Domain structures and phase diagram in 2D ferroelectrlcs under applied biaxial strains - Phase field simulations and thermodynamic calculations

The microscopic domain structures in 2D ferroelectrics under applied biaxial strains are investigated using a phase field model based on the time-dependent Ginzburg-Landau equation that takes both long-range electric and -elastic interactions into account, The stable polarization patterns are simulated at different temperatures and applied inequiaxial strains. The results show that the ferroelectrics transfer from multi-domain state to single-domain state when temperature surpasses a critical value, On the other hand, the macroscopic equilibrium polarization states are also studied through a nonlinear thermodynamic theory. The corresponding transition from a₁a ₂ state (P₁ ≠ 0, P₂ ≠ 0) to a₁ state (P₁ ≠ 0, P₂ = 0) or a₂ state (P ₂ ≠ 0, P₁ = 0) is also found from the "strain-strain-temperature" phase diagram, which is constructed by minimizing Helmholtz free energy.