粉末晶体(ZrO2)x(Bi2O3)1-x(x=1.0, 0.97) 晶体结构分析

为了确定ZrO2和(ZrO2)0.97(Bi2O3)0.03的晶体结构和原子热振动各向同性温度因子B，对该粉末晶体进行X射线衍射实验，建立了晶体结构模型，进行晶体结构分析。首先，采用共沉淀法和高温固相烧结法制备了纳米氧化锆ZrO2和(ZrO2)0.97(Bi2O3)0.03粉末晶体，接着，使用X射线测试仪对两种样品进行了衍射实验（XRD），利用Rietveld 精修方法的 RIETAN-2000程序对所得实验结果进行了晶体结构分析，获得了晶体结构参量和原子热振动各向同性温度因子B。通过Maximum Entropy Method（MEM）解析得到了粉末晶体(ZrO2)x(Bi2O3)1-x(x=1.0，0.97)的等高电子密度分布可视化图谱。结果表明，(ZrO2)0.97(Bi2O3)0.03的晶胞体积比ZrO2的晶胞体积大分别为140.6850 Å3和140.5637Å3；ZrO2晶体的原子热振动各向同性温度因子B(Zr)、BO(1)、BO(2)和 B（Bi）分别为0.690、0.269、 0.178 和 0 Å2，(ZrO2)0.97(Bi2O3)0.03晶体的分别为0.460 、0.583 、0.121 和0.581 Å2。 确定了(ZrO2)0.97(Bi2O3)0.03的晶体结构属于单斜晶系，实现了等高电子密度分布三维（3D）和二维（2D）的可视化，进一步确定了晶体结构和原子位置。     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Identifying aspirin polymorphs from combined DFT-based crystal structure prediction and solid-state NMR

A combined experimental and computational approach was used to distinguish between different polymorphs of the pharmaceutical drug aspirin. This method involves the use of ab initio random structure searching (AIRSS), a density functional theory (DFT)-based crystal structure prediction method for the high-accuracy prediction of polymorphic structures, with DFT calculations of nuclear magnetic resonance (NMR) parameters and solid-state NMR experiments at natural abundance. AIRSS was used to predict the crystal structures of form-I and form-II of aspirin. The root-mean-square deviation between experimental and calculated ¹H chemical shifts was used to identify form-I as the polymorph present in the experimental sample, the selection being successful despite the large similarities between the molecular environments in the crystals of the two polymorphs.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

基于Rietveld精修方法解析Bi2O3的原子热振动

三氧化二铋(Bi₂O₃)是氧离子导电体,为了获得它的原子热振动各向同性温度因子,对该粉末晶体进行X射线衍射实验,建立了晶体结构模型,利用Rietveld 精修方法的RIETAN-2000 程序对所得实验结果进行了晶体结构精修,通过最大熵方法(MEM)解析得到了粉末晶体的等高电子密度分布三维(3D) 和二维(2D)可视化图谱。结果表明,各原子Bi₍₁₎、Bi₍₂₎、O₍₁₎、O₍₂₎和O₍₃₎的原子热振动各向同性温度因子分别为0.004 938 nm²、0.004 174 nm²、0.007 344 nm²、0.007 462 nm²、和0.007 857 nm²,等高电子密度分布的可视化,进一步验证了晶体结构模型和原子位置的准确性,这些参数对研究晶体材料的热性质具有一定参考意义。     

田字形地震超材料甚低频宽带隙机理

在地球中传播的地震波主要有体波和表面波,而表面波中Rayleigh波对建筑物造成的破坏最为强烈。针对Rayleigh波的振动控制,提出一种田字形超材料结构。相比于传统的地震超材料,这种超材料屏障是由外部口字形框体内部嵌套十字形柱体组成,形成4个可填充区域,其外部框体采用部分埋入的方式,具有高强度、强稳定性、填充方式灵活的特点。应用有限元法计算了田字形超材料的能带结构和传输特性,并通过分析带隙边界处模态振型可知,带隙的打开是由于柱体的局域共振。结合带隙机理可知,柱体结构中土壤填充量不同可改变柱体的质量,形成不同的谐振频率,产生甚低频带隙。为进一步拓宽带隙,设计研究了正、负梯度的质量填充方式,均可得到3.3~13.1 Hz甚低频宽带隙,在谐振频率范围内两者的隔震方式分别为Rayleigh波彩虹捕获和Rayleigh波到体波的转化。最后,采用EI-Centro地震波对填充屏障进行了时程验证,加速度最大幅值衰减超过80%,为地震超材料在减震隔震方面应用提供了新的设计思路和方法。     

Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

Enhancement of thermoelectric properties of D-A conjugated polymer through constructing random copolymers with more electronic donors

Developing new D-A conjugated polymer system for thermoelectric (TE) application is highly desirable. Herein, a series of random copolymers by incorporating 3,4-ethylenedioxythiophene (EDOT) electron rich units into a diketopyrrolopyrrole (DPP) D-A conjugated polymer were designed and synthesized. Compared to the alternating conjugated copolymer PDPP-3T, the HOMO level of the random copolymers are increased as part of the electron deficiency acceptor DPP units in the polymer chain were superseded by electron rich EDOT, which could contribute to effective p-doping. Moreover, through incorporating EDOT to construct random copolymers, it can also induce an orientation change from face-on dominated to edge-on dominated orientation as well as enhance the packing of copolymer chains, which is beneficial to the charge transport. Under same doping condition, the electrical conductivities of the doped polymers increase and the Seebeck coefficient decrease as the increasing of EDOT content, resulting in an optimized power factor of 6.4 μW m⁻¹ K⁻² for the random polymer with EDOT content of 40% which is four times higher than that of alternating conjugated copolymer PDPP-3T. These results demonstrated that constructing random copolymers by incorporating more electronic donors into D-A conjugated polymers may be a promising strategy for developing TE conjugated polymers.