Aperiodic Crystals

From Modulated Phases to Quasicrystals: Structure and Properties

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Until the 1970s all materials studied consisted of periodic arrays of unit cells, or were amorphous. A new class of solid state matter called aperiodic crystals has since been uncovered. It is a long range ordered structure, but without lattice periodicity. It is found in a wide range of materials: organic and anorganic compounds, minerals (including a substantial portion of the earths crust), and metallic alloys, under various pressures and temperatures. Because of the lack of periodicity, the usual techniques for the study of structure and physical properties no longer work, and new techniques have to be developed. This book deals with the characterisation of the structure, the structure determination and the study of the physical properties, especially dynamical and electronic properties of aperiodic crystals. The treatment is based on a description in a space with more dimensions than three, the so-called superspace. This allows us to generalise the standard crystallography and to look differently at the dynamics. The three main classes of aperiodic crystals, modulated phases, incommensurate composites and quasicrystals are treated from a unified point of view, which stresses similarities of the various systems. The book assumes as a prerequisite a knowledge of the fundamental techniques of crystallography and the theory of condensed matter, and covers the literature at the forefront of the field. Since the first edition of this book in 2007, the field of aperiodic crystals has developed considerably, with the discovery of new materials and new structures. Progress has been made in structure determination, in the interpretation and understanding of the structural characteristics and in the calculation of electrons and phonons. This new edition reflects these new developments, and it includes discussions of natural quasicrystals, incommensurate magnetic and multiferroic structures, photonic and mesoscopic quasicrystals. The second edition also includes a number of new exercises that give the reader an opportunityt to check their understanding of the material.

Weniger Details

Ted Janssen studied mathematics and physics at the University of Utrecht. He later moved to the University of Nijmegen, from which he graduated with a PhD in 1968. He spent a year at the ETH in Zurich and returned to Nijmegen as an Associate Professor. He became a full professor at the University of Utrecht and, in 1994, he moved again to Nijmegen where he spent the rest of his career. He has been invited as guest Professor in Leuwen, Dijon, Lausanne, Paris, Orsay, Nagoya and Sendai. He has oriented his research activities to the fields of group theory in physics, crystallography and properties of aperiodic crystals, friction theory and nonlinear dynamics. In 1998, he received the Amino Prize from the Swedish Academy of Science along with P.M. de Wolff and A. Janner. In 2014, along with A. Janner, he received the Ewald Prize awarded by the International Union of Crystallography (IUCr). Gervais Chapuis graduated in physical chemistry at the Swiss Federal School of Technology in Zurich (ETHZ) in 1971. He later obtained his PhD in crystallography at the same institution. He continued his research in the field of resonant scattering for three years at the Lawrence Berkeley Laboratory in California. He then returned to Switzerland, to the Institute of Crystallography of the Physics Department at the University of Lausanne. In 1991, he became full professor and in 2003 moved to the Swiss Federal School of Technology in Lausanne (EPFL). Chapuis has published over 250 research papers on structures and properties of aperiodic crystals and is the author of several textbooks in the field of crystallography. As an active member of the IUCr, he is editor and co-editor of a number of scientific journals and media, and the chair and member of various committees. Marc de Boissieu obtained his PhD in Material Sciences in 1989 at Écoles des Mines in Nancy. He then joined the CNRS as a researcher in the laboratory LTPCM, now Science et Ingénierie des Matériaux et Procédés in Grenoble. He has oriented his research in the field of quasicrystals and complex intermetallic compounds, studying their atomic structure, defects and lattice dynamics using x-ray and neutron scattering techniques, associated with atomic scale modelling and simulations. His work is conducted through international collaboration with several groups in Europe, Japan and USA. Since 2009, he has been the director of the European network C-MAC. As an active member of the IUCr, he has been chair of the commission on aperiodic crystals and is co-editor of Acta B.