十二次对称准周期结构的自相似变换及准晶胞构造

研究十二次对称准晶体模型的几何结构性质.修正了Socolar在正方形-菱形-六边形拼图模型中自相似变换的错误.在Stampfli-Ghler正方形-菱形-三角形拼图模型的基础上,成功地构造出了准晶胞,使得十二次对称准周期结构可以用覆盖理论描述. 关键词： 准晶体 拼图模型 自相似变换 覆盖理论     

Configurations and Self-similar Transformation of Octagonal Quasilattice

We study the structural properties of a two-dimensional quasilattice constructed by covering of identical octagonal clusters. The covering cases and nearest-neighbour configurations are presented. A self-similar transformation is introduced to generate an octagonal covering model in a direct way.     

Critical behavior of three-state Potts model on decagonal covering quasilattice

The three-state Potts model on a 2D decagonal covering quasilattice is investigated by means of the Monte Carlo simulation. The periodic boundary conditions are realized on a rhombus-like covering pattern. By use of the finite-size scaling analysis, we obtain the critical temperature and the critical exponents. The critical temperature is higher than that of the square lattice mainly due to the larger mean coordination number of the covering model. The critical exponents are close to the corresponding values of the 2D periodic lattices, which means that the Potts model on the covering structure may belong to the same universal class as that of the periodic lattices.     

Monte Carlo simulation of Ising model on decagonal covering structure

We study the Ising model on a two-dimensional quasilattice developed from the decagonal covering structure. The periodic boundary conditions are applied to a patch of rhombus-like covering pattern. By means of the Monte Carlo simulation and the finite-size scaling analysis the critical temperature is estimated as 2.317±0.002. Two critical exponents are obtained being 1/v=0.992±0.003 and η=0.247±0.002, which are close to the values of the two-dimensional regular lattices as well as the Penrose tilings.     

Electronic properties of a two-dimensional quasicrystal model based on octagonal covering structure

A two-dimensional quasilattice with eight-fold rotational symmetry is formed by covering of identical octagonal clusters; a tight-binding Hamiltonian is presented based on it. We study the electronic properties by analyzing the energy spectrum and wave functions. The main energy levels are obtained and the gaps are labeled. The wave functions with different localization features are found and the self-similar distribution is shown.     

Crystallographic features of the approximant H (Mn7Si2V) phase in the Mn–Si–V alloy system

The intermetallic compound H (Mn₇Si₂V) phase in the Mn–Si–V alloy system can be regarded as an approximant phase of the dodecagonal quasicrystal as one of the two-dimensional quasicrystals. To understand the features of the approximant H phase, in this study, the crystallographic features of both the H phase and the (σ → H) reaction in Mn–Si–V alloy samples were investigated, mainly by transmission electron microscopy. It was found that, in the H phase, there were characteristic structural disorders with respect to an array of a dodecagonal structural unit consisting of 19 dodecagonal atomic columns. Concretely, penetrated structural units consisting of two dodecagonal structural units were presumed to be typical of such disorders. An interesting feature of the (σ → H) reaction was that regions with a rectangular arrangement of penetrated structural units (RAPU) first appeared in the σ matrix as the initial state, and H regions were then nucleated in contact with RAPU regions. The subsequent conversion of RAPU regions into H regions eventually resulted in the formation of the approximant H state as the final state. Furthermore, atomic positions in both the H structure and the dodecagonal quasicrystal were examined using a simple plane-wave model with 12 plane waves.     

正方点阵上Fibonacci超元胞声子晶体的带结构

用平面波展开方法研究了水柱体作为填充物, 按照二维Fibonacci排列成超元胞填充在Hg基体中构成的声子晶体的声频带结构. 结果发现, 随着超元胞中准晶格常数的变化, 各个能带均出现三分裂. 对声场分布的研究发现了居间态的存在. 这些现象体现了准周期结构的特征. 关键词： Fibonacci排列 声子晶体 能带结构     

Modeling of dodecagonal quasicrystal lattices

We consider a method for constructing dodecagonal quasi-lattices, which involves the recurrent multiplication of the initial group of sites that are vertices of a regular dodecagon. The algorithm of modeling of reciprocal lattices of dodecagonal quasicrystals has been analyzed. The proposed modeling method is compared with the traditional projection method. We have performed indexing of the diffraction pattern from dodecagonal quasicrystals, which is analogous to indexing proposed by Cahn for icosahedral quasicrystals. The ambiguity of the choice of the basis vectors of the quasicrystal reciprocal lattice has been considered.     

A Landau’s octagonal quasilattice

An Ammam-Beenker 2D octagonal quasilattice is derived from a Landau like method starting from an octagonal seed. The level of stability of this quasilattice, i.e. the level of difficulty in creating defects, is directly measured.Received: 28 November 2003, Published online: 28 May 2004PACS: 61.44.Br Quasicrystals     

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：     

Bravais quasilattices of icosahedral quasicrystals

A classification of icosahedral quasicrystals based the mutual-local-derivability (MLD) concept is performed. There are eighteen MLD classes within the reservation that the faces of the hyperatoms (windows) are perpendicular to the two-, three-, or fivefold axes. Each MLD class has a representative member to be called the Bravais quasilattice from which the structure of each member of the class is derived by decorating it according to a local rule depending on the member.     

Continuous transformation from quasicrystals to approximants in Al–Cu–Fe alloys

Continuous transformation of icosahedral quasicrystals as observed in Al-Cu-Fe alloys proceeds through intermediate modulated structures towards rational approximants with a rhombohedral structure. Corresponding to the diffuse scattering in the electron diffraction during the transformation, a tweed contrast emerges throughout the icosahedral phase matrix. High-resolution electron microscopy reveals a complex modulated structure which tends to evolve into rhombohedral microdomains. The observed distortion of the reciprocal quasilattice due to the structural modulation has been simulated on a computer by introducing linear phason strains into the quasicrystals.     

Substitutions of vertex configuration of Ammann-Beenker tiling in framework of Ammann lines

The Ammann-Beenker tiling is a typical model for two-dimensional octagonal quasicrystals. The geometric properties of local configurations are the key to understanding its formation mechanism. We study the configuration correlations in the framework of Ammann lines, giving an in-depth inspection of this eightfold symmetric structure. When both the vertex type and the orientation are taken into account, strict confinements of neighboring vertices are found. These correlations reveal the structural properties of the quasilattice and also provide substitution rules of vertex along an Ammann line.     

Structure and stability of moving domain walls

Simple and fundamental considerations suggest that quasicrystalline order is not the privilege of metallic phases. The aim of this paper is to call attention to a non-standard approach to quasicrystals. Out of the possible theoretical models an illustrative example is picked out here. This is a hypothetical organic quasicrystal structure consisting of dodecahedrane (C₂₀H₂₀) skeletons which, by suitable face-sharing, can be built together to form an icosahedral Penrose-Mackay type quasilattice.     

Magnetoelastic nature of the dodecagonal anisotropy in holmium metal

We have investigated the magnetoelastic nature of the dodecagonal anisotropy in the magnetic anisotropy energy (MAE) in the basal plane of the hcp crystalline structure in holmium single crystal. We have proved that the origin of the second harmonic of the hexagonal symmetry in MAE clearly lies on a sixth-order magnetoelastic coupling term. The appearance of a 12-fold anisotropy in MAE in a single crystal having hexagonal symmetry provides a new insight on how the magnetic anisotropy can be modified in a magnetic material with giant spin-lattice coupling.     

Vertex configuration rules to grow an octagonal Ammann–Beenker tiling

Based on vertex configurations in the Ammann–Beenker tiling, we propose an algorithm for aggregation of square and rhombus tiles to generate an octagonal quasilattice, which mimics the growth process of a two-dimensional quasicrystal. Local matching rules with configuration selection are used to guide the way that tiles are joined to a cluster and form Ammann lines according to a generalized Fibonacci sequence. Our results reveal that vertex configuration selection can improve the performance of the algorithm, which provides an approach for growing a perfect octagonal quasiperiodic structure.     

Bi_2Sr_2CaCu_2O_8单晶中的反常尖锋效应

使用牛津震动样品磁强计 (VSM)研究了Bi2 Sr2 CaCu2 O8单晶的磁滞回线 .在 2 0到 40K温度之间发现了反常的尖锋效应 ,随样品O含量的增加 ,发生尖锋效应的外场也相应提高 .可以认为在尖峰效应处发生了由涡漩物质的有序固态到无序固态的相变 ,在有少量点缺陷存在的BSCCO单晶相图上 ,Bsp线终止于 2 0K温度处 ,在 2 0K以下温区没有发生准格子到涡漩玻璃的相变 ,涡漩固相始终以准格子形式存在 ;可以认为尖峰效应是外场、温度、无序的复杂函数     

Ultrasonic nonlinear parameters and sound speed of alcohol-water mixtures

Changes in the nonlinear parameter B/A caused by the addition of monohydric alcohols to water have been investigated. The measurements, made by using an aqueous solution of n-propanol, isopropanol, and t-butanol, show that as the alcohol concentration is increased, B/A decreases to a minimum at approximately 10% concentration (by volume). Further increase in alcohol concentration raises B/A rapidly to a maximum at about 80% by volume. This complex variation in B/A is attributed to solute-solvent interaction which is believed to be due to an enhancement of water structure in the water-rich region. These results suggest that the magnitude of B/A may be closely related to the quasilattice structure of water, which to a first approximation can be expressed by relative amounts of bound and unbound water.