Natural Quasicrystal with Decagonal Symmetry
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WHAT IS...A Quasicrystal?, Volume 53, Number 8
?WHAT IS... a Quasicrystal? Marjorie Senechal The long answer is: no one is sure. But the short an- diagrams? The set of vertices of a Penrose tiling does— swer is straightforward: a quasicrystal is a crystal that was known before Shechtman’s discovery. But with forbidden symmetry. Forbidden, that is, by “The what other objects do, and how can we tell? The ques- Crystallographic Restriction”, a theorem that confines tion was wide open at that time, and I thought it un- the rotational symmetries of translation lattices in two- wise to replace one inadequate definition (the lattice) and three-dimensional Euclidean space to orders 2, 3, with another. That the commission still retains this 4, and 6. This bedrock of theoretical solid-state sci- definition today suggests the difficulty of the ques- ence—the impossibility of five-fold symmetry in crys- tion we deliberately but implicitly posed. By now a tals can be traced, in the mineralogical literature, back great many kinds of aperiodic crystals have been to 1801—crumbled in 1984 when Dany Shechtman, a grown in laboratories around the world; most of them materials scientist working at what is now the National are metals, alloys of two or three kinds of atoms—bi- Institute of Standards and Technology, synthesized nary or ternary metallic phases. None of their struc- aluminium-manganese crystals with icosahedral sym- tures has been “solved”. (For a survey of current re- metry. The term “quasicrystal”, hastily coined to label search on real aperiodic crystals see, for example, the such theretofore unthinkable objects, suggests the website of the international conference ICQ9, confusions that Shechtman’s discovery sowed. -
Appendix F. Glossary
Appendix F. Glossary 2DEG 2-dimensional electron gas A/D Analog to digital AAAR American Association for Aerosol Research ADC Analog-digital converter AEM Analytical electron microscopy AFM Atomic force microscope/microscopy AFOSR Air Force Office of Scientific Research AIST (Japan) Agency of Industrial Science and Technology AIST (Japan, MITI) Agency of Industrial Science and Technology AMLCD Active matrix liquid crystal display AMM Amorphous microporous mixed (oxides) AMO Atomic, molecular, and optical AMR Anisotropic magnetoresistance ARO (U.S.) Army Research Office ARPES Angle-resolved photoelectron spectroscopy ASET (Japan) Association of Super-Advanced Electronics Technologies ASTC Australia Science and Technology Council ATP (Japan) Angstrom Technology Partnership ATP Adenosine triphosphate B Magnetic flux density B/H loop Closed figure showing B (magnetic flux density) compared to H (magnetic field strength) in a magnetizable material—also called hysteresis loop bcc Body-centered cubic BMBF (Germany) Ministry of Education, Science, Research, and Technology (formerly called BMFT) BOD-FF Bond-order-dependent force field BRITE/EURAM Basic Research of Industrial Technologies for Europe, European Research on Advanced Materials program CAD Computer-assisted design CAIBE Chemically assisted ion beam etching CBE Chemical beam epitaxy 327 328 Appendix F. Glossary CBED Convergent beam electron diffraction cermet Ceramic/metal composite CIP Cold isostatic press CMOS Complementary metal-oxide semiconductor CMP Chemical mechanical polishing -
Quasicrystals a New Kind of Symmetry Sandra Nair First, Definitions
Quasicrystals A new kind of symmetry Sandra Nair First, definitions ● A lattice is a poset in which every element has a unique infimum and supremum. For example, the set of natural numbers with the notion of ordering by magnitude (1<2). For our purposes, we can think of an array of atoms/molecules with a clear sense of assignment. ● A Bravais lattice is a discrete infinite array of points generated by linear integer combinations of 3 independent primitive vectors: {n1a1 + n2a2 + n3a3 | n1, n2, n3 ∈ Z}. ● Crystal structures = info of lattice points + info of the basis (primitive) vectors. ● Upto isomorphism of point groups (group of isometries leaving at least 1 fixed point), 14 different Bravais lattice structures possible in 3D. Now, crystals... ● Loosely speaking, crystals are molecular arrangements built out of multiple unit cells of one (or more) Bravais lattice structures. ● Crystallographic restriction theorem: The rotational symmetries of a discrete lattice are limited to 2-, 3-, 4-, and 6-fold. ● This leads us to propose a “functional” definition: A crystal is a material that has a discrete diffraction pattern, displaying rotational symmetries of orders 2, 3, 4 and 6. ● Note: Order 5 is a strictly forbidden symmetry → important for us. Tessellations aka tilings Now that we have diffraction patterns to work with, we consider the question of whether a lattice structure tiles or tessellates the plane. This is where the order of the symmetry plays a role. The crystals are special, as they display translational symmetries. As such, the tiling of their lattice structures (which we could see thanks to diffraction patterns) are periodic- they repeat at regular intervals. -
A Review of Transmission Electron Microscopy of Quasicrystals—How Are Atoms Arranged?
crystals Review A Review of Transmission Electron Microscopy of Quasicrystals—How Are Atoms Arranged? Ruitao Li 1, Zhong Li 1, Zhili Dong 2,* and Khiam Aik Khor 1,* 1 School of Mechanical & Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore; [email protected] (R.L.); [email protected] (Z.L.) 2 School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore * Correspondence: [email protected] (Z.D.); [email protected] (K.A.K.); Tel.: +65-6790-6727 (Z.D.); +65-6592-1816 (K.A.K.) Academic Editor: Enrique Maciá Barber Received: 30 June 2016; Accepted: 15 August 2016; Published: 26 August 2016 Abstract: Quasicrystals (QCs) possess rotational symmetries forbidden in the conventional crystallography and lack translational symmetries. Their atoms are arranged in an ordered but non-periodic way. Transmission electron microscopy (TEM) was the right tool to discover such exotic materials and has always been a main technique in their studies since then. It provides the morphological and crystallographic information and images of real atomic arrangements of QCs. In this review, we summarized the achievements of the study of QCs using TEM, providing intriguing structural details of QCs unveiled by TEM analyses. The main findings on the symmetry, local atomic arrangement and chemical order of QCs are illustrated. Keywords: quasicrystal; transmission electron microscopy; symmetry; atomic arrangement 1. Introduction The revolutionary discovery of an Al–Mn compound with 5-fold symmetry by Shechtman et al. [1] in 1982 unveiled a new family of materials—quasicrystals (QCs), which exhibit the forbidden rotational symmetries in the conventional crystallography. -
Some Considerations Relating to the Dynamics of Quasicrystals
Some considerations relating to the dynamics of quasicrystals M. Pitk¨anen Email: [email protected]. http://tgdtheory.com/public_html/. November 12, 2012 Contents 1 The dynamics of quasicrystals, the dynamics of K¨ahleraction, symbolic dynamics, and the dynamics of self-organization 1 1.1 The non-determinism for the dynamics of quasicrystals contra non-determinism of K¨ahleraction . .1 1.2 The dynamics of quasicrystals as a model for fundamental dynamics or high level sym- bolic dynamics? . .2 1.3 Could ordered water layers around biomolecules be modelled as quasicrystal like structure?3 2 What could be the variational principle behind self-organization? 4 2.1 Why Negentropy Maximization Principle should favor quasicrystals? . .5 2.2 Maximal capacity to represent information with minimal metabolic energy costs as a basic variational principle? . .5 2.3 A possible realization for 4-D dynamics favoring quasicrystal like structures . .6 2.4 Summary . .7 1 The dynamics of quasicrystals, the dynamics of K¨ahlerac- tion, symbolic dynamics, and the dynamics of self-organization The dynamics of quasicrystals looks to me very interesting because it shares several features of the dynamics of K¨ahleraction defining the basic variational principle of classical TGD and defining the dynamics of space-time surfaces. In the following I will compare the basic features of the dynamics of quasicrystals to the dynamics of preferred extremals of K¨ahleraction [K1]. Magnetic body carrying dark matter is the fundamental intentional agent in TGD inspired quantum biology and the cautious proposal is that magnetic flux sheets could define the grid of 3-planes (or more general 3-surfaces) defining quasi-periodic background fields favoring 4-D quasicrystals or more general structures in TGD Universe. -
Thirty-Fourth List of New Mineral Names
MINERALOGICAL MAGAZINE, DECEMBER 1986, VOL. 50, PP. 741-61 Thirty-fourth list of new mineral names E. E. FEJER Department of Mineralogy, British Museum (Natural History), Cromwell Road, London SW7 5BD THE present list contains 181 entries. Of these 148 are Alacranite. V. I. Popova, V. A. Popov, A. Clark, valid species, most of which have been approved by the V. O. Polyakov, and S. E. Borisovskii, 1986. Zap. IMA Commission on New Minerals and Mineral Names, 115, 360. First found at Alacran, Pampa Larga, 17 are misspellings or erroneous transliterations, 9 are Chile by A. H. Clark in 1970 (rejected by IMA names published without IMA approval, 4 are variety because of insufficient data), then in 1980 at the names, 2 are spelling corrections, and one is a name applied to gem material. As in previous lists, contractions caldera of Uzon volcano, Kamchatka, USSR, as are used for the names of frequently cited journals and yellowish orange equant crystals up to 0.5 ram, other publications are abbreviated in italic. sometimes flattened on {100} with {100}, {111}, {ill}, and {110} faces, adamantine to greasy Abhurite. J. J. Matzko, H. T. Evans Jr., M. E. Mrose, lustre, poor {100} cleavage, brittle, H 1 Mono- and P. Aruscavage, 1985. C.M. 23, 233. At a clinic, P2/c, a 9.89(2), b 9.73(2), c 9.13(1) A, depth c.35 m, in an arm of the Red Sea, known as fl 101.84(5) ~ Z = 2; Dobs. 3.43(5), D~alr 3.43; Sharm Abhur, c.30 km north of Jiddah, Saudi reflectances and microhardness given. -
Aperiodic Mineral Structures
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Infoscience - École polytechnique fédérale de Lausanne EMU Notes in Mineralogy, Vol. 19 (2017), Chapter 5, 213–254 Aperiodic mineral structures L. BINDI1 and G. CHAPUIS2 1 Dipartimento di Scienze della Terra, Universita` di Firenze, Via La Pira 4, I-50121 Firenze, Italy 2 Laboratoire de Cristallographie, E´cole Polytechnique Fe´de´rale de Lausanne, CH-1015 Lausanne, Switzerland The three-dimensional periodic nature of crystalline structures was so strongly anchored in the minds of scientists that the numerous indications that seemed to question this model struggled to acquire the status of validity. The discovery of aperiodic crystals, a generic term including modulated, composite and quasicrystal structures, started in the 1970s with the discovery of incommensurately modulated structures and the presence of satellite reflections surrounding the main reflections in the diffraction patterns. The need to use additional integers to index such diffractograms was soon adopted and theoretical considerations showed that any crystal structure requiring more than three integers to index its diffraction pattern could be described as a periodic object in a higher dimensional space, i.e. superspace, with dimension equal to the number of required integers. The structure observed in physical space is thus a three-dimensional intersection of the structure described as periodic in superspace. Once the symmetry properties of aperiodic crystals were established, the superspace theory was soon adopted in order to describe numerous examples of incommensurate crystal structures from natural and synthetic organic and inorganic compounds even to proteins. Aperiodic crystals thus exhibit perfect atomic structures with long-range order, but without any three-dimensional translational symmetry. -
Previously Unknown Quasicrystal Periodic Approximant Found in Space Received: 13 August 2018 Luca Bindi 1, Joyce Pham 2 & Paul J
www.nature.com/scientificreports OPEN Previously unknown quasicrystal periodic approximant found in space Received: 13 August 2018 Luca Bindi 1, Joyce Pham 2 & Paul J. Steinhardt3,4 Accepted: 16 October 2018 We report the discovery of Al Ni Fe , the frst natural known periodic crystalline approximant Published: xx xx xxxx 34 9 2 to decagonite (Al71Ni24Fe5), a natural quasicrystal composed of a periodic stack of planes with quasiperiodic atomic order and ten-fold symmetry. The new mineral has been approved by the International Mineralogical Association (IMA 2018-038) and ofcially named proxidecagonite, which derives from its identity to periodic approximant of decagonite. Both decagonite and proxidecagonite were found in fragments from the Khatyrka meteorite. Proxidecagonite is the frst natural quasicrystal approximant to be found in the Al-Ni-Fe system. Within this system, the decagonal quasicrystal phase has been reported to transform at ~940 °C to Al13(Fe,Ni)4, Al3(Fe,Ni)2 and the liquid phase, and between 800 and 850 °C to Al13(Fe,Ni)4, Al3(Fe,Ni) and Al3(Fe,Ni)2. The fact that proxidecagonite has not been observed in the laboratory before and formed in a meteorite exposed to high pressures and temperatures during impact-induced shocks suggests that it might be a thermodynamically stable compound at high pressure. The most prominent structural motifs are pseudo-pentagonal symmetry subunits, such as pentagonal bipyramids, that share edges and corners with trigonal bipyramids and which maximize shortest Ni–Al over Ni–Ni contacts. 1,2 Te frst decagonal quasicrystalline (QC) phase found in nature, decagonite Al71Ni24Fe5 , was discovered in the Khatyrka meteorite, a CV3 carbonaceous chondrite3–8. -
Development of Rotation Electron Diffraction As a Fully Automated And
Bin Wang Development of rotation electron Development of rotation electron diffraction as a fully automated and accurate method for structure determination and accurate automated as a fully diffraction electron of rotation Development diffraction as a fully automated and accurate method for structure determination Bin Wang Bin Wang was born in Shanghai, China. He received his B.Sc in chemistry from Fudan University in China in 2013, and M.Sc in material chemistry from Cornell University in the US in 2015. His research mainly focused on method development for TEM. ISBN 978-91-7797-646-2 Department of Materials and Environmental Chemistry Doctoral Thesis in Inorganic Chemistry at Stockholm University, Sweden 2019 Development of rotation electron diffraction as a fully automated and accurate method for structure determination Bin Wang Academic dissertation for the Degree of Doctor of Philosophy in Inorganic Chemistry at Stockholm University to be publicly defended on Monday 10 June 2019 at 13.00 in Magnélisalen, Kemiska övningslaboratoriet, Svante Arrhenius väg 16 B. Abstract Over the past decade, electron diffraction methods have aroused more and more interest for micro-crystal structure determination. Compared to traditional X-ray diffraction, electron diffraction breaks the size limitation of the crystals studied, but at the same time it also suffers from much stronger dynamical effects. While X-ray crystallography has been almost thoroughly developed, electron crystallography is still under active development. To be able to perform electron diffraction experiments, adequate skills for using a TEM are usually required, which makes ED experiments less accessible to average users than X-ray diffraction. Moreover, the relatively poor data statistics from ED data prevented electron crystallography from being widely accepted in the crystallography community. -
79Th Annual Meeting of the Meteoritical Society (2016) 6017.Pdf
79th Annual Meeting of the Meteoritical Society (2016) 6017.pdf DISCOVERY OF NEW Al-Cu-Fe MINERALS IN THE KHATYRKA CV3 METEORITE. Chi Ma1,*, Chaney Lin2, Luca Bindi3, Paul J. Steinhardt2. 1Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA; 2Department of Physics, Princeton University, Princeton, NJ 08544, USA; 3Dipartimento di Scienze della Terra, Università di Firenze, Via La Pira 4, I-50121 Florence, Italy; *Email: [email protected]. Introduction: During a nanomineralogy investigation of the Khatyrka CV3 carbonaceous chondrite, we have identified two new alloy minerals (AlCu with a Pm-3m CsCl structure and Al3Fe with a C2/m structure) and associ- ated icosahedrite (quasicrystal Al63Cu26Fe11 with a five-fold symmetry) at micron scales in section 126A of USNM 7908. The section belongs to the larger Grain 126, which is one of the fragments recovered from an expedition to the Koryak Mountains in far eastern Russia in 2011 [1] as a result of a search for samples that would provide infor- mation on the origin of the quasicrystal mineral icosahedrite [2,3,4]. The recovered fragments have meteoritic (CV3- like) oxygen isotopic compositions and are identified collectively as coming from the Khatyrka meteorite [5], which formed 4.5 billion years ago during the earliest stages of the solar system. Khatyrka is unique, so far being the only meteorite to host metallic Al component. Field-emission scanning electron microscope with energy-dispersive X-ray spectrometer and electron back- scatter diffraction (EBSD), and electron probe microanalyzer (EPMA) were used to characterize chemical composi- tions and structures of the minerals in section 126A. -
Cosmic History and a Candidate Parent Asteroid for the Quasicrystal-Bearing Meteorite Khatyrka
COSMIC HISTORY AND A CANDIDATE PARENT ASTEROID FOR THE QUASICRYSTAL-BEARING METEORITE KHATYRKA Matthias M. M. Meier1*, Luca Bindi2,3, Philipp R. Heck4, April I. Neander5, Nicole H. Spring6,7, My E. I. Riebe1,8, Colin Maden1, Heinrich Baur1, Paul J. Steinhardt9, Rainer Wieler1 and Henner Busemann1 1Institute of Geochemistry and Petrology, ETH Zurich, Zurich, Switzerland. 2Dipartimento di Scienze della Terra, Università di Firenze, Florence, Italy. 3CNR-Istituto di Geoscienze e Georisorse, Sezione di Firenze, Florence, Italy. 4Robert A. Pritzker Center for Meteoritics and Polar Studies, Field Museum of Natural History, Chicago, USA. 5De- partment of Organismal Biology and Anatomy, University of Chicago, Chicago, USA. 6School of Earth and Environ- mental Sciences, University of Manchester, Manchester, UK. 7Department of Earth and Atmospheric Sciences, Uni- versity of Alberta, Edmonton, Canada. 8Current address: Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, USA. 9Department of Physics, and Princeton Center for Theoretical Science, Princeton University, Princeton, USA. *corresponding author: [email protected]; (office phone: +41 44 632 64 53) Submitted to Earth and Planetary Science Letters. Abstract The unique CV-type meteorite Khatyrka is the only natural sample in which “quasicrystals” and associated crystalline Cu,Al-alloys, including khatyrkite and cupalite, have been found. They are suspected to have formed in the early Solar System. To better understand the origin of these ex- otic phases, and the relationship of Khatyrka to other CV chondrites, we have measured He and Ne in six individual, ~40-μm-sized olivine grains from Khatyrka. We find a cosmic-ray exposure age of about 2-4 Ma (if the meteoroid was <3 m in diameter, more if it was larger). -
EXPERIMENTAL IMPACTS of ALUMINUM PROJECTILES INTO QUARTZ SAND: FORMATION 1,2 1,3 of KHATYRKITE (Cual2) and REDUCTION of QUARTZ to SILICON
Bridging the Gap III (2015) 1071.pdf EXPERIMENTAL IMPACTS OF ALUMINUM PROJECTILES INTO QUARTZ SAND: FORMATION 1,2 1,3 OF KHATYRKITE (CuAl2) AND REDUCTION OF QUARTZ TO SILICON. C. Hamann , D. Stöffler , and W. U. Reimold1,3. 1Museum für Naturkunde, Leibniz-Institut für Evolutions- und Biodiversitätsforschung, In- validenstraße 43, 10115 Berlin, Germany ([email protected]; dieter.stö[email protected]; [email protected]); 2Institut für Geologische Wissenschaften, Freie Universität Berlin, Malteserstraße 74– 100, 12249 Berlin, Germany, 3Humboldt-Universität zu Berlin, Unter der Linden 6, 10099 Berlin, Germany. Introduction and Rationale: Impact cratering is a melt particles, shock-lithified sand with and without basic geologic process in the solar system, which was distinct shock effects (PDF, diaplectic glass), and frac- predominant over endogenic geologic processes in the tured quartz grains (for details, see the companion early evolution of geologically active planetary bodies. abstract by Wünnemann et al. [10]). Since this study Since most planetary surfaces are highly porous and/or focuses on chemical projectile–target interaction, we composed of non-cohesive materials (e.g., the lunar will only consider impact melt particles that obviously regolith), understanding the influence of pore space show a crust of projectile melt on their top sides. and non-cohesiveness of materials on the impact pro- The bulk compositions of projectile and target were cess is crucial for gaining insights into the evolution of determined with EMPA and XRF, respectively. Impact planetary regoliths. To this end, numerous theoretical melt particles were studied with optical microscopy, and experimental studies have been conducted (e.g., SEM-EDX, and EMPA.