Phase diagram of polar states in doped ferroelectric systems

We report a complete phase diagram that describes the relationships among all polar states in doped ferroelectrics, including the paraelectric (polar liquid), ferroelectric (polar crystal), relaxor (polar glass), and precursory states (partially frozen nanopolar domains). We employ a model that considers a randomly distributed local polarization field associated with point defects, which breaks the symmetry of the Landau free energy with respect to polarization. In the meantime, the model also takes into account the effect of point defects on the overall stability of the ferroelectric phase. Based on this model, the phase field simulations reproduce all the polar states and important characteristics associated with ferroelectric-glass (relaxor) transition observed in experiments, including rugged free energy, wide relaxation time, nanosized ferroelectric domain structure, diffuse transition, temperature dependence of third-order dielectric susceptibility, nonergodicity, frequency dependence of dielectric loss, and domain switching.