准晶的弹性、塑性与位错

本文较系统地综述了适合准晶的线弹性理论,准品位错的基本理论和实验鉴定,准晶位错的弹性理论,以及准晶高温塑性形变的微观机制。     

准晶的对称性和物理性质

本文较系统地论述了准晶的对称性和物理性质，内容涉及准晶的对称性与点群，群的表示理论与准晶的弹性性质，准晶的平衡性质热力学与物理性质张量等诸多方面，其中也包含了本研究小组近年来在这方面的工作和所取得的重要成果     

准晶的对称性和物理性质

本文较系统地论述了准晶的对称性和物理性质,内容涉及准晶的对称性与点群,群的表示理论与准晶的弹性性质,准晶的平衡性质热力学与物理性质张量等诸多方面,其中也包含了本研究小组近年来在这方面的工作和所取得的重要成果     

Ti-Zr-Ni单相准晶合金的室温力学性能研究

以Ti40₄₀Zr40₄₀Ni20₂₀合金为研究对象，用铜 模吸铸法制备出直径为3mm的致密单相准晶棒，通过维氏显微硬度测定和单向压缩实验方 法研究了该合金的室温力学性能 .结果表明：Ti40₄₀Zr40₄₀Ni20₂₀准晶具有良好 的弹性变形能力，室温弹性应 变可达125%.同时，它具有相对高的室温硬度（约55GPa），是普通Ti合金的15倍.T i40_{40 关键词： 准晶 Ti-Zr-Ni合金 解理断裂}     

准晶切割投影图的计算与图示

基于准晶结构的投影描述法，发展了一种准晶的切割投影图的计算方法，并将这种方法用于十次准晶。首先用计算机计算了完整十次准晶平行于准周期平面的切割投影图，然后对沿周期方向有无限长直位错的十次准晶，分别计算了仅引入相位子应变和同时引入相位子、声子应变的平行于准周期平面的切割投影图。     

十次对称准晶的光电导率

讨论了十次对称准晶的光电导率，推导了十次对称准晶在周期方向和准周期平面不同的光电导率的计算公式，并以此计算了十次对称准晶Al₆₅Co₁₇Cu₁₈的光电导率，得到了与实验值相当符合的结果. 关键词： 准晶 光电导率     

一维准晶的振动性质

木本简单介绍了准晶的概念和一维Ｆｉｂｏｎａｃｃｉ准晶的结构，研究了一维准昂链所特有的Ｃａｎｔｏｒ－ｌｉｋｅ积分振动态密度．在准晶的振动本征态中，除了低频区的扩展态和禁带中的局域态外，还有一种以在周期及无序结构中都没有的临界态．文章还讨论了在准晶中引入掺杂和错位等无序后对准晶原子链振动的影响．以上的研究为一种人工准晶体─—准晶超晶格的振动研究提供了理想的模型．     

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     

单棱镜共光路干涉法制作多结构二维光子准晶

提出一种共路干涉装置用于复杂结构亚微米尺度光子准晶的大面积制作.改变样品旋转角度和曝光次数,设计多种不同旋转对称性的准晶结构,并给出相应的衍射模式以证明其多重旋转对称性.利用该装置可以制作任意复杂结构、任意旋转对称度的准晶结构.同时,分析了旋转轴和旋转角存在偏差时对准晶结构的影响.另外,采用该装置实验制作了十重准晶结构,并用原子力显微镜和衍射测量表征该准晶的长程指向性和十重旋转对称性,实验结果表明:十重晶格结构的直径为1.2μm,最小结构单元尺寸为377nm,与理论设计尺寸1.25μm和392.5nm相比,误差为4%.理论设计和实验结果一致性很好,对研究以光子带隙为基础的纳米光子学器件具有重要的指导意义.     

孪晶对Be材料冲击加-卸载动力学影响的数值模拟研究

在高压、高应变率加载条件下,孪晶变形对材料的塑性变形具有重要的贡献,而目前孪晶对金属材料的动态屈服强度、冲击响应等的影响还没有被充分揭示.为此,本文考虑孪晶变形和晶粒碎化,针对铍(Be)材料在高应变率加载下的动态力学响应发展了含孪晶的热弹-黏塑性晶体塑性模型.经过和实验结果的对比,发现该模型可以更准确地预测Be材料在动态加载下,尤其是高压动态加载下的屈服强度.进一步,基于该塑性模型研究了Be材料在冲击加载下的准弹性卸载行为,结果表明剪切波速随着压力和剪应变的变化而发生变化是材料产生准弹性卸载现象的主要原因.此外,研究了冲击波卸载过程中Be材料孪晶的演化过程,发现Be材料卸载过程中也伴随着孪晶的产生.     

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.     

Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.     

Decagonal quasicrystals

Following the discovery of two dimensional quasicrystals in rapidly solidified Al-Mn alloys by us and L. Bendersky in 1985, a number of fascinating studies has been conducted to unravel the atomic configuration of quasicrystals with decagonal symmetry. A comprehensive mapping of the reciprocal space of decagonal quasicrystals is now available. The interpretation of the diffraction patterns brings out the comparative advantages of various indexing schemes. In addition, the nature of the variable periodicity can be addressed as a form of polytypism. The relation between decagonal quasicrystals and their crystalline homologues will be explored with emphasis on Al₆₀Mn₁₁Ni₄ and ‘Al₃Mn’. It will also be shown that decagonal quasicrystals are closely related to icosahedral quasicrystals, icosahedral twins and vacancy ordered phases.     

Group-theoretical method for physical property tensors of quasicrystals

In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis （or a set of basis functions） in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.     

Recent advances in the study of quasicrystals

Some recent advances in the study of quasicrystals at Ames Laboratory are reviewed. In particular, growth from the melt of large, high-quality, single-grain quasicrystals is described in detail for icosahedral R-Mg-Zn and decagonal Al-Ni-Co. In addition, the magnetic properties of the rare-earth-containing icosahedral R-Mg-Zn quasicrystals are discussed.     

Quasicrystals

After some introductory remarks about quasicrystals, ME spectra of icosahedral AlMnFe-, AlCuFe- and TiNiFeSi-alloys are summarised. The results are interpreted in terms of the current understanding of the structure of quasicrystals. Further a ME-application to the stability criteria of quasicrystals is discussed. A dominant factor is the band splitting factor or the Hume-Rothery rule.     

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.     

Basics of NMR line shape in quasicrystals

The measurement and analysis of broad nuclear magnetic resonance (NMR) spectra of quasicrystals require experimental methods and theoretical interpretations different from NMR investigations of regular periodic crystals. Frequency- and field-sweep methods for recording quasicrystalline NMR spectra are described and compared with the measurement of²⁷Al NMR spectra of icosahedral AlPdMn and decagonal AlNiCo quasicrystals. The nuclear spin interactions that determine the NMR line shape are the same for both types of the above Al-based quasicrystals, where the electric quadrupolar interaction with the broad distribution of its electric field gradient parameters predominantly determines the shape of the broad satellite “background” intensity. The essential observations are an almost isotropic²⁷Al NMR spectrum of the icosahedral quasicrystals and a strong angular dependence of the spectrum of decagonal quasicrystals.