Week 1: Geometrical crystallography: crystals, lattice and motif, lattice points and translation vectors, unit cells: primitive and non-primitive. Miller indices of planes and directions.
Week 2: Reciprocal lattice, use of reciprocal lattice in crystallographic calculations, angle between planes, angle between a plane and a direction, d-spacing of planes, volume of a crystal. Structure and metric matrices.
Week 3: Concept of Symmetry, Symmetry operations. Proper and Improper operations. Point and Space operations. Rotation axes: Roto-reflection and Roto-inversion axes. Mirror and glide planes. Inversion centre. Screw axes.
Week 4: Definition and properties of mathematical groups. Subgroups. Cosets. Lagrange’s theorem.
Week 5: Stereographic projection and matrix representation of symmetry operations.
Week 6: Symmetry based Classification of lattices: 7 crystal systems and 14 Bravais lattices. 17 plane groups.
Week 7: Symmetry based classification of crystals: 32 Crystal classes and 230 space groups. Possible proper rotation axes for crystals. Possible combination of pure rotation axes: Euler’s construction.
Week 8: Development of 32 point groups.
Week 9: Space groups and International Tables.
Week 10: Cartesian tensors: definition, rank, representation quadric, magnitude of a property in a given direction.
Week 11: Second-rank tensor properties: electrical and thermal conductivity, thermal expansion coefficient.
Week 12: Elasticity and fourth rank tensors. Elastic stiffness and compliance. Calculation of useful elastic properties such as modulus, Poisson ratio etc using tensor methods.
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