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This web page contains 15 lectures and handout notes given by Dr. Cora Lind-Kovacs for her Chem 4980/6850/8850: X-ray Crystallography course at the University of Toledo (Ohio). The preparation of these lectures was in part supported by National Science Foundation CAREER award DMR-0545517. Thanks to Prof. Lind and the University of Toledo Department of Chemistry for permission to post these videos and notes. Lecture notes are in PDF format and have been updated since the time these lectures were recorded (original versions are here). Also of possible interest is MIT Open Course 3.60 (Symmetry, Structure, and Tensor Properties of Materials) taught by Prof. Bernhardt Wuensch in 2005 (41 video lectures) |
| Lecture 1: Introduction |
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This lecture introduces crystallography, including the history and generation of x-rays. (Note that refractive optics for x-rays are used at the APS, in contrast to what is mentioned in the lecture). |
| Lecture 2: Crystals |
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Presentation (see original versions for slides) This lecture discusses what is a crystal, defines the concept of a unit cell and defines the seven classes of unit cells. Growth of crystals is also discussed. The sharp facets of crystals are determined by the underlying symmetry of the unit cell; these facets are described by Miller indices. |
| Lectures 3 & 4: Symmetry and Point Groups |
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Lecture 3 relates the unit cell to the concept of the lattice and introduces the 14 Bravais lattice types. Then point symmetry elements -- the symmetry that can be found in discrete objects -- are introduced. Lecture 4 expands from symmetry of discrete objects to those of infinitely repeating patterns that fill space. This requires additional types of symmetry elements. Symmetry operations can be combined in a limited number of ways. For discrete objects there are 32 point groups, for infinite objects there are 230 space groups. |
| Lecture 5: Plane and Space Groups |
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Presentation or Sides | Examples This talk provides an overview of space group symbols and then introduces how to read a space group description in the International Tables of Crystallography, volume A. The lecture ends with a description of sub- and super-group relationships. |
| Lecture 6: Diffraction |
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This lecture introduces the basic physics of diffraction. Bragg's law, which relates diffraction to planes (of atoms), is shown and related to the concept of Miller indices, introduced earlier. |
| Lecture 7: Reciprocal Space |
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Presentations: Part 1, Part 2 or Slides This lecture introduces the concept of the reciprocal lattice and how to relate this to the scattering from a crystal. The second part starts with a review and then covers the Ewald sphere concept, which allows one to visualize the geometry of diffraction; the formulae for computing the d-space using real and reciprocal lattice constants and ending with a contrast between single crystal and powder diffraction. In the 2nd half of the lecture Prof. Lind reviews symmetry with the class, which may be of little value via video. |
| Lectures 8 & 9: Structure Factors & Fourier Transforms |
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Presentations: Structure Factors, Fourier Transforms or Slides Structure factors provide both intensity and phases for the diffracted beams. This presentation shows how the structure factor equation arises from the positions of atoms in the unit cell. This equation is used to show how systematic absences occur, where classes of reflections are required to have zero intensity by symmetry. The second lecture introduces the concept of the Fourier transform and shows how the the electron density in a unit cell is related to the Fourier transform of the structure factors, and the converse. |
| Lecture 10: Data Collection |
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This lecture describes sources of x-rays and neutrons, and how diffraction intensities are collected. |
| Lecture 11: Structure Solution |
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Presentation: Part 1 | Part 2 or Slides These talks outline a number of approaches used for determining approximate crystal structures from a set of diffraction intensities (typically from single-crystal measurements). |
| Additional Lectures (not available as video) |
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