Second-Order Phase Transitions and the Irreducible Representation of Space Groups PDF Download
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Author: Hugo F. Franzen
Publisher: Springer Science & Business Media
ISBN: 3642489478
Category : Science
Languages : en
Pages : 108
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Book Description
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.
Author: Hugo F. Franzen
Publisher: Springer Science & Business Media
ISBN: 3642489478
Category : Science
Languages : en
Pages : 108
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Book Description
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.
Author: Nikolai B. Melnikov
Publisher: Springer Nature
ISBN: 3031139917
Category : Science
Languages : en
Pages : 343
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Book Description
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.
Author: Hugo Friedrich Franzen
Publisher: Springer
ISBN: 9780387119588
Category : Crystallography, Mathematical
Languages : en
Pages : 98
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Book Description
Author: Pierre Tol‚dano
Publisher: World Scientific
ISBN: 9789810223649
Category : Science
Languages : en
Pages : 424
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Book Description
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.
Author: Dorian M Hatch
Publisher: World Scientific
ISBN: 9814522392
Category : Science
Languages : en
Pages : 621
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Book Description
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.
Author: Yurii Aleksandrovich Izyumov
Publisher: Springer Science & Business Media
ISBN: 9400919204
Category : Science
Languages : en
Pages : 462
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Book Description
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.
Author: Dietmar Heidrich
Publisher: Springer Science & Business Media
ISBN: 3642934994
Category : Science
Languages : en
Pages : 193
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Book Description
Contemporary chemical reaction theory is the characterization of Potential Energy Hypersurfaces (PES). The authors critically analyze chemically and mathematically suitable reaction path definitions. The book presents a simple mathematical analysis of stationary and critical points of the PES. It provides tools for studying chemical reactions by calculating reaction paths and related curves. A further aspect of the book is the dependence of PES properties on approximations used for the analysis. Recent quantum chemical calculations, particularly of single proton transfer processes, and experimental data are compared. The book addresses students and researchers in Theoretical Chemistry, Chemical Kinetics and related fields.
Author: Sandor Fliszar
Publisher: Springer Science & Business Media
ISBN: 3642514928
Category : Science
Languages : en
Pages : 182
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Book Description
Chemical bonds, their intrinsic energies in ground-state molecules and the energies required for their actual cleavage are the subject of this book. The theory, modelled after a description of valence electrons in isolated atoms, explains how intrinsic bond energies depend on the amount of electronic charge carried by the bond-forming atoms. It also explains how bond dissociation depends on these charges. While this theory vividly explains thermochemical stability, future research could benefit from a better understanding of bond dissociation: if we learn how the environment of a molecule affects its charges, we also learn how it modifies bond dissociation in that molecule. This essay is aimed at theoretical and physical-organic chemists who are looking for new perspectives to old problems.
Author: Wolfram Hergert
Publisher: John Wiley & Sons
ISBN: 3527413014
Category : Science
Languages : en
Pages : 411
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Book Description
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.
Author: Boris K. Vainshtein
Publisher: Springer Science & Business Media
ISBN: 9783540565581
Category : Juvenile Nonfiction
Languages : en
Pages : 520
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Book Description
From the reviews: "[...] an excellent reference book. I have no doubt it will become a much-thumbed resource for students and researchers in mineralogy and crystallography." Geological Magazine
