Direct observation of a local thermal vibration anomaly in a quasicrystal

Quasicrystals have long-range order with symmetries that are incompatible with periodicity, and are often described with reference to a higher-dimensional analogue of a periodic lattice. Within the context of this 'hyperspace' crystallography, lattice dynamics of quasicrystals can be described by a combination of lattice vibrations and atomic fluctuations--phonons and phasons. However, it is difficult to see localized fluctuations in a real-space quasicrystal structure, and so the nature of phason-related fluctuations and their contribution to thermodynamic stability are still not fully understood. Here we use atomic-resolution annular dark-field scanning transmission electron microscopy to map directly the change in thermal diffuse scattering intensity distribution in the quasicrystal, through in situ high-temperature observation of decagonal Al72Ni20Co8. We find that, at 1,100 K, a local anomaly of atomic vibrations becomes significant at specific atomic sites in the structure. The distribution of these localized vibrations is not random but well-correlated, with a quasiperiodic length scale of 2 nm. We are able to explain this feature by an anomalous temperature (Debye-Waller) factor for the Al atoms that sit at the phason-related sites defined within the framework of hyperspace crystallography. The present results therefore provide a direct observation of local thermal vibration anomalies in a solid.     

Observation of random-phase lattice solitons

The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or 'discrete') solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.     

Quasicrystalline valence bands in decagonal AlNiCo

Quasicrystals are metallic alloys that possess perfect long-range structural order, in spite of the fact that their rotational symmetries are incompatible with long-range periodicity. The exotic structural properties of this class of materials are accompanied by physical properties that are unexpected for metallic alloys. Considerable progress in resolving the geometric structures of quasicrystals has been made using X-ray and neutron diffraction, and concepts such as the quasi-unit-cell model have provided theoretical insights. But the basic properties of the valence electronic states--whether they are extended as in periodic crystals or localized as in amorphous materials--are still largely unresolved. Here we investigate the electronic bandstructure of quasicrystals through angle-resolved photoemission experiments on decagonal Al71.8Ni14.8Co13.4. We find that the s-p and d states exhibit band-like behaviour with the symmetry of the quasiperiodic lattice, and that the Fermi level is crossed by dispersing d-bands. The observation of free-electron-like bands, distributed in momentum space according to the surface diffraction pattern, suggests that the electronic states are not dominated by localization.     

Experimental measurement of the photonic properties of icosahedral quasicrystals

Quasicrystalline structures may have optical bandgap properties-frequency ranges in which the propagation of light is forbidden-that make them well-suited to the scientific and technological applications for which photonic crystals are normally considered. Such quasicrystals can be constructed from two or more types of dielectric material arranged in a quasiperiodic pattern whose rotational symmetry is forbidden for periodic crystals (such as five-fold symmetry in the plane and icosahedral symmetry in three dimensions). Because quasicrystals have higher point group symmetry than ordinary crystals, their gap centre frequencies are closer and the gaps widths are more uniform-optimal conditions for forming a complete bandgap that is more closely spherically symmetric. Although previous studies have focused on one-dimensional and two-dimensional quasicrystals, where exact (one-dimensional) or approximate (two-dimensional) band structures can be calculated numerically, analogous calculations for the three-dimensional case are computationally challenging and have not yet been performed. Here we circumvent the computational problem by doing an experiment. Using stereolithography, we construct a photonic quasicrystal with centimetre-scale cells and perform microwave transmission measurements. We show that three-dimensional icosahedral quasicrystals exhibit sizeable stop gaps and, despite their quasiperiodicity, yield uncomplicated spectra that allow us to experimentally determine the faces of their effective Brillouin zones. Our studies confirm that they are excellent candidates for photonic bandgap materials.     

Supramolecular dendritic liquid quasicrystals

A large number of synthetic and natural compounds self-organize into bulk phases exhibiting periodicities on the 10(-8)-10(-6) metre scale as a consequence of their molecular shape, degree of amphiphilic character and, often, the presence of additional non-covalent interactions. Such phases are found in lyotropic systems (for example, lipid-water, soap-water), in a range of block copolymers and in thermotropic (solvent-free) liquid crystals. The resulting periodicity can be one-dimensional (lamellar phases), two-dimensional (columnar phases) or three dimensional ('micellar' or 'bicontinuous' phases). All such two- and three-dimensional structures identified to date obey the rules of crystallography and their symmetry can be described, respectively, by one of the 17 plane groups or 230 space groups. The 'micellar' phases have crystallographic counterparts in transition-metal alloys, where just one metal atom is equivalent to a 10(3)-10(4)-atom micelle. However, some metal alloys are known to defy the rules of crystallography and form so-called quasicrystals, which have rotational symmetry other than the allowed two-, three-, four- or six-fold symmetry. Here we show that such quasiperiodic structures can also exist in the scaled-up micellar phases, representing a new mode of organization in soft matter.     

固体中的原子相关性和Bragg衍射

提出一个描述固体结构的新方法——原子相关性方法。给出原子相关性、相关性基矢、相关性格子及其倒格子的定义,分析对比原子相关性在晶体、准晶和非晶中的不同表现。从原子相关性出发讨论了固体的衍射问题,说明准晶也能产生明锐的Bragg衍射并导出普遍形式的Laue方程。     

Growth of decagonal quasicrystal phase in laser resolidified Al72Ni12Co16

An ultra-high temperature gradient directional solidification process produced by a widened laser beam was adopted to achieve the directionally solidified microstructure of the stable decagonal quasicrystal phase in Al₇₂Ni₁₂Co₁₆ alloy. X-ray, SEM, TEM and optical microscopy techniques were used to investigate the microstructures and identify the phase. The directionally solidified decagonal quasicrystal showed the facet morphology and grew in lateral growth mode. The unusual periodic and quasiperiodic atomic structures of the decagonal quasicrystal and the epitaxial growth in the melt pool were considered to be the key factors influencing the growth morphology. The experimental results were consistent with the Toner’s theoretical atomistic growth model.     

Snapshots of cooperative atomic motions in the optical suppression of charge density waves

Macroscopic quantum phenomena such as high-temperature superconductivity, colossal magnetoresistance, ferrimagnetism and ferromagnetism arise from a delicate balance of different interactions among electrons, phonons and spins on the nanoscale. The study of the interplay among these various degrees of freedom in strongly coupled electron-lattice systems is thus crucial to their understanding and for optimizing their properties. Charge-density-wave (CDW) materials, with their inherent modulation of the electron density and associated periodic lattice distortion, represent ideal model systems for the study of such highly cooperative phenomena. With femtosecond time-resolved techniques, it is possible to observe these interactions directly by abruptly perturbing the electronic distribution while keeping track of energy relaxation pathways and coupling strengths among the different subsystems. Numerous time-resolved experiments have been performed on CDWs, probing the dynamics of the electronic subsystem. However, the dynamics of the periodic lattice distortion have been only indirectly inferred. Here we provide direct atomic-level information on the structural dynamics by using femtosecond electron diffraction to study the quasi two-dimensional CDW system 1T-TaS(2). Effectively, we have directly observed the atomic motions that result from the optically induced change in the electronic spatial distribution. The periodic lattice distortion, which has an amplitude of ～0.1??, is suppressed by about 20% on a timescale (～250 femtoseconds) comparable to half the period of the corresponding collective mode. These highly cooperative, electronically driven atomic motions are accompanied by a rapid electron-phonon energy transfer (～350 femtoseconds) and are followed by fast recovery of the CDW (～4 picoseconds). The degree of cooperativity in the observed structural dynamics is remarkable and illustrates the importance of obtaining atomic-level perspectives of the processes directing the physics of strongly correlated systems.     

Growth of decagonal quasicrystal phase in laser resolidified Al72Ni12Co16

An ultra-high temperature gradient directional solidification process produced by a widened laser beam was adopted to achieve the directionally solidified microstructure of the stable decagonal quasicrystal phase in Al72Ni12Co16 alloy. X-ray, SEM, TEM and optical microscopy techniques were used to investigate the microstructures and identify the phase. The directionally solidified decagonal quasicrystal showed the facet morphology and grew in lateral growth mode. The unusual periodic and quasiperiodic atomic structures of the decagonal quasicrystal and the epitaxial growth in the melt pool were considered to be the key factors influencing the growth morphology. The experimental results were consistent with the Toner's theoretical atomistic growth model.     

Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices

Nonlinear periodic lattices occur in a large variety of systems, such as biological molecules, nonlinear optical waveguides, solid-state systems and Bose-Einstein condensates. The underlying dynamics in these systems is dominated by the interplay between tunnelling between adjacent potential wells and nonlinearity. A balance between these two effects can result in a self-localized state: a lattice or 'discrete' soliton. Direct observation of lattice solitons has so far been limited to one-dimensional systems, namely in arrays of nonlinear optical waveguides. However, many fundamental features are expected to occur in higher dimensions, such as vortex lattice solitons, bright lattice solitons that carry angular momentum, and three-dimensional collisions between lattice solitons. Here, we report the experimental observation of two-dimensional (2D) lattice solitons. We use optical induction, the interference of two or more plane waves in a photosensitive material, to create a 2D photonic lattice in which the solitons form. Our results pave the way for the realization of a variety of nonlinear localization phenomena in photonic lattices and crystals. Finally, our observation directly relates to the proposed lattice solitons in Bose-Einstein condensates, which can be observed in optically induced periodic potentials.     

急冷Al-Mn合金中准晶相的形态和化学组成

使用透射式电子显微镜(TEM)观察了Al-12Mn和Al-10Mn-2Fe合金中准晶相的显微形态,选区电子衍射(SAD)做结构分析,用TEM的能谱附件(EDXS)分析准晶相的化学成分。结果表明,典型的准晶相具有菊花状形态,其当量组成非常接近Al_4Mn,准晶相的形态表明它的形成长大机制可能介于非晶和晶体之间;而且,铁的加入促进了合金中准晶相的形成。     

1维正方准晶的2类接触问题

利用广义复变函数方法研究了1维正方准晶的2类接触问题,即有限摩擦接触和半平面粘结接触问题,得到了刚性平底压头作用下压头下方接触应力及接触位移的显式表达式.结果表明:(i)对于有限摩擦接触问题,接触应力在压头边缘呈现-1/2±θ阶奇异性,其中θ由准晶的弹性常数和摩擦系数确定; 对于半平面粘结接触问题,接触应力在压头的边缘显现出-1/2±iε阶奇异性,其中ε由准晶的弹性常数确定;(ii)由数值算例可知,对于2类接触问题,接触应力在压头下方分布规律相似; 接触位移与声子场作用力之间成正比例关系; 接触应力在接触区边缘变化非常剧烈,且产生了应力集中现象.在一定条件下可得到1维4方和6方准晶2类接触问题的解.     

Archimedean-like tiling on decagonal quasicrystalline surfaces

Monolayers on crystalline surfaces often form complex structures with physical and chemical properties that differ strongly from those of their bulk phases. Such hetero-epitactic overlayers are currently used in nanotechnology and understanding their growth mechanism is important for the development of new materials and devices. In comparison with crystals, quasicrystalline surfaces exhibit much larger structural and chemical complexity leading, for example, to unusual frictional, catalytical or optical properties. Deposition of thin films on such substrates can lead to structures that may have typical quasicrystalline properties. Recent experiments have indeed showed 5-fold symmetries in the diffraction pattern of metallic layers adsorbed on quasicrystals. Here we report a real-space investigation of the phase behaviour of a colloidal monolayer interacting with a quasicrystalline decagonal substrate created by interfering five laser beams. We find a pseudomorphic phase that shows both crystalline and quasicrystalline structural properties. It can be described by an archimedean-like tiling consisting of alternating rows of square and triangular tiles. The calculated diffraction pattern of this phase is in agreement with recent observations of copper adsorbed on icosahedral Al(70)Pd(21)Mn(9) surfaces. In addition to establishing a link between archimedean tilings and quasicrystals, our experiments allow us to investigate in real space how single-element monolayers can form commensurate structures on quasicrystalline surfaces.     

Visualizing dislocation nucleation by indenting colloidal crystals

The formation of dislocations is central to our understanding of yield, work hardening, fracture, and fatigue of crystalline materials. While dislocations have been studied extensively in conventional materials, recent results have shown that colloidal crystals offer a potential model system for visualizing their structure and dynamics directly in real space. Although thermal fluctuations are thought to play a critical role in the nucleation of these defects, it is difficult to observe them directly. Nano-indentation, during which a small tip deforms a crystalline film, is a common tool for introducing dislocations into a small volume that is initially defect-free. Here, we show that an analogue of nano-indentation performed on a colloidal crystal provides direct images of defect formation in real time and on the single particle level, allowing us to probe the effects of thermal fluctuations. We implement a new method to determine the strain tensor of a distorted crystal lattice and we measure the critical dislocation loop size and the rate of dislocation nucleation directly. Using continuum models, we elucidate the relation between thermal fluctuations and the applied strain that governs defect nucleation. Moreover, we estimate that although bond energies between particles are about fifty times larger in atomic systems, the difference in attempt frequencies makes the effects of thermal fluctuations remarkably similar, so that our results are also relevant for atomic crystals.     

Single-spin addressing in an atomic Mott insulator

Ultracold atoms in optical lattices provide a versatile tool with which to investigate fundamental properties of quantum many-body systems. In particular, the high degree of control of experimental parameters has allowed the study of many interesting phenomena, such as quantum phase transitions and quantum spin dynamics. Here we demonstrate how such control can be implemented at the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focused laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line, and observed that our addressing scheme leaves the atoms in the motional ground state. The results should enable studies of entropy transport and the quantum dynamics of spin impurities, the implementation of novel cooling schemes, and the engineering of quantum many-body phases and various quantum information processing applications.     

Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+delta

Although the crystal structures of the copper oxide high-temperature superconductors are complex and diverse, they all contain some crystal planes consisting of only copper and oxygen atoms in a square lattice: superconductivity is believed to originate from strongly interacting electrons in these CuO2 planes. Substituting a single impurity atom for a copper atom strongly perturbs the surrounding electronic environment and can therefore be used to probe high-temperature superconductivity at the atomic scale. This has provided the motivation for several experimental and theoretical studies. Scanning tunnelling microscopy (STM) is an ideal technique for the study of such effects at the atomic scale, as it has been used very successfully to probe individual impurity atoms in several other systems. Here we use STM to investigate the effects of individual zinc impurity atoms in the high-temperature superconductor Bi2Sr2CaCu2O8+delta. We find intense quasiparticle scattering resonances at the Zn sites, coincident with strong suppression of superconductivity within approximately 15 A of the scattering sites. Imaging of the spatial dependence of the quasiparticle density of states in the vicinity of the impurity atoms reveals the long-sought four-fold symmetric quasiparticle 'cloud' aligned with the nodes of the d-wave superconducting gap which is believed to characterize superconductivity in these materials.     

准晶材料中螺型位错与圆形夹杂的干涉效应

研究了一维六方准晶材料中螺型位错与圆形夹杂的干涉效应.利用复变函数方法,得到了由复势函数表示的边界条件以及应力场和位错力的解析表达式.并详细讨论了位错位置和材料差异对位错力及平衡位置的影响.结果表明,当两种准晶材料常数满足一定条件时,夹杂附近存在一个位错平衡位置.另外,位错力受到夹杂相位子场弹性常数和声子场-相位子场耦合弹性常数的强烈影响,相位子场弹性常数和声子场-相位子场耦合弹性常数均存在可以改变位错力方向的临界值.解答的特殊情况与已有文献一致.     

Ionic colloidal crystals of oppositely charged particles

Colloidal suspensions are widely used to study processes such as melting, freezing and glass transitions. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive, short-range attractive, hard-sphere-like and dipolar, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.     

一维正方准晶的无摩擦接触问题

利用复变函数方法研究了一维正方准晶的无摩擦接触问题,得到了刚性平底压头作用下接触面上应力函数、接触应力及接触位移的显示表达式。结果表明:1接触应力在压头边缘具有-1/2阶的奇异性;2压头下方接触位移与声子场作用力成比例关系。数值算例分析并验证了结论的正确性。在一定条件下,结果可退化为一维四方和六方准晶无摩擦接触问题的解。所得结论为研究准晶材料的接触变形提供了重要的力学量。