Microphases deriving from Ba₂ZrF₈ structure type: II: Crystal structure of Sr₁₇Zr₉F₇₀ and Sr_17.145Zr₉F_70.29

Highlights: • Sr₁₇Zr₉F₇₀ structure contains zigzag parallel rows of Sr cations and ZrF₈ polyhedra. • Sr₁₇Zr₉F₇₀ derives from Ba₂ZrF₈ by a triple step of the zigzag rows. • Sr₁₇Zr₉F₇₀ presents a complex non-stoichiometry based on ordered Sr vacancies. • Sr_17.145Zr₉F_70.29 incorporates a slight amount of Sr cations inside the Sr vacant site. • A series of modulated phases close to Sr₁₇Zr₉F₇₀ is studied by XRD and TEM. - Abstract: In the domain Sr_1−xZr_xF_{2+2 ×} studied at 670 °C between the limits 0.333 ≤ x ≤ 0.353, Sr₂ZrF₈ (x = 0.333) cannot be obtained under our synthesis conditions but a new phase Sr₁₇Zr₉F₇₀ (x = 0.346) is characterized which clearly shows a great analogy with Ba₂ZrF₈ and Pb₂ZrF₈ already described. It presents the same Pnma space group and derives from this basic type by the relation: a = 28.812(10) Å = 3 × a(Ba₂ZrF₈); b = 16.566(6) Å = 3 × b(Ba₂ZrF₈); c = 11.433(4)Å = c(Ba₂ZrF₈). The superlattice along a results from a change in the step of zigzag parallel rows of respectively Sr cations and ZrF₈ polyhedra. The zigzag step is not composition-dependent but more likely depends on the size of the M²⁺ cation. The superlattice along b results from an ordered creation of Sr vacancies of multiplicity m = 3 (1 vacancy for 3 Sr) in some Sr raws which changes the Sr/Zr ratio from 2/1 to 1.889/1 (x = 0.346). Then the superstructure along b accommodates the change in stoichiometry in Sr within this phase from Sr₁₈Zr₉F₇₂ (9 × "Sr₂ZrF₈") to Sr₁₇Zr₉F₇₀. A second structure of close composition (x = 0.344) shows that the vacant Sr site can be partially occupied in a disordered way by a small proportion of Sr, giving a composition slightly closer to "Sr₂ZrF₈". Compared to Sr₁₇Zr₉F₇₀, the over-stoichiometry mechanism is a solid solution model. For Zr contents comprised between x = 0.346 and 0.353, a series of modulated phases corresponding to various more or less ordered sequences of Sr cations and Sr vacancies along b are characterized by electron diffraction and TEM lattice imaging. They can be interpreted as intermediate between limit phases Sr₁₇Zr₉F₇₀ (x = 0.346) and Sr₁₁Zr₆F₄₆ (x = 0.353), of respective multiplicities m = 3 and m = 2 along the same b direction and of modulation vectors q = 1/3b* and q = 1/2b*. Several modulated phases with q modulation vector comprised between 1/3 b* and 1/2 b* can be characterized.