Fundamentals of Crystallography | Department of Chemistry

Fundamentals of Crystallography

Crystallography in combination with X-ray or neutron diffraction yields a wealth of three-dimensional structural information unobtainable through other methods. The course has been designed to give an overview of crystallography, in general. This basic course will cover the topics such as symmetry in crystallography, crystals systems, Bravais lattices, crystal symmetry, crystallographic point groups and space groups, Miller indices, theory of X-ray diffraction, data collection, data reduction, structure factors and Fourier syntheses, electron density, phase problem, direct methods, Patterson method, crystal structure refinement etc. The course will also highlight the application of single crystal and powder X-ray diffraction techniques and will include hands on training on crystal growth, mounting, structure solution, refinement and analysis. Further, training on the use of database for structural search will also be provided.

  • Introduction - Introduction on Crystallography and discussion on course structure
  • Crystallographic Symmetry - Concept of 1D and 2D symmetry and lattices, notations of symmetry elements, space groups in 2D, 3D lattices, 32 point groups and their notations, stereographic projections, Laue symmetry; glide planes, screw axes and their notations, space groups, equivalent points, space group symmetry diagrams etc. Miller Indices, crystallographic planes and directions, close pack structures, linear density, planar density, Miller-Bravais indices for hexagonal systems.
  • Theory of X-ray diffraction - What is X-ray, generation and classification of X-ray, X-ray sources, diffraction of X-rays, Bragg’s law, the reciprocal lattice, reciprocal relationship, Bragg’s law in reciprocal space, Ewald’s sphere, Laue Method, Oscillation, rotation and precession methods.
  • Data reduction - L-P corrections, structure factor, scaling, interpretation of intensity data, temperature factor, symmetry from intensity statistics, structure factor and Fourier synthesis, Friedel’s law; exponential, vector and general forms of structure factor, determination of systematic absences for various symmetry or lattice centering, FFT, Anomalous scattering.
  • The Phase Problem - Definition, Direct Methods, structure invariants and semi invariants, probability methods, Phase determination in practice, Patterson Methods, Patterson Symmetry, completion of structure solution, F synthesis.
  • Refinement of Crystal Structures - Refinement by Fourier synthesis, refinement by F synthesis, Refinement by least squares method, weighting functions, Goodness-Of-Fit (GOF) parameter, treatment of non-hydrogen atoms, and treatment of hydrogen atoms.
  • Powder X-ray diffraction (PXRD) - Methodology, geometrical basis of powder X-ray diffraction, applications of PXRD (determination of accurate lattice parameters, identification of new/unknown phases, applications in pharmaceutical industry, structure solution from PXRD etc.), Reitveld method for structure refinement, indexing of PXRD, handling of PXRD using DASH.
  • Neutron and Electron Diffraction - Basics of neutron, synchrotron and electron diffraction and their applications.
  • Practical - Crystal growth, selection, indexing of crystals, data collection, data reduction, space group determination and structure refinement using SHELXS97, SIR and SHELXL97, introduction to International Tables for Crystallography and crystallographic packages (e.g. WinGx, PLATON, OLEX-2), IUCr validation of the structure and use of Cambridge Structural Database for structural search.

Text Book:

X-ray structure determination: A Practical Guide (2nd Ed.) by George H. Stout and Lyle H Jensen, Wiley-Interscience, New York, 1989.

Reference Books:

  1. Fundamentals of Crystallography (2nd Ed.) by C. Giacovazzo, Oxford University Press, USA, 2002.
  2. X-ray analysis and The Structure of Organic Molecules (2nd Ed.) by Jack D. Dunitz, Wiley-VCH, New York, 1996.
  3. Chemical Applications of Group Theory (3rd Ed.) by F. A. Cotton, Wiley-India Edition, India, 2009.
  4. International Table of Crystallography.
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