Thermodynamics and Ferroelectric Properties of Pb_1-xSr_xTiO₃ Solid Solutions

Pb_1-xSr_xTiO₃ solid solutions have been utilized to compositionally tune the phase transitions and ferroelectric properties and thus are attractive for potential applications in tunable microwave devices and pyroelectric energy harvesters. However, a reliable thermodynamic description of the Pb_1-xSr_xTiO₃ system is currently lacking. Here, we establish a thermodynamic free energy density function for the Pb_1-xSr_xTiO₃ solid solution system taking into account both the polarization and octahedral tilt, and validated it by reproducing the experimentally measured polarization, lattice parameters, and dielectric constant values. Based on the thermodynamic model, we successfully explain the experimentally observed dielectric anomalies by analyzing the interactions between ferroelectric and octahedral tilt order parameters and constructed a comprehensive temperature-composition Pb_1-xSr_xTiO₃ phase diagram which can be used to guide future experimental synthesis and thin film growth. The thermodynamic model developed in this work can be employed not only to predict the ferroelectric and structural states and their properties for compositions that have not yet been synthesized but also used as input to model the formation of mesoscale domain structures using the phase-field method.