Investigation into the Crystal Structure of the Perovskite Lead Hafnate, PbHfO₃

The room-temperature crystal structure of the perovskite lead hafnate PbHfO₃ is investigated using both low-temperature single crystal X-ray diffraction (Mo Kα radiation, λ = 0.71069 Å) and polycrystalline neutron diffraction (D1A instrument, ILL, λ = 1.90788 Å). Single crystal X-ray data at 100 K: space group Pbam, a = 5.856 (1), b = 11.729 (3), c = 8.212 (2) Å, V = 564.04 ų with Z = 8, μ = 97.2 mm^-1, F(000) = 1424, final R = 0.038, wR = 0.045 over 439 reflections with F >1.4σ(F). Polycrystalline neutron data at 383 K: a = 5.8582 (3), b = 11.7224 (5), c = 8.2246 (3) Å, V = 564.80 ų with χ² = 1.62. Although lead hafnate has been thought to be isostructural with lead zirconate, no complete structure determination has been reported, as crystal structure analysis in both these materials is not straightforward. One of the main difficulties encountered is the determination of the oxygen positions, as necessary information lies in extremely weak l = 2n + 1 X-ray reflections. To maximize the intensity of these reflections the X-ray data are collected at 100 K with unusually long scans, a procedure which had previously been found successful with lead zirconate. In order to establish that no phase transitions exist between room temperature and 100 K, and hence that the collected X-ray data are relevant to the room-temperature structure, birefringence measurements for both PbZrO₃ and PbHfO₃ are also reported.