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

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.

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 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.

An Introduction to the Crystallogenesis of Biological Macromolecules

1999 ◽  
Author(s):  
R. Giegé ◽  
A. Ducruix
Keyword(s):  
Physical Properties ◽  
Three Dimensional ◽  
Building Blocks ◽  
Point Of View ◽  
Biological Macromolecules ◽  
Practical Applications ◽  
Space Groups ◽  
Non Linear Optics ◽  
Unit Cells ◽  
Long Time

The word ‘crystal’ is derived from the Greek root ‘krustallos’ meaning ‘clear ice’. Like ice, crystals are chemically well defined, and many among of them are of transparent and glittering appearance, like quartz, which was for a long time the archetype. Often they are beautiful geometrical solids with regular faces and sharp edges, which probably explains why crystallinity, even in the figurative meaning, is taken as a symbol of perfection and purity. From the physical point of view, crystals are regular three-dimensional arrays of atoms, ions, molecules, or molecular assemblies. Ideal crystals can be imagined as infinite and perfect arrays in which the building blocks (the asymmetric units) are arranged according to well-defined symmetries (forming the 230 space groups) into unit cells that are repeated in the three-dimensions by translations. Experimental crystals, however, have finite dimensions. An implicit consequence is that a macroscopic fragment from a crystal is still a crystal, because the orderly arrangement of molecules within such a fragment still extends at long distances. The practical consequence is that crystal fragments can be used as seeds (Chapter 7). In laboratory-grown crystals the periodicity is never perfect, due to different kinds of local disorders or long-range imperfections like dislocations. Also, these crystals are often of polycrystalline nature. The external forms of crystals are always manifestations of their internal structures and symmetries, even if in some cases these symmetries may be hidden at the macroscopic level, due to differential growth kinetics of the crystal faces. Periodicity in crystal architecture is also reflected in their macroscopic physical properties. The most straightforward example is given by the ability of crystals to diffract X-rays, neutrons, or electrons, the phenomenon underlying structural chemistry and biology (for introductory texts see refs 1 and 2), and the major aim of this book is to present the methods employed to produce three-dimensional crystals of biological macromolecules, but also two-dimensional crystals (Chapter 12), needed for diffraction studies. Other properties of invaluable practical applications should not be overlooked either, as is the case of optical and electronic properties which are at the basis of non-linear optics and modern electronics (for an introduction to physical properties of molecular crystals see ref. 3).

Colorimetric research of self-luminous objects in software and hardware environments by the method of multidimensional scales implementation

2020 ◽  
pp. 43-50
Author(s):  
Yauheniya N. Saukova
Keyword(s):  
Metrological Traceability ◽  
Point Of View ◽  
Intermediate Precision ◽  
Technical Vision ◽  
Wide Range ◽  
Chromaticity Coordinates ◽  
Unity Of Measurements ◽  
Software And Hardware ◽  
Luminous Objects ◽  
Reference Samples

It is shown that the issues of metrological traceability for extended self-luminous objects with a wide range of brightness have not yet been resolved, since the rank scales of embedded systems are used for processing digital images. For such scales, there is no “fixed” unit, which does not allow you to get reliable results and ensure the unity of measurements. An experiment is described to evaluate the accuracy of determining the intensity (coordinates) of the color of self-luminous objects. In terms of repeatability and intermediate precision compared to the reference measurement method, the color and chromaticity coordinates of self-luminous objects (reference samples) were determined by their multiple digital registration using technical vision systems. The possibilities of the developed methodology for colorimetric studies in hardware and software environments from the point of view of constructing a multidimensional conditional scale are determined.

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

Academy Journal No.3(15), 2019/ Chief Editors Susan Belih & Jaak Järv /OEAPS Inc.(Open European Academy of Public Sciences) & Estonian Academy of Sciences. Tallinn, Estonia. 09.03.2019: OEAPS Inc., 2019. - 88 P. ISBN: 9781797440507 ISSN 1736-7530 (electronic)

2019 ◽  
Author(s):  
Inc. OEAPS
Keyword(s):  
Service Sector ◽  
Point Of View ◽  
Scientific Quality ◽  
Final Decision ◽  
Research Subjects ◽  
Wide Range ◽  
Peer Reviewers ◽  
Verification Process ◽  
Scientific Research Articles ◽  
Monthly Journal

"Academy Journal" is an international, peer-reviewed monthly journal. It is devoted to the publication of original scientific research articles dealing with various academic disciplines.Articles that may be of interest to a wide range of researchers are welcome, and not limited to those who work on specific research subjects."Academy Journal" has an open archive, according to which published articles are available immediately after publication, excluding embargoes.Expert reviewThere is one blind verification process in the journal. All articles will be initially evaluated by the editor for compliance with the journal. Manuscripts that are considered appropriate are then usually sent to at least two independent peer reviewers to assess the scientific quality of the article. The editor is responsible for the final decision on whether to accept or reject the article. The editor's decision is final.The main criterion used in assessing the manuscript submitted to the journal is: uniqueness or innovation in the work from the point of view of the methodology being developed and / or its application to a problem of particular importance in the public sector or service sector and / or the setting in which the efforts, for example, in the developing region of the world. That is, the very model / methodology, application and context of problems, at least one of them must be unique and important.Additional criteria considered in the consideration of the submitted document are its accuracy, organization / presentation (ie logical flow) and recording quality.

ANACONDA ALLOY 268

Alloy Digest ◽  
1982 ◽  
Vol 31 (8) ◽  
Keyword(s):  
Corrosion Resistance ◽  
Physical Properties ◽  
Tensile Properties ◽  
Cold Working ◽  
Heat Treating ◽  
Zinc Alloy ◽  
Wide Range ◽  
Copper Zinc ◽  
Cold Worked

Abstract ANACONDA Alloy 268 is a copper-zinc alloy with excellent cold-working properties; it can be cold worked by all the conventional fabrication processes. Its corrosion resistance is excellent-to-good in most environments. This alloy has a wide range of applications including items such as springs, bathroom fixtures, automotive radiators, lamp sockets and sanitary traps. This datasheet provides information on composition, physical properties, hardness, elasticity, and tensile properties as well as fatigue. It also includes information on corrosion resistance as well as forming, heat treating, machining, and joining. Filing Code: Cu-442. Producer or source: Anaconda American Brass Company.

CENTRI-CAST GRAY IRON 50

Alloy Digest ◽  
1981 ◽  
Vol 30 (8) ◽  
Keyword(s):  
Tensile Strength ◽  
Shear Strength ◽  
Physical Properties ◽  
Machine Tools ◽  
Heat Treating ◽  
Gray Iron ◽  
Centrifugally Cast ◽  
Wide Range ◽  
Nominal Tensile Strength ◽  
Cast Gray Iron

Abstract CENTRI-CAST GRAY IRON 50 is a centrifugally cast gray iron with a nominal tensile strength of 50,000 psi. It is cast in the form of tubing which has a wide range of uses in applications where size and shape are of paramount importance and freedom from pattern cost is an important consideration. Among its many applications are farm machinery, seals, bushings, machine tools and general machinery uses. This datasheet provides information on composition, physical properties, microstructure, hardness, elasticity, tensile properties, and compressive and shear strength as well as fatigue. It also includes information on casting, heat treating, machining, and surface treatment. Filing Code: CI-51. Producer or source: Federal Bronze Products Inc..

CENTRI-CAST GRAY IRON 55

Alloy Digest ◽  
1979 ◽  
Vol 28 (9) ◽  
Keyword(s):  
Tensile Strength ◽  
Shear Strength ◽  
Physical Properties ◽  
Surface Treatment ◽  
Heat Treating ◽  
Gray Iron ◽  
Centrifugally Cast ◽  
Wide Range ◽  
Nominal Tensile Strength ◽  
Cast Gray Iron

Abstract CENTRI-CAST GRAY IRON 55 is a centrifugally cast gray iron with a nominal tensile strength of 55,000 psi. It is produced in the form of tubing which has a wide range of uses in applications where size and shape are of paramount importance and freedom from pattern cost is an important consideration. Typical applications are seals, bushings, farm machinery, casings and general machinery uses. This datasheet provides information on composition, physical properties, microstructure, hardness, elasticity, tensile properties, and compressive and shear strength as well as fatigue. It also includes information on casting, heat treating, machining, and surface treatment. Filing Code: CI-48. Producer or source: Federal Bronze Products Inc..

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