The Diagonal Functors

We obtain new categorical proofs that generalize the diagonal principles introduced in Castillo and Moreno (Israel J. Math. 140:253–270, 2004) to study the automorphic and partially automorphic character of Banach spaces. We then introduce and study the automorphy index for a Banach space, showing that while . This research has been supported in part by project MTM2004-02635.     

Research on Molecular Structure and Electronic Properties of Ln3+ (Ce3+, Tb3+, Pr3+)/Li+ and Eu2+ Co-Doped Sr2Si5N8 via DFT Calculation

We use density functional theory (DFT) to study the molecular structure and electronic band structure of Sr₂Si₅N₈:Eu²⁺ doped with trivalent lanthanides (Ln³⁺ = Ce³⁺, Tb³⁺, Pr³⁺). Li⁺ was used as a charge compensator for the charge imbalance caused by the partial replacement of Sr²⁺ by Ln³⁺. The doping of Ln lanthanide atom causes the structure of Sr₂Si₅N₈ lattice to shrink due to the smaller atomic radius of Ln³⁺ and Li⁺ compared to Sr²⁺. The doped structure’s formation energy indicates that the formation energy of Li⁺, which is used to compensate for the charge imbalance, is the lowest when the Sr2 site is doped. Thus, a suitable Li⁺ doping site for double-doped lanthanide ions can be provided. In Sr₂Si₅N₈:Eu²⁺, the doped Ce³⁺ can occupy partly the site of Sr₁²⁺ ([SrN₈]), while Eu²⁺ accounts for Sr₁²⁺ and Sr₂²⁺ ([SrN₁₀]). When the Pr³⁺ ion is selected as the dopant in Sr₂Si₅N₈:Eu²⁺, Pr³⁺ and Eu²⁺ would replace Sr₂²⁺ simultaneously. In this theoretical model, the replacement of Sr²⁺ by Tb³⁺ cannot exist reasonably. For the electronic structure, the energy level of Sr₂Si₅N₈:Eu²⁺/Li⁺ doped with Ce³⁺ and Pr³⁺ appears at the bottom of the conduction band or in the forbidden band, which reduces the energy bandgap of Sr₂Si₅N₈. We use DFT+U to adjust the lanthanide ion 4f energy level. The adjusted 4f-CBM of Ce_Sr1Li_Sr1-Sr₂Si₅N₈ is from 2.42 to 2.85 eV. The energy range of 4f-CBM in Pr_Sr1Li_Sr1-Sr₂Si₅N₈ is 2.75–2.99 eV and its peak is 2.90 eV; the addition of Ce³⁺ in Eu_Sr1Ce_Sr1Li_Sr1 made the 4f energy level of Eu²⁺ blue shift. The addition of Pr³⁺ in Eu_Sr2Pr_Sr2Li_Sr1 makes part of the Eu²⁺ 4f energy level blue shift. Eu²⁺ 4f energy level in Eu_Sr2Ce_Sr1Li_Sr1 is not in the forbidden band, so Eu²⁺ is not used as the emission center.     

The effect of impurities Pb,Bi, and PbO on erosion properties of Lead-Bismuth Eutectic alloy on Fe3O4 oxide film by first principle calculations

The first-principle calculation was performed to study the effect of impurities Pb, Bi, and PbO on erosion properties of liquid lead-bismuth eutectic alloy on the metal oxide (Fe₃O₄) and its surfaces. We found that whether in the bulk or on the surface of Fe₃O₄ the formation energy by substitution of Fe with Bi is slightly larger than that with Pb substitution and the formation energy by substitution of Fe with PbO is much larger than those with Pb and Bi, indicating that PbO has weaker corrosion potential than Pb/Bi. The calculation results show that a tetrahedral site in Fe₃O₄ should be the weakest position where Fe₃O₄ is attacked by these exotic impurities. The corrosion process on the oxide film will be initialized at that position. It can be seen that for the doping case the dissociation energy of Fe atom in the (110) surface has the smallest value, a medium value in (100) surface, and the largest value in (111) surface. Correspondingly, the corrosion resistance of doping Fe₃O₄ film in (110) surface is the weakest one among these surfaces. For the doping-free case, the (100) surface has the weakest corrosion resistance. By comparing the doping case with no-doping case it can be seen that the impurities of Pb, Bi, and PbO will weaken the corrosion resistance of Fe₃O₄ film further. The doping has a negative impact on the stability of the structure and on the corrosion resistance of Fe₃O₄ film. From present results, it is also seen that the replacement of Fe in Fe₃O₄ by multiple impurities is more likely to occur than the replacement of only single impurity.     

具有可调电学和光学性质的双层和三层Janus Ga2SSe

将二维(2D)层状材料的单层堆叠成双层或者少数层,可以很好的调节其光电性质,为该领域发展提供了新的机遇.本文采用第一性原理方法系统地研究了堆叠层数和堆叠次序对双层和三层Janus Ga₂SSe的电学和光学性质的影响.我们发现这些结构的层间距差别很大,而结合能差异却很小.尽管所有的双层和三层Janus Ga₂SSe具有间接带隙,然而其带隙值和载流子有效质量与堆叠层数和堆叠次序密切相关.此外,在Janus Ga₂SSe中,通过增加层数,可以增强其在可见光和紫外区域的吸收系数.同时,通过控制层间堆叠模式,进一步调制其吸收系数,导致在可见光和近紫外区域产生多个吸收峰.我们的结果为双层和三层Janus III族单硫化合物的可调节电学和光学性质提供了有价值的见解,这表明其可能在纳米电子和光电子器件中有着广阔的应用前景.     

Nitrogen‐doped C60 as a robust catalyst for CO oxidation

The O₂ activation and CO oxidation on nitrogen‐doped C₅₉N fullerene are investigated using first‐principles calculations. The calculations indicate that the C₅₉N fullerene is able to activate O₂ molecules resulting in the formation of superoxide species ( ) both kinetically and thermodynamically. The active superoxide can further react with CO to form CO₂ via the Eley–Rideal mechanism by passing a stepwise reaction barrier of only 0.20 eV. Ab initio molecular dynamics (AIMD) simulation is carried out to evidence the feasibility of the Eley–Rideal mechanism. In addition, the second CO oxidation takes place with the remaining atomic O without any activation energy barrier. The full catalytic reaction cycles can occur energetically favorable and suggest a two‐step Eley–Rideal mechanism for CO oxidation with O₂ catalyzed by the C₅₉N fullerene. The catalytic properties of high percentage nitrogen‐doped fullerene (C₄₈N₁₂) is also examined. This work contributes to designing higher effective carbon‐based materials catalysts by a dependable theoretical insight into the catalytic properties of the nitrogen‐doped fullerene. © 2017 Wiley Periodicals, Inc.     

Van der Waals Effects on semiconductor clusters

Van der Waals (vdW) interactions play an important role on semiconductors in nanoscale. Here, we utilized first‐principles calculations based on density functional theory to demonstrate the growth mode transition from prolate to multiunit configurations for Ge_n (n = 10–50) clusters. In agreement with the injected ion drift tube techniques that “clusters with n < 70 can be thought of as loosely bound assemblies of small strongly bound fragments (such as Ge₇ and Ge₁₀),” we found these stable fragments are connected by Ge₆, Ge₉, or Ge₁₀ unit (from bulk diamond), via strong covalent bonds. Our calculated cations usually fragment to Ge₇ and Ge₁₀ clusters, in accordance with the experiment results that the spectra Ge₇ and Ge₁₀ correspond to the mass abundance spectra. By controlling a germanium cluster with vdW interactions parameters in the program or not, we found that the vdW effects strengthen the covalent bond from different units more strikingly than that in a single unit. With more bonds between units than the threadlike structures, the multiunit structures have larger vdW energies, explaining why the isolated nanowires are harder to produce. © 2015 Wiley Periodicals, Inc.     

无网格方法中本质边界条件的处理

基于新的离散模定义，采用移动最小二乘近似方法，给出了场变量的近似表达形式；从约束变分原理出发，给出了无网格方法中新的本质边界条件的处理方案——罚函数法；对权函数、罚函数的选择对计算精度的影响进行了研究。数值计算结果表明该方法不仅简单合理，而且具有较高的精度和稳定性。     

On Material Equations in Second Gradient Electroelasticity

The concern of this work is the derivation of material conservation and balance laws for second gradient electroelasticity. The conservation laws of material momentum, material angular momentum and scalar moment of momentum on the material manifold are derived using Noether's theorem and the exact conditions under which they hold are rigorously studied. The corresponding balance laws are also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

饱和多孔介质耦合系统的几类变分原理

采用变积方法，建立了一组等温准静态下饱和多孔介质的六类变量的广义变分原理，在此基础上，引入约束条件得到五类变量，四类变量，三类变量和二类变量的变分原理，为建立饱和多孔介质的有限元模型提供了基础。     

金属修饰Ti_2N MXene吸附分解H_2S的第一性原理计算

通过第一性原理计算研究了Ti_2NO_2 MXene对H_2S的吸附、分解行为. Ti_2NO_2对H_2S气体分子的吸附结果表明,两者之间为弱的物理吸附, Ti_2NO_2无法有效吸附H_2S气体.采用过渡金属(Sc、 V)修饰Ti_2NO_2的研究结果表明,Sc和V可以在Ti_2NO_2表面上稳定存在,不易发生团聚,其最稳定吸附位为N原子上方.进一步研究了Sc、 V修饰的Ti_2NO_2对H_2S气体分子的吸附行为,结果表明金属修饰后其吸附H_2S的能力明显提高.此外还发现, H_2S分子可以在Sc/Ti_2NO_2和V/Ti_2NO_2表面直接解离为HS*和H*,而后HS*中的H原子再与H*进一步结合形成H_2, S原子则与过渡金属成键. HS*在V/Ti_2NO_2表面解离的势垒为1.69 eV,低于在Sc/Ti_2NO_2表面的2.08 eV,表明V/Ti_2NO_2有望成为吸附、分解H_2S气体的理想候选材料.