Pressure-Induced Phase Transitions in PbTiO₃:  A Query for the Polarization Rotation Theory

Abstract

Our first-principles computations show that the ground state of PbTiO3 under hydrostatic pressure transforms discontinuously from P4mm to R3c at 9 GPa. Spontaneous polarization decreases with increasing pressure so that the R3c phase transforms to the centrosymmetric Rc phase at around 27 GPa. The first-order phase transition between the tetragonal and rhombohedral phases is exceptional since there is no evidence for a bridging phase. The essential feature of the R3c and Rc phases is that they allow the oxygen octahedron to increase its volume VB at the expense of the cuboctahedral volume VA around a Pb ion. This is further supported by the fact that neither the R3m nor Cm phase, which keep the VA/VB ratio constant, is a ground state within the pressure range between 0 and 40 GPa. Thus, tetragonal strain is dominant up to 9 GPa, whereas at higher pressures, efficient compression through oxygen octahedra tilting plays the central role for PbTiO3. Previously predicted pressure induced colossal enhancement of piezoelectricity in PbTiO3 corresponds to unstable Cm and R3m phases. This suggests that the phase instability, in contrast to the polarization rotation, is responsible for the large piezoelectric properties observed in systems like Pb(Zr,Ti)O3 in the vicinity of the morphotropic phase boundary.

Strain on ferroelectric thin films

“…At low temperature and still for PbTiO 3 , a monoclinic phase was calculated [69] and then observed [61], even though this last result and its implication have been questioned [63]. The rotation of the oxygen octahedra as a pressure-accommodating mechanism [70] is a common feature of the observations on lead titanate, as well as for Pb(Zr 1-x Ti x )O 3 . We will see that this stress-accommodation has not yet been taken into account in the theoretical descriptions of PZT thin films.…”

Piezoelectricity in Lead-Zirconate-Titanate Ceramics – Extrinsic and Intrinsic Contributions

“…For more details, see refs. (Frantti et al, 2007) and (Frantti et al, 2008a). It is the opinion of the authors that after the intrinsic and extrinsic contributions are properly taken into account, an accurate and sufficient description for piezoelectricity is achieved.…”

“…There are, however, cases in which the linearity assumption ceases to be accurate. The most obvious is the vicinity of the phase transition which may result in large changes in piezoelectric constants (Frantti et al, 2007), which is an intrinsic contribution. This means that when a phase is about to change to another phase or orientation state (domain switching) external stimulus (temperature, stress, electric field) can cause large changes in the materials response (strain or induced charge).…”

“…In the context of pressure induced transitions in PbTiO 3 the phase stability issues were addressed in refs. (Frantti et al, 2007;2008a). Recent inelastic neutron scattering study suggests that a phase instability induced by a polar nanoregion-phonon interaction contributes to the ultrahigh piezoelectric response of Pb(Zn 1/3 Nb 2/3 )O 3 -4.5%PbTiO 3 and related relaxor ferroelectric materials (Xu et al, 2008).…”

“…One way to bypass this problems is to mimic the 'chemical pressure' (partial substitution of Ti by Zr) by hydrostatic pressure. Density-functional theory (DFT) computations predict that at 0 K (ground state) a phase transition between tetragonal P4mm and rhombohedral R3c phase take place at 9.5 GPa pressure (Frantti et al, 2007), which suggests that some insight about the PZT system can be drawn. Significant increase of certain piezoelectric constants, notably the d 15 , was observed once the phase transition was approached.…”