Advanced Crystallography: Symmetry, Order, and Complexity in Materials

Catalog description

This course aims to provide a comprehensive understanding of crystal structures and their properties across length scales-from atomic to mesoscale structures-and across classes of materials (e.g., metals, oxides, polymer micelles, nanoparticles). After a quick review of crystallographic symmetry and notation, the course will follow an integrated approach, covering different crystal structure types and materials classes in a case-study-like manner, and the consequences of chemical and structural properties of the building blocks and emerging ordered structures. In the context of each class of structure types, the following aspects will be discussed: crystallographic nomenclature (symmetry groups), crystal structure geometry and topology (bond angles, coordination polyhedra, nets), types of order and disorder motifs (unit cells, modulations, stochasticity), crystal-chemical interpretation and chemical bonding (interactions between particles and resulting structural motifs), phase diagram context (phase stability, surrounding phases), structure-based properties (electric, mechanical, photonic, etc.). Topics include typical crystal structures in metals, oxides, ionic compounds, mesoscale systems, as well as complex periodic structures, aperiodic structures, non-periodic structures.