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Single-pushout transformation in a category of spans, in some sense a generalization of the usual notion of partial morphism, is studied in this paper. Contrary to the usual notion of partial morphism, spans are single objects instead of equivalence classes. A necessary condition for the existence of the pushout of two spans is established which involves properties of the base category, from which the category of spans is derived, as well as properties of the spans themselves. Several interesting categories of partial morphisms of hypergraphs are proved to satisfy the necessary condition.

Technology at the nanoscale has become one of the main challenges in science as new physical effects appear and can be modulated at will. Materials for spintronics, electronics, optoelectronics, sensing, energy applications and new generations of functionalized materials are taking advantage of the low dimensionality, improving their properties and opening a new range of applications. As developments in materials science are pushing to the size limits of physics and chemistry, there is a critical need for understanding the origin of these unique physical and/or chemical properties and relate them to the changes originated at the atomic scale, e.g.: catalyst active sites related to surface states. In particular, the development of technologies for H2 production or CO2 reduction strongly relies on an abundant supply of protons and electrons liberated by water oxidation. [1-2] Therefore, photoelectrochemical (PEC) water oxidation is an important anodic half-cell process in the development of a sustainable artificial solar fuel system. In the PEC devices design, coupling water oxidation catalysts with active photoanode materials has become the most promising methodology, since the attachment/integration of the catalyst on the semiconductor light absorbers could kinetically facilitate interfacial charge transfer reactions. In the present work, I will show how combining advanced electron microscopy imaging with related spectroscopies in an aberration corrected STEM will allow us to probe the elemental composition and electronic structure simultaneously with the optical properties in unprecedented spatial detail. We have fabricated ITO/Fe2O3/Fe2TiO5/FeNiOOH multi-layers nanowire heterostructures via combination of sputtering, hydrothermal, ALD, photo-electrodepositon methods for photoelectrochemical (PEC) oxygen evolution application. Structural, spectroscopic and electrochemical investigations disclose that the origin of the superior catalytic performance is owing to the interfacial coupling effect of ITO underlayer (Sn doping and conductivity promoter), ultrathin Fe2TiO5 coating (Ti doping, energetics and surface state density modulation) and FeNiOOH eletrocatalyst (varying surface state energy level). [2] Meanwhile, an alternative earth-abundant CoFe prussian blue analogues (CoFe PBA) is incorporated in core-shell Fe2O3/Fe2TiO5 type II heterojunction nanowires as photoanodes for PEC water oxidation. The observed photocurrent is improved from 0.12 mA cm-2 to 1.25 mA cm-2 at 1.23 V vs. RHE under illumination by involvement of ultrathin Fe2TiO5 layer and CoFe PBA WOCs coating. Further investigation of the PEC mechanisms via photoelectrochemical impedance spectroscopy unveils that the enhanced PEC performance of hematite nanowires is attributed to the enhanced charge transfer efficiency owing to the tuned energy level and density of surface state. [3-4] References [1] Félix Urbain, Pengyi Tang, Nina M. Carretero, Teresa Andreu, Luís G. Gerling, Cristóbal Voz, Jordi Arbiol, Joan R. Morante, Energy & Environmental Science , 10, 2256-2266 (2017). [2] Pengyi Tang, HaiBing Xie, Carles Ros, LiJuan Han, Martí Biset-Peiró, Yongmin He, Wesley Kramer, Alejandro Perez-Rodriguez, Edgardo Saucedo, Jose Galan-Mascaros, Teresa Andreu, Joan R. Morante, Jordi Arbiol, Energy & Environmental Science , 10, 2124-2136 (2017). [3] Lijuan Han, Pengyi Tang, Alvaro Reyes-Carmona, Barbara Rodriguez-Garcia, Mabel Torrens, Joan Ramon Morante, Jordi Arbiol, Jose Ramon Galan-Mascaros, Journal of the American Chemical Society , 138, 16037-16045 (2016). [4] PengYi Tang, LiJuan Han, Paul Paciok, Marti Biset Peiro, Hong-Chu Du, Xian-Kui Wei, Lei Jin, Hai-Bing Xie, Qin Shi, Teresa Andreu, Joan Ramon Morante, Mónica Lira-Cantú, Marc Heggen, Rafal E. Dunin-Borkowski, José Ramón Galán-Mascarós, Jordi Arbiol, to be submitted.