Second Order Phase Transitions And The Irreducible Representation Of Space Groups
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Second Order Phase Transitions And The Irreducible Representation Of Space Groups
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Author : Hugo F. Franzen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Second Order Phase Transitions And The Irreducible Representation Of Space Groups written by Hugo F. Franzen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Isotropy Subgroups Of The 230 Crystallographic Space Groups
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Author : Dorian M Hatch
language : en
Publisher: World Scientific
Release Date : 1989-01-01
Isotropy Subgroups Of The 230 Crystallographic Space Groups written by Dorian M Hatch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Science categories.
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.
Second Order Phase Transitions And The Irreducible Representation Of Space Groups
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Author : Hugo Friedrich Franzen
language : en
Publisher: Springer
Release Date : 1982-01-01
Second Order Phase Transitions And The Irreducible Representation Of Space Groups written by Hugo Friedrich Franzen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Crystallography, Mathematical categories.
Space Group Representations
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Author : Nikolai B. Melnikov
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Space Group Representations written by Nikolai B. Melnikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
This book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.
Group Theory In Solid State Physics And Photonics
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Author : Wolfram Hergert
language : en
Publisher: John Wiley & Sons
Release Date : 2018-05-29
Group Theory In Solid State Physics And Photonics written by Wolfram Hergert and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Science categories.
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
Phase Transitions And Crystal Symmetry
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Author : Yurii Aleksandrovich Izyumov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Phase Transitions And Crystal Symmetry written by Yurii Aleksandrovich Izyumov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
About half a century ago Landau formulated the central principles of the phe nomenological second-order phase transition theory which is based on the idea of spontaneous symmetry breaking at phase transition. By means of this ap proach it has been possible to treat phase transitions of different nature in altogether distinct systems from a unified viewpoint, to embrace the aforemen tioned transitions by a unified body of mathematics and to show that, in a certain sense, physical systems in the vicinity of second-order phase transitions exhibit universal behavior. For several decades the Landau method has been extensively used to an alyze specific phase transitions in systems and has been providing a basis for interpreting experimental data on the behavior of physical characteristics near the phase transition, including the behavior of these characteristics in systems subject to various external effects such as pressure, electric and magnetic fields, deformation, etc. The symmetry aspects of Landau's theory are perhaps most effective in analyzing phase transitions in crystals because the relevant body of mathemat ics for this symmetry, namely, the crystal space group representation, has been worked out in great detail. Since particular phase transitions in crystals often call for a subtle symmetry analysis, the Landau method has been continually refined and developed over the past ten or fifteen years.
Reconstructive Phase Transitions In Crystals And Quasicrystals
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Author : Vladimir Dmitriev
language : en
Publisher: World Scientific
Release Date : 1996-09-30
Reconstructive Phase Transitions In Crystals And Quasicrystals written by Vladimir Dmitriev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-30 with Science categories.
This book deals with the phenomenological theory of first-order structural phase transitions, with a special emphasis on reconstructive transformations in which a group-subgroup relationship between the symmetries of the phases is absent. It starts with a unified presentation of the current approach to first-order phase transitions, using the more recent results of the Landau theory of phase transitions and of the theory of singularities. A general theory of reconstructive phase transitions is then formulated, in which the structures surrounding a transition are expressed in terms of density-waves, providing a natural definition of the transition order-parameters, and a description of the corresponding phase diagrams and relevant physical properties. The applicability of the theory is illustrated by a large number of concrete examples pertaining to the various classes of reconstructive transitions: allotropic transformations of the elements, displacive and order-disorder transformations in metals, alloys and related structures, crystal-quasicrystal transformations.
Crystal Symmetries
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Author : B. K. Vainshtein
language : en
Publisher: Elsevier
Release Date : 2017-07-26
Crystal Symmetries written by B. K. Vainshtein and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Science categories.
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.
Fundamentals Of Crystals
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Author : Boris K. Vainshtein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fundamentals Of Crystals written by Boris K. Vainshtein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
Early in this century, the newly discovered x-ray diffraction by crystals caused a complete change in crystallography and in the whole science of the atomic structure of matter, thus giving a new impetus to the development of solid-state physics. Crystallographic methods, primarily x-ray diffraction analysis, pene trated into materials sciences, molecular physics, and chemistry, and also into may other branches of science. Later, electron and neutron diffraction structure analyses became important since they not only complement x-ray data, but also supply new information on the atomic and the real structure of crystals. Electron microscopy and other modern methods of investigating matte- optical, electronic paramagnetic, nuclear magnetic, and other resonance tech niques - yield a large amount of information on the atomic, electronic, and real crystal structures. Crystal physics has also undergone vigorous development. Many remark able phenomena have been discovered in crystals and then found various practical applications. Other important factors promoting the development of crystallography were the elaboration of the theory of crystal growth (which brought crystallography closer to thermodynamics and physical chemistry) and the development of the various methods of growing synthetic crystals dictated by practical needs. Man made crystals became increasingly important for physical investigations, and they rapidly invaded technology. The production of synthetic crystals made a tremendous impact on the traditional branches: the mechanical treatment of materials, precision instrument making, and the jewelry industry.
Modern Crystallography 2
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Author : Boris K. Vainshtein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modern Crystallography 2 written by Boris K. Vainshtein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Structure of Crystals describes the ideal and real atomic structure of crystals as well as the electronic structures. The fundamentals of chemical bonding between atoms are given, and the geometric representations in the theory of crystal structure and crystal chemistry, as well as the lattice energy, are considered. The important classes of crystal structures in inorganic compounds as well as the structures of polymers, liquid crystals, biological crystals, and macromolecules are treated. This edition is complemented with recent data on many types of crystal structures - e.g., the structure of fullerenes, high-temperature superconductors, minerals, and liquid crystals.