9th International Conference on Quasicrystals
May 22 - 26, 2005
Scheman Building
Iowa State University
Ames, IA 50011 USA
ICQ9@ameslab.gov
(515) 294-4896
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Invited Speakers
(in alphabetical order)
"Quantum Dynamical Properties of Quasicrystals"
David Damanik1
1California Institute of Technology, Pasadena, CA 91125 USA
Presentation Type: Invited Talk
Topic: MathematicsAbstract:
To analyze electronic transport properties of a quasicrystal model one has to study spectral and quantum dynamical properties of the associated Schrödinger operator. In this talk, we will survey methods and results dealing with this issue. The situation in one dimension is particularly well understood. The occurrence of extended states for isolated energies in certain models, observed in the early 1990's, was recently shown to have strong quantum dynamical implications. We will explain this connection and the resulting lower bounds on quantum transport. Higher-dimensional models and results, along with a number of open problems, will be discussed as well.
"Phonon Dynamics in the Icosahedral and 1/1 Periodic Approximant of the CdYb and ZnMgSc Phase"
Marc de Boissieu1, Sonia Francoual1, Kaoru Shibata2, Roland Currat3
1LTPCM, UMR CNRS 5614, ENSEEG BP 75 38402 St Martin d'Hères Cedex, France
2Neutron Science Research Center, Tokai Research Establishment, Japan Atomic Energy Research Institute, Japan
3Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
Presentation Type: Invited Talk
Topic: Thermal and Dynamical PropertiesAbstract:
The recent discovery of the i-Cd5.7Yb and i-Zn80Mg5Sc15 QC phases, for which both the icosahedral and the 1/1 cubic approximant phases can be easily grown as single grains, opened new possibilities for the understanding of the dynamics of quasicrystals. Quasicrystals and approximants can be described as a compact quasiperiodic or periodic packing of the same icosahedral atomic clusters. Comparing the phonon dynamics in both systems should allow a better understanding of what is the respective influence of the local order (atomic clusters) and of the long range quasiperiodic order on the dynamical response of the system. Moreover, the atomic clusters which constitute the CdYb and ZnMgSc phases are of a new kind, i.e., neither of Mackay type as in i-AlPdMn nor of Bergman type as in i-ZnMgY. We present a detailed comparative study of the phonon dynamics carried out on single-grains of the i- and approximant phases of the CdYb and ZnMgSc systems using Inelastic X-ray and Neutron Scattering. Those results will be compared with the one obtained in crystalline phases of moderated structural complexity for which dynamical calculations can be performed more easily.
"Scanning Tunneling Spectroscopy and High Resistivity in Quasicrystalline Alloys"
Julien Delahaye1, Thomas Schaub1, Claire Berger1
1LEPES - CNRS, 38042 Grenoble Cedex 9 France
Presentation Type: Invited Talk
Topic: SurfacesAbstract:
Very low electrical conductivity σ is experimentally observed in a number of Al-based icosahedral alloys containing transition metals. Conductance scaling laws [1] and detailed analysis [2] of the temperature dependence of conductivity σ(T) all point to a metal-insulator transition in icosahedral Al-Pd-Re. The conductivity is essentially determined by the electronic mobility and the density of states (DOS) at the Fermi level EF, which we will address here. There is a consensus for the presence of a broad pseudogap, about 1eV wide around EF, but the structure of the DOS on a smaller energy scale (1-100meV) is still debated. We present our results obtained by low temperature Scanning Tunneling Spectroscopy (STS) [3] on three icosahedral phases (i-Al-Pd-Mn, i-Al-Cu-Fe and i-Al-Pd-Re). The measurements give evidence for the presence of a narrow square root energy-dependent pseudogap centered at EF. Similar square root dependence was observed in disordered systems close to the Mott-Anderson metal-insulator transition. We propose a scenario to explain the similarity between disordered and quasicrystalline systems that give a coherent picture of the metal-insulator transition in these icosahedral phases. We also compare our results with other tunneling spectroscopy studies of quasicrystalline alloys.
[1] J. Delahaye et al. Phys. Rev. B 64, 094203 (2001).
[2] J. Delahaye et al. . J. Phys.: Condens. Matter 15 8753 (2003).
[3] J. Delahaye et al. Phys. Rev. B 64, 214201 (2003).
"Cluster-Based Composition Rules for Quasicrystals"
Chuang Dong1, Jianbing Qiang1, Yingmin Wang1, Patricia Thiel2
1State Key Lab. of Materials Modification, Dalian University of Technology, 116024 Dalian, China
2Ames Laboratory, Ames, IA 50011 US
Presentation Type: Invited Talk
Topic: Structural Evolution and Phase StabilityAbstract:
Although hundreds of quasicrystals have been found, little is known about their quantitative composition rules that can help design new materials. In this paper we propose cluster-based composition criteria that are related to quasicrystal structure and stabilization mechanisms. For a binary quasicrystal of the icosahedral glass type, the composition is mainly determined by topological close packing of the atoms in the basic 1st-shell icosahedron. A ternary quasicrystal is located at the crossing point of two kinds of specific lines in a ternary phase diagram, which we term e/a-constant and e/a-variant lines, respectively. The e/a-constant line reflects the common electronic structure shared by the quasicrystal and its e/a-constant approximants. The e/a-variant line, defined by linking the composition of a binary cluster composition, to the third element, implies the growth pathway of a basic cluster towards final quasicrystalline and crystalline phases along the line. These simple rules are general in quasicrystalline systems. Applications of these rules in two exemplary systems, Al-Ni-Fe and Zr-Ti-Ni, are presented. Similar rules are also extended to the bulk metallic glass forming systems.
"Tunneling Spectroscopy of Tb-Mg-Zn Quasicrystals"
Roberto Escudero1
1Universidad Nacional Autönoma de México, Mexico, DF 04710 MEXICO
Presentation Type: Invited Talk
Topic: Electronic and Magnetic PropertiesAbstract:
Theoretical studies on quasicrystals (QC) predict that the electronic density of states will have a rich and fine spiky structure, and a pseudo-gap. Experimentally the pseudo-gap feature has been found at the Fermi level and determined by different spectroscopic techniques and by specific heat measurements. However, the predicted rich and fine spiky structural characteristics on the density of states have not been observed and it has been very elusive. The problem with its absence has been related, from the experimental point of view, to poor structural characteristics of the studied QCs specimens. From the theoretical point of view recent calculation have shown that the fine structure indeed exist, but only for approximants phases. The understanding and improvement for fabrication of single grain QCs, actually have had great advances. Today single grain materials can be prepared with good quasicrytalline perfection and purity. In this report we are presenting tunnelling studies performed in samples of very high quality. We have observed for the first time, a spiky structure on the electronic density of states. Our results open again the debate about the theoretical predictions, and support the picture of the spiky nature on the density of states, and also confirm the existence of the pseudogap at the Fermi level. We found that in general the structural features and the pseudo-gap are distinguished only at low temperatures.
R. Escudero.
Email: escu@servidor.unam.mx
"Complex Metallic Alloys: Structures, Defects and Plasticity"
Michael Feuerbacher1
1Forschungszentrum Juelich GmbH, 52425 Juelich Germany
Presentation Type: Invited Talk
Topic: Mechanical Properties and ApplicationsAbstract:
Complex metallic alloys (CMAs) represent a class of materials increasingly attracting interest. These materials show characteristic structural features substantially deviating from those of simple metals. They possess large lattice constants and correspondingly a high number of atomic positions per unit cell. As a result, a novel type of local order can form, which is frequently dominated by icosahedral-symmetric atom coordinations. These salient structural features open up the possibility for novel physical properties.
Representing a new field in materials science, the physical properties of CMAs have hardly been investigated to date. However, as a result of the particular structure of CMA phases, principle physical questions arise. In this talk, we will focus on the plasticity of these materials, and the following questions will be addressed: Is the macroscopic plastic behaviour comparable to that of ordinary crystals with simpler structures? What is the structure of defects, particularly of dislocations, if the translational invariant distances are much larger than energetically acceptable Burgers-vector lengths? What are the mechanisms of dislocation movement in such complex structures? Will planar faults be introduced upon dislocation movement?
In this contribution current work in the field of plasticity of complex intermetallic alloys will be reviewed. We will present experimental results on the plastic behaviour of a number of CMAs with up to 1500 atoms per unit cell. It will be demonstrated that completely novel mechanisms occur, involving new types of defect such as the recently discovered metadislocation [H. Klein, M. Feuerbacher, P. Schall and K. Urban, Phys. Rev. Lett. 82, 1999, 3468] and uncommon macroscopic plastic behaviour [M. Feuerbacher, H. Klein and K. Urban, Phil. Mag. Lett. 81, 2001, 639].
"Bi Nano-Structures Grown on the 5-Fold Surface of Al-Cu-Fe"
Vincent Fournée1, Hem-Raj Sharma2, Masahiko Shimoda2, Amy Ross3, Tom Lograsso3, An-Pang Tsai2
1CNRS- Nancy, 54 042 Nancy France
2NIMS, 1-2-1 Sengen, Tsukuba-shi, Ibaraki 305-0047 Japan
3Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
Presentation Type: Invited Talk
Topic: SurfacesAbstract:
The growth of a Bi thin film deposited on the 5-fold surface of an Al63Cu24Fe13 icosahedral quasicrystal is investigated by scanning tunnelling microscopy (STM) and reflection high energy electron diffraction (RHEED). The growth was investigated both at high temperature (250°C) and at room temperature. For deposition at high temperature, we basically observe the formation of the pseudomorphic layer expected based on the previous report by Franke et al. At submonolayer coverage, we found that the island density vary from terrace to terrace, suggesting that nucleation of Bi islands occurs at specific quasilattice sites having a density that is also terrace specific. For room temperature deposition, we observe the formation of crystalline Bi islands with flat tops and steep edges on top of a Bi wetting layer. The Bi islands exist in five different orientations (five-fold twinning) and they have uniform heights corresponding to two atomic layers (~ 6Å) or a multiple of this height. We will argue that the driving force for the island height selection is related to quantum size effects (QSE): the minimization of the energy of the electron confined within the Bi islands favors a preferred thickness. This shows that the unusual electronic structure of the substrate influences the film morphology, in producing a confinement barrier for the electron at the film/substrate interface.
"On Structural Complexity without Local Pentagonal Symmetry"
Yuri Grin1, Magnus Botroem1
1Max-Planck-Institut fuer Chemische Physik fester Stoffe, 01187 Dresden Germany
Presentation Type: Invited Talk
Topic: StructureAbstract:
Local pentagonal or pseudo pentagonal symmetry is one of the basic characteristics of the crystal structures of approximants (cf. Mackay or Bergman clusters). Several binary and ternary transition metal compounds with aluminium and gallium in the concentration region close to quasicrystalline phases and their approximants reveal this feature resulting in a strong structural complexity in different variations.
Detailed investigations were performed in binary systems of 4d and 5d transition metals (i.e., rhodium and iridium) with aluminium and gallium. Several new compounds with large crystal structures and different levels of complexity occur in the aluminium-or gallium-rich regions. Here, the complexity appears without local pentagonal or pseudo pentagonal symmetry, e.g., the binary compound Ir13Al45 is the first representative of a newstructure type (Pearson symbol oP232). The structure shows a partial local disorder in vicinity of some aluminium positions. This feature resembles many approximant structures. But, in contrary to the latter, covalent interactions between Ir and Al result in very irregular coordination of the iridium atoms. This causes low-symmetrical columnar packing of aluminium polyhedra centred by iridium atoms showing a pseudo pentagonal motif only in very rough approximation.
Chemical bonding in different structures belonging to this group is attempted to be interpreted applying the electron localization function. This kind of bonding analysis allows preliminary classifying of interatomic contacts in different groups and reveals a transition from two-centre to multi-centre bonds even in the neighbouring regions of the crystal structure.
"Short-Range Order in Undercooled and Stable Melts Forming Quasicrystals and Approximants"
Dirk Holland-Moritz1
1DLR, Institut fuer Raumsimulation, D-51147 Koeln Germany
Presentation Type: Invited Talk
Topic: Structural Evolution and Phase StabilityAbstract:
Following the pioneering work by Frank, an icosahedral short-range order should be energetically favored in undercooled metallic melts. This hypothesis was recently experimentally confirmed by diffraction experiments on stable and undercooled melts of pure metals.
In this work systematic in-situ studies on the short-range order of stable and undercooled liquids of alloys (Al13(Co,Fe)4, Al-Cu-Fe and Al-Cu-Co) forming quasicrystalline and polytetrahedral phases are presented. The liquids were containerlessly processed und undercooled by use of the electromagnetic levitation technique, which was combined with elastic neutron scattering and with energy dispersive diffraction of synchrotron radiation, in order to determine the structure factors of the liquids.
The diffraction studies indicate that an icosahedral topological short-range order prevails in all of the investigated stable and undercooled melts. For Al13(Co,Fe)4 melts partial structure factors were determined by variation of the Co/Fe ratio. This allows to analyze both the topological and the chemical short-range order as a function of the temperature. The partial structure factors indicate that the icosahedral topological short-range order is accompanied by a pronounced chemical short-range order such that the first coordination shell around the transition metal atoms consists preferentially of Al-atoms. An enhancement of the topological and the chemical short-range order is observed, if the temperature is decreased. The influence of the short-range order in the liquid phase on the nucleation behavior of solid phases in undercooled liquids is discussed.
This work was supported by Deutsche Forschungsgemeinschaft (DFG) under contract Nos. Ho1942/1, Ho1942/2 and Ho1942/4.
"Hydrogen Storage in Ti-Zr- and Ti-Hf- Based Quasicrystals"
Kenneth Kelton1
1Washington University, St. Louis, MO 63130 USA
Presentation Type: Invited Talk
Topic: Mechanical Properties and ApplicationsAbstract:
The depletion of the world's petroleum reserves and the increased environmental impact of conventional combustion-engine-powered automobiles are leading to renewed interest in hydrogen storage materials. The numerous tetrahedral interstitial sites in icosahedral quasicrystals, structurally favorable sites for hydrogen adsorption, give these novel phases potential technological importance. The most promising are the Ti-Zr-Ni and Ti-Hf-Ni i-phases, due to their favorable alloy chemistry and the low-cost of the constituent materials. While several years ago, these were demonstrated to store large amounts of hydrogen (to a weight percent of 2.5%, exceeding that of LaNi5) with relatively rapid absorption, the hydrogen equilibrium vapor pressures of the hydrogenated quasicrystals were too low at reasonable desorption temperatures to be practically important. Recent advances, however, have improved their prospects. We have recently discovered a relatively flat plateau at high pressures (100 – 200 psi) for hydrogen concentrations up to 2.8 hydrogen atoms per metal atom (H/M = 2.8) in a Ti41.5Zr41.5Ni17 quasicrystal, exceeding a weight percent of 4%. Hydrogen desorption from H/M = 2.8 to 1.6 was demonstrated at temperatures between 100 °C and 200 °C. Absorption and cycling are improved in mechanically milled powders that contain nanometer i-phase grains. The formation of a crystal hydride in Ti41.5Zr41.5Ni17 during absorption from the gas phase is dramatically decreased in Ti40Hf40Ni20 quasicrystals, suggesting an improved cycling ability for those quasicrystals. An overview of research on hydrogen in quasicrystals will be presented, focusing both on their potential for technological applications and the fundamental insight that can be gained by using hydrogen as a probe of quasicrystal structure and dynamics.
*Supported by the National Science Foundation under grant DMR 03-07410.
"Tile-Decoration Model of Co-rich d-AlCoNi Derived from W-AlCoNi Approximant"
Marek Mihalkovic1, Christopher Henley2, Nan Gu3, Michael Widom4
1Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava Slovakia
4Carnegie Mellon University, Pittsburgh, PA 15213 USA
Presentation Type: Invited Talk
Topic: StructureAbstract:
We use ab-initio total energy calculations to refine chemical ordering of the W-AlCoNi approximant structure (Sugiyama et al., 2002), and calculate its stability relative to other ternary and binary competing compounds. The approximant structure has 8Å stacking periodicity along pseudo-5-fold axis, but due to its monoclinic centering the 8Å periodicity results from stacking two identical 4Å thick bilayers, with stacking vector not parallel to the pseudo-5-fold axis. We show how this ordering generalizes into a tile-decoration model of a quasicrystal phase, in which 4Å bilayers are bound to a "binary" (3-level) version of Hexagon-Boat-Star decagonal tiling with 6.5Å edge length, while tilings adjacent along the stacking direction may exhibit mismatches bounded within octagonal supertiles, analogical with octagonal clusters facilitating tile-reshuffling update move for binary Penrose tiling. In such description, the approximant structure is a dense packing of the octagon clusters, suggesting a negative energy coefficient for the mismatched regions, and 8Å superorder at low temperatures.
"The Hume-Rothery Electron Concentration Rule for a Series of γ-Brasses Studied by FLAPW Band Calculations"
Uichiro Mizutani1, Ryoji Asahi2, Hirokazu Sato3, Tsunehiro Takeuchi4
1Nagoya University, Dept.Cryst.Mat.Sci., 464-8603 Nagoya Japan
2Toyota Central R&D Laboratories, Inc., Nagakute, Aichi, 480-1192, Japan
3Department of Physics, Aichi University of Education, Kariya-shi, Aichi, 448-8542, Japan
4Ecotopia Science Institute, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Presentation Type: Invited Talk
Topic: Electronic and Magnetic PropertiesAbstract:
The theoretical interpretation of the Hume-Rothery electron concentration rule has been attempted by performing the FLAPW (Full-Potential Linearized Augmented Plane Wave) band calculations for a series of γ-brasses, which include Cu5Zn8, Cu9Al4, Pd2Zn11, Ni2Zn11, Co2Zn11 and Fe2Zn11. In the past, the LMTO band calculations, in which the wave function is composed of the atomic orbitals or muffin-tin orbitals, had been exclusively employed for structurally complex alloy phases like 1/1-cubic approximants and consistently pointed to the importance of orbital hybridization effects on the formation of the pseudogap. This is, however, not always best suited to explore the Hume-Rothery electron concentration rule. We believe the FLAPW method to extract most transparently the Fermi surface-Brillouin zone interaction responsible for the formation of the pseudogap, regardless of the degree of orbital hybridizations, and to allow us to discuss the Hume-Rothery rule in a more straightforward manner. We evaluated the Fourier spectrum of the FLAPW wave function for states at the point N on the {110} zone plane at energy eigenvalues sustaining the pseudogap. It directly proved that the {330} and {411} zones do play a crucial role in the formation of the pseudogap below the Fermi level for Cu5Zn8, Cu9Al4, Pd2Zn11 and Ni2Zn11 γ-brasses. This is taken as a straightforward demonstration of the empirical Hume-Rothery matching rule for γ-brasses beyond the oversimplified free electron model by Mott and Jones in 1936. There exist, however, exceptions to this universal behavior. In the case of the Co2Zn11 and Fe2Zn11, the pseudogap is still formed by resonating with {330} and {411} zones but is positioned above the Fermi level because of the presence of Co- and Fe-3d states across the Fermi level. The discussion will be focused on what is meant on the Hume-Rothery electron concentration rule for all γ-brasses studied by taking into account both the FLAPW band calculations and equilibrium phase diagrams.
"Electronic Transport Behaviors of Bulk Insulating QC AlPdRe Samples"
Ralph Rosenbaum1
1Tel Aviv University, 69978 Ramat Aviv Israel
Presentation Type: Invited Talk
Topic: Electronic and Magnetic PropertiesAbstract:
Zero field resistivity and magnetoresistance (MR) data on a 3D insulating QC AlPdRe sample are presented in the temperature range from 300 K to 0.0204 K and in a magnetic field range from 0 T to 18 T. This QC sample had a resistance temperature ratio of 66. From 300 K to 90 K, the conductivity exhibited a simple temperature power law dependence with an exponent z = 1.55. Below 90 K, there was a crossover to a weaker power law having an exponent z = 0.90, valid below 10 K to 0.5 K. Below 0.5 K, there was a second crossover to an activated variable-range hopping (VRH) law having a hopping exponent y = 0.294 and characteristic temperature T0 = 3.65 K. The presence of a second phase in this sample made a major contribution to the measured conductivity below 1 K; in order to study the QC conductivity contribution, this second phase conductivity was estimated at T = 0 K and its value was subtracted off from the measured conductivity values. At 1 K the MR data can be explained using the saturation conductivity and the forward interference theory of Lien Van Nyugen and the wave function shrinkage model of Ioselevich and Schoepe. The MR behavior below 0.2 K is highly anomalous at very small fields where the MR follows a B0.63 law dependence; this is to be contrasted to the quadratic B2 dependence that is predicted theoretically in many MR theories.
Data on other less insulating AlPdRe QC samples will be presented and compared.
Samples were fabricated using the arc melting technique by Prof. Shui-Tien Lin's group in Tainan, Taiwan. This work was performed at the National High Magnetic Field Lab (NHMFL) under NSF Cooperative Agreement #DMR 9527053 and by the State of Florida.
"Tilings, Tiling Spaces and Topology"
Lorenzo Sadun1
1University of Texas, Austin, TX 78712 USA
Presentation Type: Invited Talk
Topic: MathematicsAbstract:
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations (or the Euclidean group) acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the spectrum of the translation operator) are closely related to bulk properties of individual tilings (such as the diffraction pattern). The topology of the space of tilings, particularly the Cech cohomology, gives information on how original tiling may be deformed. Tiling spaces can be constructed as inverse limits of branched manifolds. These constructions apply to tilings with infinitely many allowed orientations (like the pinwheel), on which the entire Euclidean group acts, as well as to tilings (like the Penrose tiling) on which only translations act.
"Experimental Investigations on the Electronic Structure and the Low-Temperature Stability of Cd-Based Quasicrystals and their 1/1, 2/1 Cubic Approximants"
Ryuji Tamura1, Ken Minoda1, Shin Takeuchi1, Tsunehiro Takeuchi2, Keiichi Edagawa3, Takayuki Kiss4, Takayoshi Yokoya4, Shiku Shin4
1Tokyo University of Science, Noda, Chiba 278-8510 Japan
2RCAWEM, Nagoya Univ., Nagoya 464-8603, Japan
3IIS, Univ. of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
4ISSP, Univ. of Tokyo, Kashiwa, Chiba 277-8581, Japan
Presentation Type: Invited Talk
Topic: StructureAbstract:
Valence band spectra near the Fermi edge were investigated with ultrahigh energy resolution down to 7 meV for icosahedral (i) phases, 2/1 and 1/1 cubic approximants in the Cd-Yb and Cd-Ca systems. For all the studied compounds, a sharp Fermi edge, indicative of sizable density of states at the Fermi level, was clearly observed and the Fermi levels are found to be located not at the bottom of the pseudogap but at its shoulder. In addition, a peak structure appears across the Fermi level for the Cd-Ca system, which is also obtained for the Cd-Yb system when subtracting strong Yb 4f derived peaks from the spectra. Ca 2p-3d resonant photoemission spectroscopies on the Cd-Ca compounds reveal contributions from Ca 3d states at the Fermi level and they were successfully separated, which means that the Ca 3d states are descended below the Fermi level as a result of hybridization with the Cd sp states. The above features are in a satisfactory agreement with the LMTO calculations performed on the Cd6Ca 1/1 approximant.
The low-temperature stability of the Cd-based compounds was probed by various techniques such as electrical resistivity, magnetic susceptibility, specific heat measurements, X-ray and electron diffraction experiments. They all exhibit an occurrence of a phase transition at 110K and 100K for Cd6Yb and Cd6Ca, respectively. In addition, the transition temperatures are found to increase substantially under pressure up to 2 GPa for both compounds, indicating that the low-temperature phases have a higher atomic density. Formation of a superlattice with slight tetragonal-type distortion of the lattice was observed. The transitions can be understood by an orientational ordering of Cd tetrahedron located at the center of the icosahedral clusters. Moreover, a similar transition has been also observed in a number of Cd6RE (RE=rare earth metals) compounds, suggesting that it is a common feature of the Cd6M-type compounds with disordered cluster cores. The stability of the 2/1 and i phases at low temperatures will be also reported in the presentation.
"Quasiperiodic States in Linear Surface-Wave Experiments"
M. Torres1, J. Adrados1, P. Cobo2, G. Chiappe3, E. Louis3, J. Miralles3, J. Vergès4, J. Aragòn5
1Instituto de Física Aplicada, CSIC, Serrano 144, 28006 Madrid, Spain
2Instituto de Acústica, CSIC, Serrano 144, 28006 Madrid, Spain
3Departamento de Física Aplicada and Unidad Asociada of the CSIC, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain
4Departamento de Teoría de la Materia Condensada, Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, 28049 Madrid, Spain
5Centro de Física Aplicada y Tecnología Avanzada, UNAM, Apartado Postal 1-1010, Querétaro 76000, México
Presentation Type: Invited Talk
Topic: New FrontiersAbstract:
A subtle procedure to confine quasiperiodic hydrodynamic modes on the free surface of a fluid is presented here. The experiment consists of a square vessel with an immersed square central well vibrating vertically so that the surface waves generated by the meniscus at the vessel boundary interfere with the bound states of the well. This is a classical analogy of a quantum well where some fundamental phenomena, such as bonding of states and interference between free waves and bound states, can be visualized and controlled. The above mentioned interference leads to an hydrodynamic transition from quasiperiodic to periodic patterns for the first time. As it will be shown, the quantum analogs of the present experiment suggest that our results could be transferred to design quantum confinements exhibiting electronic quasiperiodic surface states and their rational approximants. On the other hand, Bloch-like surface waves associated with a quasiperiodic structure are observed in a revisited classic wave propagation experiment which consists of pulse propagation with a shallow fluid covering a quasiperiodically drilled bottom. We show that a transversal pulse propagates as a plane wave with quasiperiodic modulation, emphasizing the idea that analogous concepts to Bloch functions can be applied to hydrodynamic quasicrystals under certain circumstances.
"Investigations of Phason Statics and Dynamics"
Hans-Rainer Trebin1, Ulrich Koschella1, Mazahiro Umezaki2, Takashi Odagaki2
1ITAP, Stuttgart University, D-70550 Stuttgart Germany
2Department of Physics, Faculty of Science, Kyushu University, Fukuoka 812, Japan
Presentation Type: Invited Talk
Topic: Thermal and Dynamical PropertiesAbstract:
The experimental observation of phason fluctuations, both static and dynamic, is well established and has been interpreted within the frame of a hydrodynamical theory. Theoretically, it is still open in what temperature range a hydrodynamical description of phasons is applicable. It has been proposed in the literature that towards low temperatures the hydrodynamical regime is terminated because the form of the phason elastic energy changes from harmonic to nonanalytical. Here we report on two contributions to the field: First, for a two-dimensional binary model quasicrystal at zero temperature we have investigated the relation between atomic two-body potentials and the phason elastic energy. It turns out that there are indeed certain potentials that can induce a nonanalytic phason elastic energy. But these must have very peculiar features in their long range part rendering their existence highly improbable. Second, one solution of the hydrodynamical equations is a phasonic excitation riding a phonon. We have studied the atomistic counterpart via a nonlinear chain with double well potentials, which resembles a dynamical fibonacci sequence. We see correlated phason flips propagating with phonon excitations and can extract observables like waiting times of the particles in the wells.
"Self-Assembled Micellar Liquid Quasicrystal"
X.-B. Zeng1, G. Ungar1, Y. Liu1, V. Percec2, A. Dulcey2
1University of Sheffield, Department of Engineering Materials, Sheffield, U.K.
2University of Pennsylvania, Department of Chemistry, Philadelphia, U.S.A.
Presentation Type: Invited Talk
Topic: New FrontiersAbstract:
Taper-shaped molecules, such as benzylether dendrons with n-alkyl terminal groups, self-organize in a variety of bulk thermotropic mesophases with periodicities in the range 3-30 nm. The molecules can assemble into spheres ("micelles", or supramolecular dendrimers), which then pack on three periodic 3-d lattices with symmetries Im3m(bcc)1, Pm3n(cubic)2 and the recently discovered P42/mnm (tetragonal).3 The tetragonal and the m3n phases belong to tetrahedrally close packed (tcp) structures, or Frank-Kasper phases4, which are widespread in transition metal alloys. This indicates the commonality of transition metal atoms and supramolecular dendrimers. Here we report on the first quasicrystalline phase in a supramolecular systems, a scaled-up "micellar" version of metallic quasicrystals, presenting a new mode of organization of soft matter.
The quasicrystalline (the fourth "micellar") phase has been observed in a number of dendrimers. We have succeeded in growing monodomains of this liquid crystal phase. On the basis of small-angle X-ray diffraction of such a domain and backed by AFM imaging, it was possible to establish that the structure possesses 12-fold rotational symmetry, and is thus a dodecagonal quasicrystal.5 We have constructed a model of the structure and the simulated diffraction pattern gives a reasonable match with that recorded for all orientations. Due to their exceptionally high symmetry, the prospect of growing self-assembled quasicrystals with "periodicities" on the optical scale (still some way off) opens exciting possibilities for generating materials with a wide 3-d photonic bandgap through supramolecular self-assembly.
1 Duan, H., Hudson, S. D., Ungar, G., Holerca M. N. and Percec, V. Chem. Eur. J., 7, 4134 (2001).
2 Balagurusamy, V. S. K., Ungar, G., Percec, V., Johansson, G. J. Am. Chem. Soc., 119, 1539 (1997).
3 Ungar, G., Liu, Y. S., Zeng, X. B., Percec, V., Cho, W.-D. Science, 299, 1208 (2003).
4 Frank, F. C., Kasper, J. S. Acta Cryst., 11, 184 (1958).
5 Zeng, X.-B., Ungar, G., Liu, Y., Percec, V., Dulcey, A. E., Hobbs J. K. Nature, 428, 157 (2004).
"Recent Development in Structure Determination of Quasicrystals"
Akiji Yamamoto1, Hiroyuki Takakura2
1Advanced Materials Laboratory, NIMS, Tsukuba, Ibaraki 305-0044 Japan
2Research Center for Molecular Thermodynamics, Osaka Univ.
Presentation Type: Invited Talk
Topic: StructureAbstract:
An accurate structure determination of quasicrystal structures based on a higher-dimensional approach is made by two steps.[1] They are a model building and a structure refinement. This paper describes a recent progress in both stages.
So far, the information for an initial model in x-ray structure refinements has been given by high-resolution electron microscopy (HRTEM) images for decagonal quasicrystals (d-QCs) together with their crystal approximant (CA) structures. On the other hand, for icosahedral quasicrystals (i-QCs), it is mainly obtained by the low-density elimination method (LDEM) [2] and CA structures, since it is difficult to extract the location of atoms or clusters from HRTEM images because of the non-periodicity of i-QCs. Recently, it was clarified that the LDEM is applicable to any kinds of aperiodic crystals, including d-QCs and modulated structures. The applications of the LDEM to a d-QC and an incommensurate crystallographic shear (CS) structure[3] together with a primitive i-QC [4] will be demonstrated as examples. It will be shown that incommensurate CS structures have diffraction patterns similar to those of quasicrystals with incommensurate linear phason strain and can be described by occupation domains as well as quasicrystals. The LDEM gives a rough positions and sizes of ODs and the distribution of atoms within ODs.
In the structure refinement, each OD is subdivided into smaller ones which are occupied by different atoms or same atoms but in different local environments. In the latter case, there exists an ambiguity for the choice of subdivided ODs. There are two ways for the choice. Since quasicrystals have no period in two dimensional subspace or entire three-dimensional space, there exists no atom positions which have exactly same local environments. In one approximation, if some atoms are surrounded by similar near neighbor atoms, they are regarded as the same local environment. This leads to subdivided small ODs, which is parallel to the internal space. This method was applied to several quasicrystal structure refinements and its efficiency was verified.[5] However, this requires smaller ODs if we take into account the difference in local environments in farther neighbor. In order to prevent the increase of the number of ODs, it may be efficient to introduce continuously modulated ODs. The merit and demerit of this method will be discussed.
[1] A. Yamamoto Acra Crystallogr, A52 (1996) 509.
[2] H. Takakura et al. Phys. Rev. Lett. 86 (2001) 236.
[3] Y. Michiue, et al. Acta Crystallogr. (2004) submitted.
[4] H. Takakura Proc. ICQ9 submitted.
[5] A. Yamamoto et al. Feroelectrics, 305 (2004) 223.