Preparation and Crystal Structure of Ruthenium Metaphosphate Ru(PO₃)₃ with an 8-fold Superstructure. Analysis of Structural Frustration with a Simple Model

Monoclinic Ru(PO3)3 was prepared as the third form of RuP3O9, and the structure was determined by the single-crystal X-ray technique. It contains infinite spiral chains of polyphosphate ions and RuO6 octahedra as found in other C-form metaphosphates. While other C-form metaphosphates have 3-fold superstructures, monoclinic Ru(PO3)3 has a superstructure with an 8-fold b-axis. The space group is P21/a, and the cell parameters are a = 10.578(5) Å, b = 51.154(5) Å, c = 9.394(4) Å, and β = 97.74(4)°. The comparison between the real structure and the parent subcell structure with the space group I2/a shows that the deviations of the O1 atoms, which bridge two phosphorus atoms, are larger than those of other atoms. The displacements of the O1 atoms exhibit a static longitudinal sine wave along the b-axis with a wavelength of b/3. The bond angle P−O1−P is 180° in the parent subcell structure, and the shifts of the O1 atoms to attain more stable bond angles cause mechanical frustration, which leads to the superstructure. The observed superstructures of the monoclinic Ru(PO3)3 and C-form metaphosphates can be explained by a simple analytical model, in which neighboring O1 atoms are mechanically coupled through polyhedral chains to cause opposite displacements.