Incommensurate versus Commensurate Description of the A_xBX₃ Hexagonal Perovskite-Type Structure. Sr_1.2872NiO₃ Incommensurate Composite Compound Example

Abstract

We report a new structure determination of the Sr1.2872NiO3 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 (R3̄m(00γ)0s superspace group; a = 9.5177(7) Å, c = 2.5739(2) Å, q = 0.64359(4)c*, V = 201.93(4) Å3, and Z = 3). The use of crenel functions notably improves previously reported results. New structural features are evidenced for Sr1.2872NiO3: (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.

Structural studies of a mixed-valence state in the incommensurate composite crystal Sr1.261CoO3

“…In the case of the hexagonal A 2γ (A , B)O 3 system, a sawtooth function or a crenel function is often used for the modulation function [9][10][11]14]. In this study, we employed a Fourier series description to approximate the modulation function [12,13]:…”

“…In figure 3, the obtained Fourier-series modulation function y(O) approximates a step-like function. The difference between the Fourier-series function and the crenel function (discontinuous function [9,10]) is the sharpness of the step boundary atx s4 = τ and τ + 1/2 and the amplitude of the modulation around each step, A or B. The Fourier-series function has a smoothened step (continuous change of y) and a large modulation amplitude around the average y (ȳ A andȳ B ) for each step, as compared with the crenel function.…”

“…For instance, Sr 14 Co 11 O 33 [9] would require a fractional number of m = 5/3 if this formula is applied to the compound. In addition, the 3D formalism is not applicable to incommensurate structure compounds such as Sr 1.2872 NiO 3 [10], Sr 1+x (Co x Mn 1−x )O 3 [11], [Ba] x [(Pt, Cu)O 3 ] [12], or Sr 1.145 TiS 3 [13].…”

The aperiodic double chain model applied to composition flexible compounds

“…The family of compounds, related to hexagonal perovskites, and with formula A 1+x (A x B 1−x )O 3 [2,5] may be described as incommensurate composites. One subsystem consists of incommensurate columns of octahedra and triangular prisms.…”

Structure Determination of Ba8CoRh6O21, a New Member of the 2H-Perovskite Related Oxides

“…As shown previously, a better structural formulation of such composites is A 1+x (A' x B 1-x )O 3 , where x = n/(3m+2n) and ranges continuously between 0 and 1/2, corresponding to chains containing all face-shared octahedra and alternating face-sharing octahedra and trigonal prisms, respectively. [27][28][29] For simple fractional values of x such as 1/5, 2/7, or 1/3, the structure is commensurate and the endmembers, the 2H perovskite (BaNiO 3 , x = 0) and the K 4 CdCl 6 (x = 1/2) structure type, are well known.…”