The Cayley graphs of ℤ<Superscript>d</Superscript> and the limits of vertex-primitive graphs of <Emphasis Type="Italic">HA</Emphasis>-type

We study the limits of the finite graphs that admit some vertex-primitive group of automorphisms with a regular abelian normal subgroup. It was shown in [1] that these limits are Cayley graphs of the groups ?^d. In this article we prove that for each d > 1 the set of Cayley graphs of ?^d presenting the limits of finite graphs with vertex-primitive and edge-transitive groups of automorphisms is countable (in fact, we explicitly give countable subsets of these limit graphs). In addition, for d < 4 we list all Cayley graphs of ?^d that are limits of minimal vertex-primitive graphs. The proofs rely on a connection of the automorphism groups of Cayley graphs of ?^d with crystallographic groups.     

Synthesis and properties of 1,6-methano[10]annuleno[3,4-c]thiophene and its 1,3-dicyano derivative

New thiophene-annulated 1,6-methano[10]annulene 1 and 2 were synthesized. The anisotropic deshielding effect from the π-electron system, based on the chemical shift values of the bridged methylene protons, is reduced compared with that of 3, and their crystal structures show clear bond alternation.     

Stereoselective Methods for the Synthesis of 4-Benzoyl-1-benzoylamino-3-(2-chlorophenyl)-2-cyano-1-methylthio-1-butene and Its Structure

Selective methods were developed for the synthesis of 4-benzoyl-1-benzoylamino-3-(2-chlorophenyl)-2-cyano-1-methylthio-1-butene on the basis of the reaction of N-methylmorpholinium and piperidinium 5-benzoyl-4-(2-chlorophenyl)-3-cyano-6-hydroxy-6-phenyl-1,4,5,6-tetrahydropyridine-2-thiolates with methyl iodide. The structure of the product was established by X-ray crystallographic analysis.     

Quantum chemical geometry optimizations in proteins using crystallographic raw data

A method is developed for the combination of quantum chemical geometry optimizations and crystallographic structure refinement. The method is implemented by integrating the quantum chemical software Turbomole with the crystallographic software Crystallography and NMR System (CNS), using three small procedures transferring information between the two programs. The program (COMQUM-X)is used to study the binding of the inhibitor N-methylmesoporphyrin to ferrochelatase, and we show that the method behaves properly and leads to an improvement of the structure of the inhibitor. It allows us to directly quantify in energy terms how much the protein distort the structure of the bound inhibitor compared to the optimum vacuum structure (4-6 kJ/mol). The approach improves the standard combined quantum chemical and molecular mechanics (QC/MM) approach by guaranteeing that the final structure is in accordance with experimental data (the reflections) and avoiding the risk of propagating errors in the crystal coordinates. The program can also be seen as an improvement of standard crystallographic refinement, providing an accurate empirical potential function for any group of interest. The results can be directly interpreted in standard crystallographic terms (e.g., R factors or electron density maps). The method can be used to interpret crystal structures (e.g., the protonation status of metal-bound water molecules) and even to locally improve them.     

Method for performing LCAO band structure calculations in crystalline solids: Application to rubidium

In this work we present a method for performing LCAO (linear combination of atomic orbitals) band structure calculations (tight binding) in crystalline solids. In the first part of the article we apply group theoretical methods to the establishment of a least‐squares scheme for the calculation of the matrix of the crystal potential: This scheme is based on a well‐defined choice of independent parameters for the Bloch vector‐dependent matrix elements and on the considerations of the symmetries between these independent parameters and their Fourier coefficients. In the second part of this work we deal with the representation of the matrices of the identity operator and of the operator of the kinetic energy by linear combinations in terms of two center integrals: We express these linear combinations by a closed formula, which can be easily programmed on a computer, and we mention a method by which the two center integrals can be evaluated numerically fast and accurately. Finally we apply our theory to the derivation of numerical results: We determine the electronic states and the high‐momentum components of Compton rates in the alkali metal rubidium and we compare the results obtained with those of augmented plane‐wave (APW) calculations. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 212–225, 2000     

考虑两种晶界的各向异性双晶和三晶体晶界附近弹塑性应力场分析

采用率相关的晶体滑移有限元程序对具有不同晶体取向的双晶体晶界附近及三晶体三晶粒交汇处的弹塑性应力场进行了计算,考虑了几何晶界和物理晶界的影响.计算结果表明:双晶体及三晶体考虑几何晶界和物理晶界时,这两种晶界具有相同的应力分布趋势,只是物理晶界比几何晶界的应力集中程度小,双晶体晶界附近有较大的应力梯度,存在应力集中现象.三晶体三晶粒交汇处可能是应力集中之地也可能不造成应力集中,这主要取决于晶粒晶体取向及加载方向.由此可见,要准确理解金属材料的断裂过程,还需要从细观的角度对晶界的力学响应进行细致和深入的研究.     

一种镍基单晶超合金高温低周疲劳的晶体取向相关性模型

在950℃t对[001]、[012]、[112]、[011]和[114]晶体取向的镍基单晶超合金DD3试样进行了对称循环低周疲劳(ICF)试验。应变率取1.0×10-2,1.33×10-3,0.33×10-3s-1.试验结果表明,LCF特性显着地取决于晶体取向和应变率。试样断口细观分析表明,除了[001]取向试样外,其余所有试样断口上均有明显的等间距疲劳纹。这些疲劳纹由微裂纹组成,其间距取决于试样的晶体取向和总应变范围。基于晶体滑移理论,建立了疲劳纹间距和总分切应变范围及取向和应变率函数的一个简单关系。对Lall-Chin-Pope(LCP)模型进行修正并推广应用于循环塑性和疲劳寿命研究,提出了一个晶体取向和应变率参数,该参数可以很好地描述镍基单晶超合金高温低周疲劳循环塑性和疲劳寿命的晶体取向和应变率相关性。     

(Nb2O5)1-x(TiO2)x陶瓷的制备及其介电性能的研究

我们采用传统固态反应方法烧结制备(Nb2O5)1-x(TiO2)x陶瓷,给出了掺杂量x从0.01到0.13陶瓷的介电性能.在本工艺条件下,所有样品的介电系数均大于120.当样品中TiO2的掺杂量为5mol;时,陶瓷的介电性能最佳:介电系数和损耗分别为217和0.078.XRD测试实验给出,当x≤0.05时,陶瓷的主要相结构为Nb2O5;当x≥0.07时,主相为TiNb24O62.     

镍基单晶合金蠕变变形过程的描述

基于强化相γ’的筏化－解筏和粗化的细观过程,本文推导了一组用于描述基单在合金蠕变变形过程的蠕变方程,并在９５０℃和７６０℃标定了国产ＤＤ３镍基单晶合金不同晶体取向的模型参数,与实验结果比较,所提模型可以准确地描述蠕变的主要阶段。     

Determination of the crystallographic parameters of a fcc metal by means of electron channelling patterns

Indexing and mapping of selected area electron channelling patterns (SAECPs) of an Al‐Zn‐Mg alloy have been performed. Although, channelling patterns are similar for crystals having the same system, since the interplanar spacing and the angular band width depend on lattice parameter, the details of the map will differ for every material. Angles between the poles and the angular separations of channelling bands were measured on the micrographs and calculated with the well known equations and found to be well in agreement within the error limits. Also the channelling line widths were calculated with the help of extinction distances of the reflecting planes. Structure factors and atomic scattering factors for selected reflections were also calculated for the present alloy whose a = 4.054 Å.