(3 + 1)-dimensional structure refinement of the fresnoite framework-structure type compound Ba(2)TiGe(2)O(8).

The incommensurately modulated structure of the fresnoite framework-structure type compound Ba(2)TiGe(2)O(8) has been solved using a (3 + 1)-dimensional superspace approach. The structure is orthorhombic and adopts the superspace group Cmm2(0,beta,1/2)s00 with beta approximately 0.635 at room temperature. The refinement was based on neutron powder diffraction data obtained from a powdered single crystal grown by Czochralski pulling. The modulation parameters that were obtained support the idea that frozen-in rigid-unit modes cause the modulation. The modulation is mainly manifested by positional displacements of O atoms. Barium ions are either eightfold, ninefold or tenfold coordinated in the one-dimensional modulated structure. A significant improvement of the bond-valence sum for both barium positions is achieved by the introduction of the positional modulation. This finding strongly suggests that underbonded barium positions are critically involved in provoking the incommensurate modulation in Ba(2)TiGe(2)O(8).