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The crystal structures of the three high-temperature polymorphs of K(3)AlF(6) 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 (K(2)KAlF(6)) which result from noncooperative tilting of the AlF(6) 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 AlF(6) 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 AlF(6) 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 AlF(6) 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 Fm ̅3m, 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 AlF(6) octahedra undergo large-amplitude rotations which are accompanied by off-center displacements of the K(+) ions that occupy the 12-coordinate A-sites.
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