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 directions
Symmetry elements in crystallographic patterns; symmetry restrictions; introduction to mathematical groups, specifically crystallographic point groups
Combining 2D point symmetry operations through (i) geometrical and (ii) matrix representation; developing the 10 crystallographic point groups in 2D
Classification of 2D lattices based on symmetry; adding translation to 2D point groups; combining rotation, reflection and translation using geometry and matrices
Derivation of the 17 plane groups; Decoding the International Tables for Crystallography-I; Combination of rotation axes in 3D
Development of 3D point groups; Derivation of the Bravais Lattices; Space Groups, Screw Axis, Glide Planes; Decoding the International Tables for Crystallography-II
X-Ray Diffraction: Laue Conditions and Braggs Law; Structure Factor
Reciprocal Lattice: use for deriving the equations for interplanar spacing; representation of diffraction conditions in reciprocal lattice space; Decoding the International Tables for Crystallography-III
Experimental Techniques of X-Ray Diffraction: applications
Physical properties of crystals: representation by tensors; transformation of tensors; extend to other second rank tensor properties
Electrical Conductivity of crystals: second-rank tensor property; extend to other second rank tensor properties, such as,:thermal conductivity, thermal expansion
Third rank tensor property: piezoelectricity; Fourth rank tensor property: elastic stiffness and elastic compliance