Abstract
A complete study of the lattice-dynamical behavior of the ferroelectric tetragonal perovskite PbTi has been carried out using Raman spectroscopy. The temperature dependence of all the long-wavelength mode frequencies are determined. We show that a damped-harmonic-oscillator model with a frequency-independent damping coefficient is sufficient to explain the observed shape of the soft mode in the ferroelectric phase at all temperatures below °C. Moreover, by combining our experimental mode-frequency data with pyroelectric measurements of the change in spontaneous polarization with temperature, we obtain values of μC/ and μC/. This is in excellent agreement with a recent direct experimental measurement. The temperature dependence of all the mode strengths has also been determined to . These results are used to extract the temperature dependence of the clamped dielectric constants. In PbTi the dielectric constant along the ferroelectric axis is determined primarily by the lowest frequency mode at all temperatures to , in contrast to BaTi where in the ferroelectric phase the lowest mode determines only of . In PbTi the dielectric constant perpendicular to the axis is also determined by the lowest mode at all temperatures. The possibility of observing critical effects near in the soft-mode data of PbTi has been examined. These effects are not observed. Also, it is shown that very careful fitting of the soft-mode temperature dependence to a functional form containing a minimum number of separately determined parameters is required before critical effects can be invoked in first-order phase transitions of the displacive type.
- Received 12 June 1972
DOI:https://doi.org/10.1103/PhysRevB.7.3088
©1973 American Physical Society