Workshop on Structural Analysis of Incommensurate Crystals
Bayreuth, Germany, March, 2009
Lectures on Aperiodic order in crystalline materials, Superspace description of modulated structures, Superspace symmetry and Diffraction by incommensurate structures provided an overview and introduced the fundamentals of the (3+d)-dimensional superspace approach as a mathematical tool for the description of crystal structures of incommensurately modulated compounds. Fourier methods in superspace and Modulation functions by the Maximum Entropy Method presented techniques for finding atomic modulation functions. Structure solution by Charge-Flipping described a method of ab initio direct structure determination in higher-dimensional superspace. Modulated structures of Lazurite minerals - a case study, Disorder and aperiodic order and Modulated molecular compounds described using the superspace approach for a unified and simplified description of complex superstructures, crystal-chemical aspects of aperiodic structures and potential problems and their solution during measurement and data collection.
In the afternoons participants practiced structure solution and refinement on their own desktop computers using programs such as JANA2006 (V. Petricek, M. Dusek and L. Palatinus, Prague) and SUPERFLIP (L. Palatinus and G. Chapuis, Lausanne) that had been installed on the computers in the Bayreuth U data centre. A script with selected examples of different levels of difficulty gave a step-by-step introduction to the procedure of structure analysis of aperiodic crystals. The questions and exercises in the script served as motivation for working out the various aspects of structure analysis in superspace. The lecturers served as tutors to discuss, help, advise and solve problems.