Syllabus

Module-1: The development of structure and types of matter: Gaseous, liquid, amorphous and crystalline states. Symmetry operations, point symmetry operations, lattice, basis, unit cell, crystal structure and crystal systems. Centering of lattice, The 14 Bravais lattices, The Wigner-Seitz unit cell. (8 hours)

Module-2: Crystallographic point groups: Point group, Hermann-Mauguin symbols for point groups. Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange’s theorem, conjugation, Factor group and Homomorphism, Group actions, Conjugate subgroup and normalizers. Development of 32 crystallographic point groups. Stereographic projection and its use for the derivation of crystallographic point groups. Laue classes. (8 hours)

Module-3: Space groups and their description: Space groups - general introduction. Space group operators, The Symmorphic and non-symmorphic space groups, Matrix-column presentation of screw axes and glide planes, Structure of space groups: point groups of space groups. Coset decomposition of the space group with respect to its translation subgroup, Space-group diagrams. General and special positions, site-symmetry groups, Derivation of space groups, Orthogonal projections of space groups. Exercises on space-group diagrams from Volume A of the International Tables for Crystallography. (6 hours)

Module-4: Fundamental principles of x-ray diffraction, Scattering of x-ray by electron, atom and small crystal, Structure factor and Intensity. Typical crystal structure determinations from x-ray powder diffraction data. Determination of crystallite size and strain from x-ray diffraction patterns. (6 hours)

Module-5: Crystal Physics: Crystal symmetry and macroscopic physical properties, Physical Properties, Polar Tensor and Tensor properties, Axial tensor properties, Neuman’s Principle, Symmetry of higher rank tensors and their applications to crystal properties: pyroelectricity, ferroelectricity, electrical conductivity, piezoelectricity, magnetic susceptibility and elasticity tensors.
(8 hours)

To impart knowledge on
1. Basic aspects of crystallographic symmetry and point symmetry operations.

2. The concept of lattice, crystal systems and bravias lattices.

3. Development of the point groups, space groups and their descriptions.

4. The basic of X-ray diffractions and determination of crystal structure.
5. Use of symmetry in tensor representation of crystal properties.

At the end of course, students will be able to:
CO1: Explain the different types of point symmetry operations.
CO2: Describe the application of symmetry operations to a lattice for classifying seven crystal systems and 14 bravias lattices.
CO3: Explain the determination of crystallographic point groups and descriptions on space groups.
CO4: Gain knowledge on the theory of X-ray diffraction along with the x-ray methods used to determine the crystal structure of materials.
CO5: Correlate the crystal symmetry on the macroscopic physical properties of crystalline solids.

G. Burns and A. M. Glazer, Space Group for Solid State Scientist,, Academic Press, USA, (2013).

J. F. Nye, Physical properties of crystals, Oxford University Press: New York, (2004).

Ulrich Muller, Symmetry Relationships Between Crystal Structures, Oxford University Press, UK, 1st Edition (2013).

C. Suryanarayana, M. Grant Norton, X-ray diffraction: A practical approach, Plenum Press, New York, (1998).