Study of formation of nano-quasicrystals and crystallization kinetics of Zr-Al-Ni-Cu metallic glass

The formation of nano-quasicrystals on isothermal annealing of melt-spun ribbons of Zr_69.5Al_7.5Ni₁₁Cu₁₂ metallic glass has been investigated using transmission electron microscopy (TEM). The crystallization study of this metallic glass has been carried out using differential scanning calorimetry (DSC) in non-isothermal (linear heating) mode. It exhibits two-stage crystallization where the first stage corresponds to the precipitation of icosohedral nano-quasicrystalline phase. This has been confirmed with the help of TEM investigations. The crystallization parameters like the activation energy (E _c) and frequency factor (k ₀) have been derived using the Kissinger peak shift analysis. The activation energies for the first and second crystallization peak are found to be 278 and 295 kJ mol^–1, respectively. The frequency factors obtained for the two peaks are respectively 7.16·10¹⁹ and 1.42·10²⁰ s^–1. E _c, k ₀ and the Avrami exponent (n) have also been derived by fitting the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation for the transformed volume fraction (x) to the crystallization data. JMAK results of E _c for the first and second crystallization peak turn out to be 270 and 290 kJ mol^–1 respectively. However, k ₀ and n are found to be heating rate dependent as reported in similar studies. The values of n for the first crystallization stage ranges between 1.66 and 2.57 indicating diffusion-controlled transformation in agreement with earlier reports.     

The relation between the generalised Eshelby integral and the generalised BCS and DB modelsvspace1mm

The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the same results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy--momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.     

准晶体的研究进展

准晶体是一种介于晶体和非晶体之间的固体。按照其准周期维数的分类方法分为一维、二维、三维准晶体,具有力学性能、电学性能和磁性能。利用其优良的性能特点,可将其应用于表面改性材料和结构材料增强相中。对准晶体的基础研究主要在其原子结构测定、形成因素、成分预测、单质组元的寻找和物理性质的有效调控等方面;而应用研究主要包括其薄膜技术和微纳米化的研究等。     

Symmetries of Quasicrystals

We consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant—rings instead of Bragg peaks. They can be distinguished from glasses by self-similarity of the pattern of radii of the rings.     

Transport coefficients of quasicrystals

The transport coefficients for the nine point groups —which represent the symmetry groups of the quasicrystals in two and three dimensions—have been evaluated and tabulated in this work, employing group-theoretical methods.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

Localization in Two-Dimensional Quasicrystalline Lattices

We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.     

一维六方准晶压电材料反平面Ⅲ型裂纹电塑性分析

论文基于一维六方准晶压电材料反平面问题的基本方程,对Ⅲ型裂纹的电塑性区进行分析.采用条带模型并假设在电塑性区的切应力保持为常数,得到了电塑性区大小的表达式.这种假设方式消除了电场和应力在裂纹尖端的奇异性,这与实际情况相符合,也为一维六方准晶压电材料的断裂分析提供了理论基础.     

Discrete unbounded sets in a finite dimensional space and beyond

Discrete infinite sets in a finite dimensional space, i.e., infinite sets without finite limit points appear in various branches of analysis (zero and pole sets of meromorphic functions, various models in the mathematical theory of quasicrystals, and so on). Here we introduce some notions and present some new theorems connected with such sets.