MSE638A - Symmetry and Properties of Crystals

Introduction 1 Symmetries in 1 D, 2D and 3D, Examples of patterns showing various, symmetries, Symmetries and Lattices in 2D space : Operations of Translation, Rotation and Reflection, standard symbols, Lattices and Unit Cells, Permissible rotational symmetries, Derivation of lattices: oblique, rectangular, centered rectangular, square, hexagonal Point Groups in 2D 4 : Set of symmetry operations, Group Theory Essentials, Evolution of 2D crystallographic point groups, 2D Space Groups (Plane Groups) Glide Planes: combination of lattice translation and reflection, Derivation of all the 17 plane groups, Understanding the Plane Group entries in the International Tables, of Crystallography3D Point Groups 4 : Combination of rotation axes in 3D, Development of the 32 point groups, Laue Groups3D Brava's Lattices Addition of a third translation to the plane groups, Derivation of Brava's Lattices3D Space Groups Screw Axes: combination of lattice translation and rotation, Development of the 230 space groups, Understanding the Space Groups entries in the International Tables of Crystallography.