Structure of ferroelectric Pb₅Al₃F₁₉ at 160 K, polarization reversal and relationship to ferroelectric Pb₅Cr₃F₁₉ at 295 K

Pb₅Al₃F₁₉ at 160 K is ferroelectric, crystallizing in the tetragonal system. With M_r = 1477.9, the space group is I4cm and a = 14.07 (2), c = 7.30 (1) Å, V = 1445 (3) ų, Z = 4, D_x = 6.793 Mg m⁻³. For λ(Mo Kα) = 0.71073 Å, μ = 56.36 mm⁻¹. F(000) = 2480 Pb₅Al₃F₁₉ undergoes a first-order phase transition on cooling at 120 K and on heating at 270 K. The structure was determined from 656 independent F(hkl) with I> 3σ(I) and refined by least squares to R = 0.0527, wR = 0.0480, S = 1.065. No atom is further than 0.83 Å, from the hypothetical I4/mcm atomic positions, hence the crystal is structurally ferroelectric. The mean atomic polar displacement of the two independent Al atoms from the zero spontaneous-polarization location, allowing for the F atoms, is 0.207 (28) Å, which leads to a predicted T_c = 860 (230) K. Several additional phase transitions are known to form before the hypothetical phase is attained. Each independent Al atom occupies a fluorine octahedron with average Al—F distance either 1.818 (5) or 1.824 (1) Å. One Pb atom is nine coordinated, occupying a distorted tricapped trigonal prism with average Pb—F = 2.66 (22) Å. The other is ten coordinated, forming a distorted bicapped cuboid, with average Pb—F = 2.61 (28) Å. Pyroelectric pulses are readily detectable in crystals cooled below 120 K, or subsequently on heating to 270 K. Similarly, numerous piezoelectric resonances are observed in the same thermal ranges; the compression mode at ~1197 kHz has been identified by its characteristic admittance circle. The mechanical quality factor Q_m for ferroelectric Pb₅Al₃F₁₉, determined from the admittance-circle-derived equivalent circuit, is ~423.

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