Lattice dynamics in the paraelectric phase of PbHfO₃studied by inelastic x-ray scattering

Abstract

We report the results of an inelastic x-ray scattering study of the lattice dynamics in the paraelectric phase of the antiferroelectric lead hafnate PbHfO3. The study reveals an avoided crossing between the transverse acoustic and transverse optic phonon modes propagating along the [1 1 0] direction with [1 -1 0] polarization. The static susceptibility with respect to the generally incommensurate modulations is shown to increase on cooling for the entire Γ-M direction. We consider different approaches to the data analysis that correspond to different models for the temperature evolution of the dynamic susceptibility function. A number of similarities and differences between the lattice dynamics of PbHfO3 and PbZrO3 are described.

Critical scattering and incommensurate phase transition in antiferroelectric PbZrO3 under pressure

“…It is thus possible to obtain the ħ ω( q ) dependence knowing the mode energy at one of the relevant wavevectors and the integral intensity wavevector dependence. For estimating the phonon energy we have used the spectrum at q = (0.1, 0, 0.1), in which the two pairs of the phonon resonances are resolvable in accord with the ambient pressure results for PbZrO 3 28 and PbHfO 3 29 . The damped harmonic oscillator fit of the spectrum yields the energy E 1 = 3.1 ± 1 meV and damping Γ 1 = 4.1 ± 2.5 meV for the lower-energy phonon and E 2 = 7.8 ± 1.5 meV and damping Γ 2 = 5.6 ± 3 meV for the higher-energy phonon.…”

Crystallographic and optical study of PbHfO3 crystals

“…An initial soak at 1473 K for 24 h was followed by cooling at 3.5 K h À1 to 1200 K. As-grown crystals were decanted and then cooled to room temperature at a rate of 10 K h À1 . The PbHfO 3 crystals formed 1 Â 1 Â 0.1 mm plates and traces of the solidified flux were removed by etching with acetic acid (Burkovsky et al, 2015).…”

The complexity of structural phase transitions in Pb(Hf0.92Sn0.08)O3 single crystals

“…23 Strong softening of the LA mode and noticeable broadening of the LA mode are consistent with the assumption that precursor polar regions already exist in the PE phase. The lattice-dynamical theory described in 3,4,38 predicts the existence of precursor, noncentrosymmetric polar regions that appear in the centrosymmetric matrix due to the specific coupling of the zone center transverse optic mode, and located near the zone-center acoustic mode. The local polar regions in the paraelectric phase grow in size and change their character from dynamic to static near T p .…”