Skip to main content
European Commission logo print header
Content archived on 2022-12-23

A combinatorial approach to the geometry and topology of crystal structures

Exploitable results

In spite of the large amount of crystallographic software available today, chemists still have to rely on building, and playing with, plastic models to discover new possible crystal-structures. This is because the appropriate mathematics for periodic 3-dimensional structures is only just being developed (Smith 88). In the past ten years much progress has been made at Bielefeld University in developing a combinatorial theory for describing periodic structures in terms of so-called Delaney symbols, which capture the important topological and symmetry-related features (Dress84,87 Huson93 and Dress, Huson, Molnar 93). The long-term goal is to develop algorithms for the systematic enumeration of possible periodic 3D structures. This requires bringing together geometry and combinatorics with computational methods and crystallography. In this project algorithms have been developed and implemented that, given data from a crystal-structure database as input, compute as output the corresponding periodic Delone tiling and it's so-called Delaney symbol. The latter is a combinatorial description of the given structure. This work will enable a systematic study of the topological and symmetry-related properties of know crystals. As a first application, these methods are now being used to investigate known zeolite structures. The approach is proving to work well in many cases, especially in those with high symmetry. Currently, working is being done on a generalisation of the concept of Delone tiling that promises to be appropriate for less symmetric crystal-structures. Moreover, useful mathematical results addressing the problem of determining whether a given cluster of atoms can grow into a crystal, and the systematic enumeration of all structures accommodating a given cluster, have been gained.

Searching for OpenAIRE data...

There was an error trying to search data from OpenAIRE

No results available