Perovskite-like K₃TiOF₅ Exhibits (3 + 1)-Dimensional Commensurate Structure Induced by Octahedrally Coordinated...

Elpasolite- and cryolite-type oxyfluorides can be regarded as superstructures of perovskite and exhibit structural diversity. While maintaining a similar structural topology with the prototype structures, changes in the size, electronegativity, and charge of cation and/or anion inevitably lead to structural evolution. Therefore, the nominal one-to-one relation suggested by a doubled formula of perovskite does not guarantee a simple 2-fold superstructure for many cases. Herein, the commensurately modulated perovskite-like K₃TiOF₅ was refined at 100 K from single-crystal X-ray diffraction data by using a pseudotetragonal subcell with lattice parameters of a = b = 6.066(2) Å and c = 8.628(2) Å. The length of the modulation vector was refined to 0.3a* + 0.1b* + 0.25c*. In the commensurate supercell of K₃TiOF₅, the B-site Ti⁴⁺ and K⁺ cations in [TiOF₅]^3- and [KOF₅]^6- octahedral units were found to be significantly displaced from the average atomic positions refined in the subcell. The displacements of the K⁺ cations are ±0.76 Å, and those for the Ti⁴⁺ cations are approximately ±0.13 Å. One- and two-dimensional solid-state ¹⁹F NMR measurements revealed two tightly clustered groups of resonances in a ratio of ca. 4:1, assigned to equatorial and axial fluorine, respectively, consistent with local [TiOF₅]^3- units. S/TEM results confirmed the average structure. Electronic structure calculations of the idealized I4mm subcell indicate the instability to a modulated structure arises from soft optical modes that is controlled by the octahedrally coordinated B-site potassium ions in the cryolite-type structure.