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.

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 author's own interpretation of the properties with respect to their unique structure.

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.

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 are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.

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.

A comprehensive and up-to-date review, covering the broad range of this outstanding class of materials among intermetallic alloys. Starting with metallurgy and characterization, the authors continue on to structure and mathematical modeling. They use this basis to move on to dealing with electronic, magnetic, thermal, dynamic and mechanical properties, before finally providing an insight into surfaces and thin films. The authors belong to a research program on quasicrystals, sponsored by the German Research Society and managed by Hans-Rainer Trebin, such that most of the latest results are pre.