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

Module PH2191

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of SS 2017

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022SS 2021SS 2020SS 2019SS 2018SS 2017SS 2014

Basic Information

PH2191 is a semester module in German or English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 40 h 5 CP

Responsible coordinator of the module PH2191 in the version of SS 2017 was Markus Lackinger.

Content, Learning Outcome and Preconditions


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.

Learning Outcome

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

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

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

Module Exam

Description of exams and course work

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

Exam Repetition

The exam may be repeated at the end of the semester.

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