of polymer electrolyte membrane fuel cells

Shape-controlled Pt-Ni alloys usually offer an exceptional electrocatalytic activity toward the oxygen reduction reaction(ORR)of polymer electrolyte membrane fuel ceils(PEMFCs),whose tricks lie in welldesigned structures and surface morphologies.In this paper,a novel synthesis of truncated octahedral PtNi_(3.5) alloy catalysts that consist of homogeneous Pt-Ni alloy cores enclosed by NiO-Pt double shells through thermally annealing defective heterogeneous PtNi35 alloys is reported.By tracking the evolution of both compositions and morphologies,the outward segregation of both PtOv and NiO are first observed in Pt-Ni alloys.It is speculated that the diffusion of low-coordination atoms results in the formation of an energetically favorable truncated octahedron while the outward segregation of oxides leads to the formation of NiO-Pt double shells.It is very attractive that after gently removing the NiO outer shell,the dealloyed truncated octahedral core-shell structure demonstrates a greatly enhanced ORR activity.The asobtained truncated octahedral Pt_(2.1)Ni core-shell alloy presents a 3.4-folds mass-specific activity of that for unannealed sample,and its activity preserves 45.4%after 30000 potential cycles of accelerated degradation test(ADT).The peak power density of the dealloyed truncated octahedral Pt2jNi core-shell alloy catalyst based membrane electrolyte assembly(MEA)reaches 679.8 mW/cm^(2),increased by 138.4 mW/cm^(2) relative to that based on commercial Pt/C.

A mild one-step solvothermal route to truncated octahedral magnetite crystals

Perfect truncated octahedral magnetite crystals were successfully synthesized from FeCl3.6H2O and poly（acrylic acid） （PAA） in an alkaline ethylene glycol solution via a mild one-step solvothermal process. The structure and morphologies of the obtained products were characterized by powder X-ray diffraction （XRD）, Raman spectroscopy, scanning electron microscopy （SEM）, and transmission electron microscopy （TEM）. The effects of synthetic parameters including reaction temperature, reaction time, and the amount of alkali on the morphological evolution of the truncated octahedral magnetite crystals were systematically explored. 160℃ was found to be the optimum temperature for the formation of truncated octahedral magnetite crystals. Below 160 ℃, little magnetite was formed. Above 160℃, the truncated octahedrons were gradually transformed into irregular-shaped polyhedrons. Alkali is indispensable in promoting the formation of magnetite at mild temperatures. The truncated octahedral magnetite crystals were found to be ferromagnetic and had a saturation magnetization of about 83 emu/g.

Platinum nickel alloy-MXene catalyst with inverse opal structure for enhanced hydrogen evolution in both acidic and alkaline solutions

The development of an efficient Pt-based electrocatalyst in acidic and alkaline electrolytes is of great significance to the field of electrocatalytic hydrogen evolution.Herein,we report a strategy for in situ growth of Pt_(3)Ni truncated octahedrons on Ti3C2Tx nanosheets and then obtain an ordered porous catalyst via a template method.Meanwhile,we use the finite element calculation to clarify the relationship between the component structure and performance and find that the performance of the spherical shell microstructure catalyst is higher than that of the disc structure catalyst,which is also verified by experiments.The experimental analysis shows that the ordered porous catalyst is conducive to enhancing electrocatalytic hydrogen evolution activity in acidic and alkaline electrolytes.In an acidic solution,the overpotential is 25 mV(10 mA·cm^(−2)),and the Tafel slope is 22.86 mV·dec−1.In an alkaline solution,the overpotential is 44.1 mV(10 mA·cm^(−2)),and the Tafel slope is 39.06 mV·dec−1.The synergistic coupling between Ti3C2Tx and Pt_(3)Ni nanoparticles improves the stability of the catalyst.The in situ growth strategy and design of microstructure with its correlation with catalytic performance represent critical steps toward the rational synthesis of catalysts with excellent catalytic activity.