Thermal equations of state and phase relation of PbTiO3: A high P-T synchrotron x-ray diffraction study

Abstract

The phase relation of tetragonal and cubic PbTiO3 and their unit-cell parameters have been determined by synchrotron x-ray diffraction at pressures up to 7.8 GPa and temperatures up to 1074 K with a cubic anvil apparatus. From these measurements, a pressure-temperature phase boundary between the tetragonal and cubic phases has been established. With increasing temperature or pressure, the c/a ratio of the ferroelectric, tetragonal PbTiO3 becomes closer to unity, suggesting that both heating and compression favor the paraelectric, cubic structure. Using a modified high-T Birch-Murnaghan equation of state and a thermal-pressure approach, we have derived the thermoelastic parameters of tetragonal and cubic PbTiO3, including the ambient bulk modulus K0, temperature derivative of bulk modulus at constant pressure, volumetric thermal expansivity, pressure derivative of thermal expansion, and temperature derivative of bulk modulus at constant volume. Our obtained K0 value for tetragonal PbTiO3 is consistent with previously reported results, while that for cubic PbTiO3 is smaller than earlier results probably due to differences in the experimental techniques used (cubic anvil apparatus versus diamond anvil cell) and related stress conditions of the samples. All other thermoelastic parameters for both tetragonal and cubic PbTiO3 have been determined for the first time. Compared with previous high-temperature data at atmospheric pressure, our P-V-T dataset for tetragonal PbTiO3 infers a pressure-induced crossover in volumetric thermal expansion from negative to positive between 0 and 1 GPa, an phenomenon that is of fundamentally interest and practically important.