Article

# The High-Temperature Polymorphs of K3AlF6

Lujan Neutron Scattering Center, Los Alamos National Laboratory, MS H805, Los Alamos, New Mexico 87545, USA.

Inorganic Chemistry (Impact Factor: 4.76). 08/2011; 50(16):7792-801. DOI: 10.1021/ic200956a Source: PubMed

**ABSTRACT**

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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**ABSTRACT:**The crystal structures of the three high-temperature polymorphs of the title compound are determined by neutron powder diffraction, synchrotron powder XRD, and electron diffraction. - [Show abstract] [Hide abstract]

**ABSTRACT:**For many disordered materials, knowing their average crystal structure is insufficient for explaining and predicting their macroscopic properties. It has been found that a description of the short-range atomic arrangements is needed to understand such materials. In order to understand the conduction pathways in ionic conductors which have random distributions of vacancies it is imperative to know the local structures which are present. In this study the local structures of three oxygen-deficient double perovskites, Sr(2)MSbO(5.5) (M = Ca, Sr, Ba), have been investigated by neutron pair distribution function analysis. The ions in these compounds are all found to have local coordination environments which are radically different than those given by their average structures. While there is no long-range ordering of the oxygen vacancies in these compounds, a considerable amount of short-range order does exist. The conditions which drive the short-range ordering are discussed as are the possible mechanisms for achieving it. It is proposed that the SbO(5) polyhedra form distorted trigonal bipyramids by moving oxygen atoms into interstitial positions. In the M = Sr compound 45° rotations of SbO(6) octahedra are also present, which add additional oxygen atoms into the interstitial sites. Large displacements of the Ca(2+), Sr(2+), and Ba(2+) cations are also present, the directions of which are correlated with the occupancies of the interstitial oxygen sites. Reverse Monte Carlo modeling of the pair distribution function data has provided the actual bond length distributions for the cations. - [Show abstract] [Hide abstract]

**ABSTRACT:**The room temperature crystal structures of α-K3MoO3F3 and α-Rb3MoO3F3 have been solved via combined Rietveld refinements of synchrotron and neutron powder diffraction data. These two compounds are part of a broader family of A2BMO3F3 compounds that have been studied for their dielectric properties, but until now the complex crystal structures of the ferroelectric phases of these compounds were not known. At room temperature and below, these two isostructural compounds are tetragonal with I41 space group symmetry and unit cell parameters of a = 19.38613(3) Å, c = 34.86739(8) Å for α-K3MoO3F3 and a = 20.0748(4) Å, c = 36.1694(1) Å for α-Rb3MoO3F3. Their structures are related to the cubic double perovskite structure but are considerably more complicated due to noncooperative octahedral tilting and long-range orientational ordering of the polar MoO3F33– units. The pattern of octahedral tilting is equivalent to that seen in the α-K3AlF6 structure, which has I41/a symmetry, but orientational ordering of MoO3F33– units lowers the symmetry to I41. The polar space group symmetry is consistent with earlier reports of ferroelectricity in these compounds. Hence orientational ordering of the MoO3F33– units is directly responsible for the ferroelectric behavior.