Course Details
Subject {L-T-P / C} : PH6351 : Crystal Symmetry and Crystal Physics { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Dillip Kumar Pradhan
Syllabus
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.
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.
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.
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.
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.
Course Objectives
- To define the basic concepts of crystallographic symmetry, which are essential for the understanding of arrangement of atoms and molecules in space for crystalline solids.
- To introduce the concept of symmetry operations, to derive the point groups and space groups with practical applications of crystalline solids.
- To provide the basic qualitative knowledge of X-ray diffractions and crystal structure determination to put this knowledge on a quantitative basis.
- To establish the correlation between the crystal symmetry and physical properties of the crystalline materials.
Course Outcomes
The students after completion of the course will get basic knowledge of elemental crystallography, fundamentals of X-ray diffraction, crystal structure determination, and the correlation of the crystal symmetry on the macroscopic physical properties of crystalline solids.
Essential Reading
- G. Burns and A. M. Glazer, Space Group for Solid State Scientist,, Academic Press, USA, 2013.
- J. F. Nye, Physical properties of crystals, Oxford Science Publication, Oxford University Press: New York, 2004.
Supplementary Reading
- B. E. Warren, X-ray diffraction,, Addison-Wesley Publishing Company, London, 1969.
- C. Suryanarayana, M. Grant Norton, X-ray diffraction: A practical approach, Plenum Press, New York, 1998.