Ferroelectric structure and related properties of Pb5W3O9F1

Abstract

Lead tungsten oxyfluoride, Pb5W3O9F10, is a new ferroelectric material that crystallizes in the tetragonal system with space group I4 and four formulas in the unit cell. The lattice constants at 295 K are a=14.583(3) and c=7.365(1) Å for λ(MoKα1,2)=0.709 30, 0.713 59 Å. The integrated intensities of all 10 757 reflections within a reciprocal hemisphere of radius (sin θ)/λ ≤0.91 Å−1 were measured on a CAD-4 diffractometer with MoKα radiation and resulted in 7080 F2m ≥2σF2m. Correction for linear anisotropic radiation damage, followed by averaging the symmetry equivalent reflections, gave 2933 independent 〈 F2m〉≥2σ〈 F2m〉 with internal agreement factor Rint〈Fm〉 =0.0289. The crystal structure was solved from the Patterson function and difference Fourier series and refined on w〈 F2m〉 by the method of least squares. The final agreement factors between measurement and model were R=0.0382 and wR=0.0329 on 〈 Fm〉. The as-grown crystal contained equal volumes of ±Z domains. The three independent tungsten atoms form WO6, WO3F3, and WO2F4 octahedra, and the three independent lead atoms form two different PbO4F5 and a PbO4F4 polyhedron. The major local dipole contribution to the spontaneous polarization is associated with a tungsten atom that is displaced 0.172(43) Å from the center of its octahedron. The corresponding predicted Curie temperature is 590(260) K, in agreement with the experimental value of 785(15) K. All six metal atoms undergo anharmonic thermal vibrations, which are fitted either to fifth or sixth order in a Gram–Charlier expansion of the probability density function. The average interatomic distances are W–F=1.798(8) Å, W–O=1.944(18) Å, Pb–F=2.68(19) Å, and Pb–O=2.72(21) Å: standard deviations are from Bessel’s relationship. The atomic rearrangement required in forming Pb5W3O9F10 from PbF2 and WO3 is discussed, and similarities and contrasts between the related families for which Pb5W3O9F10, SrAlF5, and Sr3(FeF6)2 provide the archetype structures are considered. All three families exhibit ferroelectric behavior.