Structural modulations in the intermediate phase of antiferroelectric PbHfO₃

We determine the crystal structure of the intermediate antiferroelectric (A₂) phase of PbHfO₃ by a Rietveld method using X-ray and neutron diffraction. The structure can be described by modulations associated with the lattice vibrational mode Σ₃(TO) with q (0.15,0.15,0)and the R^xy ₂₅ mode, although the latter modulation is relatively distorted. The size of the orthorhombic unit cell is p2 × 10p2 × 2 times as large as that of the high-temperature cubic cell. The space group is Pbam-D⁹ _2h (No. 55), and is the same as that of the room-temperature antiferroelectric (A₁) phase of PbHfO₃.