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).

The formation and functioning of electroactive coatings based on fullerenes and their derivatives. The role of Non-covalent interactions

“…(b) String of the MEM electron density representing the atom Cr in incommensurately modulated Cr 2 P 2 O 7 . X-ray diffraction data from[20].…”

About systematic errors in charge-density studies

“…Since the corresponding cif file of Li et al (2010) did not contain all relevant information for set No. 22, the cif file from the original publication (Palatinus et al, 2006), which was cited in Li et al (2010), was consulted. The conventional R factor for all 2409 reflections found in this cif file, 0.0494, is considerably smaller than the recalculated conventional R factor, 0.0705.…”

Validating the model of a (3 + 1)-dimensional incommensurately modulated structure as generator of a family of compounds for the Eu2(MoO4)3scheelite structure

“…Both approaches are just alternative descriptions of the same structure [15,16]. In order to validate the hypothesis which postulates the KNd(MoO 4 ) 2 compound as a superspace model for the description of the commensurately modulated Eu 2 (MoO 4 ) 3 structure, we refined the latter compound from synchrotron powder diffraction data by using both the superspace and traditional 3D descriptions.…”