Pressure dependence of the Raman frequency calculated from the volume data close to the ferroelectric-paraelectric transition in PbTiO₃

ABSTRACT

We calculate the pressure dependence of the Raman frequencies of some Raman modes by using the observed volume data through the mode Grüneisen parameters for the ferroelectri-paraelectric transition in PbTiO₃. The mode Grüneisen parameters which we have determined using the observed Raman frequencies for the soft modes, increase considerably with increasing pressure toward the transition pressure (P_C11 GPa) from the tetragonal (ferroelectric) to the cubic (paraelectric) phase in PbTiO₃. Variation of the mode Grüneisen parameter with the pressure is rather smooth for the other Raman modes studied as compared to the drastic change at P_C for the soft modes in this ferroelectric material. Raman frequencies (energy shifts) of the modes which we have calculated, decrease from the ferroelectric to the paraelectric phase with the exception of the optical modes of E(3LO) and E(3TO) whose Raman frequencies increase with increasing pressure.

This decrease and/or increase in the energy shifts for the Raman modes which we have calculated as also observed experimentally, shows a continuous manner, indicating a second order character rather that the first order transition from the tetragonal to the cubic phase in PbTiO₃.

KEYWORDS:

• Raman modes
• Grüneisen parameter
• tetragonal-cubic transition
• PbTiO₃