scholarly journals Phonon and phasons : from incommensurate phases to quasicrystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C9-C9
Author(s):  
Marc de Boissieu
Keyword(s):  
Physical Properties ◽  
Long Range ◽  
Lattice Dynamics ◽  
General Introduction ◽  
Modulated Phases ◽  
Aperiodic Order ◽  
Ordered Phases ◽  
Diffusive Modes ◽  
Aperiodic Crystals ◽  
Incommensurate Phases

Aperiodic crystals are long range ordered phases, which lack translational symmetry. They encompass incommensurately modulated phases, incommensurate composites phases and quasicrystals (1). Whereas their atomic structure is now well understood, even for the case of quasicrystals, the understanding of their physical properties remains a challenging problem. In particular, because of the aperiodic long range order, the lattice dynamics present a specific behavior. In particular, it can be shown theoretically that besides phonon, a supplementary excitation exits in all aperiodic phases named phason. Phason modes arise from the degeneracy of the free energy of the system with respect to a phase shift and are always diffusive modes (1). After a general introduction on the different class of aperiodic crystals, we will illustrate experimental results on phason modes. We will in particular demonstrate that these phason modes lead to a flexibility of the structure that might have important consequences for physical properties. We will also discuss their importance for the understanding of stabilizing mechanisms that lead to the long-range aperiodic order.

scholarly journals Ted Janssen and aperiodic crystals

2019 ◽  
Vol 75 (2) ◽  
pp. 273-280 ◽  
Author(s):  
Marc de Boissieu
Keyword(s):  
Physical Properties ◽  
Long Range ◽  
Atomic Structure ◽  
Ordered Structures ◽  
Detailed Understanding ◽  
3D Space ◽  
Modulated Phases ◽  
The Stability ◽  
Aperiodic Crystals

This article reviews some of Ted Janssen's (1936–2017) major contributions to the field of aperiodic crystals. Aperiodic crystals are long-range ordered structures without 3D lattice translations and encompass incommensurately modulated phases, incommensurate composites and quasicrystals. Together with Pim de Wolff and Aloysio Janner, Ted Janssen invented the very elegant theory of superspace crystallography that, by adding a supplementary dimension to the usual 3D space, allows for a deeper understanding of the atomic structure of aperiodic crystals. He also made important contributions to the understanding of the stability and dynamics of aperiodic crystals, exploring their fascinating physical properties. He constantly interacted and collaborated with experimentalists, always ready to share and explain his detailed understanding of aperiodic crystals.

scholarly journals Aperiodic Crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1-C1 ◽  
Author(s):  
Ted Janssen ◽  
Aloysio Janner
Keyword(s):  
Physical Properties ◽  
Dimensional Space ◽  
X Rays ◽  
New Techniques ◽  
New Family ◽  
Modulated Phases ◽  
Open Questions ◽  
Higher Dimensional ◽  
Lattice Periodicity ◽  
Aperiodic Crystals

2014 is the International Year of Crystallography. During at least fifty years after the discovery of diffraction of X-rays by crystals, it was believed that crystals have lattice periodicity, and crystals were defined by this property. Now it has become clear that there is a large class of compounds with interesting properties that should be called crystals as well, but are not lattice periodic. A method has been developed to describe and analyze these aperiodic crystals, using a higher-dimensional space. In this lecture the discovery of aperiodic crystals and the development of the formalism of the so-called superspace will be described. There are several classes of such materials. After the incommensurate modulated phases, incommensurate magnetic crystals, incommensurate composites and quasicrystals were discovered. They could all be studied using the same technique. Their main properties of these classes and the ways to characterize them will be discussed. The new family of aperiodic crystals has led also to new physical properties, to new techniques in crystallography and to interesting mathematical questions. Much has been done in the last fifty years by hundreds of crystallographers, crystal growers, physicists, chemists, mineralogists and mathematicians. Many new insights have been obtained. But there are still many questions, also of fundamental nature, to be answered. We end with a discussion of these open questions.

Aperiodic Crystals

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Physical Properties ◽  
Inorganic Compounds ◽  
Point Of View ◽  
Periodic Arrays ◽  
New Class ◽  
Modulated Phases ◽  
Lattice Periodicity ◽  
Wide Range ◽  
Unit Cells ◽  
Aperiodic Crystals

Until the 1970s all materials studied consisted of periodic arrays of unit cells, or were amorphous. In the following decades a new class of solid state matter, called aperiodic crystals, has been found. It is a long-range ordered structure, but without lattice periodicity. It is found in a wide range of materials: organic and inorganic compounds, minerals (including a substantial portion of the earth’s 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 characterization of the structure, the structure determination, and the study of the physical properties, especially the 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 generalize 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 the 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.

scholarly journals Aperiodic crystals and beyond

2014 ◽  
Vol 70 (a1) ◽  
pp. C521-C521
Author(s):  
Uwe Grimm ◽  
Michael Baake
Keyword(s):  
Bragg Diffraction ◽  
Penrose Tiling ◽  
General Introduction ◽  
Ordered Structures ◽  
Model Sets ◽  
Higher Dimensional ◽  
Aperiodic Order ◽  
Discrete Structures ◽  
Aperiodic Crystals ◽  
Recent Monograph

Following Dan Shechtman's discovery of quasicrystals in 1982, the realm of crystallography has been extended to include structures that lack translational periodicity. While periodic crystals can be modelled as decorations of lattices, aperiodic crystals require more general discrete structures such as point sets or tilings in space for the description of their structure. For a mathematical introduction to the field of aperiodic order, we refer to the recent monograph [1]. Interesting examples are obtained by projections from higher-dimensional lattices, leading to model sets which have pure Bragg diffraction, though the Bragg peaks are, in general, dense in space. All symmetries that have been experimentally observed in quasicrystals can be reproduced in this way, and some of the resulting structures are standard examples of tilings that are frequently used in quasicrystal modelling, such as the famous Penrose tiling. But there exists a plethora of ordered structures beyond cut and project sets, some of which have even weirder properties. After a general introduction to aperiodically ordered structures, a couple of examples of such systems are briefly described, offering a glimpse at the largely unexplored world of order beyond (aperiodic) crystals.

Description and symmetry of aperiodic crystals

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Time Reversal ◽  
Mathematical Concept ◽  
New Materials ◽  
Magnetic Systems ◽  
Atomic Structures ◽  
Modulated Phases ◽  
Quasiperiodic Functions ◽  
Aperiodic Crystals ◽  
Superspace Description

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

scholarly journals Nanoscale bubble domains with polar topologies in bulk ferroelectrics

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jie Yin ◽  
Hongxiang Zong ◽  
Hong Tao ◽  
Xuefei Tao ◽  
Haijun Wu ◽  
...  
Keyword(s):  
Physical Properties ◽  
Bulk Material ◽  
Condensed Matter ◽  
Time Dependent ◽  
Morphology Evolution ◽  
Contrast Imaging ◽  
Ferroelectric Films ◽  
Modulated Phases ◽  
Ferroelectric Memories ◽  
Z Contrast

AbstractMultitudinous topological configurations spawn oases of many physical properties and phenomena in condensed-matter physics. Nano-sized ferroelectric bubble domains with various polar topologies (e.g., vortices, skyrmions) achieved in ferroelectric films present great potential for valuable physical properties. However, experimentally manipulating bubble domains has remained elusive especially in the bulk form. Here, in any bulk material, we achieve self-confined bubble domains with multiple polar topologies in bulk Bi0.5Na0.5TiO3 ferroelectrics, especially skyrmions, as validated by direct Z-contrast imaging. This phenomenon is driven by the interplay of bulk, elastic and electrostatic energies of coexisting modulated phases with strong and weak spontaneous polarizations. We demonstrate reversable and tip-voltage magnitude/time-dependent donut-like domain morphology evolution towards continuously and reversibly modulated high-density nonvolatile ferroelectric memories.

scholarly journals Quasi-1D XY antiferromagnet Sr2Ni(SeO3)2Cl2 at Sakai-Takahashi phase diagram

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
E. S. Kozlyakova ◽  
A. V. Moskin ◽  
P. S. Berdonosov ◽  
V. V. Gapontsev ◽  
S. V. Streltsov ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Long Range ◽  
Density Functional ◽  
Uniaxial Anisotropy ◽  
Exchange Interactions ◽  
Spin Liquid ◽  
Functional Theory ◽  
One Dimensional ◽  
Ordered Phases ◽  
Experimental Findings

AbstractUniform quasi-one-dimensional integer spin compounds are of interest as a potential realization of the Haldane conjecture of a gapped spin liquid. This phase, however, has to compete with magnetic anisotropy and long-range ordered phases, the implementation of which depends on the ratio of interchain J′ and intrachain J exchange interactions and both uniaxial D and rhombic E single-ion anisotropies. Strontium nickel selenite chloride, Sr2Ni(SeO3)2Cl2, is a spin-1 chain system which passes through a correlations regime at Tmax ~ 12 K to long-range order at TN = 6 K. Under external magnetic field it experiences the sequence of spin-flop at Bc1 = 9.0 T and spin-flip transitions Bc2 = 23.7 T prior to full saturation at Bsat = 31.0 T. Density functional theory provides values of the main exchange interactions and uniaxial anisotropy which corroborate the experimental findings. The values of J′/J = 0.083 and D/J = 0.357 place this compound into a hitherto unoccupied sector of the Sakai-Takahashi phase diagram.

scholarly journals Physical properties and lattice dynamics of bixbyite-type V2O3

2017 ◽  
Vol 32 (12) ◽  
pp. 2397-2404 ◽  
Author(s):  
Dominik A. Weber ◽  
Christian Schwickert ◽  
Anatoliy Senyshyn ◽  
Martin Lerch ◽  
Rainer Pöttgen
Keyword(s):  
Physical Properties ◽  
Lattice Dynamics ◽  
Image Position

Abstract

scholarly journals Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Long Range ◽  
Topological Order ◽  
Fractional Statistics ◽  
Microscopical Level ◽  
Macroscopic Level ◽  
Emergent Phenomena ◽  
Quantum Matter ◽  
Ordered Phases ◽  
Zero Viscosity

We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.

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