title: The incommensurately and commensurately modulated crystal structures of chromium(II) diphosphate.
abstract: Chromium(II) diphosphate, Cr(2)P(2)O(7), has an incommensurately modulated structure at ambient conditions with a = 7.05, b = 8.41, c = 4.63 A, beta = 108.71 degrees and q = (-0.361, 0, 0.471). It undergoes a phase transition towards a commensurate structure with a commensurate q vector, q = (-1/3, 0, 1/2), at T(c) = 285 K. The incommensurate structure has been solved by the charge-flipping method, which yielded both the basic positions of the atoms and the shapes of their modulation functions. The structure model for the commensurate structure was derived directly from the incommensurate structure. The structure analysis shows that the modulation leads to a change of the coordination of the Cr(2+) ions from distorted octahedra in the average structure towards a sixfold coordination in the form of a more regular octahedron and a fivefold coordination in the form of a square pyramid. The fivefold and sixfold coordination polyhedra alternate along the lattice direction a with the pattern 5-6-5 5-6-5 in the commensurate structure. In the incommensurate structure this pattern is occasionally disturbed by a 5-6-5-5 motif. Both structures can be described in superspace using the same superspace group and a similar modulated structure model. The same superspace model can also be used for the low-temperature phases of other metal diphosphates with the thortveitite stucture type at high temperature. Their low-temperature structures can be obtained from the superspace model by varying the q vector and the origin in the internal dimension t(0).
authors.affiliation: Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague, Czechia. palat@fzu.cz
authors.forename: Lukás
authors.initials: L
authors.lastname: Palatinus
authors.forename: Michal
authors.initials: M
authors.lastname: Dusek
authors.forename: Robert
authors.initials: R
authors.lastname: Glaum
authors.forename: Brahim
authors.initials: B
authors.lastname: El Bali