Ferroelectric materials exhibit spontaneous polarization, spontaneous strain and domain structures below the Curie temperature. The phase field approach has been used to simulate the formation of ferroelectric domain structures and the ferroelectric-antiferroelectric phase transformation. The evolution of phases and domain structures was simulated in ferroelectric single crystals by solving the time dependent Ginzburg-Landau (TDGL) equation with polarization as the order parameter. In the TDGL equation the free energy of a ferroelectric crystal is written as a function of polarization and applied fields. Change of temperature as well as application of stress and electric field leads to change of free energy level and therefore evolution of phase and domain states. In this work the temporal evolution of polarization field was computed by solving the TDGL equation with explicit time integration scheme. The finite difference method was implemented for the spatial description of the polarization. Cubic to tetragonal, cubic to rhombohedral and ferroelectric to antiferroelectric (tetragonal or rhombohedral) phase transformations were modeled and the formation of domain structures were simulated. Field induced polarization switching and the macroscopic material responses were simulated.
Relaxor ferroelectric PZN-xPT and PMN-xPT single crystals exhibit excellent electromechanical coupling properties that depend on crystallographic orientations. In this study compressive stress and electric field were applied to relaxor single crystals [Pb(Zn<sub>1/3</sub>Nb<sub>2/3</sub>)O<sub>3</sub>]<sub>0.955</sub>-[PbTiO<sub>3</sub>]<sub>0.045</sub> (PZN-4.5%PT) in a series of crystal orientations between <001> and <111>, and the corresponding strain and electric displacement were measured. It was found that as the angle of the orientation cut is rotated from <001> to <111>, the piezoelectric coefficient d33 drops and hysteresis increases dramatically. A crystal variant based approach was used to model the piezoelectric coefficients and remnant electric displacement. The bipolar electro-mechanical response of these crystals is presented. Observed hysteresis and nonlinear phenomena related to polarization reorientation and phase transitions is discussed. In actuator design and performance control, these results give a guideline regarding appropriate external fields in order to prevent depolarization, heat generation and damage.
Rhombohedral relaxor single crystals are a class of materials that includes PZN-xPT and PMN-xPT in a certain range of compositions. This work presents an approach to predicting the physical properties of engineered domain state crystals. A model based on the properties of the crystal variants and volume averaging provides a method for determining a full set of the piezoelectric coefficients for the rhombohedral <111> single domain. The model suggests there is a large d15 and the existence of d16 for the <111> orientation cuts of PZN-PT and PMN-PT crystals. The approach has led to the identification of engineered domain states with properties optimized for specific applications such as the large transverse piezoelectric coefficients of the <110> orientation. This cut has optimal properties for actuator and sensor applications that utilize the transverse mode piezoelectric coupling coefficients (d<sub>31</sub> and d<sub>32</sub>).
The constitutive behavior of relaxor rhombohedral single crystal is discussed in terms of the constitutive behavior of crystal variants. The domain engineered cut gives rise to a stable domain state. Resulting crystal behavior is described. The cut and poled single crystal should display the volume average behavior of single domain crystal variants, but comparison of a crystal variant model with measured properties leads to the identification of inconsistencies. Several possible reasons for these inconsistencies are discussed.