Solid State Physics Yuanxu Wang School of Physics and Electronics Henan University 双语教学示范课程

Page  2 Why does not exist fivefold axis? The crystal periodicity and translation symmetry. Quasicrystal : Long-range orientation, no long-range translation symmetry §1.6 Symmetry Operation  Fivefold axis?

Page  3 Why does not exist fivefold axis? A and B are nearest points of O. Array A’B’ are certainly parallel to array AB Thus, m is integer number Consequently

Page  4 The physical constants of a crystal is strongly depended on its symmetry. Such as dielectric constant, piezoelectric constant, elastic constant Application of symmetry operation  Dielectric constant and symmetry Applying matrix of symmetry operation, then The dielectric constant should be unchanged with symmetry operating.

Page  5 1) Applying the rotating 90 degree along x (a) axis 2) Applying the rotating 90 degree along y (a) axis 3) Applying (1.22), we can obtain (1.22) (1.23) (1.24)

Page  6 3) Applying (1.24) to (1.23), we obtain (1.24)  Thus, the number of the individual dielectric constants for a cubic crystal is only one. Mention: the symmetry is very important for the properties of crystals.

Page  7 §7 Classification of crystal structure According to the crystal cell Cubic Tetragonal Triclinic Monoclinic Hexagonal Trigonal orthorhombic According to the function electric conductor semiconductor Insulator Magnetic medium Dielectric Superconductor According the mode of combination Molecular crystals Ionic crystals Covalent crystals Metallic crystal Hydrogen bond crystal

Page  8 CrystalFeaturesBravais lattice The point group (international symbol) Triclinica ≠b ≠c a ≠b ≠g simple triclinic(Without shaft) Neither the symmetry axis nor the symmetry plane Monoclinica ≠b ≠c a = b = 90° ≠g Simple monoclinic;Bsae- centered monoclinic One C2, mirror symmetry Orthorhombica ≠b ≠c a = b = g = 90° Simple orthogonal;Bsae- centered orthorhombic;Body- centered orthogonal;Face- centered orthogonal Three mutually perpendicular C2 Trigonal a = b = c a = b = g ≠90° TrigonalOne C3 Tetragonala = b ≠c a = b = g = 90° Simple tetragonal;Body- centered tetragonal one C4 Hexagonala = b ≠c a=b= 90°;g =120° Hexagonalone C6 Cubica = b = c a = b = g = 90° simple cubic; body- centered cubic; face-centered cubic Four C3