ABOUT THE COURSE:A thorough understanding of crystallographic symmetry: 2D/3D point groups and space groups. An understanding of the underlying symmetry as the basis of the 14 Bravais Lattices. Principles of X-Ray diffraction, relation of reflection conditions with crystal symmetry. Tensors and their uses in symmetry operations and representation of the physical properties of crystals. Applications to pyroelectricity, dielectric susceptibility, piezoelectricity, elasticity and other symmetry dependent properties, such as, optical properties, conductivity, ferroelectricity.INTENDED AUDIENCE: Undergraduate and Postgraduate students of Metallurgy, Materials Science, Mechanical Engineering, Chemical Engineering, Chemistry, PhysicsINDUSTRY SUPPORT: R&D divisions of materials development in industry, e.g., Tata Steel
Crystal Symmetry, X-Ray Diffraction and Physical Properties
Overview
Syllabus
Week 1: Introduction to Crystallography: common misconceptions, lattice, motif and crystals; translation vectors; unit cells; Miller indices of planes and directions; interplanar spacing, angular relationships between planes and directionsWeek 2:Symmetry elements in crystallographic patterns; symmetry restrictions; introduction to mathematical groups, specifically crystallographic point groupsWeek 3:Combining 2D point symmetry operations through (i) geometrical and (ii) matrix representation; developing the 10 crystallographic point groups in 2DWeek 4:Classification of 2D lattices based on symmetry; adding translation to 2D point groups; combining rotation, reflection and translation using geometry and matricesWeek 5:Derivation of the 17 plane groups; Decoding the International Tables for Crystallography-I; Combination of rotation axes in 3DWeek 6:Development of 3D point groups; Derivation of the Bravais Lattices; Space Groups, Screw Axis, Glide Planes; Decoding the International Tables for Crystallography-IIWeek 7:X-Ray Diffraction: Laue Conditions and Braggs Law; Structure FactorWeek 8:Reciprocal Lattice: use for deriving the equations for interplanar spacing; representation of diffraction conditions in reciprocal lattice space; Decoding the International Tables for Crystallography-IIIWeek 9:Experimental Techniques of X-Ray Diffraction: applicationsWeek 10:Physical properties of crystals: representation by tensors; transformation of tensors; extend to other second rank tensor properties: Week 11:Electrical Conductivity of crystals: second-rank tensor property; extend to other second rank tensor properties, such as,:thermal conductivity, thermal expansionWeek 12:Third rank tensor property: piezoelectricity; Fourth rank tensor property: elastic stiffness and elastic compliance
Taught by
Prof. Sandeep Sangal
