Abstract
The phonon-dispersion relations for cubic PbTiO ( K) have been determined along the , , and directions at K using inelastic neutron scattering. A set of the transverse optical (TO) branches drops sharply toward the zone center. The TO phonon curves for cubic PbTiO are nearly isotropic, in contrast to the distinct dependence of the TO branches for tetragonal PbTiO. The zone-center TO mode energy softens with decreasing temperature from 1173 to 793 K. Moreover, the transverse acoustic (TA) branch along [] shows significant softening around and . The anomaly around the midpoint suggests a tendency toward forming a fourfold periodicity along the direction, whereas the anomaly toward the point results from the softening of the oxygen octahedron rotation. These two anomalies persist up to 1173 K and are weakly temperature dependent. The TA branches along and soften in the entire range as the temperature approaches . Although the phonon softening occurs simultaneously, the softening of the zone-center TO mode plays an important role in the single phase transition. The phonon dispersion relations for PbTiO are discussed in connection with the simple perovskite oxides and the Pb-based relaxors.
6 More- Received 2 July 2012
DOI:https://doi.org/10.1103/PhysRevB.86.134306
©2012 American Physical Society