Superspace-symmetry determination and multidimensional refinement of the incommensurately modulated structure of natural fresnoite.

The structure of natural fresnoite, Ba2TiSi2O8, from the sanbornite deposits of eastern Fresno County, California, has been solved and refined as an incommensurate structure in five-dimensional superspace. The structure is tetragonal, superspace group P4bm(alpha, alpha, 1/2)(-alpha, alpha, 1/2)0gg, cell parameters a=8.5353 (6), c=10.4128 (7) A, modulation vectors q1=0.3020 (3) (a*+b*), q2=0.3020 (3) (-a*+b*). Data collection was performed on an Xcalibur CCD diffractometer at 110 K. The structure was refined from 3452 reflections to final R=0.0123. The model includes modulation of both atomic positions and displacement parameters. As a consequence of the Ba and O positional modulation, eight-, nine- and tenfold Ba coordinations occur throughout the structure. The change of coordination around the Ba atom is clearly represented by the deformation of the pentagonal rings, as seen from a projection along [001]. The deformed pentagonal rings correspond to Ba atoms with eight- and ninefold coordinations and form octagonal clusters closely resembling those observed in the incommensurate structure of melilite-type compounds.