Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this study a cubic to tetragonal phase transformation and the evolution of domain structures in ferroelectric crystals are simulated by using the time-dependent Ginzburg-Landau equation. The effects of electric boundary conditions on the formation of domain patterns and field induced polarization switching are discussed. The phase field model is used to simulate the formation of domain structures, domain wall motion and the macroscopic response of ferroelectric materials under external fields.

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