Site Symmetry in Crystals: Theory and ApplicationsSpringer Science & Business Media, 06.12.2012 - 274 Seiten 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. |
Inhalt
2 | |
5 | |
of Irreducible Representation Generation | 26 |
Irreducible Representations on the Setting | 81 |
Site Symmetry and Induced Representations of Symmetry Groups | 89 |
97 | 193 |
Application of Induced Representations of Space Group | 204 |
Induced Representations of Space Groups in Phonon Spectroscopy | 213 |
Site Symmetry in Magnetic Crystals | 237 |
Site Symmetry in Permutation Inversion Symmetry Groups | 251 |
265 | |
271 | |
Häufige Begriffe und Wortgruppen
a₁ a₂ atomic functions axis b₁ b₂ basis vectors Bloch functions Bravais lattice Brillouin zone C₂ calculations cluster coefficients consider contains coordinates corep corresponding coset representatives crystalline crystallographic crystallographic point groups cyclic model cyclic system decomposition electronic structure elements g energy bands energy levels G₁ group G group irreps Hamiltonian hybrid orbitals induced representations invariant subgroup irreducible irreps of G isomorphic k-basis left cosets linear combinations little group localized functions localized orbitals matrix molecular molecule notations obtained phonon point defect point group point q point symmetry primitive r₁ reciprocal lattice respect rotation Sect Simple induced representations simple induced reps small irreps space group space group D14 span the space subduced subgroup H superlattices symmetry group symmetry points tetragonal tion transform according translation group translation vectors unit cell valence bands wave functions wave vector Wigner-Seitz unit cell Wyckoff positions