Incommensurate versus Commensurate Description of the AxBX3 Hexagonal Perovskite-Type Structure. Sr1.2872NiO3 Incommensurate Composite Compound Example

We report a new structure determination of the Sr 1.2872 NiO 3 incommensurate composite hexagonal perovskite compound. Three different refinement strategies are presented: (i) a 3D supercell approximation with a nonharmonic development of the atomic displacement factor, (ii) an original (3+1)D incommensurate composite description with the use of crenel functions, and (iii) a (3+1)D commensurate composite model. The three strategies are discussed and compared to previous refinements carried out for the hexagonal perovskites in a classical way or with the superspace group formalism. Out of the three methods, the incommensurate composite approach gives slightly better results with a final global R value of 2.89% for 635 independent reflections (at a I /σ( I ) > 2 level) and only 60 parameters ( R 3̄ m (00γ)0s superspace group; a = 9.5177(7) Å, c = 2.5739(2) Å, q = 0.64359(4) c*, V = 201.93(4) Å 3, and Z = 3). The use of crenel functions notably improves previously reported results. New structural features are evidenced for Sr 1.2872 NiO 3: (i) an incommensurate character, (ii) a splitting of the trigonal prismatic nickel atoms over 5 positions, (iii) a definite stoichiometry which induces a perfect charge balance, and (iv) a nonharmonic behavior of some Sr atoms. Those characteristics seem general to most hexagonal perovskite compounds and essential for correctly interpreting their interesting magnetic properties. Finally, a new generic formulation is proposed, which explains the various stoichiometries observed and suggests a new compound possibility.