Unified (3 + 1)-dimensional superspace description of the 2212-type stair-like [Bi2Sr3Fe2O9]m[Bi4Sr6Fe2O16] family of compounds.

The (3 + 1)-dimensional superspace approach is applied to describe and refine a series of sheared compounds related to layered high T(c) superconducting oxides. Two commensurate members (m = 4, 5) of the 2212 stair-like [Bi(2)Sr(3)Fe(2)O(9)](m)[Bi(4)Sr(6)Fe(2)O(16)] family of compounds, previously studied using single-crystal diffraction data, are analyzed. A common average unit cell has been identified and a composition-dependent modulation wavevector is proposed. The model is built using only three independent atomic domains, one for the metal atoms and two for the O atoms. The three Sr, Bi and Fe species are described using close-connected crenel-like functions forming a continuous atomic domain along the internal space. The two oxygen domains are represented by crenel functions and the displacive modulation functions are built up by Legendre polynomials recently implemented in the program JANA2006. Surprisingly, the results of the refinements show a striking similarity of the displacive modulations for the two compounds analyzed, indicating that a unique model can be used to describe the correlations between the atomic displacements of the 2212 stair-like series. This final model is then applied to predict the structure of new members of the family.