Structure Determination, Building Principles, and Synthesis of Crystalline Materials in Two and Three Dimensions

Many materials in nature and technology are crystalline, i.e. their atomic structure is periodic. For a microscopic understanding of physical properties and their anisotropy and as a prerequisite for simulations, detailed knowledge of the atomic structure is essential. The lecture aims at providing fundamentals for structure determination by means of diffraction, i.e. determination of the unit cell as well as type and coordinates of the atoms contained. Since structure determination takes advantage of symmetries, an overview will be given over symmetry operations, the difference between coupling and combination, as well as the classification in point and space groups. Moreover, important methods for the growth of inorganic crystals as well as synthesis of novel organic crystalline materials as Metal-Organic-Frameworks und Covalent-Organic-Frameworks will be introduced. Finally, in relation to nano-materials, we discuss both synthesis and structure determination of two-dimensional materials.

The module covers the following aspects:

1) basic knowledge of crystallography in 2D and 3D:
-lattices and compatible symmetries
-recognition and application of simple and coupled symmetry operations
-determination of point symmetry groups of objects
-determination of point space groups of periodic structures

2) fundamentals of structure resolution by diffraction:

-Laue equations
-reciprocal lattices: calculation and meaning
-structure factors: calculation and meaning of
-extinction rules for centerings, screw-axis, glide planes
-Bragg equation and analysis of powder diffractograms
-Ewald-Konstruktion in 2D and 3D
-principal solution strategies for phase problem
-differences x-ray vs. electron diffraction

3) overview crystal growth:

-elementary processes (nucleation and growth)
-overview over the most important methods

Keine Vorkenntnisse nötig, die über die Zulassungsvoraussetzungen zum Masterstudium hinausgehen

lecture, beamer presentation, board work

worksheets, lecture slides

1) Werner Massa and Robert O. Gould: Crystal Structure Determination, Springer
2) Walter Borchardt-Ott and Robert O. Gould: Crystallography: An Introduction, Springer 2011

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions, symmetry determinations and sample calculations.

For example an assignment in the exam might be:

• Determination of the 2D space group of periodic structure
• Determination of the structure factor for a given unit cell
• Determination of the coordinatioes when a given symmetry element (e.g. glide plane, screw axis) acts on a point (x,y,z)
• Interpretation of a given powder diffractogramm
• Explain what a Laue classes are