Site Symmetry in Crystals

1. Front Matter

   Pages I-XI

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2. Introduction

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 1-3

3. Finite Groups and Their Representations

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 5-30

4. Symmetry Groups and Their Representations

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 31-87

5. Site Symmetry and Induced Representations of Symmetry Groups

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 89-124

6. Application of Induced Representations in the Electron Theory of Molecules and Crystals

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 125-184

7. Induced Representations in the Theory of Imperfect Crystals

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 185-203

8. Application of Induced Representations of Space Group to Second Order Phase Transitions

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 205-212

9. Induced Representations of Space Groups in Phonon Spectroscopy of Crystals

   • Robert A. Evarestov, Vyacheslav P. Smirnov

   Pages 213-236

10. Site Symmetry in Magnetic Crystals and Induced Corepresentations

    • Robert A. Evarestov, Vyacheslav P. Smirnov

    Pages 237-250

11. Site Symmetry in Permutation — Inversion Symmetry Groups of Nonrigid Crystals

    • Robert A. Evarestov, Vyacheslav P. Smirnov

    Pages 251-264

12. Back Matter

    Pages 265-276

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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.

• Group theory
• Lattice
• chemistry
• induced representations of space groups
• lattice dynamics
• layer groups
• localized and delocalized states in crystals
• site symmetry in crystals
• surface

• Department of Chemistry, St. Petersburg University St. Peterhoff, St. Petersburg, Russia

  Robert A. Evarestov

• Department of Theoretical Physics, Institute of Fine Mechanics and Optics, St. Petersburg, Russia

  Vyacheslav P. Smirnov

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