# Quasicrystals

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## Quasicrystals

Author | : D. P. DiVincenzo,Paul J. Steinhardt |

Publsiher | : World Scientific |

Total Pages | : 634 |

Release | : 1999 |

ISBN | : 9789810241568 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

Quasicrystals: The State of the Art has proven to be a useful introduction to quasicrystals for mathematicians, physicists, materials scientists, and students. The original intent was for the book to be a progress report on recent developments in the field. However, the authors took care to adopt a broad, pedagogical approach focusing on points of lasting value. Many subtle and beautiful aspects of quasicrystals are explained in this book (and nowhere else) in a way that is useful for both the expert and the student. In this second edition, some authors have appended short notes updating their essays. Two new chapters have been added. Chapter 16, by Goldman and Thiel, reviews the experimental progress since the first edition (1991) in making quasicrystals, determining their structure, and finding applications. In Chapter 17, Steinhardt discusses the quasi-unit cell picture, a promising, new approach for describing the structure and growth of quasicrystals in terms of a single, repeating, overlapping cluster of atoms.

## Quasicrystals

Author | : Christian Janot |

Publsiher | : OUP Oxford |

Total Pages | : 427 |

Release | : 2012-10-18 |

ISBN | : 0191021792 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

In 1984 physicists discovered a monster in the world of crystallography, a structure that appeared to contain five-fold symmetry axes, which cannot exist in strictly periodic structures. Such quasi-periodic structures became known as quasicrystals. A previously formulated theory in terms of higher dimensional space groups was applied to them and new alloy phases were prepared which exhibited the properties expected from this model more closely. Thus many of the early controversies were dissolved. In 2011, the Nobel Prize for Chemistry was awarded to Dan Shechtman for the discovery of quasicrystals. This primer provides a descriptive approach to the subject for those coming to it for the first time. The various practical, experimental, and theoretical topics are dealt with in an accessible style. The book is completed by problem sets and there is a computer program that generates a Penrose lattice.

## Crystallography of Quasicrystals

Author | : Steurer Walter,Sofia Deloudi |

Publsiher | : Springer Science & Business Media |

Total Pages | : 384 |

Release | : 2009-08-26 |

ISBN | : 3642018998 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Crystallography of Quasicrystals Book Excerpt:**

From tilings to quasicrystal structures and from surfaces to the n-dimensional approach, this book gives a full, self-contained in-depth description of the crystallography of quasicrystals. It aims not only at conveying the concepts and a precise picture of the structures of quasicrystals, but it also enables the interested reader to enter the field of quasicrystal structure analysis. Going beyond metallic quasicrystals, it also describes the new, dynamically growing field of photonic quasicrystals. The readership will be graduate students and researchers in crystallography, solid-state physics, materials science, solid- state chemistry and applied mathematics.

## Quasicrystals and Discrete Geometry

Author | : Jiri Patera |

Publsiher | : American Mathematical Soc. |

Total Pages | : 289 |

Release | : 1998-01-01 |

ISBN | : 9780821871683 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals and Discrete Geometry Book Excerpt:**

## Useful Quasicrystals

Author | : Jean-Marie Dubois |

Publsiher | : World Scientific |

Total Pages | : 506 |

Release | : 2005 |

ISBN | : 9810232543 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Useful Quasicrystals Book Excerpt:**

The aim of this book is to acquaint the reader with what the authors regard as the most basic characteristics of quasicrystals -- structure, formation and stability, and properties -- in relationship with the applications of quasicrystalline materials. Quasicrystals are fascinating substances that form a family of specific structures with strange physical, chemical and mechanical properties as compared to those of metallic alloys. This, on the one hand, requires a generalization of the crystallographic description of solids and is still stimulating intensive research to understand the most basic properties of quasicrystals. On the other hand, these properties open the way to technological applications, demonstrated or potential, mostly regarding energy savings. This valuable book discusses those various facets of quasicrystals in six chapters, ending with the authors' own interpretation of the properties with respect to their unique structure.

## Quasicrystals

Author | : J.-B. Suck,M. Schreiber,P. Häussler |

Publsiher | : Springer Science & Business Media |

Total Pages | : 564 |

Release | : 2013-04-17 |

ISBN | : 3662050285 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

The book provides an introduction to all aspects of the physics of quasicrystals. The chapters, each written by an expert in this field, cover quasiperiodic tilings and the modeling of the atomic structure of quasicrystals. The electronic density of states and the calculation of the electronic structure play a key role in this introduction, as does an extensive discussion of the atomic dynamics. The study of defects in quasicrystals by high resolution electron microscopy and the computer simulations of defects and fracture in decorated tilings are important subjects for the application of these aperiodic crystals.

## Quasicrystals

Author | : Enrique Maciá-Barber |

Publsiher | : CRC Press |

Total Pages | : 284 |

Release | : 2020-12-18 |

ISBN | : 1351209132 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

promoting the very notion of quasiperiodic order, and to spur its physical implications and technological capabilities. It, therefore, explores the fundamental aspects of intermetallic, photonic, and phononic quasicrystals, as well as soft-matter quasicrystals, including their intrinsic physical and structural properties. In addition, it thoroughly discusses experimental data and related theoretical approaches to explain them, extending the standard treatment given in most current solid state physics literature. It also explores exciting applications in new technological devices of quasiperiodically ordered systems, including multilayered quasiperiodic systems, along with 2D and 3D designs, whilst outlining new frontiers in quasicrystals research. This book can be used as a reader-friendly introductory text for graduate students, in addition to senior scientists and researchers coming from the fields of physics, chemistry, materials science, and engineering. Key features: • Provides an updated and detailed introduction to the interdisciplinary field of quasicrystals in a tutorial style, considering both fundamental aspects and additional freedom degrees provided by designs based on quasiperiodically ordered materials. • Includes 50 fully worked out exercises with detailed solutions, motivating, and illustrating the different concepts and notions to provide readers with further learning opportunities. • Presents a complete compendium of the current state of the art knowledge of quasicrystalline matter, and outlines future next generation materials based on quasiperiodically ordered designs for their potential use in useful technological devices. Dr. Enrique Maciá-Barber is Professor of condensed matter physics at the Universidad Complutense de Madrid. His research interests include the thermoelectric properties of quasicrystals and DNA biophysics. In 2010 he received the RSEF- BBVA Foundation Excellence Physics Teaching Award. His book Aperiodic Structures in Condensed Matter: Fundamentals and Applications (CRC Press, Boca-Raton, 2009) is one of the Top Selling Physics Books according to YBP Library Services.

## Quasicrystals

Author | : Anonim |

Publsiher | : Elsevier |

Total Pages | : 374 |

Release | : 2007-12-17 |

ISBN | : 9780080555973 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

This book is aimed at researchers who are working in a field of quasicrystals to provide a reference to recent developments and ideas in the field and also at graduate students, who intend to study quasicrystals, to provide introduction of ideas. Topics in this book cover an entire field of quasicrystals, both experimental and theoretical, including new developments: the state of the art in quasicrystallography, new families of quasicrystals, phasons in aperiodic solids, ab initio studies on stability mechanism, quantum transport phenomena, elastic/plastic properties and surface of quasicrystals. · Comprehensive reviews by experts in the field · Complete reference of original papers and new topics · Intelligible introduction of quasicrystals by experts

## Quasicrystals

Author | : Hans-Rainer Trebin |

Publsiher | : John Wiley & Sons |

Total Pages | : 668 |

Release | : 2006-05-12 |

ISBN | : 3527606785 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

Quasicrystals form a new state of solid matter beside the crystalline and the amorphous. The positions of the atoms are ordered, but with noncrystallographic rotational symmetries and in a nonperiodic way. The new structure induces unusual physical properties, promising interesting applications. This book provides a comprehensive and up-to-date review and presents most recent research results, achieved by a collaboration of physicists, chemists, material scientists and mathematicians within the Priority Programme "Quasicrystals: Structure and Physical Properties" of the Deutsche Forschungsgemeinschaft (DFG). Starting from metallurgy, synthesis and characterization, the authors carry on with structure and mathematical modelling. On this basis electronic, magnetic, thermal, dynamic and mechanical properties are dealt with and finally surfaces and thin films.

## Quasicrystals

Author | : Esther Belin-Ferr |

Publsiher | : World Scientific |

Total Pages | : 552 |

Release | : 2000 |

ISBN | : 9789810242817 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

This book focuses on current topics in quasicrystal science and research. Various themes are addressed, such as atomic structure, growth of quasicrystals, statistical physics and thermodynamics, magnetism, phasons, propagation of waves, surfaces and technological potential of quasicrystals. Insight into basics in physics and chemistry is also given, with examples from metallurgy, the surface of alloys, plasticity, etc., in order to point out the possible genuine aspects of quasicrystals and allow a better comparison with conventional alloys.

## Natural Quasicrystals

Author | : Luca Bindi |

Publsiher | : Springer Nature |

Total Pages | : 89 |

Release | : 2020-04-20 |

ISBN | : 3030456773 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Natural Quasicrystals Book Excerpt:**

This book describes the discovery of quasicrystals (icosahedral and decagonal) in an extraterrestrial rock from the Koryak Mountains of Far Eastern Russia. After a decade-long search for a natural quasicrystal, this discovery opened a new avenue in mineralogy and crystallography that could lead to further discoveries in geoscience, astronomy, condensed matter physics, and materials engineering. For the first time, minerals have been discovered that violate the symmetry restrictions of conventional crystallography. The natural occurrence of such crystals was unexpected, involving previously unknown processes. The fact that the quasicrystals were found in a meteorite formed in the earliest moments of the solar system means these processes have been active for over 4.5 billion years and have influenced the composition of the first objects to condense around the Sun. Finding quasicrystals formed in these extreme environments also informed the longstanding debate concerning the stability and robustness of quasicrystals. Recent shock experiments lend support to the hypothesis that the extraterrestrial quasicrystals formed as a result of hypervelocity impacts between objects in the early Solar system, and that they are probably less rare in the Milky Way.

## Beyond Quasicrystals

Author | : Francoise Axel,Denis Gratias |

Publsiher | : Springer Science & Business Media |

Total Pages | : 619 |

Release | : 2013-06-29 |

ISBN | : 3662031302 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Beyond Quasicrystals Book Excerpt:**

This book is the collection of most of the written versions of the Courses given at the Winter School "Beyond Quasicrystals" in Les Houches (March 7-18, 1994). The School gathered lecturers and participants from all over the world and was prepared in the spirit of a general effort to promote theoretical and experimental interdisciplinary communication between mathematicians, theoretical and experimental physicists on the topic of the nature of geometric order in solids beyond standard periodicity and quasi periodicity. The overall structure of the book reflects the wish of the editors to pose this fundamental question of geometric order in solids from both the experimental and theoretical point of view. The first part is devoted more specifically to quasicrystals. These materials were the common starting point of most of the audience and present a first concrete example of a non-trivial geometric order. We chose to focus on a few fundamental aspects of quasicrystals related to hidden symmetries in solids which are not easily found in standard textbooks on the topic, not to reach an exhaustive survey which is already available elsewhere.

## Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Author | : Tianyou Fan |

Publsiher | : Springer Science & Business Media |

Total Pages | : 350 |

Release | : 2011-05-25 |

ISBN | : 3642146430 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Mathematical Theory of Elasticity of Quasicrystals and Its Applications Book Excerpt:**

This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.

## Generalized Dynamics of Soft Matter Quasicrystals

Author | : Tian-You Fan,Wenge Yang,Hui Cheng,Xiao-Hong Sun |

Publsiher | : Springer Nature |

Total Pages | : 235 |

Release | : 2022-01-17 |

ISBN | : 9811666288 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Generalized Dynamics of Soft Matter Quasicrystals Book Excerpt:**

This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

## Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Author | : Tian-You Fan |

Publsiher | : Springer |

Total Pages | : 452 |

Release | : 2016-09-20 |

ISBN | : 9811019843 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Mathematical Theory of Elasticity of Quasicrystals and Its Applications Book Excerpt:**

This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science.

## The Physics of Quasicrystals

Author | : P J Steinhardt,S Ostlund |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 788 |

Release | : 1987-12-31 |

ISBN | : 9813103841 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**The Physics of Quasicrystals Book Excerpt:**

This book comprises an introductory lecture outlining the basic concepts and challenges in the field. This is followed by a collection of reprinted articles which are important in understanding the subject. The book will focus mainly on mathematical and physical foundations of the subject rather than experimental progress. By concentrating on theoretical topics, this volume has long-lasting as well as immediate value to physicists, crystallographers, metallurgists and mathematicians. Request Inspection Copy

## Quasicrystals

Author | : Paul Steinhardt,David DiVincenzo |

Publsiher | : World Scientific |

Total Pages | : 536 |

Release | : 1991-10-22 |

ISBN | : 9814566535 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Book Excerpt:**

This review volume provides the most up-to-date and authoritative description of research on icosahedral solids, which has advanced rapidly since the discovery of these unique materials in 1984. The present book, intended as a companion volume to the reprint volume on The Physics of Quasicrystals edited by P Steinhardt and S Ostlund, will be invaluable to graduate students and workers in the field as a comprehensive reference. Scientists in related fields can use it as a readable introduction to the important current problems in quasicrystals. The chapters have been written by many of the most prominent theorists and experimentalists on quasicrystals, both physicists and materials scientists, from around the world. Especially exciting are the details of the recent discovery of “perfect quasi-crystals”, new materials which promise to be an ideal form of quasiperiodic matter with little or no disorder. Other topics include: electron, X-ray and neutron quasi-crystallography, scanning tunneling microscopy studies, electronic transport experiments, quasicrystal faceting and statistical mechanics, growth rules and matching rules for quasicrystals, group theory and elasticity theory. Contents:Progress and Current Issues in Quasicrystals (D P DiVincenzo & P J Steinhardt)Order and Disorder in Icosahedral Alloys (P A Bancel); Neutron Scattering Approaches to Quasicrystals (Ch Janot & M de Boissieu)High-Resolution Electron Microscopy of Quasicrystals (K Hiraga)Scanning Tunneling Microscopy Studies of Quasicrystals (R S Becker & A R Kortan)(Quasi) Crystallography is Better in Fourier Space (N D Mermin)Matching Rules for Quasicrystalline Tilings (K Ingersent)Growth Rules for Quasicrystals (J E S Socolar)Continuous Atomic Surfaces (L S Levitov)Chiral Smectics as Quasicrystals (T C Lubensky et al.)Experimental Studies of Electronic Transport in Quasicrystals (K Kimura & S Takeuchi)Electronic Structure and Transport of Quasicrystals (T Fujiwara & H Tsunetsugu)Electronic-Structure and Total-Energy Calculation for Quasicrystals and Related Crystals (A E Carlsson & R Phillips)Faceting and Surface Roughening in Quasicrystals (T-L Ho)Random Tiling Models (C L Henley) Readership: Condensed matter physicists, crystallographers, materials scientists, metallurgists and mathematicians. keywords:Quasicrystal;Phason;Icosahedral Symmetry;Penrose Tilings;Random Tilings;Quasiperiodicity;Pinning;Fibonacci Lattice;Quasilattice;Quasicrystallography;Localization;Critical States “… timely and useful … I recommend this book to those in the field and to everyone interested in quasicrystals …” Marjorie Senechal Science

## From Quasicrystals to More Complex Systems

Author | : F. Axel,F. Denoyer,J.P. Gazeau |

Publsiher | : Springer Science & Business Media |

Total Pages | : 375 |

Release | : 2013-06-29 |

ISBN | : 3662042533 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**From Quasicrystals to More Complex Systems Book Excerpt:**

This book is a collection of part of the written versions of the Physics Courses given at the Winter School "Order, Chance and Risk: Aperiodic Phenomena from Solid State to Finance" held at the Les Houches Center for Physics, between February 23 and March 6, 1998. The School gathered lecturers and participants from all over the world. On a thematic level, the content of the school can be viewed both as a continuation (aperiodic phenomena in solid state physics) and an extension (mathematical aspects of fmance and economy) of the previous "Beyond Quasicrystals", also held at Les Houches, March 7-18 1994 and published in the same ·series. One of its important goals was to promote in-depth concrete scientific exchanges between theoretical physicists, experimental physicists and mathematicians on the one hand, and on the other hand practitioners of the economico-fmancial sphere and specialists of financial mathematics. Therefore, besides the mathematical tools and concepts at work in theoretical descriptions, relevant experimental data were also presented together with methods allowing their interpretation. As a result of this choice, the School was stimulated by experimentalists and fmancial market operators who joined the theoretical physicists and mathematicians at the conference. The present volume deals with the theoretical and experimental studies on aperiodic solids with long range order, incommensurate phases, quasicrystals, glasses, and more complex systems (fractal, chaotic), while a second volume to appear in the same series is devoted to the finance and economy facet.

## Quasicrystals Proceedings Of The 5th International Conference

Author | : Janot C,Mosseri R |

Publsiher | : World Scientific |

Total Pages | : 856 |

Release | : 1995-12-22 |

ISBN | : 9814548650 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Quasicrystals Proceedings Of The 5th International Conference Book Excerpt:**

This volume presents the newest results and developments in the fast-moving field of astroparticle physics. The following topics are covered: dark matter, baryogenesis, neutrino physics and astrophysics, inflation, topological defects, cosmic ray physics and cosmological implications of grand unification, supersymmetry, superstrings and extra dimensions.

## Fractals Quasicrystals Chaos Knots and Algebraic Quantum Mechanics

Author | : Anton Amann,L. Cederbaum,Werner Gans |

Publsiher | : Springer Science & Business Media |

Total Pages | : 346 |

Release | : 2012-12-06 |

ISBN | : 9400930054 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Fractals Quasicrystals Chaos Knots and Algebraic Quantum Mechanics Book Excerpt:**

At the end of the workshop on "New Theoretical Concepts in Physical Chemistry", one of the participants made an attempt to present a first impression of its achievements from his own personal standpoint. Appar ently his views reflected a general feeling, so that the organizers thought they would be suitable as a presentation of the proceedings for future readers. That is the background from which this foreword was born. The scope of the workshop is a very broad one. There are contribu tions from mathematics, physics, crystallography, chemistry and biology; the problems are approached either by means of axiomatic and rigorous methods, or at an empirical phenomenological level. This same diversifi cation can be found in the new basic concepts presented. Some arise from pure theoretical investigation in C*-algebra or in quantum probability theory; others from an analysis of very complex experimental data like nuclear energy levels, or processes on the frontier between classical and quantum physics; others again have their origin in the discovery of new ordered structures like the icosahedral crystal phases, or the knots of DNA molecules; others follow from the application of ideas like frac tals or chaos to new fields like spectral theory or chemical reactions. It is to be expected that readers will have to face the same sort of difficulties as did the participants in understanding such diverse languages, in applying themselves to subjects possibly far from their own experience, and in grasping highly sophisticated new concepts.