Lattice modes in ferroelectric perovskites: PbTiO3

Abstract

A complete study of the lattice-dynamical behavior of the ferroelectric tetragonal perovskite PbTiO3 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 E(1TO) mode in the ferroelectric phase at all temperatures below Tc=493 °C. Moreover, by combining our experimental mode-frequency data with pyroelectric measurements of the change in spontaneous polarization Ps with temperature, we obtain values of Ps(25 C)=81 μC/cm2 and Ps(Tc)=42 μC/cm2. This is in excellent agreement with a recent direct experimental measurement. The temperature dependence of all the mode strengths has also been determined to Tc. These results are used to extract the temperature dependence of the clamped dielectric constants. In PbTiO3 the dielectric constant along the ferroelectric axis εc is determined primarily by the lowest frequency A1(1TO) mode at all temperatures to Tc, in contrast to BaTiO3 where in the ferroelectric phase the lowest mode determines only 25% of εc. In PbTiO3 the dielectric constant perpendicular to the c axis εa is also determined by the lowest E(1TO) mode at all temperatures. The possibility of observing critical effects near Tc in the soft-mode data of PbTiO3 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. © 1973 The American Physical Society.