Evarestov / Smirnov Site Symmetry in Crystals

Theory and Applications
Erscheinungsjahr 2012
ISBN: 978-3-642-97442-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 108, 274 Seiten, eBook

Reihe: Springer Series in Solid-State Sciences

The history of applications of space group theory to solid state physics goes back more than five decades. The periodicity of the lattice and the definition of a k-space were the corner-stones of this application. Prof. Volker Heine in Vol. 35 of Solid State Physics (1980) noted that, even in perfect crystals, where k-space methods are appropriate, the local properties (such as the charge densi ty, bond order, etc.) are defined by the local environment of one atom. Natural ly, "k-space methods" are not appropriate for crystals with point defects, sur faces and interfaces, or for amorphous materials. In such cases the real-space approach favored by chemists to describe molecules has turned out to be very useful. To span the gulf between the k-space and real space methods it is helpful to recall that atoms in crystalline solids possess a site symmetry defined by the symmetry of the local environment of the atom occupying the site. The site symmetry concept is familiar to crystallographers and commonly used by them in the description of crystalline structures. However, in the application of group theory to solid state physics problems, the site symmetry approach has been used only for the last ten to fifteen years. In our book Methods oj Group Theory in the Quantum Chemistry oj Solids published in Russian in 1987 by Leningrad University Press we gave the first results of this application to the theory of electronic structure of crystals.

Zielgruppe

Research

Autoren/Hrsg.

Evarestov, Robert A.

Smirnov, Vyacheslav P.

Inhaltsverzeichnis

1. Introduction.- 2. Finite Groups and Their Representations.- 2.1 Elements of Group Theory.- 2.2 Elements of Group Representation Theory.- 2.3 Generation of Representations.- 3. Symmetry Groups and Their Representations.- 3.1 The Euclidean Group and Its Subgroups.- 3.2 Point Symmetry Groups.- 3.3 Space Groups.- 3.4 Site Symmetry in Space Groups.- 3.5 Symmetry Operations in Quantum Mechanics.- 3.6 Irreducible Representations of Rotation and Full Orthogonal Groups.- 3.7 Representations of Point Groups.- 3.8 Representations of Space Groups.- 4. Site Symmetry and Induced Representations of Symmetry Groups.- 4.1 Induced Representations of Point Groups. Correlation Tables.- 4.2 Induced Representations of Space Groups.- 4.3 Double-Valued Induced Representations.- 4.4 Generation of the Simple Induced Representations of the Space Group D144h.- 4.5 The Twenty-Four Most Common Space Groups: Crystal Structures and Tables of Simple Induced Representations.- 5. Application of Induced Representations in the Electron Theory of Molecules and Crystals.- 5.1 Adiabatic and One-Electron Approximations.- 5.2 Induced Representations in the Electron Theory of Molecules.- 5.3 One-Electron Approximation for Crystals.- 5.4 Induced Representations and the Theory of Chemical Bonding in Crystals.- 5.5 Energy Bands and Localized States.- 5.6 Localized Orbitals in Molecular Models of Crystals.- 6. Induced Representations in the Theory of Imperfect Crystals.- 6.1 Point Defects in Crystals.- 6.2 Diperiodic Space Groups. Surface Electron States.- 7. Application of Induced Representations of Space Group to Second Order Phase Transitions.- 7.1 Symmetry Rules in the Landau Theory of Second Order Phase Transitions.- 7.2 Tensor Fields in Crystals and Induced Representations of Space Groups. Tensor Fields forSpace Group D144h.- 7.3 Vibrational Field Representation and Phase Transitions in High-Temperature Superconductors.- 8. Induced Representations of Space Groups in Phonon Spectroscopy of Crystals.- 8.1 Phonon Symmetry Analysis.- 8.2 Infrared and Raman Spectra Selection Rules.- 8.3 Phonon Symmetry and Optical Spectra Selection Rules in Semiconductor Superlattices.- 8.4 Phonon Symmetry in High-Temperature Superconductors.- 8.5 Phonon Symmetry in Diperiodic Systems.- 9. Site Symmetry in Magnetic Crystals and Induced Corepresentations.- 9.1 Shubnikov Space Groups of Symmetry of Magnetic Crystals.- 9.2 Site Symmetry in Magnetic Crystals.- 9.3 Corepresentations of Shubnikov Space Groups.- 9.4 Induced Corepresentations of Magnetic Space Groups.- 9.5 Corepresentations of the Space Groups of Antiferromagnetic La2CuO4.- 10. Site Symmetry in Permutation — Inversion Symmetry Groups of Nonrigid Crystals.- 10.1 Symmetry Groups of Nonrigid Crystals.- 10.2 Irreducible Representations of a Nonrigid Crystal Symmetry Group.- References.