Abstract

Most of the “classical” methods for “ab initio” solution of crystal structures from powder diffraction diagrams depend on the knowledge of the intensity for each reflection I(hkl), in analogy to single crystal methods. Unfortunately, in many cases a severe overlap of different reflections makes it difficult to determine these values with sufficient accuracy.

For this reason, the so called "direct space methods" propose a structural model independent of the powder diffraction diagram, just from the given unit cell parameters and -contents. Beginning with some arbitrarily chosen starting configuration, the difference between the calculated and the measured diffraction pattern (cost function) is minimized through repeated change of the atomic arrangement.

Direct space methods have shown to be very successful in the solution of molecular crystal structures, however, for most ionic or metallic crystalline solids (which consist more or less of single atoms), this prescription results in the system quickly getting trapped in some minimum that does not correspond to a physically reasonable atomic arrangement. The reason for this lies in the landscape of the cost function which includes numerous deep local minima, owing to the low data/parameters ratio.

In order to include additional knowledge about physically reasonable atomic arrangements in the structure solution process, our program "Endeavour" uses a combined optimization of the difference between the calculated and the measured diffraction pattern and of the potential energy of the system. Relatively simple empirically parametrized effective potentials have shown to be generally sufficient for calculating the potential energy in the context of structure solution if they are used in combination with diffraction data.

Endeavour was tested successfully on a large variety of especially ionic and intermetallic compounds, some of which will be demonstrated.