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.     

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.     

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.     

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.     

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.     

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.     

Microstructure of a composite with a quasicrystalline phase fraction obtained by directional solidification of Al61Cu27Fe12 alloy

The microstructure of a composite containing a quasicrystal phase, i.e. so-called crystal–quasicrystal (CQ) composite, was studied. The CQ composite was obtained by the Bridgman method via solidification of Al₆₁Cu₂₇Fe₁₂ alloy (numbers indicate at%). The process was conducted at a pull out rate of v = 0.07 mm/min. The average temperature gradient in the heating zone was 43 K/cm. The composite matrix consisted of cubic β phase Al(Fe, Cu), with reinforcement of λ-phase rod-shaped fibres surrounded by a quasicrystal icosahedral ψ phase, which also existed in the fibre core. The fibres were rhomboidal in cross-section. The composite was studied using X-ray and electron diffraction, light-optical and scanning electron microscopy (SEM), X-ray topography and Laue diffraction.     

Phase transformation behaviour in continuously cooled Zr65Al7.5Ni10Cu17.5− x Pd x (x = 0 − 17.5) glass-forming alloys and consequences for structure and property control

Continuous cooling transformation (CCT) diagrams were successfully constructed for Zr₆₅Al_7.5Ni₁₀Cu_{17.5? x} Pd _x (x?=?0???17.5) glass-forming alloys, comparing phase-transformation features in the alloy system to composition. While a low-Pd alloy (x?=?5) showed a single transformation curve, corresponding to the formation of a crystalline phase on the high-temperature side of the undercooled-liquid region, for a given time-scale, a high-Pd alloy (x?=?17.5) revealed an additional curve, corresponding to quasicrystalline phase formation on the lower temperature side. The result provides a clue to the structural and property control on the alloy system. Glassy specimens of the same size but with different intrinsic structure, evaluated by structural relaxation during continuous heating, could be fabricated for the low-Pd alloy (x?=?5). Plasticity was found to increase proportionally with the relaxation enthalpy. On the other hand, the critical size for glass formation could be improved considerably from 5 to 7 mm in diameter for the high-Pd alloy (x?=?17.5).     

Icosahedral symmetry in clusters

First principles calculations and simulations based on interatomic potentials together with experimental studies of abundance spectrum suggest icosahedral structures to be common for some magic clusters of diverse systems such as rare gases, metals, covalently bonded systems and water. Close packing models obtained from pair potentials are shown to be good representations of the structure of rare gas clusters. However, the electronic structure is found to play the important role in the atomic structure and related properties of other clusters. Results of recent studies of fullerenes, their derivatives as well as some large icosahedral metal clusters containing several thousand atoms are also presented. Further results on doped icosahedral clusters are discussed which hold promise for the development of new materials and for understanding the occurrence of icosahedral order in several aluminum alloys.