# Quasicrystals

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## Quasicrystals

- Author : D. P. DiVincenzo,Paul J. Steinhardt
- Publisher :
- Release Date :1999
- Total pages :618
- ISBN : 9789810241568

**Summary :** 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
- Publisher :
- Release Date :2012-10-18
- Total pages :409
- ISBN : 0199657408

**Summary :** This primer provides a descriptive approach to the subject of quasicrystals 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.

## Quasicrystals

- Author : Jens-Boie Suck,M. Schreiber,P. Häussler
- Publisher :
- Release Date :2002-07-23
- Total pages :564
- ISBN : 9783540642244

**Summary :** 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 : Esther Belin-Ferr
- Publisher :
- Release Date :2000
- Total pages :532
- ISBN : 9789810242817

**Summary :** 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.

## Quasicrystals

- Author : Hans-Rainer Trebin
- Publisher :
- Release Date :2006-05-12
- Total pages :668
- ISBN : 3527606785

**Summary :** 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 : Antony J. Bourdillon
- Publisher :
- Release Date :2010-04-01
- Total pages :112
- ISBN : 1449083951

**Summary :** Quasicrystalline material contained, for twenty five years, the most fundamental unsolved structural problem in condensed matter physics. Quasicrystals' 2D tiles in 3D superclusters compiles further illustrations of the solution proposed in Quasicrystals - and quasi drivers. "This is new...and interesting." Reviews scatter widely as is expected for novel theories. The structural driving force is the icosahedral subcluster. Agglomerations 'rapidly solidify' into clusters and superclusters. The icosahedra share edges that outline 2D tiles. The tiles close the surface of a regular dodecahedron. In 3D, the tiles become pseudo space filling. The superclusters are supertiles that 'stretch' and 'force the border'. As in the diffraction pattern, the periodicity on the superclusters is 'logarithmic.' In this geometry, the tiles, clusters and superclusters are uniquely oriented. New physical effects became apparent from the simulation of diffraction patterns: Angular Filtering that is responsible for the sharp diffraction; a Compromise Spacing Effect that determines dimensions; Logarithmically Periodic electronic band structures and dispersion curves, etc. Quasi science? Referees who can't answer rebuttals are zero, hence this book. The internet is free...

## Quasicrystals and Geometry

- Author : Marjorie Senechal
- Publisher :
- Release Date :1996-09-26
- Total pages :286
- ISBN : 9780521575416

**Summary :** This first-ever detailed account of quasicrystal geometry will be of great value to mathematicians at all levels with an interest in quasicrystals and geometry, and will also be of interest to graduate students and researchers in solid state physics, crystallography and materials science.

## Useful Quasicrystals

- Author : Jean-Marie Dubois
- Publisher :
- Release Date :2005
- Total pages :482
- ISBN : 9789812567888

**Summary :** The aim of this book is to acquaint the reader with what the author regards as the most basic characteristics of quasicrystals structure, formation and stability, properties in relationship with the applications of quasicrystalline materials. Quasicrystals are fascinating substances that form a family of specific structures with strange physical and mechanical properties as compared to those of metallic alloys. This, on the one hand, is stimulating intensive research to understand the most basic properties of quasicrystals in the frame of a generalized crystallography. 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 five chapters, ending with the authorOCOs own interpretation of the properties with respect to their unique structure."

## Physical Properties of Quasicrystals

- Author : Zbigniew M. Stadnik
- Publisher :
- Release Date :1998-11-30
- Total pages :443
- ISBN : 9783540651888

**Summary :** Quasicrystals are a new form of the solid state which differ from the other two known forms, crystalline and amorphous, by possesing a new type of long-range translational order, called quasiperiodicty, and a noncrystallographic orientational order. This book provides an up-to-date description of the unusual physical properties of these new materials. Emphasis is placed on the experimental results, which are compared with those of the corresponding crystalline and amorphous systems and discussed in terms of modern theoretical models. Written by leading authorities in the field, the book will be of great use both to experienced workers in the field and to uninitiated graduate students.

## Quasicrystals

- Author : Christian Janot,Professor C Janot
- Publisher :
- Release Date :1992
- Total pages :320
- ISBN :

**Summary :** 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.

## Crystallography of Quasicrystals

- Author : Steurer Walter,Sofia Deloudi
- Publisher :
- Release Date :2009-08-26
- Total pages :384
- ISBN : 3642018998

**Summary :** 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
- Publisher :
- Release Date :1998-01-01
- Total pages :289
- ISBN : 9780821871683

**Summary :** The common topic of the eleven articles in this volume is ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This emerging field of study is found at the crossroads of algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. The volume brings together contributions by leading specialists. Important advances in understanding the foundations of this new field are presented.

## Quasicrystals

- Author : N.A
- Publisher :
- Release Date :2007-12-17
- Total pages :374
- ISBN : 9780080555973

**Summary :** 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

## Mathematical Theory of Elasticity of Quasicrystals and Its Applications

- Author : Tianyou Fan
- Publisher :
- Release Date :2011-05-25
- Total pages :350
- ISBN : 3642146430

**Summary :** 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.

## Introduction to the Mathematics of Quasicrystals

- Author : Marko V. Jaric
- Publisher :
- Release Date :2012-12-02
- Total pages :238
- ISBN : 0323159478

**Summary :** Introduction to the Mathematics of Quasicrystals provides a pedagogical introduction to mathematical concepts and results necessary for a quantitative description or analysis of quasicrystals. This book is organized into five chapters that cover the three mathematical areas most relevant to quasicrystals, namely, the theory of almost periodic functions, the theory of aperiodic tilings, and group theory. Chapter 1 describes the aspects of the theory of tiling in two- and three-dimensional space that are important for understanding some of the ways in which “classical mathematical crystallography is being generalized; this process is to include possible models for aperiodic crystals. Chapter 2 examines the non-local nature of assembly “mistakes that might have significance to the quasicrystals growth. This chapter also describes how closely a physical quasicrystal might be able to approximate a three-dimensional version of tilings. Chapter 3 discusses the theoretical background and concepts of group theory of icosahedral quasicrystals. Chapter 4 presents the local properties of the three-dimensional Penrose tilings and their global construction is described through the projection method. This chapter emphasizes the relationship between quasiperiodic sets of points and quasiperiodic tiling. Chapter 5 explores the analysis of defects in quasicrystals and their kinetics, as well as some properties of the perfect system. This book is of great value to physicists, crystallographers, metallurgists, and beginners in the field of quasicrystals.

## Introduction to Quasicrystals

- Author : Marko Jaric
- Publisher :
- Release Date :2012-12-02
- Total pages :296
- ISBN : 0323140645

**Summary :** Aperiodicity and Order, Volume 1: Introduction to Quasicrystals deals with various aperiodic types of order in quasicrystals as well as the basic physics of quasicrystalline order and materials. Questions about the nature of order and the order of nature are addressed. This volume is comprised of six chapters; the first of which introduces the reader to icosahedral coordination in metallic crystals, with emphasis on the structural principles of metallic materials that are crystalline and may be expected to carry over to aperiodic materials. The discussion then turns to short- and long-range icosahedral orders in glass, crystals, and quasicrystals. The origins of icosahedral order are explained, and the physical properties of icosahedral materials are described. The chapters that follow focus on the metallurgy of quasicrystals, the crystallography of ideal icosahedral crystals, and stability and deformations in quasicrystalline solids. The book concludes with a discussion on symmetry, elasticity, and hydrodynamics in quasiperiodic structures. A pedagogical review of continuum elastic-hydrodynamic theory for quasicrystals and related structures is presented. This book is intended primarily as an introduction for new students in the field and as a reference for active researchers.

## Metric, Myth & Quasicrystals

- Author : Antony J. Bourdillon
- Publisher :
- Release Date :2012-08-30
- Total pages :122
- ISBN : 9781477247853

**Summary :** Metric, Myth & Quasicrystallography describes the first measurement of the metric in quasicrystals and the first measurement at atomic scale. Quasicrystals are ordinary as window glass, but they have been mistified owing to their sharp diffraction patterns with 5-fold symmetries, impossible in crystals. Out of the fog, the patterns are not in Bragg order; the series is not properly Fibonacci: simplified indexation of the pattern is used to simulate a structure due to a single, aligned, edge-sharing unit-cell that is consistent with all data. Since it is unlikely that the sharp diffraction pattern is due to unmeasured poly polyhedra, does the International Union of Crystallography have to redefine crystals yet again? In modern physics, the metric relates the covariant components of invariant vectors with corresponding contravariant components. In crystallography it relates dimensions in momentum space to atomic locations in real space. In quasicrystals, the pattern in momentum space is logarithmic. Theory and simulation show why this has to be. Consequences follow. In particular, we show not only where the atoms are but also why they are there. A debate is reported so that the reader will be encouraged to make his own mind. When logarithmic periodicity is discovered and explained in one branch of physics, it should be expected in others.

## Quasicrystals and Quasi Drivers

- Author : Antony J. Bourdillon
- Publisher :
- Release Date :2008-09-17
- Total pages :116
- ISBN : 1438955898

**Summary :** The Book Quasicrystals - quasi drivers - quasi everything. The book is in two parts: the first tells about one set of quasi drivers who are nameless; the second describes the chemical force that drives the structure of quasicrystals. Quasicrystals contained, for twenty five years, the most fundamental unsolved structural problem in condensed matter physics. The first problem in quasicrystals is whether the extraordinary data represent conventional Bragg diffraction. They don't because the order, n, is logarithmic instead of linear. The second problem is structural: it is not necessary to model with more than one unit cell. The patterns can be indexed and simulated using a single structural unit, as is normal in crystallography. The unit is the key driving force that creates logarithmic periodicity. Quasi science? Everything that suffers biased reviewing. Science may be censored in journals, but not on the new age internet. The book recommends more open, more responsible, more reliable and more realistic science, to engage with modern communications.

## Scanning Tunneling Microscopy and Spectroscopy of Aluminum Based Quasicrystals and Approximants

- Author : Ruben Rafael Mäder
- Publisher :
- Release Date :2010
- Total pages :154
- ISBN : 3832526757

**Summary :** On the nanometer scale, the local variation of the electronic density of states of aluminum based complex metallic alloys (quasicrystals and approximants) is experimentally investigated by low temperature scanning tunneling spectroscopy. We report on the correlation between the local variations of the electronic density of states and the electrical resistivity. The surface structure is investigated by scanning tunneling microscopy, low energy electron diffraction, and X-ray photoemission diffraction. Experimental results are interpreted on the basis of the respective bulk structure models.

## What Periodicities Can be Found in Diffraction Patterns of Quasicrystals?.

- Author : N.A
- Publisher :
- Release Date :2014
- Total pages :329
- ISBN :

**Summary :** Abstract The structure of quasicrystals is aperiodic. Their diffraction patterns, however, can be considered periodic. They are composed solely of series of peaks which exhibit a fully periodic arrangement in reciprocal space. Furthermore, the peak intensities in each series define the so‐called `envelope function'. A Fourier transform of the envelope function gives an average unit cell, whose definition is based on the statistical distribution of atomic coordinates in physical space. If such a distribution is lifted to higher‐dimensional space, it becomes the so‐called atomic surface – the most fundamental feature of higher‐dimensional analysis.