Abstract: The crystal structures of the three high-temperature polymorphs of K3AlF6 have been solved from neutron powder diffraction, synchrotron X-ray powder diffraction, and electron diffraction data. The β-phase (stable between 132 and 153 °C) and γ-phase (stable between 153 to 306 °C) can be described as unusually complex superstructures of the double-perovskite structure (K2KAlF6) which result from noncooperative tilting of the AlF6 octahedra. The β-phase is tetragonal, space group I4/m, with lattice parameters of a = 13.3862(5) Å and c = 8.5617(3) Å (at 143 °C) and Z = 10. In this phase, one-fifth of the AlF6 octahedra are rotated about the c-axis by 45° while the other four-fifths remain untilted. The large 45° rotations result in edge sharing between these AlF6 octahedra and the neighboring K-centered polyhedra, resulting in pentagonal bipyramidal coordination for four-fifths of the K+ ions that reside on the B-sites of the perovskite structure. The remaining one-fifth of the K+ ions on the B-sites retain octahedral coordination. The γ-phase is orthorhombic, space group Fddd, with lattice parameters of a = 36.1276(4) Å, b = 17.1133(2) Å, and c = 12.0562(1) Å (at 225 °C) and Z = 48. In the γ-phase, one-sixth of the AlF6 octahedra are randomly rotated about one of two directions by 45° while the other five-sixths remain essentially untilted. These rotations result in two-thirds of the K+ ions on the B-site obtaining 7-fold coordination while the other one-third remain in octahedral coordination. The δ-phase adopts the ideal cubic double-perovskite structure, space group Fmm, with a = 8.5943(1) Å at 400 °C. However, pair distribution function analysis shows that locally the δ-phase is quite different from its long-range average crystal structure. The AlF6 octahedra undergo large-amplitude rotations which are accompanied by off-center displacements of the K+ ions that occupy the 12-coordinate A-sites.

Abstract: The crystal structure of α-K3AlF6 was solved and refined from a combination of powder X-ray and neutron diffraction data (a = 18.8385(3)Å, c = 33.9644(6)Å, S.G. I41/a, Z = 80, RP(X-ray) = 0.037, RP(neutron) = 0.053). The crystal structure is of the A2BB′X6 elpasolite type with the a = b ≈ ae√5, c = 4ae superstructure (ae, parameter of the elpasolite subcell) and rock-salt-type ordering of the K and Al cations over the B and B′ positions, respectively. The remarkable feature of α-K3AlF6 is a rotation of 2/5 of the AlF6 octahedra by π/4 around one of the crystal axes of the elpasolite subcell, coinciding with the 4-fold symmetry axes of the AlF6 octahedra. The rotation of the AlF6 octahedra replaces the corner-sharing between the K and Al polyhedra by edge-sharing, resulting in an increase of coordination numbers of the K cations at the B positions up to 7 and 8. Due to significant deformations of the K polyhedra, the corner-sharing connectivity of the octahedral elpasolite framework is broken and the rotations of the AlF6 octahedra do not have a cooperative character. Elpasolites and double perovskites with similar structural organization are discussed. The difference in ionic radii of the B and B′ cations as well as the tolerance factor are proposed to be the parameters governing the formation of elpasolites and double perovskites with broken corner-sharing connectivity of the octahedral framework.