| 1 |
Introduction
Overview, textbooks, history of crystallography
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| 2 |
Symmetry in 2D
Definition of symmetry, introduction of symmetry operators
Compatibility of symmetry operators with translation
Combining symmetry operations and determination of plane groups
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| 3 |
Symmetry in 3D
Extension of the plane groups concept to the third dimension: space groups
Introduction of screw axes and glide planes
Point groups vs. space groups
The unit cell and crystallographic conventions
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| 4 |
X-rays and matter
X-ray generation
Diffraction experiment with optical grids and laser pointers
Convolution theorem and Fourier transformation
Introduction of Bragg's law and Miller indices
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Student presentations of current homework assignment due two days after Lec #4 |
| 5 |
Geometry of diffraction
Reciprocal space vs. real space
Ewald construction as a geometric interpretation of Bragg's law
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| 6 |
Structure factors
Real atoms are no point atoms (atomic form factors) and show thermal motion (atomic displacement factors)
Having more than one atom per unit cell leads to structure factors
Fourier transformation gives rise to electron density; crystallographic resolution
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Student presentations of current homework assignment due two days after Lec #6 |
| 7 |
Structure factors II
Complex numbers, Euler's equation and the argand plane
Introduction of the phase problem
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| 8 |
Symmetry in reciprocal space
Introduction of Friedel's law and laue groups
Space group determination: |E2-1| statistics, systematic absences, crystallographic directions for triclinic, monoclinic, orthorhombic and tetragonal systems
Introduction of the Patterson function and Harker sections, as well as direct methods for structure solution
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Student presentations of current homework assignment due two days after Lec #8 |
| 9 |
Structure refinement
Different types of electron density maps (Fo, Fc, Fo-Fc, etc.)
Introduction of anisotropic displacement parameters
Minimization functions: the least-squares approach and different R-factors
Crystallographic parameters, constraints and restraints
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| 10 |
Structure refinement II
Problems and pitfalls: wrong space group, atom type assignment (all electrons are blue), disorder, twinning
What are artifacts (libration, C-C triple bonds, Fourier truncation ripples, etc.)?
Finding the hydrogen atoms, "riding model"
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Student presentations of current homework assignment due two days after Lec #10 |
| 11 |
Anomalous scattering
Absorption of X-ray photons leads to loss of symmetry in orbital geometry, which results in a violation of Fridel's law
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| 12 |
Practical aspects and related methods
Growing crystals and keeping them alive (never remove the mother liquor!)
Mounting crystals onto the diffractometer
Short introduction of powder diffraction, neutron diffraction and EXAFS
Crystallographic data bases (ICSD, CSD, PDB, reciprocal net)
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Student presentations of current homework assignment due two days after Lec #12 |
| 13 |
Quick recap
Symmetry, Bragg's law, Miller indices, real space vs. reciprocal space, Ewald construction, structure factors, electron density, symmetry in reciprocal space, laue groups vs. point groups vs. space groups, space group determination, Patterson function, structure refinement, parameters/constraints/restraints, anisotropic displacement parameters, libration, hydrogen atoms
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| 14 |
Exam
You have 50 minutes to answer all questions. You can use pens, a calculator, ruler and compass, as well as a letter sized piece of paper with anything written on it. No books or other material is allowed.
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