Second-Order Phase Transitions and the Irreducible Representation of Space Groups
Second-Order Phase Transitions and the Irreducible Representation of Space Groups

Author: Hugo F. Franzen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 108

ISBN-13: 3642489478

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The lecture notes presented in this volume were developed over a period of time that originated with the investigation of a research problem, the distortion from NiAs-type to MnP-type, the group-theoretical implications of which were investigated in collaboration with Professors F. Jellinek and C. Haas of the Laboratory for Inorganic Chemistry at the University of Groningen during the 1973-1974 year. This distortion provides the major example that is worked through in the notes. The subject matter of the notes has been incorporated in part in the lectures of a course in Solid State Chemistry taught several times at Iowa State University, and formed the basis of a series of lectures presented at the Max-Planck Institute for Solid State Research in Stuttgart during 1981- 19821 and as part of a Solid State Chemistry course taught during the spring of 1982 at Arizona State University in Tempe. I wish here to express my gratitude to the Max-Planck Institute for Solid State Research and to Arizona State University for the opportunity and support they provided during the time I was developing and writing the lecture notes of this volume. I wish also to thank the many colleagues and students who have offered comments and suggestions that have improved the accuracy and readability of the notes, and who have provided stimulation through discussion of the ideas presented here. am especially indebted to Professors C. Haas and F.

Crystal Symmetries
Crystal Symmetries

Author: B. K. Vainshtein

Publisher: Elsevier

Published: 2017-07-26

Total Pages: 330

ISBN-13: 1483299104

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Crystal Symmetries is a timely account of the progress in the most diverse fields of crystallography. It presents a broad overview of the theory of symmetry and contains state of the art reports of its modern directions and applications to crystal physics and crystal properties. Geometry takes a special place in this treatise. Structural aspects of phase transitions, correlation of structure and properties, polytypism, modulated structures, and other topics are discussed. Applications of important techniques, such as X-ray crystallography, biophysical studies, EPR spectroscopy, crystal optics, and nuclear solid state physics, are represented. Contains 30 research and review papers.

Site Symmetry in Crystals
Site Symmetry in Crystals

Author: Robert A. Evarestov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 292

ISBN-13: 3642604889

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Site Symmetry in Crystals is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids. The efficiency of this approach, which is based on the concepts of simple induced and band representations of space groups, is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Tables of simple induced respresentations are given for the 24 most common space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.

Isotropy Subgroups Of The 230 Crystallographic Space Groups
Isotropy Subgroups Of The 230 Crystallographic Space Groups

Author: Dorian M Hatch

Publisher: World Scientific

Published: 1989-01-01

Total Pages: 621

ISBN-13: 9814522392

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This book gives a rather exhaustive list of isotropy subgroups of the 230 crystallographic space groups. The symmetry changes for the vast majority of observed phase transitions in crystalline solids can be found in the list. With each entry, information is given concerning both physical and abstract characteristics of the phase transitions.

Discontinuous Phase Transitions In Condensed Matter: Symmetry Breaking In Bulk Martensite, Quasiperiodic And Low-dimensional Nanostructures
Discontinuous Phase Transitions In Condensed Matter: Symmetry Breaking In Bulk Martensite, Quasiperiodic And Low-dimensional Nanostructures

Author: Vladimir Dmitriev

Publisher: World Scientific

Published: 2023-01-19

Total Pages: 469

ISBN-13: 1800612931

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Discontinuous (first-order) phase transitions constitute the most fundamental and widespread type of structural transitions existing in Nature, forming a large majority of the transitions found in elemental crystals, alloys, inorganic compounds, minerals and complex fluids. Nevertheless, only a small part of them, namely, weakly discontinuous transformations, were considered by phenomenological theories, leaving aside the most interesting from a theoretical point of view and the most important for application cases. Discontinuous Phase Transitions in Condensed Matter introduces a density-wave approach to phase transitions which results in a unified, symmetry-based, model-free theory of the weak crystallization of molecular mixtures to liquid-crystalline mesophases, strongly discontinuous crystallization from molten metals and alloys to conventional, fully segregated crystals, to aperiodic, quasi-crystalline structures. Assembly of aperiodic closed virus capsids with non-crystallographic symmetry also falls into the domain of applicability of the density-wave approach.The book also considers the applicability domains of the symmetry-based approach in physics of low-dimensional systems. It includes comparisons of stability of different surface superstructures and metal monoatomic coverage structures on the surface of single-crystalline substrates. The example of the twisted graphene bilayer demonstrates how parametrization in the spirit of an advanced phenomenological approach can establish symmetry-controlled, and therefore model-free, links between geometrical parameters of the twisted bilayer structure and reconstruction of its Brillouin zone and energy bands.

Pyrochlore Ceramics
Pyrochlore Ceramics

Author: Anirban Chowdhury

Publisher: Elsevier

Published: 2022-06-09

Total Pages: 492

ISBN-13: 0323886469

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Present-day interest in pyrochlore materials is immense. Academic and industrial researchers working with pyrochlore materials need a fundamental understanding of what pyrochlores are and their potential applications. Pyrochlore Ceramics: Properties, Processing, and Applications provides key knowledge and information needed on pyrochlore materials. With an emphasis on recent research developments, the contents review a broad spectrum of pyrochlore systems, focusing on their structures, their successful synthesis, multifaceted properties, and applications. The book brings all aspects together and presents recent research findings on pyrochlore materials. It will be the definitive text for all researchers who aim to venture into the eclectic world of pyrochlores. In addition, the book will be of interest to researchers who are already working on pyrochlore materials, providing them with novel information on the uncommon virtues of pyrochlore systems. All chapters presented in the book are at the cutting edge of research and have never been assembled in book form before. Any researcher working in related fields will gain not only a historical perspective but also a comprehensive overview of recent developments. The book will be a valuable reference resource for academic and industrial researchers working in ceramics and materials science, mechanical, electronics, and chemical engineering, as well as physical and chemical science. - Provides an extensive review of novel pyrochlore material systems - Compares different types of pyrochlore materials, including their structure, properties, and performance - Describes potential applications

Systematics and the Properties of the Lanthanides
Systematics and the Properties of the Lanthanides

Author: Shyama P. Sinha

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 650

ISBN-13: 9400971753

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Science is not a mere collection of facts. It is the correlation of facts, the interpretative synthesis of the available knowledge and its application that excite the imagination of a scientist. Even in these days of modern technology, the need for quick and accurate dissemination of new information and current concepts still exists. Conferences and Symposia offer one direct method of communication. The Summer Schools are another approach. The success of a Summer School is mainly due to that human factor and under standing that goes with it and allows for extensive and often time-unrestricted discussions. During the course of the past 20 years, one of the most in tensively studied groups of elements in the Periodic Table is the Lanthanides. In this period, we have increased our knowledge on these once exotic elements, which were once considered to be a part of a lean and hungry industry, many-fold due to the involve ment of scientists from various disciplines. The purpose of our Summer School was to bring a group of ex perts and participants together for the exchange of ideas and in formation in an informal setting and to promote interdisciplinary interactions. Out of many conceivable topics, we selected the following five as the main basis to broaden our knowledge and understanding I) Systematics 2) Structure 3) Electronic and Magnetic Proper ties 4) Spectroscopic Properties and 5) Lanthanide Geochemistry.

Alloy Phase Stability
Alloy Phase Stability

Author: G.M. Stocks

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 638

ISBN-13: 9400909152

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One of the ultimate goals of materials research is to develop a fun damental and predictive understanding of the physical and metallurgical properties of metals and alloys. Such an understanding can then be used in the design of materials having novel properties or combinations of proper ties designed to meet specific engineering applications. The development of new and useful alloy systems and the elucidation of their properties are the domain of metallurgy. Traditionally, the search for new alloy systems has been conducted largely on a trial and error basis, guided by the skill and intuition of the metallurgist, large volumes of experimental data, the principles of 19th century thermodynamics and ad hoc semi-phenomenological models. Recently, the situation has begun to change. For the first time, it is possible to understand the underlying mechanisms that control the formation of alloys and determine their properties. Today theory can begin to offer guidance in predicting the properties of alloys and in developing new alloy systems. Historically, attempts directed toward understanding phase stability and phase transitions have proceeded along distinct and seemingly diverse lines. Roughly, we can divide these approaches into the following broad categories. 1. Experimental determination of phase diagrams and related properties, 2. Thermodynamic/statistical mechanical approaches based on semi phenomenological models, and 3. Ab initio quantum mechanical methods. Metallurgists have traditionally concentrated their efforts in cate gories 1 and 2, while theoretical physicists have been preoccupied with 2 and 3.

Group Theory and Quantum Mechanics
Group Theory and Quantum Mechanics

Author: Michael Tinkham

Publisher: Courier Corporation

Published: 2012-04-20

Total Pages: 354

ISBN-13: 0486131661

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This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.