Jan Simons


Global optimisation: structure determination of medium sized structures from
low resolution x-ray powder diffraction data.

Crystal structure determination from resolution limited x-ray powder diffraction data - esp. in the case of medium sized inorganic structures with a high number of independent parameters - even by today's standards is still
considered a very challenging task:
Off-the-shelf algorithms for structural optimisation against measured intensity data tend to work rather sluggish or unreliable for high dimensional problems and often fail to reach the global optimum of the multi-modal target function.

This research project aims at finding and exploring novel optimisation algorithms that are tailored to fit the structure of the target function by exploiting its inherent properties and that therefore can effectively solve
crystal structures.

So far two candidate algorithms have shown high potential that is and has been studied during our research. Those algorithms will be released as an easy to use free open source tool at the end of this dissertation:

1. optimal configuration search (OCS):
Due to basic crystal chemical considerations its possible to allow only certain sites within the asymmetric unit. Thus discretising the continuous high-dimensional optimisation problem into a combinatoric one with finite number of configurations. Iterating all of those configurations seems doable in acceptable time scales for medium sized structures.

2. successive line scans (SLS):
The target function shows a characteristic trench like structure that helps to find the global optimum with high certainty via a series of 1-dimensional line scans through parameter space.

The systematic exploration, implementation, and extension of those two candidate algorithms should help in making structure determination from low resolution x-ray powder diffraction data more accessible and therefore lead to a better understanding of materials that cannot (or only with hard labour) be made into single crystals.