Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

Effect of an abrupt change in pulling rate on microstructures of directionally solidified Al2O3-Er3Al5O12 eutectic and off-eutectic composite ceramics

Directionally solidified microstructures of Al₂O₃-Er₃Al₅O₁₂ eutectic and off-eutectic in situ composite ceramics were explored under abrupt-change pulling rate conditions. Corresponding temperature distributions and interface locations were studied. In eutectic composition, fluctuation of eutectic spacing occurred when the pulling rate increased abruptly. A gradually increase or abrupt increase in eutectic spacing was observed when the pulling rate decreased abruptly. In hypoeutectic and hypereutectic compositions, formation of the primary phases were suppressed when the pulling rate increased abruptly from 10?µm/s to 100?µm/s, while primary phases precipitated when the pulling rate decreased abruptly from 100?µm/s to 10?µm/s. The interface altitude decreased after the pulling rate increased abruptly, but increased after the pulling rate decreased abruptly. The liquid composition restriction (around the eutectic composition) at the eutectic interface plays an important role in the suppression of the primary dendrite and coupled eutectic oxides can be obtained in off-eutectic compositions even under higher solidification rate conditions.     

离子液体水热法辅助合成稀土Ce掺杂ZnO纳米材料的制备及其应用研究

以1-甲基咪唑和氯代正丁烷为原料,合成1-丁基-3-甲基咪唑氯盐离子液体;以醋酸锌[Zn(Ac)2]、硫酸锌(ZnSO4)和氯化锌(ZnCl2)为锌源,在1-丁基-3-甲基咪唑氯盐离子液体和丙氨酸体系中与硝酸铈反应,经水热合成法制备得到Ce掺杂的纳米ZnO。采用扫描电子显微镜(SEM)、紫外-可见光吸收光谱(UV-Vis)、X射线衍射仪(XRD)、X射线光电子能谱分析(XPS)和红外光谱(FT-IR)对产品进行表征。以亚甲基蓝(MB)为目标降解物,采用UV-Vis检测,考察了Ce掺杂的纳米ZnO的光催化活性。研究表明,焙烧温度对光催化的晶体结构和光催化活性产生较大的影响;2%Ce/ZnO、焙烧温度为500℃、催化时间为30 min、亚甲基蓝用量0.05 g、pH值为10时降解率可达99.5%以上。     

Porous sunflower plate-like NiFe2O4/CoNi–S heterostructure as efficient electrocatalyst for overall water splitting

Constructing high-efficient and nonprecious electrocatalysts is of primary importance for improving the efficiency of water splitting. Herein, a novel sunflower plate-like NiFe₂O₄/CoNi–S nanosheet heterostructure was fabricated via facile hydrothermal and electrodeposition methods. The as-fabricated NiFe₂O₄/CoNi–S heterostructure array exhibits remarkable bifunctional catalytic activity and stability toward oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) in alkaline media. It presents a small overpotential of 219 mV and 149 mV for OER and HER, respectively, to produce a current density of 10 mA cm^?2. More significantly, when the obtained electrodes are used as both the cathode and anode in an electrolyzer, a voltage of 1.57 V is gained at 10 mA cm^?2, with superior stability for 72 h. Such outstanding properties are ascribed to: the 3D porous network structure, which exposes more active sites and accelerates mass transfer and gas bubble emission; the high conductivity of CoNi–S, which provides faster charge transport and thus promotes the electrocatalytic reaction of the composites; and the effective interface engineering between NiFe₂O₄ (excellent performance for OER) and CoNi–S (high activity for HER), which leads to a shorter transport pathway and thus expedites electron transfer. This work provides a new strategy for designing efficient and inexpensive electrocatalysts for water splitting.