Direct space methods of crystal structure determination from powder diffraction applied to intermetallic compounds
Chem. Met. Alloys 1 (2008) 120-127
Direct space methods of structure determination from powder diffraction of non-molecular compounds (inorganics, extended solids, intermetallic compounds etc.) are reviewed. They do not need powder pattern decomposition, and are based on a global optimization of a structural model to improve the agreement between the observed and calculated diffraction patterns. The success of the method depends very much on a proper modeling of the structure from building blocks. The modeling from larger building blocks improves the convergence of the global optimization algorithm by a factor of up to ten. The correctness of the building block like its rigidity, deformation, bonding distances and ligand identity must be examined carefully. Dynamical Occupancy Correction implemented in the direct space program FOX has shown to be useful when merging excess atoms, and even larger building blocks like coordination polyhedra. It allows also joining smaller blocks into larger ones in the case when the connectivity is not a priori evident from the structural model. The available computer programs working in direct space are listed.
Solving a structure ab-initio in direct space implies describing the structure through a number (N) of Degrees of Freedom (DoF): translation and rotation of the molecule or polyhedron, and internal DoF like torsion angles, bond length and bond angles. These parameters must then be randomly changed in order to find the minimal cost (usually the best agreement between the calculated and experimental powder pattern). This corresponds to exploring a N-dimensional hypersurface until the global minimum is found. The surface represented here corresponds to a 2D cut of the hypersurface corresponding to the variation of one torsion angle and one translation.
Structure solution / Powder diffraction / Inorganic compound / Simulated annealing / Genetic algorithm