Computer simulation of crystal structures applied to the solution of the superstructure of cubic silicondiphosphate

The superstructure of cubic SiP₂O₇ has a volume 27 times as large as the substructure of this compound. Because conventional methods failed in solving the superstructure, computer simulation of the structure was applied. Computer simulation depends on the accurate prediction of individual interatomic distances in a structure and on an appropriate weighting scheme. The predicted distances are treated as observations in a distance least-squares refinement, in which the positional coordinates of the atoms are varied until the calculated distances conform to the predicted values. Cubic SiP₂O₇ (a = 22.418Å, space group Pa3, Z = 108, D_x = 3.22) has 50 atoms in the asymmetric unit. The initial R-value for the simulated structure was 0.18, which dropped to 0.061 after three cycles of least squares refinement using F_obsd = 1382. In the substructure, all POP angles in the diphosphate groups are straight because of symmetry requirements, and the angles POSi are 164°. In the superstructure, the average angle POP is 150°; the average POSi angle is 149°. The tendency to decrease these angles may be responsible for the formation of the superstructure. However, two diphosphate groups retain, even in the superstructure, the 180° configuration. Such a feature is usually only observed in high temperature polymorphs and is explainable as a positional disorder of bent P₂O₇ groups, or by the assumption of a highly anisotropic motion of the bridging oxygen atom. The silicon atoms in cubic SiP₂O₇ are octahedrally coordinated, as they are in the two monoclinic polymorphs of SiP₂O₇. However, the three modifications are topologically distinct from each other as can be proved by considering the three-dimensional nets on which the three structures are based.