SYMMETRY OF CRYSTALS

The following sections are included:

• Symmetric Group of Crystals

• Crystallographic Point Groups

  • Elements in a Crystallographic Point Group

  • Proper Crystallographic Point Groups

  • Improper Crystallographic Point Group

• Crystal Systems and Bravais Lattice

  • Restrictions on Vectors of Crystal Lattice

  • Triclinic Crystal System

  • Monoclinic Crystal System

  • Orthorhombic Crystal System

  • Trigonal and Hexagonal Crystal System

  • Tetragonal Crystal System

  • Cubic Crystal System

• Space Group

  • Symmetric Elements

  • Symbols of a Space Group

  • Method for Determining the Space Groups

  • Example for the Space Groups in Type A

  • Example for the Space Groups in Type B

  • Analysis of the Symmetry of a Crystal

• Linear Representations of Space Groups

  • Irreducible Representations of $\mathcal{T}$

  • Star of Wave Vectors and Group of Wave Vectors

  • Representation Matrices of Elements in $\mathcal{S}$

  • Irreducible Representations of $\mathcal{S}(k_1)$

  • The Bloch Theorem

  • Energy Band in a Crystal

• Exercises