Three-dimensional computer simulation of ferroelectric domain formation

Three-dimensional (3-D) computer simulations of ferroelectric domain formation and evolution were performed, using a computer simulation model based on the time-dependent Ginsburg-Landau equations. A cubic-to-tetragonal ferroelectric phase transition is considered. It is shown that the initial stage of the transition during the annealing of a quenched cubic paraelectric phase involves the nucleation and growth of the ferroelectric domains, followed by the domain coarsening leading to the formation of 90° and 180° domain structures. Part of the 3-D results reported here confirm our conclusions made earlier for the two-dimensional (2-D) case, namely, the nonlocal elastic interactions are critical to the formation of twin structure and the dipole-dipole interactions are responsible for the head-to-tail arrangements of dipoles at twin boundaries. In contrast to our previous work, and others; the effect of the depolarization energy was explicitly incorporated into the simulation model. It is found that when there are no surface charges to compensate the Lorentz field due to the polarization charges, and if the system is mechanically clamped, both 90° and 180° domains are thermodynamically stable.