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 Gruneisen parameters for the ferroelectri-paraelectric transition in PbTiO3. The mode Gruneisen parameters which we have determined using the observed Raman frequencies for the soft modes, increase considerably with increasing pressure toward the transition pressure (PC similar to 11 GPa) from the tetragonal (ferroelectric) to the cubic (paraelectric) phase in PbTiO3. Variation of the mode Gruneisen parameter with the pressure is rather smooth for the other Raman modes studied as compared to the drastic change at PC 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.