X-RAY CRYSTALLOGRAPHY

Explore the fundamentals and advanced concepts of X-ray crystallography in this comprehensive 16-week course offered by the Indian Institute of Science Bangalore. Delve into crystalline and amorphous materials, their physical properties, and various crystal growth techniques. Learn to select suitable crystals, understand unit cells and symmetries, and study important space groups. Examine diffraction principles, including Bragg's Law and reciprocal lattice concepts. Investigate scattering power, structure factor equations, and three-dimensional intensity data collection using diffractometers. Master the process of structure solution, from phase determination to electron density map computation. Gain practical skills in analyzing crystal structures, calculating geometries, and interpreting crystallographic data.

COURSE LAYOUT

Module 1-4:
The understanding of a Crystalline/amorphous materials and some of their physical properties viz., melting point, anisotropic/isotropic in nature, electrical resistance, refractive index and conductivity. Methods of obtaining single crystal by different techniques Viz., slow evaporation either by single / mixer of solvents, Vapour diffusion techniques- combination of solvents, the crystallization process involved- either exothermic/endothermic, controlling the evaporation rate.

Module 5-7:
Selecting a suitable Crystals viz., the suitable size, the defects associated with the crystals, how to choose a crystal free from defects by microscope, use of polarizing microscope. Understanding Crystalline substance may be a powder or a single crystal as a grating plate and use as a diffraction Grating for the X-Ray diffraction studies.

Module 7-13:
The unit cell and the symmetries associated, the basic symmetry in the seven Crystal systems, The 32 point groups associated with them and the symmetry operations, equivalent points, Viz., rotation, reflection, screw-rotation followed by translation along the rotation axis, glide- reflection followed by translation in the plane of reflection, and symmetry generated equivalent points.

Module 13-23:
Selected important Space groups viz., Triclinc-2, Monoclinic 15, orthorhombic 25,(centro symmetric and non-centrosymmetric) space groups with their packing symmetries, equivalent points, generated higher symmetry points.

Module 24-30:
Condition for Diffraction , Wavelength of the source and its relation with the slit width, How the Crystal acts as a Diffraction Grating with respect to X- Ray as a source. Braggs Law and Laue equation for diffraction, Concept of Reciprocal Lattice, constructing the Miller Indices from reciprocal lattice, Braggs law in reciprocal lattice.

Module 31-36:
Scattering Power of an atom, Structure Factor Equation, Derivation and Interpretation of Structure Factor Equation. Proving the Systematic absent condition from the structure factor equations.Using the Reciprocal lattice understanding the Diffraction Pattern, Indexing the Powder Pattern or single Crystal pattern.

Module 37- 40:
Three dimensional Intensity data collection: description about the Diffractometer, X-ray tube, the geometry of the diffractometer and understanding their significance, the three/four circles viz., Phi, Omega, Kappa and two Theta. Deciding the crystal quality from rotation, still picture, resolution from the matrix and obtaining the Cell parameters, refinement, deciding the system. Data collection strategy, Selecting the parameters like, time of exposure depending on the crystal quality, the data collection based on the system namely- quadrant, hemisphere, or full sphere for data collection, Refinement of the Cell parameters from the full data, further Data Integration. Selection of suitable parameters for data process, determining the Crystal System, Analyzing the systematic absent conditions, Space group Determination.

Module 41-50:
Structure Solution: Considering the Intensity as a wave form, converting Intensity into Structure factor, amplitude of the wave, the PHASE associated, solve the PHASE problem, determining the PHASES, structure solution, Understanding the Fourier Equation as a wave function and its application in Computing the electron density map. Obtaining the fractional coordinates, calculating the geometries like Bond Length, Bond angles, the torsional angles and mean plane calculation, the dihedral angle between the mean planes.