Pressure and temperature dependence of the ferroelectric-paraelectric phase transition in PbTiO₃

Synchrotron X-ray powder diffraction patterns were collected at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) on powderosamples of PbTiO₃ (tetragonal, Z = 1 P4mm a = 3.9036(1) Å and c = 4.1440(2) Å at room conditions) applying external pressure using a diamond anvil cell. Data were collected at four different temperatures (room temperature, 462, 538 and 623 K) up to the phase transition to the cubic phase (Z = 1, Pm3m a = 3.8647(4) Å at RT and 11.6 GPa). Analyzing the behavior of the cell parameters obtained by the Rietveld refinement, we were able to extract the dependence of the critical temperature on external pressure. The bulk moduli of the lead titanate were calculated for the first time. The progressive decrease of the distortion of the Pb and Ti coordination polyhedra with pressure allows to propose a structural explanation of the first-/second-order cross-over in the ferroelectric-paralectric phase transition on applying pressure.