One possibility of determining the atomic structure of nanosized particles using diffuse-scattering data

A method based on using the Fourier transform of finite functions has been developed to reconstruct the distribution function of interatomic vectors in a nanoparticle from x-ray diffuse scattering data. This distribution is similar to the Patterson function used in the structure analysis of single crystals. The method for determining the structure has been developed and verified for an actual cluster consisting of 36 atoms. The atomic cluster structure was previously determined in single crystals with the fluorite structure (Cd_0.90Tb_0.10F_2.10. The vectors between heavy atoms are localized on the distribution of interatomic vectors and are used to construct superpositional synthesis. This synthesis yields the positions of the atoms in the nanoparticle. The method is also applicable to the nanocrystals with a limited number of unit cells.     

准晶结构的激光全息人工制作

报道了用激光全息刻写技术结合感光聚合材料体系制作介观尺度二维准周期结构(准晶). 并在前期工作的基础上，研究了不同曝光量对二维空气柱孔径的影响，不同偏振对准晶结构花样的影响. 实验结果显示，可以制作的二维准晶的空气柱孔径可达100nm，而且结构均匀，无缺陷面积大. 用此实验系统可以制作多种花样二维甚至是三维准晶结构. 目前，除激光全息刻写技术外，用其他传统精密机械加工技术来人工制作介观准晶体尚存在很大挑战性. 关键词： 准晶结构 光子晶体 激光全息技术     

Surface structure analysis of metal adsorbed Si(1 1 1) surfaces by Patterson function with LEED I-V curves

Wu and Tong proposed the calculation method of Patterson function obtained directly from the LEED I-V curves which shows the relative position of surface atoms as an image. We have made the calculation program of Patterson function and applied to the structural analysis of the Si(1 1 1)1 × 1-Fe surface. Surface structure was able to be expressed almost correctly by the Patterson function obtained from the theoretical I-V curves for the model structure. In the Patterson function obtained from the experimental I-V curves, the locational relation between the atoms of subsurface layer was in agreement with the CsCl type structure. More over, because the faint peak, by which we can distinguish the model, can be seen, it seems that the model B8 is preferable to the model A8. This result is consistent with the model shown by Walter et al.     

A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations

In this paper, we consider band structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they discretize the interface alone and can achieve high order accuracy in complicated geometries. In order to handle the quasi-periodic conditions which are imposed on the unit cell, the free-space Green’s function is typically replaced by its quasi-periodic cousin. Unfortunately, the quasi-periodic Green’s function diverges for families of parameter values that correspond to resonances of the empty unit cell. Here, we bypass this problem by means of a new integral representation that relies on the free-space Green’s function alone, adding auxiliary layer potentials on the boundary of the unit cell itself. An important aspect of our method is that by carefully including a few neighboring images, the densities may be kept smooth and convergence rapid. This framework results in an integral equation of the second kind, avoids spurious resonances, and achieves spectral accuracy. Because of our image structure, inclusions which intersect the unit cell walls may be handled easily and automatically. Our approach is compatible with fast-multipole acceleration, generalizes easily to three dimensions, and avoids the complication of divergent lattice sums.     

Disorder diffuse scattering from quasicrystals

Very sharp Bragg reflections accompanied by diffuse scattering phenomena are typical for most stable quasicrystals. The correlation length of the quasiperiodic average structure can reach several micrometers as proved by high-resolution X-ray diffraction experiments. This corresponds to a structural perfection of some quasicrystals similar to that of silicon. Nevertheless, the omnipresent diffuse scattering indicates significant deviations from a strictly ordered quasiperiodic structure especially in the case of decagonal phases. These structural deviations may be caused by phason fluctuations, by disorder in the packing of the basic atomic clusters, by the formation of nanodomains, by chemical disorder, or by superstructure formation on a short-range scale. Characteristic examples of different types of structural disorder present in icosahedral and decagonal quasicrystals are reported. The diffuse scattering phenomena in decagonal Al-Co-Ni as a function of composition and temperature are discussed in more detail.     

二维Fibonacci准晶电子能谱

基于重整化群技术,我们用分解-消元方法研究二维Fibonacci准晶电子能谱性质,得到了具有多种分支结构的能谱,这与一维Fibonacci的单一分支结构完全不同。同时,利用晶格的四重旋转对称性将哈密顿量化简,然后进行数值模拟计算,计算结果与分析结果完全一致。 关键词：     

脲嘧啶3′,5′—环核苷酸(c-UMP)的晶体结构研究

脲嘧啶3′,5′-环核苷酸(c-UMP)结晶为无色透明晶体,分子式为C₉,H₁₁O₈N₂P,属单斜晶系,空间群C₂¹P2。晶胞参数α=10.767(6)?,b=7.152(4)?,c=1O.414(5)?,β=112.77(31)°,晶胞内分子数z=2。用PW-1100四圆衍射仪收集衍射强度数据,独立衍射点为1658个。应用Patterson法、直接法和Fourier综合法测定c-UMP分子结构。晶胞中呈现部分无序分布的溶剂分子。以对角矩阵最小二乘法修正结构参数,R=0.084。 关键词：     

Elliptic hole in octagonal quasicrystals

The stress potential function theory for plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method (Lekhnitskii method) for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.     

Nonsingular Greens function method for crystals

By use of simple mathematical transformations, an integral equation for the Greens function method leads to a homogeneous equation which contains only the nonsingular part of the Greens function. No limitations are imposed on the crystal potential, so the solutions may be found for any unit cell. The method is applicable to any crystal structure. Using bcc iron as an example we present various calculations which make it possible to predict ahead of time which atomic levels will form bands and which will not.Altaisk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 120–123, July, 1995.     

用直接法处理由重原子引起的四重解

溴化五味子醇乙C₂₃H₂₇O₇Br的单晶体属P2₁2₁2₁空间群,每个晶胞含4个分子。由于Br原子的y和z坐标都非常接近于1/4,无论用重原子法还是用Patterson法,相应于每一个轻原子的位置都可能出现四种不同的解,因而正常的分析无法进行下去。用作者之一提出的方法顺利地消除了重原子引起的赝解,从而求出正确的结构。 关键词：     

Elliptic holes in octagonal quasicrystals

The stress potential function theory for the plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving the elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method (Lekhnitskii method) for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.     

Average unit cell approach to diffraction analysis of some aperiodic structures — decorated fibonacci chain

The average unit cell approach has been successfully used to construct the probability distributions of atomic distances from the reference lattice points and to calculate the diffraction patterns for decorated Fibonacci chains with non-Fibonacci type of decoration. General method able to distinguish between various quasilattice decorations has been elaborated and tested for decorated Fibonacci chains. Financial support from the Polish Committee for Sci. Research under grant No. 2 P03B 041 16 is acknowledged. Presented at the DI-CRM Workshop held in Prague, 18–21 June 2000.     

Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading

Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode {\rm II} Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.     

Aluminium diffusion in decagonal quasicrystals

Aluminium is the majority element in many quasicrystals and expected to be the most mobile element, but its diffusion properties are hardly accessible to experiment. Here we investigate aluminum diffusion in decagonal Al-Ni-Co and Al-Cu-Co quasicrystals by molecular dynamics simulations, using classical effective pair potentials. Above two-thirds of the melting temperature, strong aluminum diffusion is observed. The diffusion constant is measured as a function of temperature and pressure, from which the activation enthalpies and activation volumes are determined. As there are no vacancies in the samples, the diffusion, which is anisotropic, must use a direct mechanism. The high mobility of aluminium is also relevant for structure determination, and will contribute to diffuse scattering. The qualitative behavior of the dynamics is confirmed by ab initio simulations.     

用直接法处理Patterson法中的多解问题

测定含重原子晶体的结构,通常都利用Patterson法或以其为基础的重原子法、同晶型法、反常散射法等。此类方法往往会出现多解的情况。作者之一在1965年提出了用直接法消除多解问题的方法。多年来国际上在这方面也一直有类似的探讨。这类方法不仅在分析小分子晶体时有其特点,而且其进一步发展将有助于扩大直接法在生物大分子晶体结构分析中应用的领域,为提高生物大分子晶体结构分析的技术水平作出贡献。作者之一在文献[7]中已用实例说明了此类方法在中心对称情况下的应用。本文则提供非中心对称情况下的成功例子。虽然本例只处理了含重原子晶体Patterson函数的双解问题,但所用手段同样适用于处理同晶型法和反常散射法的双解。     

Section method for projected structures of icosahedral quasicrystals and its application to electron-microscopy-image and surface analyses

A section method for projected structures of icosahedral quasicrystals (IQCs) is given. A structure projected along a specified direction can be calculated directly from a six-dimensional periodic structure by this method. The method concludes that all peaks in high-resolution transmission electron-microscopy images of an IQC have different projected atom densities in general and leads to different chemical compositions and densities for all atom layers, suggesting that all surfaces of an IQC are different. Its application to icosahedral Al-Pd-Mn quasicrystals is shown.     

Vector method for studying the second-harmonic-generation light derived from complex periodic ferroelectric domains

In this Letter, in order to overcome the disadvantages of controlling the second-harmonic-generation (SHG) light derived from the traditional one-dimensional (1D) periodic ferroelectric domains we propose a kind of so-called complex periodic ferroelectric structure (CPFS), which unit cell is composed of even layers of positive and negative domains arranged alternatively following aperiodic sequence. It is found that comparing with the traditional periodic structure, CPFS cannot offer more reciprocal vector compensations for the mismatching phase, but CPFS may provide larger effective nonlinear coefficients (ENCs) in high-order quasi-phase-matching (QPM) and possesses advantages of the amplitude modulation for SHG peaks. In this Letter we study CPFS by use of vector method (VM), where the contribution to ENC for each domain or each unit cell will be treated as a vector and the QPM condition for CPFS and the modulation effect of aperiodic unit cells have been obtained. Without any Fourier transformation VM treats the grating function in real space and will be very convenient and intuitive. Both VM and CPFS would possess potential applications in the field of SHG investigations.     

氮原子修饰点缺陷石墨烯结构和性质的理论研究

氮原子掺杂石墨烯对基于石墨烯的器件和催化研究具有重要的应用价值.本文采用基于密度泛函理论的计算方法,研究了氮原子修饰的C-Bridge(碳原子吸附在石墨烯碳碳键桥位)、C-Top(碳原子吸附在石墨烯一个碳原子上方)和C7557(碳原子对吸附在石墨烯碳环上方)三种不同点缺陷类型的石墨烯物理性质.讨论不同缺陷石墨烯结构在用氮原子进行修饰前后体系的稳定性、电子结构等;计算得到了缺陷处原子的分波态密度(PDOS)图,分析了原子间的相互作用;模拟出氮原子修饰后缺陷石墨烯恒流模式的STM图像,以便和实验上得出的图像进行对比.计算结果表明,对于所选取的三种不同缺陷,氮原子能够较稳定地吸附在缺陷表面.C-Bridge和C-Top缺陷结构本身具有磁矩,经氮原子修饰后结构磁矩消失.与之相反,C7557缺陷结构本身没有磁矩,经氮原子修饰后缺陷体系带有磁矩.另外,C-Bridge和CTop两种不同缺陷结构石墨烯经过氮原子修饰后,体系几何结构变得完全一样.     

Hardness of Al-based quasicrystals evaluated via cluster-plus-glue-atom model

In this paper, the hardness of ternary Al-based quasicrystals was assessed through an application of the cluster-plus-glue-atom model. In this model, any structure is decomposed into a first-neighbour strongly bonded cluster part and second-neighbour weakly bonded glue-atom part so that the overall structural information is condensed into a local structural unit [cluster](glue atom)_x. For quasicrystals, the averaged local units are formulated as [icosahedron] TM_0,1(Transition Metal) and could be visualized as single icosahedron packing. Then, the hardness of quasicrystals was related to the rupture of weak inter-cluster bonds. Typically, theoretical hardness values of 8–9?GPa were obtained using 19 broken inter-cluster bonds, which accounts for about half of all the surface bonds of an icosahedron in the Mackay-type environment. The unit cluster formulas would act as rigid units during deformation and cracking.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.