Local structure of Co and Ni in decagonal AlNiCo investigated by polarized EXAFS

The local structure of cobalt and nickel in single crystals of decagonal quasicrystals with composition Al_71.5Ni_15.5Co₁₃ and Al₇₅Ni_14.5Co_10.5 have been studied by polarized EXAFS. Significant differences between the Ni and Co local environments have been detected. The effective absence of the 4 ? periodicity along the decagonal axis in these QCs is confirmed and indications about its reasons are presented. Received 26 July 2000 and Received in final form 20 October 2000     

Correlation functions and the dynamical structure factor of quasicrystals

The icosahedral or decagonal symmetry of quasicrystals is well described by a periodic structure in higher dimensions. One consequence is the existence of dynamic phason modes in addition to the phonon modes. In an atomistic model phasons show up as correlated atomic jumps. We detect the phasons by the calculation of correlation functions and the dynamical structure factor in molecular dynamics simulations similar to the procedure used for phonons. In the simulations it is also possible to observe atomic jump processes directly. The models studied here represent icosahedral AlCuLi and decagonal AlCuCo quasicrystals. Ring processes are observed in the icosahedral case, and flips in the decagonal model. Received 17 March 2000 and Received in final form 8 June 2000     

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：     

On dynamic plane elasticity problems of 2D quasicrystals

In this Letter, the dynamic plane elasticity problems of 2D quasicrystals is considered. By use of the Fourier transform and matrix transformations the system is reduced to uncoupled ordinary differential equations. Fourier images of Green's functions for dynamic plane elasticity problems of 2D dodecagonal, pentagonal and decagonal quasicrystals are obtained explicitly by the suggested method.     

Disorder diffuse scattering from quasicrystals

Very sharp Bragg reflections accompanied by diffuse scattering phenomena are typical for most stable quasicrystals. The correlation length of the quasiperiodic average structure can reach several micrometers as proved by high-resolution X-ray diffraction experiments. This corresponds to a structural perfection of some quasicrystals similar to that of silicon. Nevertheless, the omnipresent diffuse scattering indicates significant deviations from a strictly ordered quasiperiodic structure especially in the case of decagonal phases. These structural deviations may be caused by phason fluctuations, by disorder in the packing of the basic atomic clusters, by the formation of nanodomains, by chemical disorder, or by superstructure formation on a short-range scale. Characteristic examples of different types of structural disorder present in icosahedral and decagonal quasicrystals are reported. The diffuse scattering phenomena in decagonal Al-Co-Ni as a function of composition and temperature are discussed in more detail.     

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.     

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.     

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.     

Covering Rules and Nearest Neighbour Configurations of the Dodecagonal Quasiperiodic Structure

A dodecagonal quasiperiodic structure can be generated by duster covering and the quasilattice is described in terms of the quasi-unit cell. We study the structural properties of the two-dimensional dodecagonal quasilattice in the covering scheme. The pair covering rules and the nearest neighbour configurations are determined. It is shown that the dodecagonal structure is more complicated than those of decagonal and octagonal quasilattices.     

The Al-Pd-Mn quasicrystalline approximant -phase revisited

A detailed investigation of the Fourier space of several Al-Pd-Mn samples with composition Al-72.6 at. %, Pd-22.9 at. %, Mn-4.5 at. % is reported. In the phase diagram of the Al-Pd-Mn ternary alloy, this composition corresponds to the so-called ξ' phase which was described as an icosahedral quasicrystalline approximant. By re-examining the Fourier space by means of X-ray diffraction (powder patterns and single crystal precession patterns), complex structures in close relation with the ξ'-phase have been observed. These long-range order complex structures are described as resulting from a periodic perturbation of the ξ' structure along the c direction. Two states with periodicities c (3 + τ) and c (5 + τ) have been observed in this study (τ: golden mean). Structural models based on periodic arrangements of “defects” layers separating layers of phase are proposed. These two states are certainly intermediate states between the phase and the metastable decagonal quasicrystalline phase. Received 11 April 2002 / Received in final form 24 June 2002 Published online 17 September 2002     

Inelastic neutron scattering study of the dynamics of the AlNiCo decagonal phase

The dynamics of the decagonal AlNiCo phase has been investigated on a single-grain quasicrystalline sample using inelastic neutron scattering. The decagonal structure can be viewed as a periodic stacking of quasiperiodic planes. The anisotropy between the modes propagating in the periodic and quasiperiodic directions is found to be much weaker than theoretically predicted. A strong resonance splitting is observed at an energy transfer of 15 meV for transverse modes polarized in the quasiperiodic plane. Received: 18 November 1998 / Accepted: 27 November 1998     

A study of the Al-Cu-Co phase diagram and the solidification of alloys containing decagonal phase

The ternary Al-Cu-Co phase diagram was studied in order to revise the region of 50–75 at.% Al. The study was carried out by optical microscopy, scanning electron microscopy, transmission electron microscopy and powder X-ray diffraction. Isothermal 800°C, 600°C and 540°C sections are presented. The development of the composition range of the decagonal phase with temperature is discussed.     

三种典型结构光子晶体光纤基本特性的比较和分析

应用多极法比较和分析了相同结构参数下的正六边形、正八边形和正十边形光子晶体光纤的色散系数、色散斜率、非线性系数和限制损耗.正六边形光子晶体光纤更适合用于色散补偿和高非线性的研究,在波长0.8 μm处的非线性系数达到了0.37 m^-1·W^-1;正十边形光子晶体光纤更适合用于色散平坦和低限制损耗的研究,在波长0.8 μm处的限制损耗相对正六边形光子晶体光纤减小了约3000个数量级,在1.4—1.65 μm波长范围内,正十边形光纤的色散系数介于-0.07—0.17 p     

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.     

Decagonal quasicrystal plate with elliptic holes subjected to out-of-plane bending moments

In the present paper, we consider only the ideal elastic behavior, neglecting the dissipation associated with the atomic rearrangements. Under these conditions, the decagonal quasicrystal plate bending problems have been discussed. The Stroh-like formalism for the bending theory of decagonal quasicrystal plate is developed. The analytical solutions for problems of decagonal quasicrystal plate with elliptic hole subjected to out-of-plane bending moments are obtained directly by using the forms. The resultant bending moments around the hole boundaries are also given explicitly. When the phonon–phason coupling is absent, the results reduce to the corresponding solutions for the isotropic elastic plates.     

Collinear second harmonic generation of 20 wavelengths in a single two-dimensional decagonal nonlinear photonic quasi-crystal

We report on the observation of quasi-phase matched collinear second harmonic generation (SHG) at 20 wavelengths in a two-dimensional nonlinear photonic quasi-crystal with decagonal lattice. We show that at some wavelengths the second harmonics are generated via standard quasi-phase matching, namely a reciprocal vector exists that equals the phase-mismatch vector, while at others the SHG is as a result of the projection-based quasi-phase matching in which the momentum conservation is satisfied up to a projection of a reciprocal vector onto the direction of propagation. In spite of different generation mechanisms, the reciprocal vectors (or their projections) involved in the collinear QPM SHG can be described by a generalized equation.     

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.     

Dissolution patterns caused by chemical etching of Al–Co–Cu and Al–Co–Ni decagonal quasicrystals with a HF–HNO3–H2O solution

Dissolution patterns essential for Al–Co–Cu and Al–Co–Ni decagonal quasicrystals (d-QCs) have been investigated in detail by chemical etching using a HF–HNO₃–H₂O solution followed by scanning electron microscopy (SEM) observations. The chemical etching of definite surface areas of the samples, which are either normal or parallel to the tenfold axes, using a solution with HF–HNO₃–H₂O (1?:?5?:?4 in volume ratio; 0°C; 5–10?min), produces a large number of microfacet pits of decagonal prismatic shape. In addition, the same etching test in combination with SEM observations was carried out on a deformed sample of the Al–Co–Ni d-QC, which had been subjected to concentrated mechanical stress at an elevated temperature of 850°C by means of the Vickers indentation technique. The morphological features of the resulting micropits and their possible origins are discussed on the basis of results obtained by SEM observations.     

Nonicosahedral equilibrium overlayers of icosahedral quasicrystals

We demonstrate that icosahedral Al-Pd-Mn quasicrystals can have nonicosahedrally ordered thermodynamic equilibrium overlayers. The formation of orthorhombic or decagonal equilibrium surface structures is determined by the phase equilibrium of the ternary alloy at given composition and temperature as well as by the surface acting as nucleation site. Nonequilibrium steady-state orthorhombic and hexagonal structures can also be derived with the same methodology when taking preferential evaporation into account. The results describe consistently all presently observed surface structures.