Elastic fields around a nanosized elliptic hole in decagonal quasicrystals

Based on the variational principle, a continuum theory of surface elasticity and new boundary conditions for qua- sicrystals is proposed. The effect of the residual surface stress on a decagonal quasicrystal that is weakened by a nanoscale elliptical hole is considered. The explicit expressions for the hoop stress along the edge of the hole are obtained using the Stroh formalism. The results show that the residual surface stress and the shape of the hole have a significant effect on the elastic state around the hole.     

Analytic solutions to a finite width strip with a single edge crack of two-dimensional quasicrystals

In this paper, we investigate the well-known problem of a finite width strip with a single edge crack, which is useful in basic engineering and material science. By extending the configuration to a two-dimensional decagonal quasicrystal, we obtain the analytic solutions of modes I and II using the transcendental function conformal mapping technique. Our calculation results provide an accurate estimate of the stress intensity factors K_I and K_II, which can be expressed in a quite simple form and are essential in the fracture theory of quasicrystals. Meanwhile, we suggest a generalized cohesive force model for the configuration to a two-dimensional decagonal quasicrystal. The results may provide theoretical guidance for the fracture theory of two-dimensional decagonal quasicrystals.     

Structure of the AlRhCu decagonal quasicrystal: I. A unit-cell approach

Structure of the Al---Rh---Cu decagonal quasicrystal has been studied by high-resolution electron microscopy. The high-resolution structure image shows an aperiodic tiling composed of three kinds of subunits, namely flattened hexagon, crown and five star. Therefore, a structural model of the Al---Rh---Cu decagonal quasicrystal has been constructed in a unit-cell approach, in which the atom arrangements in the subunits have been proposed. It is known that the phase has two layers in a period of 0.4 nm along the unique tenfold axis according to the previous study by electron diffraction method. The ideal model of the Al---Rh---Cu decagonal quasicrystal is proposed as periodic stacking of the layers with quasiperiodic tessellation of the three kinds of subunits, in each layer the two-colour Penrose tiling is obtained if different atom decorations for the same shape subunits are distinguished by white and black colours. Calculated images reproduces well the contrast features of the observed images, which means that the present model is basically correct. Structural relationship between the Al---Rh---Cu decagonal quasicrystal and the previously reported Al---Ni---Co decagonal quasicrystal, which has also a period of 0.4 nm, has also been discussed.     

A mixed problem of plate bending for doubly connected domains with partially unknown boundaries in the presence of cyclic symmetry

This paper addresses the problem of plate bending for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides.The neighborhoods of the vertices of the inner boundary are equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center,but have unknown positions.Rigid bars are attached to the linear parts of the boundary.The plate bends by the moments applied to the middle point bars.The unknown arcs are free from external stresses.The same problem of plate bending is considered for a regular hexagon weakened by a full-strength hole.Using the methods of complex analysis,the analytical image of Kolosov-Muskhelishvili's complex potentials (characterizing an elastic equilibrium of the body),the plate deflection and unknown parts of its boundary are determined under the condition that the tangential normal moment on that plate takes a constant value.Numerical analyses are also performed and the corresponding graphs are constructed.     

Structure and composition of cleaved and heat-treated tenfold surfaces of decagonal Al-Ni-Co quasicrystals

We investigated cleavage surfaces perpendicular to the tenfold direction of as-grown decagonal Al-Ni-Co quasicrystals by scanning tunneling microscopy, Auger electron spectroscopy, and scanning electron microscopy. The cleavage surface is determined by a cluster-subcluster structure. The image contrast of the smallest features, 1-2 nm in diameter, is related to the columnar atom arrangements extending perpendicular to the cleavage plane, which are predicted by current models of the decagonal quasicrystal structure. No voltage dependence of the STM images is observed. The presence of surface states and an enhanced density of states are discussed. Heat-treatments of the cleaved Al-Ni-Co quasicrystal surfaces show nearly no changes in chemical composition and structure up to about 750 °C. This is correlated with a much lower concentration of vacancies in as-grown decagonal Al-Ni-Co quasicrystals as compared to that in as-grown icosahedral Al-Pd-Mn quasicrystals.     

Atomic dynamics of a <Emphasis Type="Italic">d</Emphasis>-AlNiFe decagonal quasicrystal

The atomic dynamics of an Al_71.3Ni₂₄Fe_4.7 decagonal quasicrystal has been investigated using the isotopic contrast method for inelastic neutron scattering. The partial vibrational spectra of the Ni, Fe, and Al atoms and the spectrum of the thermal vibrations of the alloy have been reconstructed directly from the experimental data without any model assumptions. The cutoff energies and the positions of the main features of the spectra have been determined. It has been revealed that the average binding energy of the nickel atoms in the quasicrystal under investigation is lower than that of the iron atoms and the vibrational spectrum of the aluminum atoms is noticeably harder than the spectrum of the pure metal. The results obtained for the d-AlNiFe decagonal quasicrystal have been compared with the previously published data for an i-AlCuFe icosahedral quasicrystal.     

落管中Al4Mn合金的形核研究

用1.2米长的落管对Al₄Mn合金进行了形核与过冷的研究.在落管底部收集到的样品中得到了正交Al₆Mn,β-Mn,两个十次准晶相关相、一个二十面体五次准晶相关相和十次准晶畴.发现这些相的含量与样品的尺寸大小有关,根据传统的形核理论对相含量与样品尺寸大小之间的关系作了定性的分析和讨论. 关键词：     

Self-assembly of monatomic complex crystals and quasicrystals with a double-well interaction potential

For the study of crystal formation and dynamics, we introduce a simple two-dimensional monatomic model system with a parametrized interaction potential. We find in molecular dynamics simulations that a surprising variety of crystals, a decagonal, and a dodecagonal quasicrystal are self-assembled. In the case of the quasicrystals, the particles reorder by phason flips at elevated temperatures. During annealing, the entropically stabilized decagonal quasicrystal undergoes a reversible phase transition at 65% of the melting temperature into an approximant, which is monitored by the rotation of the de Bruijn surface in hyperspace.     

High-temperature surface oxidation of the decagonal AlCoNi quasicrystal

The interaction of oxygen with the 10-fold-symmetry surface of the decagonal Al_72.9Co_16.7Ni_10.4 quasicrystal at high temperatures was investigated by low-energy-electron diffraction and Auger electron spectroscopy. The results are consistent with a well-ordered aluminum-oxide layer possessing a hexagonal antiphase domain structure with a limited lateral size of about 35 Å. We claim that the separation distances of the domain boundaries, separating domains of equal orientation, are primarily a consequence of the preferential cluster nucleation on decagonal Al-Co-Ni. The domains are azimuthally oriented along one direction of the two sets of five twofold-symmetry axes lying on the decagonal surface in accordance with the local symmetry of the quasicrystal surface, while the size of the domains can be explained in terms of self-size-selecting arguments.     

PERTURBATION METHOD SOLVING ELASTIC PROBLEMS OF ICOSAHEDRAL QUASICRYSTALS CONTAINING A CIRCULAR CRACK

Perturbation method for solving elastic three-dimensional (3D) problems for 3D icosahedral quasicrystals is proposed. Considering an infinite 3D icosahedral quasicrystal weakened by a circular crack, we obtain the uniformly valid asymptotic solutions up to O(R²) for the mode I loading, where R is the elastic constant of phonon-phason coupling.     

AXISYMMETRIC ELASTICITY PROBLEM OF CUBIC QUASICRYSTAL

A method for analyzing the elasticity problem of cubic quasicrystal is developed. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the solutions of elastic field of cubic quasicrystal with a penny-shaped crack are obtained, and the stress intensity factor and strain energy release rate are determined.     

A new orthogonality relationship for orthotropic thin plate theory and its variational principle

While Hamiltonian system was led to solution of elastic theory a symplectic system-atic methodology for theory of elasticity was established and a symplectic orthogonality relationship was presented[1,2]. For two-dimensional theory of elasticity a new dual vec-tor and a new dual differential matrix were presented by putting the old dual vector[1] in a new order. It was discovered for isotropic materials that the symplectic orthogonality relationship may be decomposed into two independent and s…     

Growing perfect decagonal quasicrystals by local rules

A local growth algorithm for a decagonal quasicrystal is presented. We show that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to form on the upper layer, successive 2D PPT layers can be added on top resulting in a perfect decagonal quasicrystalline structure in bulk with a point defect only on the bottom surface layer. Our growth rule shows that an ideal quasicrystal structure can be constructed by a local growth algorithm in 3D, contrary to the necessity of nonlocal information for a 2D PPT growth.     

Decagonal quasicrystal in the Al–Pd–Mn system

Abstract

A stable decagonal quasicrystal in Al₇₀Pd_30?xMn_x alloys (x = 10–20) was examined by electron diffraction and high-resolution electron microscopy. The decagonal quasicrystalline grains are formed with definite crystallographic relationships to adjacent icosahedral and Al₃Mn crystalline grains. The structure of the decagonal phase, which is formed as the main phase at near Al₇₀Pd₁₀Mn₂₀ composition, is a mixture of decagonal quasicrystalline regions with some linear phason strain and microcrystalline regions. The structures of both regions may be interpreted in terms of quasiperiodic and periodic tilings, constructed with two types of bond lengths, S (about 2 nm) and L (= τ · S, where τ is the Golden ratio), of the same atom cluster with decagonal symmetry.     

Stress and mixed boundary conditions for two-dimensional dodecagonal quasi-crystal plates

For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the first time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.      

Extended field method free vibration solutions

An apparent paradox involving the relation between the plate bending natural frequencies of two elastic plates when one plate encloses the other is examined and dispelled. Specifically it is shown (1) that the extended field method of analysis can exactly, or with excellent numerical convergence, calculate plate bending eigenvalues, and (2) that the extended field method forced vibration solutions are not compromised by the singularities at the eigenvalues of the extended plate.     

Al70Co15Tb5Ni10合金中准晶T相和相关相的形成

 对Al₇₀Co₁₅Tb₅Ni₁₀合金进行了静高压（4.40 GPa）熔态（1 450 ℃）淬火（冷却速率为10² ℃/s）研究。首次在该系统中观察到准晶T相和一个新的十次准晶相关相形成。使用透射电镜对准晶相和准晶相关相进行了结构分析，得到了准晶相关相的晶胞参数。使用已有的理论模型对该相关相的形成进行了讨论。     

基于弹性力学的应力加工方法有限元分析

基于弹性力学理论,对应力加工方法的原理、算法及玻璃薄板对复杂面型的模拟进行了研究。在球面镜周边分布力和力矩的状态下对球面变形为轴对称非球面进行了分析,以抛物面镜为例,采用有限元法对玻璃薄板周边施加均布弯矩后产生的变形量和最大应力进行了模拟、分析和仿真计算,得出的仿真结果与球面和抛物面之间的理想变形量进行比较,验证了基于弹性力学的应力加工方法加工旋转对称非球面理论的正确性。